SAP2000. Integrated Finite Element Analysis and Design of Structures STEEL DESIGN MANUAL. Computers and Structures, Inc. Berkeley, California, USA

Transcription

1 SAP000 Integrated inite Element Analsis and Design o Structures STEEL DESIGN ANUAL Computers and Structures, Inc. Berkele, Caliornia, USA Version 7.4 Revision a 000

2 COPYRIGHT The computer program SAP000 and all associated documentation are proprietar and coprighted products. Worldwide rights o ownership rest with Computers and Structures, Inc. Unlicensed use o the program or reproduction o the documentation in an orm, without prior written authorization rom Computers and Structures, Inc., is explicitl prohiited. urther inormation and copies o this documentation ma e otained rom: Computers and Structures, Inc Universit Avenue Berkele, Caliornia USA Tel: (510) ax: (510) [email protected] We: Copright Computers and Structures, Inc., The CSI Logo is a registered trademark o Computers and Structures, Inc. SAP000 is a registered trademark o Computers and Structures, Inc.

3 DISCLAIER CONSIDERABLE TIE, EORT AND EXPENSE HAVE GONE INTO THE DEVELOPENT AND DOCUENTATION O SAP000. THE PROGRA HAS BEEN THOROUGHLY TESTED AND USED. IN USING THE PROGRA, HOWEVER, THE USER ACCEPTS AND UNDERSTANDS THAT NO WARRANTY IS EX- PRESSED OR IPLIED BY THE DEVELOPERS OR THE DIS- TRIBUTORS ON THE ACCURACY OR THE RELIABILITY O THE PROGRA. THIS PROGRA IS A VERY PRACTICAL TOOL OR THE DE- SIGN/ CHECK O STEEL STRUCTURES. HOWEVER, THE USER UST THOROUGHLY READ THE ANUAL AND CLEARLY RECOGNIZE THE ASPECTS O STEEL DESIGN THAT THE PRO- GRA ALGORITHS DO NOT ADDRESS. THE USER UST EXPLICITLY UNDERSTAND THE ASSUP- TIONS O THE PROGRA AND UST INDEPENDENTLY VER- IY THE RESULTS.

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5 Tale o Contents CHAPTER I Introduction 1 Overview...1 Organization...3 Recommended Reading....3 CHAPTER II Design Algorithms 5 Design Load Cominations...6 Design and Check Stations...7 P- Eects...8 Element Unsupported Lengths...9 Eective Length actor (K)...10 Choice o Input Units...13 CHAPTER III Check/Design or AISC-ASD89 15 Design Loading Cominations...18 Classiication o Sections...18 Calculation o Stresses... Calculation o Allowale Stresses...3 Allowale Stress in Tension...3 Allowale Stress in Compression....3 lexural Buckling...3 lexural-torsional Buckling...5 Allowale Stress in Bending...30 I-sections...30 Channel sections...33 T-sections and Doule angles...34 Box Sections and Rectangular Tues...35 Pipe Sections...36 Round Bars...36 i

6 SAP000 Steel Design anual Rectangular and Square Bars...36 Single-Angle Sections...37 General Sections...39 Allowale Stress in Shear...39 Calculation o Stress Ratios...40 Axial and Bending Stresses Shear Stresses...43 CHAPTER IV Check/Design or AISC-LRD93 45 Design Loading Cominations...48 Classiication o Sections...48 Calculation o actored orces...5 Calculation o Nominal Strengths...54 Compression Capacit...54 lexural Buckling...54 lexural-torsional Buckling...58 Torsional and lexural-torsional Buckling...58 Tension Capacit...60 Nominal Strength in Bending Yielding...61 Lateral-Torsional Buckling...61 lange Local Buckling...65 We Local Buckling...69 Shear Capacities...7 Calculation o Capacit Ratios...73 Axial and Bending Stresses Shear Stresses...74 CHAPTER V Check/Design or AASHTO Design Loading Cominations...78 Classiication o Sections...79 Calculation o actored orces...79 Calculation o Nominal Strengths...8 Compression Capacit...83 Tension Capacit...84 lexure Capacit...84 Shear Capacities...90 Calculation o Capacit Ratios...91 Axial and Bending Stresses....9 Shear Stresses...9 CHAPTER VI Check/Design or CISC94 93 Design Loading Cominations...96 Classiication o Sections...97 ii

7 Tale o Contents Calculation o actored orces...97 Calculation o actored Strengths Compression Strength Tension Strength Bending Strengths I-shapes and Boxes...10 Rectangular Bar Pipes and Circular Rods Channel Sections T-shapes and doule angles Single Angle and General Sections Shear Strengths Calculation o Capacit Ratios Axial and Bending Stresses Shear Stresses CHAPTER VII Check/Design or BS Design Loading Cominations Classiication o Sections Calculation o actored orces Calculation o Section Capacities Compression Resistance Tension Capacit...11 oment Capacit...11 Plastic and Compact Sections...11 Semi-compact Sections...1 Lateral-Torsional Buckling oment Capacit...1 Shear Capacities...15 Calculation o Capacit Ratios...15 Local Capacit Check...17 Under Axial Tension...17 Under Axial Compression...17 Overall Buckling Check...17 Shear Capacit Check...18 CHAPTER VIII Check/Design or EUROCODE 3 19 Design Loading Cominations...13 Classiication o Sections Calculation o actored orces Calculation o Section Resistances Tension Capacit Compression Resistance Shear Capacit iii

8 SAP000 Steel Design anual oment Resistance...14 Lateral-torsional Buckling Calculation o Capacit Ratios Bending, Axial Compression, and Low Shear Bending, Axial Compression, and High Shear Bending, Compression, and lexural Buckling Bending, Compression, and Lateral-Torsional Buckling Bending, Axial Tension, and Low Shear Bending, Axial Tension, and High Shear Bending, Axial Tension, and Lateral-Torsional Buckling Shear CHAPTER IX Design Output 151 Overview Graphical Displa o Design Output...15 Taular Displa o Design Output emer Speciic Inormation Reerences 157 Index 159 iv

9 Chapter I Introduction Overview SAP000 eatures powerul and completel integrated modules or design o oth steel and reinorced concrete structures. The program provides the user with options to create, modi, analze and design structural models, all rom within the same user interace. The program is capale o perorming initial memer sizing and optimization rom within the same interace. The program provides an interactive environment in which the user can stud the stress conditions, make appropriate changes, such as revising memer properties, and re-examine the results without the need to re-run the analsis. A single mouse click on an element rings up detailed design inormation. emers can e grouped together or design purposes. The output in oth graphical and taulated ormats can e readil printed. The program is structured to support a wide variet o the latest national and international design codes or the automated design and check o concrete and steel rame memers. The program currentl supports the ollowing steel design codes: U.S. AISC/ASD (1989), U.S. AISC/LRD (1994), U.S. AASHTO LRD (1997), Overview 1

10 SAP000 Steel Design anual Canadian CAN/CSA-S (1994), British BS 5950 (1990), and Eurocode 3 (ENV ). The design is ased upon a set o user-speciied loading cominations. However, the program provides a set o deault load cominations or each design code supported in SAP000. I the deault load cominations are acceptale, no deinition o additional load comination is required. In the design process the program picks the least weight section required or strength or each element to e designed, rom a set o user speciied sections. Dierent sets o availale sections can e speciied or dierent groups o elements. Also several elements can e grouped to e designed to have the same section. In the check process the program produces demand/capacit ratios or axial load and iaxial moment interactions and shear. The demand/capacit ratios are ased on element stress and allowale stress or allowale stress design, and on actored loads (actions) and actored capacities (resistances) or limit state design. The checks are made or each user speciied (or program deaulted) load comination and at several user controlled stations along the length o the element. aximum demand/capacit ratios are then reported and/or used or design optimization. All allowale stress values or design capacit values or axial, ending and shear actions are calculated the program. Tedious calculations associated with evaluating eective length actors or columns in moment rame tpe structures are automated in the algorithms. The presentation o the output is clear and concise. The inormation is in a orm that allows the designer to take appropriate remedial measures i there is memer overstress. Backup design inormation produced the program is also provided or convenient veriication o the results. Special requirements or seismic design are not implemented in the current version o SAP000. English as well as SI and KS metric units can e used to deine the model geometr and to speci design parameters. Overview

11 Chapter I Introduction Organization This manual is organized in the ollowing wa: Chapter II outlines various aspects o the steel design procedures o the SAP000 program. This chapter descries the common terminolog o steel design as implemented in SAP000. Each o six susequent chapters gives a detailed description o a speciic code o practice as interpreted and implemented in SAP000. Each chapter descries the design loading cominations to e considered; allowale stress or capacit calculations or tension, compression, ending, and shear; calculations o demand/capacit ratios; and other special considerations required the code. Chapter III gives a detailed description o the AISC ASD code (AISC 1989) as implemented in SAP000. Chapter IV gives a detailed description o the AISC LRD code (AISC 1994) as implemented in SAP000. Chapter V gives a detailed description o the AASHTO LRD steel code (AASHTO 1997) as implemented in SAP000. Chapter VI gives a detailed description o the Canadian code (CISC 1994) as implemented in SAP000. Chapter VII gives a detailed description o the British code BS 5950 (BSI 1990) as implemented in SAP000. Chapter VIII gives a detailed description o the Eurocode 3 (CEN 199) as implemented in SAP000. Chapter IX outlines various aspects o the taular and graphical output rom SAP000 related to steel design. Recommended Reading It is recommended that the user read Chapter II Design Algorithms and one o six susequent chapters corresponding to the code o interest to the user. inall the user should read Design Output in Chapter IX or understanding and interpreting SAP000 output related to steel design. A steel design tutorial is presented in the chapter Steel Design Tutorial in the SAP000 Quick Tutorial manual. It is recommended that irst time users ollow through the steps o this tutorial eore reading this manual. Organization 3

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13 Chapter II Design Algorithms This chapter outlines various aspects o the steel check and design procedures that are used the SAP000 program. The steel design and check ma e perormed according to one o the ollowing codes o practice. American Institute o Steel Construction s Allowale Stress Design and Plastic Design Speciication or Structural Steel Buildings, AISC-ASD (AISC 1989). American Institute o Steel Construction s Load and Resistance actor Design Speciication or Structural Steel Buildings, AISC-LRD (AISC 1994). American Association o State Highwa and Transportation Oicials AASHTO-LRD Bridge Design Speciications, AASHTO-LRD (AASHTO 1997). Canadian Institute o Steel Construction s Limit States Design o Steel Structures, CAN/CSA-S (CISC 1995). British Standards Institution s Structural Use o Steelwork in Building, BS 5950 (BSI 1990). European Committee or Standardization s Eurocode 3: Design o Steel Structures Part 1.1: General Rules and Rules or Buildings, ENV (CEN 199). 5

14 SAP000 Steel Design anual Details o the algorithms associated with each o these codes as implemented and interpreted in SAP000 are descried in susequent chapters. However, this chapter provides a ackground which is common to all the design codes. It is assumed that the user has an engineering ackground in the general area o structural steel design and amiliarit with at least one o the aove mentioned design codes. or reerring to pertinent sections o the corresponding code, a unique preix is assigned or each code. or example, all reerences to the AASHTO-LRD code carr the preix o AASHTO. Similarl, Reerences to the AISC-ASD89 code carr the preix o ASD Reerences to the AISC-LRD93 code carr the preix o LRD Reerences to the Canadian code carr the preix o CISC Reerences to the British code carr the preix o BS Reerences to the Eurocode carr the preix o EC3 Design Load Cominations The design load cominations are used or determining the various cominations o the load cases or which the structure needs to e designed/checked. The load comination actors to e used var with the selected design code. The load comination actors are applied to the orces and moments otained rom the associated load cases and the results are then summed to otain the actored design orces and moments or the load comination. or multi-valued load cominations involving response spectrum, time histor, moving loads and multi-valued cominations (o tpe enveloping, square-root o the sum o the squares or asolute) where an correspondence etween interacting quantities is lost, the program automaticall produces multiple su cominations using maxima/minima permutations o interacting quantities. Separate cominations with negative actors or response spectrum cases are not required ecause the program automaticall takes the minima to e the negative o the maxima or response spectrum cases and the aove descried permutations generate the required su cominations. When a design comination involves onl a single multi-valued case o time histor or moving load, urther options are availale. The program has an option to request that time histor cominations produce su cominations or each time step o the time histor. Also an option is availale to request that moving load comina- 6 Design Load Cominations

15 Chapter II Design Algorithms tions produce su cominations using maxima and minima o each design quantit ut with corresponding values o interacting quantities. or normal loading conditions involving static dead load, live load, wind load, and earthquake load, and/or dnamic response spectrum earthquake load, the program has uilt-in deault loading cominations or each design code. These are ased on the code recommendations and are documented or each code in the corresponding chapters. or other loading conditions involving moving load, time histor, pattern live loads, separate consideration o roo live load, snow load, etc., the user must deine design loading cominations either in lieu o or in addition to the deault design loading cominations. The deault load cominations assume all static load cases declared as dead load to e additive. Similarl, all cases declared as live load are assumed additive. However, each static load case declared as wind or earthquake, or response spectrum cases, is assumed to e non additive with each other and produces multiple lateral load cominations. Also wind and static earthquake cases produce separate loading cominations with the sense (positive or negative) reversed. I these conditions are not correct, the user must provide the appropriate design cominations. The deault load cominations are included in design i the user requests them to e included or i no other user deined comination is availale or concrete design. I an deault comination is included in design, then all deault cominations will automaticall e updated the program an time the user changes to a dierent design code or i static or response spectrum load cases are modiied. Live load reduction actors can e applied to the memer orces o the live load case on an element--element asis to reduce the contriution o the live load to the actored loading. The user is cautioned that i moving load or time histor results are not requested to e recovered in the analsis or some or all the rame memers, then the eects o these loads will e assumed to e zero in an comination that includes them. Design and Check Stations or each load comination, each element is designed or checked at a numer o locations along the length o the element. The locations are ased on equall spaced segments along the clear length o the element. The numer o segments in an element is requested the user eore the analsis is made. The user can reine the design along the length o an element requesting more segments. Design and Check Stations 7

16 SAP000 Steel Design anual The axial-lexure interaction ratios as well as shear stress ratios are calculated or each station along the length o the memer or each load comination. The actual memer stress components and corresponding allowale stresses are calculated. Then, the stress ratios are evaluated according to the code. The controlling compression and/or tension stress ratio is then otained, along with the corresponding identiication o the station, load comination, and code-equation. A stress ratio greater than 1.0 indicates an overstress or exceeding a limit state. P- Eects The SAP000 design algorithms require that the analsis results include the P- eects. The P- eects are considered dierentl or raced or nonswa and unraced or swa components o moments in rames. or the raced moments in rames, the eect o P- is limited to individual memer stailit. or unraced components, lateral drit eects should e considered in addition to individual memer stailit eect. In SAP000, it is assumed that raced or nonswa moments are contriuted rom the dead or live loads. Whereas, unraced or swa moments are contriuted rom all other tpes o loads. or the individual memer stailit eects, the moments are magniied with moment magniication actors as in the AISC-LRD and AASHTO-LRD codes or are considered directl in the design equations as in the Canadian, British, and European codes. No moment magniication is applied to the AISC-ASD code. or lateral drit eects o unraced or swa rames, SAP000 assumes that the ampliication is alread included in the results ecause P- eects are considered or all ut AISC-ASD code. The users o SAP000 should e aware that the deault analsis option in SAP000 is turned O or P- eect. The deault numer o iterations or P- analsis is 1. The user should turn the P- analsis ON and set the maximum numer o iterations or the analsis. No P- analsis is required or the AISC-ASD code. or urther reerence, the user is reerred to SAP000 Analsis Reerence anual (CSI 1997). The user is also cautioned that SAP000 currentl considers P- eects due to axial loads in rame memers onl. orces in other tpes o elements do not contriute to this eect. I signiicant orces are present in other tpes o elements, or example, large axial loads in shear walls modeled as shell elements, then the additional orces computed or P- will e inaccurate. 8 P- Eects

17 Chapter II Design Algorithms Element Unsupported Lengths To account or column slenderness eects, the column unsupported lengths are required. The two unsupported lengths are l 33 and l. See igure II-1. These are the lengths etween support points o the element in the corresponding directions. The length l 33 corresponds to instailit aout the 3-3 axis (major axis), and l corresponds to instailit aout the - axis (minor axis). The length l is also used or lateral-torsional uckling caused major direction ending (i.e., aout the 3-3 axis). See igure II- or correspondence etween the SAP000 axes and the axes in the design codes. Normall, the unsupported element length is equal to the length o the element, i.e., the distance etween END-I and END-J o the element. See igure II-1. The program, however, allows users to assign several elements to e treated as a single memer or design. This can e done dierentl or major and minor ending. Thereore, extraneous joints, as shown in igure II-3, that aect the unsupported length o an element are automaticall taken into consideration. igure II-1 ajor and inor Axes o Bending Element Unsupported Lengths 9

18 SAP000 Steel Design anual In determining the values or l and l 33 o the elements, the program recognizes various aspects o the structure that have an eect on these lengths, such as memer connectivit, diaphragm constraints and support points. The program automaticall locates the element support points and evaluates the corresponding unsupported element length. Thereore, the unsupported length o a column ma actuall e evaluated as eing greater than the corresponding element length. I the eam rames into onl one direction o the column, the eam is assumed to give lateral support onl in that direction. The user has options to speci the unsupported lengths o the elements on an element--element asis. igure II- Correspondence etween SAP000 Axes and Code Axes Eective Length actor (K) The column K-actor algorithm has een developed or uilding-tpe structures, where the columns are vertical and the eams are horizontal, and the ehavior is asicall that o a moment-resisting nature or which the K-actor calculation is relativel complex. or the purpose o calculating K-actors, the elements are identiied as columns, eams and races. All elements parallel to the Z-axis are classiied as columns. All elements parallel to the X-Y plane are classiied as eams. The rest are races. 10 Eective Length actor (K)

19 Chapter II Design Algorithms igure II-3 Unsupported Lengths are Aected Intermediate Nodal Points The eams and races are assigned K-actors o unit. In the calculation o the K-actors or a column element, the program irst makes the ollowing our stiness summations or each joint in the structural model: S = cx S = c EI c L c EI c L c c c x S = x S = EI L EI L x where the x and suscripts correspond to the gloal X and Y directions and the c and suscripts reer to column and eam. The local - and 3-3 terms EI l and EI l are rotated to give components along the gloal X and Y directions to orm the ( EI / l) x and ( EI / l) values. Then or each column, the joint summations at END-I and the END-J o the memer are transormed ack to the column local 1--3 coordinate sstem and the G-values or END-I and the END-J o the memer are calculated aout the - and 3-3 directions as ollows: Eective Length actor (K) 11

20 SAP000 Steel Design anual I G = S S I c I G J = S S J c J G I 33 = S S I c 33 I 33 G J 33 = S S J c 33 J 33 I a rotational release exists at a particular end (and direction) o an element, the corresponding value is set to I all degrees o reedom or a particular joint are deleted, the G-values or all memers connecting to that joint will e set to 1.0 or the end o the memer connecting to that joint. inall, i G I and G J are known or a particular direction, the column K-actor or the corresponding direction is calculated solving the ollowing relationship or α: G G I G G I J J rom which K. This relationship is the mathematical ormulation or the evaluation o K actors or moment-resisting rames assuming sideswa to e uninhiited. or other structures, such as raced rame structures, trusses, space rames, transmission towers, etc., the K-actors or all memers are usuall unit and should e set so the user. The ollowing are some important aspects associated with the column K-actor algorithm: An element that has a pin at the joint under consideration will not enter the stiness summations calculated aove. An element that has a pin at the ar end rom the joint under consideration will contriute onl 50% o the calculated EI value. Also, eam elements that have no column memer at the ar end rom the joint under consideration, such as cantilevers, will not enter the stiness summation. I there are no eams raming into a particular direction o a column element, the associated G-value will e ininit. I the G-value at an one end o a column or a particular direction is ininit, the K-actor corresponding to that direction is set equal to unit. I rotational releases exist at oth ends o an element or a particular direction, the corresponding K-actor is set to unit. The automated K-actor calculation procedure can occasionall generate artiiciall high K-actors, speciicall under circumstances involving skewed eams, ixed support conditions, and under other conditions where the program ma have diicult recognizing that the memers are laterall supported and K-actors o unit are to e used. 1 Eective Length actor (K)

21 Chapter II Design Algorithms All K-actors produced the program can e overwritten the user. These values should e reviewed and an unacceptale values should e replaced. Choice o Input Units English as well as SI and KS metric units can e used or input. But the codes are ased on a speciic sstem o units. All equations and descriptions presented in the susequent chapters correspond to that speciic sstem o units unless otherwise noted. or example, AISC-ASD code is pulished in kip-inch-second units. B deault, all equations and descriptions presented in the chapter Check/Design or AISC-ASD89 correspond to kip-inch-second units. However, an sstem o units can e used to deine and design the structure in SAP000. Choice o Input Units 13

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23 Chapter III Check/Design or AISC-ASD89 This chapter descries the details o the structural steel design and stress check algorithms that are used SAP000 when the user selects the AISC-ASD89 design code (AISC 1989). Various notations used in this chapter are descried in Tale III-1. or reerring to pertinent sections and equations o the original ASD code, a unique preix ASD is assigned. However, all reerences to the Speciications or Allowale Stress Design o Single-Angle emers carr the preix o ASD SA. The design is ased on user-speciied loading cominations. But the program provides a set o deault load cominations that should satis requirements or the design o most uilding tpe structures. In the evaluation o the axial orce/iaxial moment capacit ratios at a station along the length o the memer, irst the actual memer orce/moment components and the corresponding capacities are calculated or each load comination. Then the capacit ratios are evaluated at each station under the inluence o all load cominations using the corresponding equations that are deined in this chapter. The controlling capacit ratio is then otained. A capacit ratio greater than 1.0 indicates overstress. Similarl, a shear capacit ratio is also calculated separatel. 15

24 SAP000 Steel Design anual A = Cross-sectional area, in A e = Eective cross-sectional area or slender sections, in A = Area o lange, in A g = Gross cross-sectional area, in Av, Av3 = ajor and minor shear areas, in A w = We shear area, dt w,in C = Bending Coeicient C m = oment Coeicient C w = Warping constant, in 6 D = Outside diameter o pipes, in E = odulus o elasticit, ksi a = Allowale axial stress, ksi = Allowale ending stress, ksi 33, = Allowale major and minor ending stresses, ksi cr = Critical compressive stress, ksi e33 e = = 1 3 K l E r 1 E 3 K l r v = Allowale shear stress, ksi = Yield stress o material, ksi K = Eective length actor K 33, K = Eective length K-actors in the major and minor directions 33, = ajor and minor ending moments in memer, kip-in o = Lateral-torsional moment or angle sections, kip-in P = Axial orce in memer, kips P e = Euler uckling load, kips Q = Reduction actor or slender section, = QQ a s Q a = Reduction actor or stiened slender elements Q s = Reduction actor or unstiened slender elements S = Section modulus, in 3 S, S = ajor and minor section moduli, in 3 33 Tale III-1 AISC-ASD Notations 16

25 Chapter III Check/Design or AISC-ASD89 S e, 33, S e, = Eective major and minor section moduli or slender sections, in 3 S c = Section modulus or compression in an angle section, in 3 V, V3 = Shear orces in major and minor directions, kips = Nominal dimension o plate in a section, in longer leg o angle sections, tw or welded and 3tw or rolled ox sections, etc. e = Eective width o lange, in = lange width, in d = Overall depth o memer, in a = Axial stress either in compression or in tension, ksi = Normal stress in ending, ksi 33, = Normal stress in major and minor direction ending, ksi v = Shear stress, ksi v, v3 = Shear stress in major and minor direction ending, ksi h = Clear distance etween langes or I shaped sections ( d t ),in h e = Eective distance etween langes less illets, in k = Distance rom outer ace o lange to we toe o illet, in k c = Parameter used or classiication o sections, i ht 0.46 w 70, ht w 1 i ht w 70. l33, l = ajor and minor direction unraced memer lengths, in l c = Critical length, in r = Radius o gration, in r33, r = Radii o gration in the major and minor directions, in r z = inimum Radius o gration or angles, in t = Thickness o a plate in I, ox, channel, angle, and T sections, in t = lange thickness, in t w = We thickness, in w = Special section propert or angles, in Tale III-1 AISC-ASD Notations (cont.) 17

26 SAP000 Steel Design anual English as well as SI and KS metric units can e used or input. But the code is ased on Kip-Inch-Second units. or simplicit, all equations and descriptions presented in this chapter correspond to Kip-Inch-Second units unless otherwise noted. Design Loading Cominations The design load cominations are the various cominations o the load cases or which the structure needs to e checked. or the AISC-ASD89 code, i a structure is sujected to dead load (DL), live load (LL), wind load (WL), and earthquake induced load (EL), and considering that wind and earthquake orces are reversile, then the ollowing load cominations ma have to e deined (ASD A4): DL DL + LL (ASD A4.1) (ASD A4.1) DL WL (ASD A4.1) DL + LL WL (ASD A4.1) DL EL (ASD A4.1) DL + LL EL (ASD A4.1) These are also the deault design load cominations in SAP000 whenever the AISC-ASD89 code is used. The user should use other appropriate loading cominations i roo live load is separatel treated, i other tpes o loads are present, or i pattern live loads are to e considered. When designing or cominations involving earthquake and wind loads, allowale stresses are increased a actor o 4/3 o the regular allowale value (ASD A5.). Live load reduction actors can e applied to the memer orces o the live load case on an element--element asis to reduce the contriution o the live load to the actored loading. Classiication o Sections The allowale stresses or axial compression and lexure are dependent upon the classiication o sections as either Compact, Noncompact, Slender, or Too Slender. SAP000 classiies the individual memers according to the limiting width/thickness ratios given in Tale III- (ASD B5.1, 3.1, 5, G1, A-B5-). The deinition o the section properties required in this tale is given in igure III-1 and Tale III Design Loading Cominations

27 Chapter III Check/Design or AISC-ASD89 igure III-1 AISC-ASD Deinition o Geometric Properties Classiication o Sections 19

28 SAP000 Steel Design anual Section Description Ratio Checked Compact Section Noncompact Section Slender Section t ( rolled) t (welded) No limit 65 / kc No limit I-SHAPE d t w or or a a a ( ), / 57/. No limit No limit h t w No limit I compression onl, 53 otherwise 760 t No limit BOX d t w As or I-shapes No limit No limit h t w No limit As or I-shapes As or I-shapes Other t t w, d w None None t As or I-shapes As or I-shapes No limit d t w As or I-shapes No limit No limit CHANNEL h t w No limit As or I-shapes As or I-shapes Other No limit No limit I welded d t tw I rolled d t t w, w, w Tale III- Limiting Width-Thickness Ratios or Classiication o Sections Based on AISC-ASD 0 Classiication o Sections

29 Chapter III Check/Design or AISC-ASD89 Section Description Ratio Checked Compact Section Noncompact Section Slender Section t No limit d t w Not applicale 17 No limit T-SHAPE Other No limit No limit I welded d t tw I rolled d t t w, w, w DOUBLE ANGLES t Not applicale 76 No limit ANGLE t Not applicale 76 No limit PIPE D t 3, 300 3, 300 (Compression onl) No limit or lexure ROUND BAR Assumed Compact RECTANGLE Assumed Noncompact GENERAL Assumed Noncompact Tale III- Limiting Width-Thickness Ratios or Classiication o Sections Based on AISC-ASD (Cont.) I the section dimensions satis the limits shown in the tale, the section is classiied as either Compact, Noncompact, or Slender. I the section satisies the criteria or Compact sections, then the section is classiied as Compact section. I the section does not satis the criteria or Compact sections ut satisies the criteria or Noncompact sections, the section is classiied as Noncompact section. I the section does not satis the criteria or Compact and Noncompact sections ut satisies Classiication o Sections 1

30 SAP000 Steel Design anual the criteria or Slender sections, the section is classiied as Slender section. I the limits or Slender sections are not met, the section is classiied as Too Slender. Stress check o Too Slender sections is eond the scope o SAP000. In classiing we slenderness o I-shapes, Box, and Channel sections, it is assumed that there are no intermediate stieners (ASD 5, G1). Doule angles are conservativel assumed to e separated. Calculation o Stresses The stresses are calculated at each o the previousl deined stations. The memer stresses or non-slender sections that are calculated or each load comination are, in general, ased on the gross cross-sectional properties.: a = P/A = /S = /S = V /A v v = V /A v3 3 v3 I the section is slender with slender stiened elements, like slender we in I, Channel, and Box sections or slender langes in Box, eective section moduli ased on reduced we and reduced lange dimensions are used in calculating stresses. a = P/A (ASD A-B5.d) = /S (ASD A-B5.d) e, 33 = /S (ASD A-B5.d) e, = V /A (ASD A-B5.d) v v = V /A (ASD A-B5.d) v3 3 v3 The lexural stresses are calculated ased on the properties aout the principal axes. or I, Box, Channel, T, Doule-angle, Pipe, Circular and Rectangular sections, the principal axes coincide with the geometric axes. or Single-angle sections, the design considers the principal properties. or general sections it is assumed that all section properties are given in terms o the principal directions. or Single-angle sections, the shear stresses are calculated or directions along the geometric axes. or all other sections the shear stresses are calculated along the geometric and principle axes. Calculation o Stresses

31 Chapter III Check/Design or AISC-ASD89 Calculation o Allowale Stresses The allowale stresses in compression, tension, ending, and shear are computed or Compact, Noncompact, and Slender sections according to the ollowing susections. The allowale lexural stresses or all shapes o sections are calculated ased on their principal axes o ending. or the I, Box, Channel, Circular, Pipe, T, Doule-angle and Rectangular sections, the principal axes coincide with their geometric axes. or the Angle sections, the principal axes are determined and all computations related to lexural stresses are ased on that. I the user speciies nonzero allowale stresses or one or more elements in the SAP000 Redeine Element Design Data orm, these values will override the aove mentioned calculated values or those elements as deined in the ollowing susections. The speciied allowale stresses should e ased on the principal axes o ending. Allowale Stress in Tension The allowale axial tensile stress value a is assumed to e. a = (ASD D1, ASD SA ) It should e noted that net section checks are not made. or memers in tension, i lris greater than 300, a message to that eect is printed (ASD B7, ASD SA ). or single angles, the minimum radius o gration, r z, is used instead o r and r 33 in computing lr. Allowale Stress in Compression The allowale axial compressive stress is the minimum value otained rom lexural uckling and lexural-torsional uckling. The allowale compressive stresses are determined according to the ollowing susections. or memers in compression, i Kl r is greater than 00, a warning message is printed (ASD B7, ASD SA 4). or single angles, the minimum radius o gration, r z, is used instead o r and r 33 in computing Kl r. lexural Buckling The allowale axial compressive stress value, a, depends on the slenderness ratio Kl r ased on gross section properties and a corresponding critical value, C c, where Calculation o Allowale Stresses 3

32 SAP000 Steel Design anual Kl r K l K max, r r 33 l, and c E. (ASD E, ASD SA 4) or single angles, the minimum radius o gration, r z, is used instead o r and r 33 in computing Kl r. or Compact or Noncompact sections a is evaluated as ollows: = a Kl/r 8C ( Kl/r) c C c Kl/r 8 3 C c 3, i Kl r C c, (ASD E-1, SA 4-1) = a 1 E 3( Kl r), i Kl r C c. (ASD E-, SA 4-) I Kl r is greater than 00, then the calculated value o a is taken not to exceed the value o a calculated using the equation ASD E- or Compact and Noncompact sections (ASD E1, B7). or Slender sections, except slender Pipe sections, a is evaluated as ollows: = Q a Kl/r 8C c ( Kl/r) C c Kl/r 8C c 3 3,i Kl r C c, (ASD A-B5-11, SA 4-1) = a 1 E 3( Kl r), i Kl r C c.(asd A-B5-1, SA 4-) where, E C c. (ASD A-B5.c, ASD SA 4) Q 4 Calculation o Allowale Stresses

33 Chapter III Check/Design or AISC-ASD89 or slender sections, i Kl r is greater than 00, then the calculated value o a is taken not to exceed its value calculated using the equation ASD A-B5-1 (ASD B7, E1). or slender Pipe sections a is evaluated as ollows: a = (ASD A-B5-9) Dt The reduction actor, Q, or all compact and noncompact sections is taken as 1. or slender sections, Q is computed as ollows: Q Q Q s a, where (ASD A-B5..c, SA 4) Q s = reduction actor or unstiened slender elements, and (ASD A-B5..a) Q a = reduction actor or stiened slender elements. (ASD A-B5..c) The Q s actors or slender sections are calculated as descried in Tale III-3 (ASD A-B5.a, ASD SA 4). The Q a actors or slender sections are calculated as the ratio o eective cross-sectional area and the gross cross-sectional area. Q a A A e g (ASD A-B5-10) The eective cross-sectional area is computed ased on eective width as ollows: A A t e g e e or unstiened elements is taken equal to, and e or stiened elements is taken equal to or less than as given in Tale III-4 (ASD A-B5.). or wes in I, ox, and Channel sections, h e is used as e and h is used as in the aove equation. lexural-torsional Buckling The allowale axial compressive stress value, a, determined the limit states o torsional and lexural-torsional uckling is determined as ollows (ASD E3, C-E3): = Q a Kl/r 8 C c Kl/r C e c e Kl/r 8C c 3 e 3,i Kl/r e C c, (E-1, A-B5-11) Calculation o Allowale Stresses 5

34 SAP000 Steel Design anual Section Tpe Reduction actor or Unstiened Slender Elements (Q s ) Equation Reerence I-SHAPE Q s i t kc, t kc i kc t kc, k t i t k. c c ASD A-B5-3, ASD A-B5-4 BOX Q s 1 ASD A-B5.c CHANNEL As or I-shapes with t replaced t. ASD A-B5-3, ASD A-B5-4 T-SHAPE Q s or langes, as or langes in I-shapes. or we see elow. i d t dt, i dt, w w dt, i dt. w w w, ASD A-B5-3, ASD A-B5-4, ASD A-B5-5, ASD A-B5-6 DOUBLE- ANGLE Q s i t t, i t, t, i t., ASD A-B5-1, ASD A-B5-, SA 4-3 ANGLE Q s i t t, i t, t, i t., ASD A-B5-1, ASD A-B5-, SA 4-3 PIPE Q s 1 ASD A-B5.c ROUND BAR RECTAN- GULAR Q s 1 ASD A-B5.c Q s 1 ASD A-B5.c GENERAL Q s 1 ASD A-B5.c Tale III-3 Reduction actor or Unstiened Slender Elements, Q s 6 Calculation o Allowale Stresses

35 Chapter III Check/Design or AISC-ASD89 Section Tpe Eective Width or Stiened Sections Equation Reerence I-SHAPE h e h h, i, tw tw h 1, i. ( h t ) t w w (compression onl, P A g ) ASD A-B5-8 BOX h e e h h, i, tw tw h 1, i. ( h t ) t w, i, t t 1, i. ( h t ) t w (compression onl, P A g ) (compr., lexure, ) ASD A-B5-8 ASD A-B5-7 CHANNEL h e h h, i, tw tw h 1, i. ( h t ) t w w (compression onl, P A g ) ASD A-B5-8 T-SHAPE e ASD A-B5.c DOUBLE- ANGLE e ASD A-B5.c ANGLE e ASD A-B5.c PIPE Q a 1, (However, special expression or allowale axial stress is given.) ASD A-B5-9 ROUND BAR Not applicale RECTAN- GULAR e ASD A-B5.c GENERAL Not applicale Note: A reduction actor o 3/4 is applied on or axial-compression-onl cases and i the load comination includes an wind load or seismic load (ASD A-B5.). Tale III-4 Eective Width or Stiened Sections Calculation o Allowale Stresses 7

36 SAP000 Steel Design anual 1 E a = 3 Kl/r e, i Kl/r C e c. (E-, A-B5-1) where, E C c, and (ASD E, A-B5.c, SA 4) Q Kl/r e E e. (ASD C-E-, SA 4-4) ASD Commentar (ASD C-E3) reers to the 1986 version o the AISC-LRD code or the calculation o e. The 1993 version o the AISC-LRD code is the same as the 1986 version in this respect. e is calculated in SAP000 as ollows: or Rectangular, I, Box, and Pipe sections: e EC w z z K l 1 GJ I I 33 (LRD A-E3-5) or T-sections and Doule-angles: = e H H e ez e ez e ez (LRD A-E3-6) or Channels: = e H H e33 ez e 33 ez e 33 ez (LRD A-E3-6) or Single-angle sections with equal legs: = e H H e33 ez e 33 ez e 33 ez (ASD SA C-C4-1) or Single-angle sections with unequal legs, e is calculated as the minimum real root o the ollowing cuic equation (ASD SA C-C4-, LRD A-E3-7): 8 Calculation o Allowale Stresses

37 Chapter III Check/Design or AISC-ASD89 x0 ( e )( )( ) ( ) ( e33 e e e ez e e e e e r where, x 0 e33 0 ) 0, r, are the coordinates o the shear center with respect to the centroid, 0 or doule-angle and T-shaped memers (-axis o smmetr), 0 0 x 0 I I 33 r x = polar radius o gration aout the shear center, A g 0 H x 0 1 r 0 0, (LRD A-E3-9) e33 E K l r , (LRD A-E3-10) e E K l r, (LRD A-E3-11) ez EC w z z K l GJ Ar 1, (LRD A-E3-1) 0 K, K are eective length actors in minor and major directions, 33 K z is the eective length actor or torsional uckling, and it is taken equal to K in SAP000, l, l are eective lengths in the minor and major directions, 33 l z is the eective length or torsional uckling, and it is taken equal to l. or angle sections, the principal moment o inertia and radii o gration are used or computing e (ASD SA 4). Also, the maximum value o Kl, i.e, max( K l, K l ), is used in place o K l or K l in calculating and e e 33 in this case. Calculation o Allowale Stresses 9

38 SAP000 Steel Design anual Allowale Stress in Bending The allowale ending stress depends on the ollowing criteria: the geometric shape o the cross-section, the axis o ending, the compactness o the section, and a length parameter. I-sections or I-sections the length parameter is taken as the laterall unraced length, l, which is compared to a critical length, l c. The critical length is deined as l c 76 0, 000 A min, d, where (ASD 1-) A is the area o compression lange, ajor Axis o Bending I l is less than l c, the major allowale ending stress or Compact and Noncompact sections is taken depending on whether the section is welded or rolled and whether is greater than 65 ksi or not. or Compact sections: = 33 i, (ASD 1-1) = 33 i, (ASD 1-5) or Noncompact sections: = 33 t, i rolled and, (ASD 1-3) = 33 t k c, i welded and, (ASD1-4) = 33 i.. (ASD 1-5) I the unraced length l is greater than l c, then or oth Compact and Noncompact I-sections the allowale ending stress depends on the l r T ratio. 30 Calculation o Allowale Stresses

39 Chapter III Check/Design or AISC-ASD89 or l 10, 000C r T, 33, (ASD 1-6) or 10, 000 C l 510, 000 C r T, 33 ( l / r ) T , 000 C, and (ASD 1-6) or l 510, 000 C r T, , 000C ( l / r ) T 0, (ASD 1-7) and is taken not to e less than that given the ollowing ormula: 1, 000C l d / A (ASD 1-8) where, r T is the radius o gration o a section comprising the compression lange and 13the compression we taken aout an axis in the plane o the we, C = + a + a, where (ASD 1.3) a and are the end moments o an unraced segment o the memer and a is numericall less than ; a eing positive or doule curvature ending and negative or single curvature ending. Also, i an moment within the segment is greater than, C is taken as 1.0. Also, C is taken as 1.0 or cantilevers and rames raced against joint translation (ASD 1.3). SAP000 deaults C to 1.0 i the unraced length, l, o the memer is redeined the user (i.e. it is not equal to the length o the memer). The user can overwrite the value o C or an memer speciing it. Calculation o Allowale Stresses 31

40 SAP000 Steel Design anual The allowale ending stress or Slender sections ent aout their major axis is determined in the same wa as or a Noncompact section. Then the ollowing additional considerations are taken into account. I the we is slender, then the previousl computed allowale ending stress is reduced as ollows: R R 33 PG e 33, where (ASD G-1) R PG A A w h t , (ASD G) R e 3 A A 3 w A A w, (hrid girders) (ASD G) R e, (non-hrid girders) (ASD G) A w = Area o we, in, A = Area o compression lange, in, 33 (ASD G) 33 = Allowale ending stress assuming the section is non-compact, and 33 = Allowale ending stress ater considering we slenderness. In the aove expressions, R e is taken as 1, ecause currentl SAP000 deals with onl non-hrid girders. I the lange is slender, then the previousl computed allowale ending stress is taken to e limited as ollows. Q 33 s Q s is deined earlier., where (ASD A-B5.a, A-B5.d) 3 Calculation o Allowale Stresses

41 Chapter III Check/Design or AISC-ASD89 inor Axis o Bending The minor direction allowale ending stress is taken as ollows: or Compact sections: = i, (ASD -1) = i, (ASD -) or Noncompact and Slender sections: = t, i, (ASD -3) = i.. (ASD -) Channel sections or Channel sections the length parameter is taken as the laterall unraced length, l, which is compared to a critical length, l c. The critical length is deined as l c 76 0, 000 A min, d, where (ASD 1-) A is the area o compression lange, ajor Axis o Bending I l is less than l c, the major allowale ending stress or Compact and Noncompact sections is taken depending on whether the section is welded or rolled and whether is greater than 65 ksi or not. or Compact sections: = 33 i, (ASD 1-1) = 33 i, (ASD 1-5) or Noncompact sections: =, i rolled and 33, (ASD 1-3) t Calculation o Allowale Stresses 33

42 SAP000 Steel Design anual =, i welded and 33,(ASD 1-4) t k c = 33 i.. (ASD 1-5) I the unraced length l is greater than l c, then or oth Compact and Noncompact Channel sections the allowale ending stress is taken as ollows: 33 1, 000C l d / A (ASD 1-8) The allowale ending stress or Slender sections ent aout their major axis is determined in the same wa as or a Noncompact section. Then the ollowing additional considerations are taken into account. I the we is slender, then the previousl computed allowale ending stress is reduced as ollows: R R 33 e PG 33 (ASD G-1) I the lange is slender, the previousl computed allowale ending stress is taken to e limited as ollows: Q 33 s The deinition or r T,C, A, A w, R e, R PG,Q s, 33, and 33 inor Axis o Bending (ASD A-B5.a, A-B5.d) are given earlier. The minor direction allowale ending stress is taken as ollows: = (ASD -) T-sections and Doule angles or T sections and Doule angles, the allowale ending stress or oth major and minor axes ending is taken as, =. 34 Calculation o Allowale Stresses

43 Chapter III Check/Design or AISC-ASD89 Box Sections and Rectangular Tues or all Box sections and Rectangular tues, the length parameter is taken as the laterall unraced length, l, measured compared to a critical length, l c. The critical length is deined as l /, 100 c max ( a ) (ASD 3-) where a and have the same deinition as noted earlier in the ormula or C.Il is speciied the user, l c is taken as 100 in SAP000. ajor Axis o Bending I l is less than l c, the allowale ending stress in the major direction o ending is taken as: = 33 (or Compact sections) (ASD 3-1) = 33 (or Noncompact sections) (ASD 3-3) I l exceeds l c, the allowale ending stress in the major direction o ending or oth Compact and Noncompact sections is taken as: = 33 (ASD 3-3) The major direction allowale ending stress or Slender sections is determined in the same wa as or a Noncompact section. Then the ollowing additional consideration is taken into account. I the we is slender, then the previousl computed allowale ending stress is reduced as ollows: R R 33 e PG 33 The deinition or R e, R PG, 33, and 33 are given earlier. (ASD G-1) I the lange is slender, no additional consideration is needed in computing allowale ending stress. However, eective section dimensions are calculated and the section modulus is modiied according to its slenderness. inor Axis o Bending I l is less than l c, the allowale ending stress in the minor direction o ending is taken as: Calculation o Allowale Stresses 35

44 SAP000 Steel Design anual = (or Compact sections) (ASD 3-1) = (or Noncompact and Slender sections) (ASD 3-3) I l exceeds l c, the allowale ending stress in the minor direction o ending is taken, irrespective o compactness, as: Pipe Sections = (ASD 3-3) or Pipe sections, the allowale ending stress or oth major and minor axes o ending is taken as Round Bars = (or Compact sections), and (ASD 3-1) = (or Noncompact and Slender sections). (ASD 3-3) The allowale stress or oth the major and minor axis o ending o round ars is taken as, =. (ASD -1) Rectangular and Square Bars The allowale stress or oth the major and minor axis o ending o solid square ars is taken as, =. (ASD -1) or solid rectangular ars ent aout their major axes, the allowale stress is given =, And the allowale stress or minor axis ending o rectangular ars is taken as, =. (ASD -1) 36 Calculation o Allowale Stresses

45 Chapter III Check/Design or AISC-ASD89 Single-Angle Sections The allowale lexural stresses or Single-angles are calculated ased on their principal axes o ending (ASD SA 5.3). ajor Axis o Bending The allowale stress or major axis ending is the minimum considering the limit state o lateral-torsional uckling and local uckling (ASD SA 5.1). The allowale major ending stress or Single-angles or the limit state o lateraltorsional uckling is given as ollows (ASD SA 5.1.3): o =, i, major o o (ASD SA 5-3a) = major, i, o (ASD SA 5-3) o where, o is the elastic lateral-torsional uckling stress as calculated elow. The elastic lateral-torsional uckling stress, o, or equal-leg angles is taken as C, (ASD SA 5-5) o lt and or unequal-leg angles o is calculated as o C S I min major l ( lt r ), (ASD SA 5-6) w min w where, t min t, t, w l max l, l, 33 I min = minor principal moment o inertia, I max = major principal moment o inertia, S major = major section modulus or compression at the tip o one leg, r min = radius o gration or minor principal axis, Calculation o Allowale Stresses 37

46 SAP000 Steel Design anual w 1 I max A zw ( z ) da z, (ASD SA 5.3.) 0 z = coordinate along the major principal axis, w = coordinate along the minor principal axis, and z 0 = coordinate o the shear center along the major principal axis with respect to the centroid. w is a special section propert or angles. It is positive or short leg in compression, negative or long leg in compression, and zero or equal-leg angles (ASD SA 5.3.). However, or conservative design in SAP000, it is alwas taken as negative or unequal-leg angles. In the aove expressions C is calculated in the same wa as is done or I sections with the exception that the upper limit o C is taken here as 1.5 instead o.3. C = + a + a (ASD 1.3, SA 5..) The allowale major ending stress or Single-angles or the limit state o local uckling is given as ollows (ASD SA 5.1.1): =, major, i t, (ASD SA 5-1a) =, major, i t, (ASD SA 5-1) = Q, major, i t, (ASD SA 5-1c) where, t = thickness o the leg under consideration, = length o the leg under consideration, and Q = slenderness reduction actor or local uckling. (ASD A-B5-, SA 4) In calculating the allowale ending stress or Single-angles or the limit state o local uckling, the allowale stresses are calculated considering the act that either o 38 Calculation o Allowale Stresses

47 Chapter III Check/Design or AISC-ASD89 the two tips can e under compression. The minimum allowale stress is considered. inor Axis o Bending The allowale minor ending stress or Single-angles is given as ollows (ASD SA 5.1.1, 5.3.1, 5.3.):,minor =, i t, (ASD SA 5-1a),minor =, i t, (ASD SA 5-1),minor = Q, i t, (ASD SA 5-1c) In calculating the allowale ending stress or Single-angles it is assumed that the sign o the moment is such that oth the tips are under compression. The minimum allowale stress is considered. General Sections or General sections the allowale ending stress or oth major and minor axes ending is taken as, =. Allowale Stress in Shear The shear stress is calculated along the geometric axes or all sections. or I, Box, Channel, T, Doule angle, Pipe, Circular and Rectangular sections, the principal axes coincide with their geometric axes. or Single-angle sections, principal axes do not coincide with the geometric axes. ajor Axis o Bending The allowale shear stress or all sections except I, Box and Channel sections is taken in SAP000 as: v (ASD 4-1, SA 3-1) Calculation o Allowale Stresses 39

48 SAP000 Steel Design anual The allowale shear stress or major direction shears in I-shapes, oxes and channels is evaluated as ollows: v, i h t w 380, and (ASD 4-1) v C v, i h t w. (ASD 4-) where, C v 45, 000k ht k h k v, i, t v h tw w w v, i h t w k v, (ASD 4) k v ah ah a, i 1, h a, i 1, h (ASD 4) t w = Thickness o the we, a = Clear distance etween transverse stieners, in. Currentl it is taken conservativel as the length, l, o the memer in SAP000, h = Clear distance etween langes at the section, in. inor Axis o Bending The allowale shear stress or minor direction shears is taken as: v (ASD 4-1, SA 3-1) Calculation o Stress Ratios In the calculation o the axial and ending stress capacit ratios, irst, or each station along the length o the memer, the actual stresses are calculated or each load comination. Then the corresponding allowale stresses are calculated. Then, the capacit ratios are calculated at each station or each memer under the inluence o 40 Calculation o Stress Ratios

49 Chapter III Check/Design or AISC-ASD89 each o the design load cominations. The controlling capacit ratio is then otained, along with the associated station and load comination. A capacit ratio greater than 1.0 indicates an overstress. During the design, the eect o the presence o olts or welds is not considered. Also, the joints are not designed. Axial and Bending Stresses With the computed allowale axial and ending stress values and the actored axial and ending memer stresses at each station, an interaction stress ratio is produced or each o the load cominations as ollows (ASD H1, H, SA 6): I a is compressive and a a, the comined stress ratio is given the larger o + C a m a a ' e33 C m ' a e, and (ASD H1-1, SA 6.1) a 33 33, where (ASD H1-, SA 6.1) a, 33,, a, 33, and are deined earlier in this chapter, C m33 and C m are coeicients representing distriution o moment along the memer length. C m a, (ASD H1) or swa rame C m, or nonswa rame without transverse load C m a, or nonswa rame with transverse load and end restrained compression memer C m, and or nonswa rame with transverse load and end unrestrained compression memer C m (ASD H1), where is the ratio o the smaller to the larger moment at the ends o the a Calculation o Stress Ratios 41

50 SAP000 Steel Design anual memer, a eing positive or doule curvature ending and negative or single curvature ending. When is zero, C m is taken as 1.0. The program deaults C m to 1.0 i the unraced length actor, l, o the memer is redeined either the user or the program, i.e., i the unraced length is not equal to the length o the memer. The user can overwrite the value o C m or an memer. C m assumes two values, C m and C m33, associated with the major and minor directions. is given e 1 E e 3( Kl / r). (ASD H1) A actor o 4/3 is applied on e and i the load comination includes an wind load or seismic load (ASD H1, ASD A5.). I a is compressive and a a, a relativel simpliied ormula is used or the comined stress ratio. a a (ASD H1-3, SA 6.1) I a is tensile or zero, the comined stress ratio is given the larger o a a 33 33, and (ASD H-1, SA 6.) 33 33, where a, 33,, a, 33, and are deined earlier in this chapter. However, either 33 or need not e less than in the irst equation (ASD H-1). The second equation considers lexural uckling without an eneicial eect rom axial compression. or circular and pipe sections, an SRSS comination is irst made o the two ending components eore adding the axial load component, instead o the simple addition implied the aove ormulae. or Single-angle sections, the comined stress ratio is calculated ased on the properties aout the principal axis (ASD SA 5.3, 6.1.5). or I, Box, Channel, T, Doule-angle, Pipe, Circular and Rectangular sections, the principal axes coincide with their geometric axes. or Single-angle sections, principal axes are determined in 4 Calculation o Stress Ratios

51 Chapter III Check/Design or AISC-ASD89 SAP000. or general sections no eort is made to determine the principal directions. When designing or cominations involving earthquake and wind loads, allowale stresses are increased a actor o 4/3 o the regular allowale value (ASD A5.). Shear Stresses rom the allowale shear stress values and the actored shear stress values at each station, shear stress ratios or major and minor directions are computed or each o the load cominations as ollows: v, and v v v 3. or Single-angle sections, the shear stress ratio is calculated or directions along the geometric axis. or all other sections the shear stress is calculated along the principle axes which coincide with the geometric axes. When designing or cominations involving earthquake and wind loads, allowale shear stresses are increased a actor o 4/3 o the regular allowale value (ASD A5.). Calculation o Stress Ratios 43

52

53 Chapter IV Check/Design or AISC-LRD93 This chapter descries the details o the structural steel design and stress check algorithms that are used SAP000 when the user selects the AISC-LRD93 design code (AISC 1994). Various notations used in this chapter are descried in Tale IV-1. or reerring to pertinent sections and equations o the original LRD code, a unique preix LRD is assigned. However, all reerences to the Speciications or Load and Resistance actored Design o Single-Angle emers carr the preix o LRD SA. The design is ased on user-speciied loading cominations. But the program provides a set o deault load cominations that should satis requirements or the design o most uilding tpe structures. In the evaluation o the axial orce/iaxial moment capacit ratios at a station along the length o the memer, irst the actual memer orce/moment components and the corresponding capacities are calculated or each load comination. Then the capacit ratios are evaluated at each station under the inluence o all load cominations using the corresponding equations that are deined in this chapter. The controlling capacit ratio is then otained. A capacit ratio greater than 1.0 indicates exceeding a limit state. Similarl, a shear capacit ratio is also calculated separatel. 45

54 SAP000 Steel Design anual A = Cross-sectional area, in A e = Eective cross-sectional area or slender sections, in A g = Gross cross-sectional area, in Av, Av3 = ajor and minor shear areas, in A w = Shear area, equal dt w per we, in B 1 = oment magniication actor or moments not causing sideswa B = oment magniication actor or moments causing sideswa C = Bending coeicient C m = oment coeicient C w = Warping constant, in 6 D = Outside diameter o pipes, in E = odulus o elasticit, ksi cr = Critical compressive stress, ksi r = Compressive residual stress in lange assumed 10.0 or rolled sections and 16.5 or welded sections, ksi = Yield stress o material, ksi G = Shear modulus, ksi I = inor moment o inertia, in 4 I 33 = ajor moment o inertia, in 4 J = Torsional constant or the section, in 4 K = Eective length actor K 33, K = Eective length K-actors in the major and minor directions L = Laterall unraced length o memer, in L p = Limiting laterall unraced length or ull plastic capacit, in L r = Limiting laterall unraced length or inelastic lateral-torsional uckling, in cr = Elastic uckling moment, kip-in lt = actored moments causing sideswa, kip-in nt = actored moments not causing sideswa, kip-in n33, n = Nominal ending strength in major and minor directions, kip-in o = Elastic lateral-torsional uckling moment or angle sections, kip-in r33, r = ajor and minor limiting uckling moments, kip-in u = actored moment in memer, kip-in u33, u = actored major and minor moments in memer, kip-in P e = Euler uckling load, kips P n = Nominal axial load strength, kip P u = actored axial orce in memer, kips P = A g, kips Q = Reduction actor or slender section, = QQ a s 46 Tale IV-1 AISC-LRD Notations

55 Chapter IV Check/Design or AISC-LRD93 Q a = Reduction actor or stiened slender elements Q s = Reduction actor or unstiened slender elements S = Section modulus, in 3 S 33, S = ajor and minor section moduli, in 3 S e, 33, S e, = Eective major and minor section moduli or slender sections, in 3 S c = Section modulus or compression in an angle section, in 3 Vn, Vn3 = Nominal major and minor shear strengths, kips Vu, Vu3 = actored major and minor shear loads, kips Z = Plastic modulus, in 3 Z33, Z = ajor and minor plastic moduli, in 3 = Nominal dimension o plate in a section, in longer leg o angle sections, tw or welded and 3tw or rolled ox sections, etc. e = Eective width o lange, in = lange width, in d = Overall depth o memer, in d e = Eective depth o we, in h c = Clear distance etween langes less illets, in assumed d k or rolled sections, and d t or welded sections k = Distance rom outer ace o lange to we toe o illet, in k c = Parameter used or section classiication, 4 h t w, k c l33, l = ajor and minor direction unraced memer lengths, in r = Radius o gration, in r33, r = Radii o gration in the major and minor directions, in t = Thickness, in t = lange thickness, in t w = Thickness o we, in w = Special section propert or angles, in = Slenderness parameter c, e = Column slenderness parameters p = Limiting slenderness parameter or compact element r = Limiting slenderness parameter or non-compact element s = Limiting slenderness parameter or seismic element slender = Limiting slenderness parameter or slender element = Resistance actor or ending, 0.9 c = Resistance actor or compression, 0.85 t = Resistance actor or tension, 0.9 v = Resistance actor or shear, 0.9 Tale IV-1 AISC-LRD Notations (cont.) 47

56 SAP000 Steel Design anual English as well as SI and KS metric units can e used or input. But the code is ased on Kip-Inch-Second units. or simplicit, all equations and descriptions presented in this chapter correspond to Kip-Inch-Second units unless otherwise noted. Design Loading Cominations The design load cominations are the various cominations o the load cases or which the structure needs to e checked. or the AISC-LRD93 code, i a structure is sujected to dead load (DL), live load (LL), wind load (WL), and earthquake induced load (EL), and considering that wind and earthquake orces are reversile, then the ollowing load cominations ma have to e deined (LRD A4.1): 1.4 DL (LRD A4-1) 1. DL LL (LRD A4-) 0.9 DL 1.3 WL (LRD A4-6) 1. DL 1.3 WL (LRD A4-4) 1. DL LL 1.3 WL (LRD A4-4) 0.9 DL 1.0 EL (LRD A4-6) 1. DL 1.0 EL (LRD A4-4) 1. DL LL 1.0 EL (LRD A4-4) These are also the deault design load cominations in SAP000 whenever the AISC-LRD93 code is used. The user should use other appropriate loading cominations i roo live load is separatel treated, i other tpes o loads are present, or i pattern live loads are to e considered. Live load reduction actors can e applied to the memer orces o the live load case on an element--element asis to reduce the contriution o the live load to the actored loading. When using the AISC-LRD93 code, SAP000 design assumes that a P- analsis has een perormed so that moment magniication actors or moments causing sideswa can e taken as unit. It is recommended that the P- analsis e done at the actored load level o 1. DL plus 0.5 LL (White and Hajjar 1991). Classiication o Sections The nominal strengths or axial compression and lexure are dependent on the classiication o the section as Compact, Noncompact, Slender or Too Slender. 48 Design Loading Cominations

57 Chapter IV Check/Design or AISC-LRD93 igure IV-1 AISC-LRD Deinition o Geometric Properties Classiication o Sections 49

58 SAP000 Steel Design anual Description o Section Check COPACT ( p ) NONCOPACT r SLENDER ( slender ) t (rolled) t (welded) No limit No limit k c I-SHAPE or Pu P, 640 Pu 1 - P h c t w or P 191 P u 53 - Pu P 970 Pu P BOX h c t tw 190 As or I-shapes 38 As or I-shapes No limit CHANNEL h c t t w As or I-shapes As or I-shapes As or I-shapes As or I-shapes No limit As or I-shapes T-SHAPE t As or I-Shapes d t w Not applicale As or I-Shapes 17 No limit No limit ANGLE t Not applicale 76 No limit DOUBLE- ANGLE (Separated) t Not applicale 76 No limit PIPE D t (Compression onl) No limit or lexure ROUND BAR Assumed Compact RECTAN- GULAR Assumed Noncompact GENERAL Assumed Noncompact 50 Classiication o Sections Tale IV- Limiting Width-Thickness Ratios or Classiication o Sections in lexure ased on AISC-LRD

59 Chapter IV Check/Design or AISC-LRD93 Description o Section Width- Thickness Ratio COPACT (SEISIC ZONE) ( s ) NONCOPACT (Uniorm Compression) ( 33 0) ( r ) I-SHAPE t (rolled) t (welded) h c t w or Pu P, 50 Pu 1 - P or P P u 191 Pu 53 - P 53 BOX h c t t w Not applicale Not applicale CHANNEL T-SHAPE t hc tw As or I-shapes As or I-shapes t d t w Not applicale Not applicale As or I-shapes As or I-shapes As or I-shapes 17 ANGLE t Not applicale 76 DOUBLE-ANGLE (Separated) t Not applicale 76 PIPE D t Not applicale 3300 ROUND BAR Assumed Compact RECTANGULAR Assumed Noncompact GENERAL Assumed Noncompact Tale IV-3 Limiting Width-Thickness Ratios or Classiication o Sections (Special Cases) ased on AISC-LRD Classiication o Sections 51

60 SAP000 Steel Design anual SAP000 classiies individual memers according to the limiting width/thickness ratios given in Tale IV- and Tale IV-3 (LRD B5.1, A-G1, Tale A-1.1). The deinition o the section properties required in these tales is given in igure IV-1 and Tale IV-1. oreover, special considerations are required regarding the limits o width-thickness ratios or Compact sections in Seismic zones and Noncompact sections with compressive orce as given in Tale IV-3. I the limits or Slender sections are not met, the section is classiied as Too Slender. Stress check o Too Slender sections is eond the scope o SAP000. In classiing we slenderness o I-shapes, Box, and Channel sections, it is assumed that there are no intermediate stieners. Doule angles are conservativel assumed to e separated. Calculation o actored orces The actored memer loads that are calculated or each load comination are P u, u33, u, V u and V u3 corresponding to actored values o the axial load, the major moment, the minor moment, the major direction shear orce and the minor direction shear orce, respectivel. These actored loads are calculated at each o the previousl deined stations. or loading cominations that cause compression in the memer, the actored moment u ( u33 and u in the corresponding directions) is magniied to consider second order eects. The magniied moment in a particular direction is given : u = B nt + B 1 lt, where (LRD C1-1, SA 6) B 1 = oment magniication actor or non-sideswa moments, B = oment magniication actor or sideswa moments, nt = actored moments not causing sideswa, and lt = actored moments causing sideswa. The moment magniication actors are associated with corresponding directions. The moment magniication actor B 1 or moments not causing sideswa is given B = 1 1 C P u m P e, where (LRD C1-, SA 6-) P e is the Euler uckling load (P e A Kl, ), and r E g 5 Calculation o actored orces

61 Chapter IV Check/Design or AISC-LRD93 C m33 and C m are coeicients representing distriution o moment along the memer length. C m a, (LRD C1-3) a is the ratio o the smaller to the larger moment at the ends o the memer, a eing positive or doule curvature ending and negative or single curvature ending. or tension memers C m is assumed as 1.0. or compression memers with transverse load on the memer, C m is assumed as 1.0 or memers with an unrestrained end and as 0.85 or memers with two unrestrained ends. When is zero, C m is taken as 1.0. The program deaults C m to 1.0 i the unraced length actor, l, o the memer is redeined either the user or the program, i.e., i the unraced length is not equal to the length o the memer. The user can overwrite the value o C m or an memer. C m assumes two values, C m and C m33, associated with the major and minor directions. The magniication actor B 1, must e a positive numer. Thereore P u must e less than P e.ip u is ound to e greater than or equal to P e, a ailure condition is declared. SAP000 design assumes the analsis includes P- eects, thereore B is taken as unit or ending in oth directions. It is suggested that the P- analsis e done at the actored load level o 1. DL plus 0.5 LL (LRD C.). See also White and Hajjar (1991). or single angles, where the principal axes o ending are not coincident with the geometric axes (- and 3-3), the program conservativel uses the maximum o K l and K l or determining the major and minor direction Euler uckling capacit I the program assumptions are not satisactor or a particular structural model or memer, the user has a choice o explicitl speciing the values o B 1 and B or an memer. Calculation o actored orces 53

62 SAP000 Steel Design anual Calculation o Nominal Strengths The nominal strengths in compression, tension, ending, and shear are computed or Compact, Noncompact, and Slender sections according to the ollowing susections. The nominal lexural strengths or all shapes o sections are calculated ased on their principal axes o ending. or the Rectangular, I, Box, Channel, Circular, Pipe, T, and Doule-angle sections, the principal axes coincide with their geometric axes. or the Angle sections, the principal axes are determined and all computations except shear are ased on that. or Single-angle sections, the shear stresses are calculated or directions along the geometric axes. or all other sections the shear stresses are calculated along their geometric and principle axes. The strength reduction actor,, is taken as ollows (LRD A5.3): t = Resistance actor or tension, 0.9 (LRD D1, H1, SA, 6) c = Resistance actor or compression, 0.85 (LRD E, E3, H1) c = Resistance actor or compression in angles, 0.90 (LRD SA 4, 6) = Resistance actor or ending, 0.9 (LRD 1, H1, A-1, A-G, SA 5) = Resistance actor or shear, 0.9 (LRD, A-, A-G3, SA 3) v I the user speciies nominal strengths or one or more elements in the Redeine Element Design Data orm, these values will override the aove mentioned calculated values or those elements as deined in the ollowing susections. The speciied nominal strengths should e ased on the principal axes o ending. Compression Capacit The nominal compression strength is the minimum value otained rom lexural uckling, torsional uckling and lexural-torsional uckling. The strengths are determined according to the ollowing susections. or memers in compression, i Kl r is greater than 00, a message to that eect is printed (LRD B7, SA 4). or single angles, the minimum radius o gration, r z, is used instead o r and r 33 in computing Kl r. lexural Buckling The nominal axial compressive strength, P n, depends on the slenderness ratio, Kl r, and its critical value, c, where 54 Calculation o Nominal Strengths

63 Chapter IV Check/Design or AISC-LRD93 Kl r K l K max, r r 33 l, and c Kl r E. (LRD E-4, SA 4) or single angles, the minimum radius o gration, r z, is used instead o r and r 33 in computing Kl r. P n or Compact or Noncompact sections is evaluated or lexural uckling as ollows: P = A n g cr, where (LRD E-1) lc =, or c, and (LRD E-) cr = cr c, or c. (LRD E-3) P n or Slender sections is evaluated or lexural uckling as ollows: P = A n g cr, where (LRD A-B3d, SA 4) Qlc = Q, or c Q, and (LRD A-B5-15, SA 4-1) cr = cr c, or c Q. (LRD A-B5-16, SA 4-) The reduction actor, Q, or all compact and noncompact sections is taken as 1. or slender sections, Q is computed as ollows: Q Q Q s a, where (LRD A-B5-17, SA 4) Q s = reduction actor or unstiened slender elements, and (LRD A-B5.3a) Q a = reduction actor or stiened slender elements. (LRD A-B5.3c) TheQ s actors or slender sections are calculated as descried in Tale IV-4 (LRD A-B5.3a). The Q a actors or slender sections are calculated as the ratio o eective cross-sectional area and the gross cross-sectional area (LRD A-B5.3c). Q a A A e g (LRD A-B5-14) Calculation o Nominal Strengths 55

64 SAP000 Steel Design anual Section Tpe Reduction actor or Unstiened Slender Elements (Q s ) Equation Reerence Q s i t, t, i t, t, i t. LRD A-B5-5, LRD A-B5-6 I-SHAPE (rolled) Q s t k i c i t k, c k t k, c c k t i t k. c c (welded) LRD A-B5-7, LRD A-B5-8 BOX Q s 1 LRD A-B5.3d CHANNEL As or I-shapes with t replaced t. LRD A-B5-5, LRD A-B5-6, LRD A-B5-7, LRD A-B5-8 T-SHAPE Q s or langes, as or langes in I-shapes. or we see elow. i d t dt, i dt, w w dt, i dt. w w w, LRD A-B5-5, LRD A-B5-6, LRD A-B5-7, LRD A-B5-8, LRD A-B5-9, LRDA-B5-10 DOUBLE- ANGLE (Separated) Q s i t t, i t, t, i t., LRD A-B5-3, LRD A-B5-4 ANGLE Q s i t E, t E, i E t E, t E, i t E. LRD SA4-3 PIPE Q s 1 LRD A-B5.3d ROUND BAR RECTAN- GULAR Q s 1 LRD A-B5.3d Q s 1 LRD A-B5.3d GENERAL Q s 1 LRD A-B5.3d Tale IV-4 Reduction actor or Unstiened Slender Elements, Q s 56 Calculation o Nominal Strengths

65 Chapter IV Check/Design or AISC-LRD93 Section Tpe Eective Width or Stiened Sections Equation Reerence I-SHAPE h e h h, i, tw tw h 1, i ( h t ) t. w w (compression onl, P A g ) LRD A-B5-1 BOX h e e h h, i, tw tw h 1, i ( h t ) t. w, i, t t 1 ( t ), i w t. (compression onl, P A g ) (compr. or lexure, ) LRD A-B5-1 LRD A-B5-11 CHANNEL h e h h, i, tw tw h 1, i ( h t ) t. w w (compression onl, P A g ) LRD A-B5-1 T-SHAPE e DOUBLE- ANGLE e (Separated) ANGLE e PIPE Q a D 1, i, t D, i. Dt t (compression onl) LRD A-B5.3 LRD A-B5.3 LRD A-B5.3 LRD A-B5-13 ROUND BAR Not applicale RECTAN- GULAR e LRD A-B5.3 GENERAL Not applicale Tale IV-5 Eective Width or Stiened Sections Calculation o Nominal Strengths 57

66 SAP000 Steel Design anual The eective cross-sectional area is computed ased on eective width as ollows: A A t e g e e or unstiened elements is taken equal to, and e or stiened elements is taken equal to or less than as given in Tale IV-5 (LRD A-B5.3). or wes in I, ox, and Channel sections, h e is used as e and h is used as in the aove equation. lexural-torsional Buckling P n or lexural-torsional uckling o Doule-angle and T-shaped compression memers whose elements have width-thickness ratios less than r is given P = A n g crt, where (LRD E3-1) = crt H crz GJ Ar H cr crz cr crz, 0 cr crz, where (LRD E3-1) H x 0 1 r 0 0, r 0 = Polar radius o gration aout the shear center, x, are the coordinates o the shear center with respect to the centroid, 0 or doule-angle and T-shaped memers (-axis o smmetr), 0 0 x 0 cr is determined according to the equation LRD E-1 or lexural Kl uckling aout the minor axis o smmetr or c. r E Torsional and lexural-torsional Buckling The strength o a compression memer, P n, determined the limit states o torsional and lexural-torsional uckling is determined as ollows: P = A n g cr, where (LRD A-E3-1) 58 Calculation o Nominal Strengths

67 Chapter IV Check/Design or AISC-LRD93 Qle = Q, or e Q, and (LRD A-E3-) cr = cr e, or e Q. (LRD A-E3-3) In the aove equations, the slenderness parameter e is calculated as e e, (LRD A-E3-4) where e is calculated as ollows: or Rectangular, I, Box, and Pipe sections: e EC w z z K l 1 GJ I I 33 (LRD A-E3-5) or T-sections and Doule-angles: = e H H e ez e ez e ez (LRD A-E3-6) or Channels: = e H H e33 ez e 33 ez e 33 ez (LRD A-E3-6) or Single-angles sections with equal legs: = e H H e33 ez e 33 ez e 33 ez (LRD A-E3-6) or Single-angle sections with unequal legs, e is calculated as the minimum real root o the ollowing cuic equation (LRD A-E3-7): x0 ( e )( )( ) ( ) ( e33 e e e ez e e e e e r where, 0 e33 0 ) 0, r 0 Calculation o Nominal Strengths 59

68 SAP000 Steel Design anual x, are the coordinates o the shear center with respect to the centroid, 0 or doule-angle and T-shaped memers (-axis o smmetr), 0 0 x 0 I I 33 r x = polar radius o gration aout the shear center, A g H x 0 1 r 0 0, (LRD A-E3-9) e33 E K l r , (LRD A-E3-10) e E K l r, (LRD A-E3-11) ez EC w z z K l GJ Ar 1, (LRD A-E3-1) 0 K, K are eective length actors in minor and major directions, 33 K z is the eective length actor or torsional uckling, and it is taken equal to K in SAP000, l, l are eective lengths in the minor and major directions, 33 l z is the eective length or torsional uckling, and it is taken equal to l. or angle sections, the principal moment o inertia and radii o gration are used or computing e. Also, the maximum value o Kl, i.e, max( K l, K l ), is used in place o K l or K l in calculating and in this case e e 33 Tension Capacit The nominal axial tensile strength value P n is ased on the gross cross-sectional area and the ield stress. Pn Ag (LRD D1-1) It should e noted that no net section checks are made. or memers in tension, i lris greater than 300, a message to that eect is printed (LRD B7, SA ). or 60 Calculation o Nominal Strengths

69 Chapter IV Check/Design or AISC-LRD93 single angles, the minimum radius o gration, r z, is used instead o r and r 33 in computing Kl r. Nominal Strength in Bending The nominal ending strength depends on the ollowing criteria: the geometric shape o the cross-section, the axis o ending, the compactness o the section, and a slenderness parameter or lateral-torsional uckling. The nominal strengths or all shapes o sections are calculated ased on their principal axes o ending. or the Rectangular, I, Box, Channel, Circular, Pipe, T, and Doule-angle sections, the principal axes coincide with their geometric axes. or the Single Angle sections, the principal axes are determined and all computations related to lexural strengths are ased on that. The nominal ending strength is the minimum value otained according to the limit states o ielding, lateral-torsional uckling, lange local uckling, and we local uckling, as ollows: Yielding The lexural design strength o eams, determined the limit state o ielding is: Z S p (LRD 1-1) Lateral-Torsional Buckling Doul Smmetric Shapes and Channels or I, Channel, Box, and Rectangular shaped memers ent aout the major axis, the moment capacit is given the ollowing equation (LRD 1):, i L L, p33 p = n33 C - - p33 p33 r33 L-L L-L r p p, i L L L, p33 p r i L, cr 33 p33 r L. (LRD 1-1, 1-, 1-1) where, n33 = Nominal major ending strength, p33 = ajor plastic moment, Z S 33 33, (LRD 1.1) Calculation o Nominal Strengths 61

70 SAP000 Steel Design anual r 33 = ajor limiting uckling moment, ( r ) S or I-shapes and channels, (LRD 1-7) 33 and S e,33 or rectangular ars and oxes, (LRD 1-11) cr 33 = Critical elastic moment, C E EI GJ + I C w L L or I-shapes and channels, and C JA or oxes and rectangular ars, L r L = Laterall unraced length, l, (LRD 1-13) (LRD 1-14) L p = Limiting laterall unraced length or ull plastic capacit, 300 r or I-shapes and channels, and (LRD 1-4) 3750 r p33 JA or oxes and rectangular ars, (LRD 1-5) L r = Limiting laterall unraced length or inelastic lateral-torsional uckling, 1 1 r X 1 1 +X - r X 1 = r or I-shapes and channels, and (LRD 1-6) r JA or oxes and rectangular ars, (LRD 1-10) r S 33 EGJA, (LRD 1-8) 33 C S w 33 X = 4, (LRD 1-9) I GJ max C =, and (LRD 1-3) max A B C max,,,and are asolute values o maximum moment, 1/4 point, center o span and 3/4 point major moments respectivel, in the memer. C A B C should e taken as 1.0 or cantilevers. However, the program is unale to detect whether the memer is a cantilever. The user should overwrite C or cantilevers. The program also deaults C to 1.0 i the minor unraced length, l, o the memer is re- 6 Calculation o Nominal Strengths

71 Chapter IV Check/Design or AISC-LRD93 deined the user (i.e. it is not equal to the length o the memer). The user can overwrite the value o C or an memer. or I, Channel, Box, and Rectangular shaped memers ent aout the minor axis, the moment capacit is given the ollowing equation: = = Z S n p (LRD 1) or pipes and circular ars ent aout an axis, n = p = Z S. (LRD 1) T-sections and Doule Angles or T-shapes and Doule-angles the nominal major ending strength is given as, = n33 EI L GJ B+ 1 +B, where (LRD 1-15) S n33 33 S n33 33, or positive moment, stem in tension (LRD 1.c), or negative moment, stem in compression (LRD 1.c) B d L I. (LRD 1-16) J The positive sign or B applies or tension in the stem o T-sections or the outstanding legs o doule angles (positive moments) and the negative sign applies or compression in stem or legs (negative moments). or T-shapes and doule angles the nominal minor ending strength is assumed as, = S n. Single Angles The nominal strengths or Single-angles are calculated ased on their principal axes o ending. The nominal major ending strength or Single-angles or the limit state o lateral-torsional uckling is given as ollows (LRD SA 5.1.3): Calculation o Nominal Strengths 63

72 SAP000 Steel Design anual where, = n, major = n, major o, major, major o o major, i,, major o, major, i,,, major o, major, major = ield moment aout the major principal axis o ending, considering the possiilit o ielding at the heel and oth o the leg tips, o = elastic lateral-torsional uckling moment as calculated elow. The elastic lateral-torsional uckling moment, o, or equal-leg angles is taken as o C E t l, (LRD SA 5-5) and or unequal-leg angles the o is calculated as where, EC I l min o w min w t min t, t, w l max l, l, 33 I min = minor principal axis moment o inertia, I max = major principal axis moment o inertia, r min = radius o gration or minor principal axis, ( lt r ), (LRD SA 5-6) w 1 I max A zw ( z ) da z, (LRD SA 5.3.) 0 z = coordinate along the major principal axis, w = coordinate along the minor principal axis, and z 0 = coordinate o the shear center along the major principal axis with respect to the centroid. 64 Calculation o Nominal Strengths

73 Chapter IV Check/Design or AISC-LRD93 w is a special section propert or angles. It is positive or short leg in compression, negative or long leg in compression, and zero or equal-leg angles (LRD SA 5.3.). However, or conservative design in SAP000, it is alwas taken as negative or unequal-leg angles. General Sections or General sections the nominal major and minor direction ending strengths are assumed as, n = S. lange Local Buckling The lexural design strength, n, o Noncompact and Slender eams or the limit state o lange Local Buckling is calculated as ollows (LRD A-1): or major direction ending, p33, i, p = n33 p33 p33 r33 r p p, i, p r (A-1-3), i. and or minor direction ending, cr 33 p33 r p, i, p = n p p r r p p, i, p r (A-1-3), i. cr p r where, n33 = Nominal major ending strength, n = Nominal minor ending strength, p33 = ajor plastic moment, Z S p = inor plastic moment, Z S 33 33,, Calculation o Nominal Strengths 65

74 SAP000 Steel Design anual r 33 = ajor limiting uckling moment, r = inor limiting uckling moment, cr 33 = ajor uckling moment, cr = inor uckling moment, = Controlling slenderness parameter, p = Largest value o or which n p r = Largest value o or which uckling is inelastic. The parameters,,,,,, and p r or lange local uckling r 33 r cr 33 cr or dierent tpes o shapes are given elow: I Shapes, Channels t t, (or I sections) (LRD B5.1, Tale A-1.1), (or Channel sections) (LRD B5.1, Tale A-1.1) p, (LRD B5.1, Tale A-1.1) r k r, r c (LRD Tale A-1.1), ( ) S, (LRD Tale A-1.1) r33 r 33 S r, (LRD Tale A-1.1) cr 33 S 33 k, S c 33, (LRD Tale A-1.1) cr S k, S c, (LRD Tale A-1.1) 66 Calculation o Nominal Strengths

75 Chapter IV Check/Design or AISC-LRD93 r (LRD A-1) Boxes t t 3t t w w,, (LRD B5.1, Tale A-1.1) p, (LRD B5.1, Tale A-1.1) r, (LRD B5.1, Tale A-1.1) ( ) S, (LRD Tale A-1.1), r33 r e 33 ( ) S, (LRD Tale A-1.1), r r e S S S cr, (LRD Tale A-1.1) 33 e, 33 e, S cr e,, (LRD Tale A-1.1) r (LRD A-1) S e,33 = eective major section modulus considering slenderness, and S e, = eective minor section modulus considering slenderness. T-sections and Doule Angles No local uckling is considered or T sections and Doule angles in SAP000. I special consideration is required, the user is expected to analze this separatel. Single Angles The nominal strengths or Single-angles are calculated ased on their principal axes o ending. The nominal major and minor ending strengths or Single-angles or the limit state o lange local uckling are given as ollows (LRD SA 5.1.1): Calculation o Nominal Strengths 67

76 SAP000 Steel Design anual S c, i, t = n S c S c 1, i, i, t t, where, S c = section modulus or compression at the tip o one leg, t = thickness o the leg under consideration, = length o the leg under consideration, and Q = strength reduction actor due to local uckling. In calculating the ending strengths or Single-angles or the limit state o lange local uckling, the capacities are calculated or oth the principal axes considering the act that either o the two tips can e under compression. The minimum capacities are considered. Pipe Sections p t, (LRD Tale A-1.1), (LRD Tale A-1.1) r (LRD Tale A-1.1) = = + S r r, (LRD Tale A-1.1) 33 D t = = S, (LRD Tale A-1.1) cr 33 cr D t 68 Calculation o Nominal Strengths

77 Chapter IV Check/Design or AISC-LRD93 Circular, Rectangular, and General Sections No consideration o local uckling is required or solid circular shapes, rectangular plates (LRD Tale A-1.1). No local uckling is considered in SAP000 or circular, rectangular, and general shapes. I special consideration is required, the user is expected to analze this separatel. We Local Buckling The lexural design strengths are considered in SAP000 or onl the major axis ending (LRD Tale A-1.1). I Shapes, Channels, and Boxes The lexural design strength or the major axis ending, n, o Noncompact and Slender eams or the limit state o We Local Buckling is calculated as ollows (LRD A-1-1, A-1-3, A-G-): p33, i, p = n33 p33 p33 r33 r p p, i,(a-1,a-g1) p r S R R, i, 33 PG e cr r where, n33 = Nominal major ending strength, p33 = ajor plastic moment, Z S 33 33, (LRD 1.1) r 33 = ajor limiting uckling moment,re S 33,(LRD TaleA-1.1) = We slenderness parameter, p = Largest value o or which n p r = Largest value o or which uckling is inelastic, R PG = Plate girder ending strength reduction actor, R e = Hrid girder actor, and cr = Critical compression lange stress, ksi. The we slenderness parameters are computed as ollows, where the value o P u is taken as positive or compression and zero or tension: h t c w, Calculation o Nominal Strengths 69

78 SAP000 Steel Design anual p u 1, - - P P u P P 53, P u P P u P r u 1. - P P The parameters R PG, R e, and cr SAP000 as ollows: or slender we sections are calculated in R PG a r a r h t c w cr, (LRD A-G-3) R e a m m r a r 3 (or hrid sections), (LRD A-G) R e, (or non-hrid section), where (LRD A-G) a r, and (LRD A-G) m, taken as 1.0. (LRD A-G) min(, ) cr In the aove expressions, R e is taken as 1, ecause currentl SAP000 deals with onl non-hrid girders. The critical compression lange stress, cr, or slender we sections is calculated or limit states o lateral-torsional uckling and lange local uckling or the corresponding slenderness parameter in SAP000 as ollows: 70 Calculation o Nominal Strengths

79 Chapter IV Check/Design or AISC-LRD93, i, p = cr C i 1 1, r p p p r, (LRD A-G-4, 5, 6) C PG, i, r The parameters,,, and C p r or lateral-torsional uckling or slender we I, PG Channel and Box sections are given elow: p L r T, (LRD A-G-7), (LRD A-G-8) C r T r, (LRD A-G-9) C PG, and (LRD A-G-10) = radius o gration o the compression lange plus one-third o the compression portion o the we, and it is taken as 1 in SAP000. C = a actor which depends on span moment. It is calculated using the equation given in page 6. The parameters,,, and C p r or lange local uckling or slender we I, PG Channel and Box sections are given elow: p t, (LRD A-G-11), (LRD A-G-1) C r k c k PG c, (LRD A-G-13), and (LRD A-G-14) C 1. (LRD A-G-15) Calculation o Nominal Strengths 71

80 SAP000 Steel Design anual T-sections and Doule Angles No local uckling is considered or T-sections and Doule-angles in SAP000. I special consideration is required, the user is expected to analze this separatel. Single Angles The nominal major and minor ending strengths or Single-angles or the limit state o we local uckling are the same as those given or lange local uckling (LRD SA 5.1.1). No additional check is considered in SAP000. Pipe Sections The nominal major and minor ending strengths or Pipe sections or the limit state o we local uckling are the same as those given or lange local uckling (LRD Tale A-1.1). No additional check is considered in SAP000. Circular, Rectangular, and General Sections No we local uckling is required or solid circular shapes and rectangular plates (LRD Tale A-1.1). No we local uckling is considered in SAP000 or circular, rectangular, and general shapes. I special consideration is required, the user is expected to analze them separatel. Shear Capacities The nominal shear strengths are calculated or shears along the geometric axes or all sections. or I, Box, Channel, T, Doule angle, Pipe, Circular and Rectangular sections, the principal axes coincide with their geometric axes. or Single-angle sections, principal axes do not coincide with their geometric axes. ajor Axis o Bending The nominal shear strength,v n, or major direction shears in I-shapes, oxes and channels is evaluated as ollows: or h t w, or V = A n w, (LRD -1) < h, t w 7 Calculation o Nominal Strengths

81 Chapter IV Check/Design or AISC-LRD93 h V = A n w, and (LRD -) t w or < h t w, V = A w n ht w. (LRD -3 and A--3) The nominal shear strength or all other sections is taken as: V = A. n v inor Axis o Bending The nominal shear strength or minor direction shears is assumed as: V = A n3 v3 Calculation o Capacit Ratios In the calculation o the axial orce/iaxial moment capacit ratios, irst, or each station along the length o the memer, the actual memer orce/moment components are calculated or each load comination. Then the corresponding capacities are calculated. Then, the capacit ratios are calculated at each station or each memer under the inluence o each o the design load cominations. The controlling compression and/or tension capacit ratio is then otained, along with the associated station and load comination. A capacit ratio greater than 1.0 indicates exceeding a limit state. During the design, the eect o the presence o olts or welds is not considered. Also, the joints are not designed. Axial and Bending Stresses The interaction ratio is determined ased on the ratio P u.ip u is tensile, P n is the Pn nominal axial tensile strength and t ; and i P u is compressive, P n is the nominal axial compressive strength and c, except or angle sections c (LRD SA 6). In addition, the resistance actor or ending,. Calculation o Capacit Ratios 73

82 SAP000 Steel Design anual or P u P n, the capacit ratio is given as Pu P + 8 u 9 n 33 n33 + u n. (LRD H1-1a, SA 6-1a) or Pu P < n, the capacit ratio is given as PP + u n u33 n33 + u n. (LRD H1-1, SA 6-1a) or circular sections an SRSS (Square Root o Sum o Squares) comination is irst made o the two ending components eore adding the axial load component instead o the simple algeraic addition implied the aove ormulas. or Single-angle sections, the comined stress ratio is calculated ased on the properties aout the principal axis (LRD SA 5.3, 6). or I, Box, Channel, T, Doule angle, Pipe, Circular and Rectangular sections, the principal axes coincide with their geometric axes. or Single-angle sections, principal axes are determined in SAP000. or general sections it is assumed that the section properties are given in terms o the principal directions. Shear Stresses Similarl to the normal stresses, rom the actored shear orce values and the nominal shear strength values at each station or each o the load cominations, shear capacit ratios or major and minor directions are calculated as ollows: V v V v u V u3 V n n3, and, where v. or Single-angle sections, the shear stress ratio is calculated or directions along the geometric axis. or all other sections the shear stress is calculated along the principle axes which coincide with the geometric axes. 74 Calculation o Capacit Ratios

83 Chapter V Check/Design or AASHTO 1997 This chapter descries the details o the structural steel design and stress check algorithms that are used SAP000 when the user selects the AASHTO design code (AASHTO 1997). Various notations used in this chapter are descried in Tale V-1. The design is ased on user-speciied loading cominations. But the program provides a set o deault load cominations that should satis requirements or the design o most structures. In the evaluation o the axial orce/iaxial moment capacit ratios at a station along the length o the memer, irst the actual memer orce/moment components and the corresponding capacities are calculated or each load comination. Then the capacit ratios are evaluated at each station under the inluence o all load cominations using the corresponding equations that are deined in this section. The controlling capacit ratio is then otained. A capacit ratio greater than 1.0 indicates exceeding a limit state. Similarl, a shear capacit ratio is also calculated separatel. The design and check are limited to noncomposite, nonhrid and unstiened sections. Composite, hrid and stiened sections should e investigated the users independentl o SAP

84 SAP000 Steel Design anual A = Cross-sectional area, in A g = Gross cross-sectional area, in Av, Av3 = ajor and minor shear areas, in A w = Shear area, equal dt w per we, in C = Bending coeicient C m = oment coeicient C w = Warping constant, in 6 D = Outside diameter o pipes, in D c = Depth o we in compression, in D cp = Depth o we in compression under plastic moment, in E = odulus o elasticit, ksi cr = Critical compressive stress, ksi r = Compressive residual stress in lange assumed 10.0 or rolled sections and 16.5 or welded sections, ksi = Yield stress o material, ksi G = Shear modulus, ksi I = inor moment o inertia, in 4 I 33 = ajor moment o inertia, in 4 J = Torsional constant or the section, in 4 K = Eective length actor K 33, K = Eective length K-actors in the major and minor directions L = Laterall unraced length o memer, in L p = Limiting laterall unraced length or ull plastic capacit, in L r = Limiting laterall unraced length or inelastic lateral-torsional uckling, in cr = Elastic uckling moment, kip-in = actored moments not causing sideswa, kip-in s = actored moments causing sideswa, kip-in n33, n = Nominal ending strength in major and minor directions, kip-in p33, p = ajor and minor plastic moments, kip-in r33, r = ajor and minor limiting uckling moments, kip-in u = actored moment in memer, kip-in u33, u = actored major and minor moments in memer, kip-in P e = Euler uckling load, kips P n = Nominal axial load strength, kip P u = actored axial orce in memer, kips 76 Tale V-1 AASHTO-LRD Notations

85 Chapter V Check/Design or AASHTO 1997 S = Section modulus, in 3 S 33, S = ajor and minor section moduli, in 3 Vn, Vn3 = Nominal major and minor shear strengths, kips Vu, Vu3 = actored major and minor shear loads, kips Z = Plastic modulus, in 3 Z33, Z = ajor and minor plastic moduli, in 3 = Nominal dimension o longer leg o angles, in tw or welded and 3tw or rolled BOX (TS) sections = lange width, in d = Overall depth o memer, in h c = Clear distance etween langes less illets, in assumed d k or rolled sections and d t or welded sections k = Distance rom outer ace o lange to we toe o illet, in k c = Parameter used or section classiication, 4, k c h t w l33, l = ajor and minor direction unraced memer lengths, in r = Radius o gration, in r33, r = Radii o gration in the major and minor directions, in r z = inimum Radius o gration or angles, in t = Thickness, in t = lange thickness, in t w = Thickness o we, in = oment magniication actor or moments not causing sideswa s = oment magniication actor or moments causing sideswa = Slenderness parameter c = Column slenderness parameter p = Limiting slenderness parameter or compact element r = Limiting slenderness parameter or non-compact element = Resistance actor = Resistance actor or ending, 0.9 c = Resistance actor or compression, 0.85 = Resistance actor or tension, 0.9 v = Resistance actor or shear, 0.9 Tale V-1 AASHTO-LRD Notations (continued) 77

86 SAP000 Steel Design anual English as well as SI and KS metric units can e used or input. But the code is ased on Kip-Inch-Second units. or simplicit, all equations and descriptions presented in this chapter correspond to Kip-Inch-Second units unless otherwise noted. Design Loading Cominations The design load cominations are the various cominations o the prescried load cases or which the structure needs to e checked. There are six tpes o dead loads: dead load o structural components and nonstructural attachments (DC), downdrag (DD), dead load o wearing surace and utilities (DW), horizontal earth pressure load (EH), vertical earth pressure load (EV), earth surcharge load (ES). Each tpe o dead load case requires a separate load actor (AASHTO 3.4.1). There are six tpes o live loads: vehicular live load (LL), vehicular dnamic load allowance (I), vehicular centriugal orce (CE), vehicular raking orce (BR), pedestrian live load (PL), and live load surcharge (LS). All these live load cases require the same actor and do not need to e treated separatel (AASHTO 3.4.1). I the structure is sujected to structural dead load (DL), live load (LL), wind load (WL), and earthquake loads (EL), and considering that wind and earthquake orces are reversile, the ollowing deault load cominations have een considered or Strength and Extreme Event limit states (AASHTO 3.4.1) DL (Strength-IV) 1.5 DL LL (Strength-I) 0.90 DL 1.4 WL (Strength-III) 1.5 DL 1.4 WL (Strength-III) 1.5 DL LL 0.40 WL (Strength-V) 0.90 DL 1.0 EL (Extreme-I) 1.5 DL LL 1.0 EL (Extreme-I) These are also the deault design load cominations in SAP000 whenever the AASHTO LRD 1997 code is used. There are more dierent tpes o loads speciied in the code than are considered in the current implementation o the deault load cominations. However, the user has ull control o the deinition o loads and load cominations. The user is expected to deine the other load cominations as necessar. 78 Design Loading Cominations

87 Chapter V Check/Design or AASHTO 1997 Live load reduction actors can e applied to the memer orces o the live load case on an element--element asis to reduce the contriution o the live load to the actored loading. When using the AASHTO code, SAP000 design assumes that a P- analsis has een perormed so that moment magniication actors or moments causing sideswa can e taken as unit. It is recommended that the P- analsis e done at the actored load level (AASHTO C ) o 1.5 DL plus 1.35 LL (See White and Hajjar 1991). Classiication o Sections The nominal strengths or axial compression and lexure are dependent on the classiication o the section as Compact, Noncompact, or Slender. SAP000 classiies individual memers according to the width/thickness ratio quantities given in Tale V- (AASHTO 6). The deinitions o the section properties required in these tales are given in igure V-1. I the limits or non-compact criteria are not met, the section is classiied as Slender. Currentl SAP000 does not check stresses or Slender sections. Calculation o actored orces The actored memer loads that are calculated or each load comination are P u, u33, u,v u andv u3 corresponding to actored values o the axial load, the major moment, the minor moment, the major direction shear orce and the minor direction shear orce, respectivel. These actored loads are calculated at each o the previousl deined stations. or loading cominations that cause compression in the memer, the actored moment u ( u33 and u in the corresponding directions) is magniied to consider second order eects. The magniied moment in a particular direction is given : u= + s s, where (AASHTO ) = oment magniication actor or moments in raced mode, s = oment magniication actor or moments in sideswa mode, = actored moments not causing sideswa, and s = actored moments causing sideswa. Classiication o Sections 79

88 SAP000 Steel Design anual Description o Section Check Compact ( p ) Noncompact r t E E D t w c I-SHAPE D cp t w E E L u p re rt E BOX Assumed noncompact t CHANNEL h c t w or Pu P, 640 Pu 1 - P or P P u 191 Pu 53 - P 970 T-SHAPE t w As or Channels Not applicale As or Channels 17 ANGLE t Not applicale 76 DOUBLE- ANGLE (Sep.) t Not applicale 76 PIPE D t E E ROUND BAR Assumed compact RECTAN- GULAR Assumed Compact GENERAL Assumed Noncompact 80 Calculation o actored orces Tale V- Limiting Width-Thickness Ratio or lexure Classiication o Sections According to AASHTO

89 Chapter V Check/Design or AASHTO 1997 igure V-1 AASHTO Deinition o Geometric Properties Calculation o actored orces 81

90 SAP000 Steel Design anual The moment magniication actors are associated with corresponding directions. The moment magniication actor or moments not causing sideswa is given = 1 C m P c u P e, where (AASHTO ) P e is the Euler uckling load, P e EI ( Kl ) u, (AASHTO ) C m a, where (AASHTO ) a is the ratio o the smaller to the larger nonswa moments at the ends o the memer, a eing positive or single curvature ending and negative or doule curvature ending. or compression memers with transverse load on the memer, C m is assumed as 1.0. When is zero, C m is taken as 1.0. The program deaults C m to 1.0 i the unraced length, l, o the memer is redeined the user (i.e. it is not equal to the length o the memer). The user can overwrite the value o C m or an memer. The magniication actor, must e a positive numer. Thereore P u must e less than cp e.ip u is ound to e greater than or equal to cp e, a ailure condition is declared. SAP000 design assumes the analsis includes P- eects, thereore s is taken as unit or ending in oth directions. It is suggested that the P- analsis e done at the actored load level o 1.5 DL plus 1.35 LL (AASHTO C ). See also White and Hajjar (1991). I the program assumptions are not satisactor or a particular structural model or memer, the user has a choice o explicitl speciing the values o and s or an memer. Calculation o Nominal Strengths The nominal strengths in compression, tension, ending, and shear are computed or Compact and Non-compact sections according to the ollowing susections. The strength reduction actor,, is taken as ollows (AASHTO ): 8 Calculation o Nominal Strengths

91 Chapter V Check/Design or AASHTO 1997 = Resistance actor or ending, 1.0 (AASHTO , 6.10.) v = Resistance actor or shear, 1.0 (AASHTO , 6.10.) = Resistance actor or tension, 0.95 (AASHTO , 6.8.) = Resistance actor or compression, 0.9 (AASHTO , 6.9.) c or Slender sections and an singl smmetric and unsmmetric sections requiring consideration o local uckling, lexural-torsional and torsional uckling, or we uckling, reduced nominal strengths ma e applicale. The user must separatel investigate this reduction i such elements are used. The AASHTO design in SAP000 is limited to noncomposite, nonhrid and unstiened sections. The user must separatel investigate this reduction i such sections are used. I the user speciies nominal strengths or one or more elements in the Redeine Element Design Data, these values will override all the aove mentioned calculated values or those elements as deined in the ollowing susections. Compression Capacit The nominal axial compressive strength, P n, depends on the slenderness ratio, Kl r, and its critical value,. Kl c r is the larger o K l and K l, and r r 33 c Kl r E. (AASHTO ) P n is evaluated or lexural uckling as ollows: P = l c A n g, or c, and (AASHTO ) P = n c A, or g c. (AASHTO ) or single angles r z is used in place o r and r. or memers in compression, i 33 Kl is greater than 10, a message to that eect is printed (AASHTO 6.9.3). r In computing the column compression capacit, the sections are assumed to satis the slenderness requirements given elow: Calculation o Nominal Strengths 83

92 SAP000 Steel Design anual t k E, (AASHTO ) where the constant k ranges etween 0.56 and 1.86 depending on the supports o the outstanding elements o the sections (AASHTO Tale ). I this slenderness criteria is not satisied, it is suggested that AISC-LRD (1986) code should e used (AASHTO C ). The users are speciicall expected to consult AISC- LRD or this situation, ecause the current version o SAP000 does not consider this slenderness criteria. Tension Capacit The nominal axial tensile strength value P n is ased on the gross cross-sectional area and the ield stress. Pn Ag (AASHTO ) It should e noted that no net section checks are made. or memers in tension, i lris greater than 140, a message to that eect is printed (AASHTO 6.8.4). lexure Capacit The nominal ending strength depends on the ollowing criteria: the geometric shape o the cross-section, the axis o ending, the compactness o the section, and a slenderness parameter or lateral-torsional uckling. The nominal ending strength is the minimum value otained rom ielding, lateral-torsional uckling, lange local uckling, and we local uckling. The nominal moment capacit aout the minor axis is alwas taken to e the plastic moment capacit aout the minor axis unless as speciied elow. = = Z n p. However, the moment capacit aout the major axis is determined depending on the shapes as ollows. General Section General Sections are considered to e noncompact and their nominal moment capacit aout the major axis is given n S. 84 Calculation o Nominal Strengths

93 Chapter V Check/Design or AASHTO 1997 I-Section or compact I sections the moment capacit aout the major axis is given as: n Z (AASHTO , a, ) or noncompact I sections the moment capacit aout the major axis is given as: RRS n h, (AASHTO , a, ) where R h is the hrid actor, R h, or nonhrid sections, and (AASHTO a) R is the load shedding actor, and or nonhrid sections, R 1.0, ar D a t r w c E c D t w c E, Dc E,, t w ( a) where a r D t c t w, and (AASHTO a). (AASHTO a) or slender unstiened I sections, when the unraced length o the compression lange, L, exceeds the criteria or noncompactness L 1.76 r E t / (AASHTO d), and the we slenderness and the compression lange slenderness criteria or noncompact sections are satisied (AASHTO , c), the moment capacit aout the major axis is given as ollows (AASHTO ): Calculation o Nominal Strengths 85

94 SAP000 Steel Design anual I D t w c E, then EC R I n h L J I d L R h, ( ) i D t w c E and L L L p r, then C R R n h L L p RR h L L r p, and ( ) i D t w c E and L L, then r C R R L n h L r RR h, (AASHTO ) where, J dt t 3 3 w 3 3, (AASHTO ) L p E 1.76 rt, (AASHTO ) L r I d S 33 E, (AASHTO ), and (AASHTO ) C ( a ) ( a ). (AASHTO ) C is the moment gradient correction actor, a is the ratio o the smaller to the larger moments at the ends o the memer, a eing positive or single curvature ending and negative or doule curvature ending. When is zero, C is taken as 1.0. The program also deaults C to 1.0 i the unraced 86 Calculation o Nominal Strengths

95 Chapter V Check/Design or AASHTO 1997 length, l, o the memer is redeined the user (i.e. it is not equal to the length o the memer). The user can overwrite the value o C or an memer. r t is the minimum radius o gration taken aout the vertical axis o the compression lange plus one-third o the we in compression (AASHTO d). or slender unstiened I sections, when the compression lange exceeds the criteria or noncompactness, i.e. t E D t c c w,(aashto c), ut t E D t c cp w and the compression lange racing and the we slenderness requirements are satisied or noncompact sections (AASHTO d, ), the moment capacit aout the major axis is given as ollows (AASHTO ): n p Q Q p p Q l p, ( ) p where, Q p 3.0, and (AASHTO ) Q l Box Section 30.5 E, 0.38, D t t t w cp 4.45 E E, D t t w cp (AASHTO ) Noncomposite Box Sections are considered to e noncompact and their nominal moment capacit aout the major axis is given as ollows: n 1 Sl d t t w w S p (6.1...) AE I Calculation o Nominal Strengths 87

96 SAP000 Steel Design anual Pipe Section or compact Pipe sections (D t axis is given as: E ) the moment capacit aout the major n Z (AASHTO ) or noncompact Pipe sections ( E Dt E ) the moment capacit aout the major axis is given as: n S (AASHTO ) Circular Bar Solid Circular Bars are not sujected to lateral-torsional uckling. The are considered to e compact and their nominal moment capacit aout the major axis is given n Z. Rectangular and Channel Sections The nominal moment capacit o Rectangular and Channel Sections aout the major axis is computed according to AISC-LRD 1986 ased on ielding and Lateral-Torsional-Buckling limit states as ollows (AASHTO a): or channels and rectangular ars ent aout the major axis, i L =, n33 p33 i Lp L L r L p L -L p = C - - n33 p33 p33 r33 p33, (LRD 1-3) L -L and i L > L, r = C, (LRD 1-1) n33 cr33 r33 p33 where n33 = Nominal major ending strength, p33 = ajor plastic moment, Z S 33 33, r 33 = ajor limiting uckling moment, ( ) S or channels, (LRD 1-7) r 33 r p 88 Calculation o Nominal Strengths

97 Chapter V Check/Design or AASHTO 1997 and S 33 or rectangular ars, (LRD 1-11) cr 33 = Critical elastic moment, C E EI GJ + L L I C w or channels, and (LRD 1-13) C JA L r or rectangular ars, (LRD 1) L = Laterall unraced length, l, L p = Limiting laterall unraced length or ull plastic capacit, 300 r or channels, and (LRD 1-4) 3750 r p33 JA or rectangular ars, (LRD 1-5) L r = Limiting laterall unraced length or inelastic lateral-torsional uckling, r X 1 1 +X - r r 1 or channels, (LRD 1-6) r JA or rectangular sections, (LRD 1-10) X 1 = S r 33 EGJA, (LRD 1-8) 33 C S w 33 X = 4, (LRD 1-9) I GJ C ( a ) ( a ). (AASHTO ) or non-compact channels, the nominal ending strengths are not taken greater than that given the ormulas elow or the various local uckling modes possile or these sections. The nominal lexural strength n or the limit state o lange and we local uckling is: or major direction ending = -, ( LRD A-1-3) n33 p33 p33 r33 and or minor direction ending r p p Calculation o Nominal Strengths 89

98 SAP000 Steel Design anual = -, (LRD A-1-3) n p p r where, r r 33 = ajor limiting uckling moment, (LRD Tale A-1.1) ( r ) S or lange uckling o channels, and 33 S 33 or we uckling o channels, r = inor limiting uckling moment, (LRD Tale A-1.1) S or lange uckling o channels, = Controlling slenderness parameter, p = Largest value o or which n p r = Largest value o or which uckling is inelastic. T-Sections and Doule Angles or T-shapes and doule angles the nominal major ending strength is given as, p p n33 = C EI L GJ B+ 1 +B S, where (LRD 1-15) 33 B d L I. (LRD 1-16) J The positive sign or B applies or tension in the stem o T-sections or the outstanding legs o doule angles (positive moments) and the negative sign applies or compression in stem or legs (negative moments). Single Angles or single angles the nominal major and minor direction ending strengths are assumed as, n = S. Shear Capacities ajor Axis o Bending The nominal shear strength,v n, or major direction shears in I-shapes, oxes and channels is evaluated assuming unstiened girders as ollows (AASHTO ): 90 Calculation o Nominal Strengths

99 Chapter V Check/Design or AASHTO 1997 or d t w E, V = A n w, (AASHTO ) or E < d t E w, V = t E n w, and (AASHTO ) or d t w E, V = n 3 twe. (AASHTO ) d The nominal shear strength or all other sections is taken as: V = A. n v inor Axis o Bending The nominal shear strength or minor direction shears is assumed as: V = A n3 v3 Calculation o Capacit Ratios In the calculation o the axial orce/iaxial moment capacit ratios, irst, or each station along the length o the memer, the actual memer orce/moment components are calculated or each load comination. Then the corresponding capacities are calculated. Then, the capacit ratios are calculated at each station or each memer under the inluence o each o the design load cominations. The controlling compression and/or tension capacit ratio is then otained, along with the associated station and load comination. A capacit ratio greater than 1.0 indicates exceeding a limit state. During the design, the eect o the presence o olts or welds is not considered. Also, the joints are not designed. Calculation o Capacit Ratios 91

100 SAP000 Steel Design anual Axial and Bending Stresses The interaction ratio is determined ased on the ratio P u.ip u is tensile, P n is the Pn nominal axial tensile strength and t ; and i P u is compressive, P n is the nominal axial compressive strength and c. In addition, the resistance actor or ending,. or Pu P < n, the capacit ratio is given as PP + u n u33 n33 + u n. (AASHTO , 6.9..) or P u P n, the capacit ratio is given as Pu P + 8 u 9 n 33 n33 + u n. (AASHTO , 6.9..) or circular sections an SRSS (Square Root o Sum o Squares) comination is irst made o the two ending components eore adding the axial load component instead o the simple algeraic addition implied the aove ormulas. Shear Stresses Similarl to the normal stresses, rom the actored shear orce values and the nominal shear strength values at each station or each o the load cominations, shear capacit ratios or major and minor directions are produced as ollows: V v V v u V u3 V n n3, and. 9 Calculation o Capacit Ratios

101 Chapter VI Check/Design or CISC94 This chapter descries the details o the structural steel design and stress check algorithms that are used SAP000 when the user selects the CAN/CSA-S design code (CISC 1995). Various notations used in this chapter are descried in Tale VI-1. The design is ased on user-speciied loading cominations. But the program provides a set o deault load cominations that should satis requirements or the design o most uilding tpe structures. In the evaluation o the axial orce/iaxial moment capacit ratios at a station along the length o the memer, irst the actual memer orce/moment components and the corresponding capacities are calculated or each load comination. Then the capacit ratios are evaluated at each station under the inluence o all load cominations using the corresponding equations that are deined in this section. The controlling capacit ratio is then otained. A capacit ratio greater than 1.0 indicates exceeding a limit state. Similarl, a shear capacit ratio is also calculated separatel. English as well as SI and KS metric units can e used or input. But the code is ased on Newton-illimeter-Second units. or simplicit, all equations and descriptions presented in this chapter correspond to Newton-illimeter-Second units unless otherwise noted. 93

102 SAP000 Steel Design anual A = Cross-sectional area, mm A g = Gross cross-sectional area, mm Av, Av3 = ajor and minor shear areas, mm A w = Shear area, mm C e = Euler uckling strength, N C = actored compressive axial load, N C r = actored compressive axial strength, N C w = Warping constant, mm 6 C = Compressive axial load at ield stress, A g,n D = Outside diameter o pipes, mm E = odulus o elasticit, Pa = Speciied minimum ield stress, Pa G = Shear modulus, Pa I 33, I = ajor and minor moment o inertia, mm 4 J = Torsional constant or the section, mm 4 K = Eective length actor K 33, K = Eective length K-actors in the major and minor directions (assumed as 1.0 unless overwritten user) L = Laterall unraced length o memer, mm 33, = actored major and minor ending loads, N-mm p33, p = ajor and minor plastic moments, N-mm r33, r = actored major and minor ending strengths, N-mm u = Critical elastic moment, N-mm 33, = ajor and minor ield moments, N-mm S 33, S = ajor and minor section moduli, mm 3 T = actored tensile axial load, N T r = actored tensile axial strength, N U 1 = oment magniication actor to account or deormation o memer etween ends U = oment magniication actor ( on sideswa moments) to account or P- V, V3 = actored major and minor shear loads, N Vr, Vr3 = actored major and minor shear strengths, N Z, Z = ajor and minor plastic moduli, mm 3 33 Tale VI-1 CISC 94 Notations 94

103 Chapter VI Check/Design or CISC94 = Nominal dimension o longer leg o angles ( tw ) or welded ( 3t ) or rolled ox sections, mm = lange width, mm d = Overall depth o memer, mm h = Clear distance etween langes, taken as ( d t ),mm k = We plate uckling coeicient, assumed as 5.34 (no stieners) k = Distance rom outer ace o lange to we toe o illet, mm l = Unraced length o memer, mm l33, l = ajor and minor direction unraced memer lengths, mm r = Radius o gration, mm r33, r = Radii o gration in the major and minor directions, mm r z = inimum Radius o gration or angles, mm t = Thickness, mm t = lange thickness, mm t w = We thickness, mm = Slenderness parameter = Resistance actor, taken as = oment Coeicient, = ajor and minor direction moment coeicients 13 1 = Bending coeicient Tale VI-1 CISC 94 Notations (cont.) 95

104 SAP000 Steel Design anual Design Loading Cominations The design load cominations are the various cominations o the load cases or which the structure needs to e checked. or the CAN/CSA-S code, i a structure is sujected to dead load (DL), live load (LL), wind load (WL), and earthquake induced load (EL), and considering that wind and earthquake orces are reversile, then the ollowing load cominations ma have to e deined (CISC 7.): 1.5 DL 1.5 DL LL (CISC 7..) 1.5 DL 1.50 WL 0.85 DL 1.50 WL 1.5 DL (1.50 LL 1.50 WL) (CISC 7..) 1.00 DL 1.00 EL 1.00 DL LL 1.00 EL (CISC 7..6) These are also the deault design load cominations whenever the CISC Code is used. In generating the aove deault loading cominations, the importance actor is taken as 1. The user should use other appropriate loading cominations i roo live load is separatel treated, other tpes o loads are present, or i pattern live loads are to e considered. Live load reduction actors can e applied to the memer orces o the live load case on an element--element asis to reduce the contriution o the live load to the actored loading. When using the CISC code, SAP000 design assumes that a P- analsis has een perormed so that moment magniication actors or moments causing sideswa can e taken as unit. It is suggested that the P- analsis e done at the actored load level o 1.5 DL plus 1.05 LL. See also White and Hajjar (1991). or the gravit load case onl, the code (CISC 8.6.) requires that notional lateral loads e applied at each stor, equal to times the actored gravit loads acting at each stor. I extra load cases are used or such analsis, the should e included in the loading cominations with due consideration to the act that the notional lateral orces can e positive or negative. 96 Design Loading Cominations

105 Chapter VI Check/Design or CISC94 Classiication o Sections or the determination o the nominal strengths or axial compression and lexure, the sections are classiied as either Class 1 (Plastic), Class (Compact), Class 3 (Noncompact), or Class 4 (Slender). The program classiies the individual sections according to Tale VI- (CISC 11.). According to this tale, a section is classiied as either Class 1, Class, or Class 3 as applicale. I a section ails to satis the limits or Class 3 sections, the section is classiied as Class 4. Currentl SAP000 does not check stresses or Class 4 sections. Calculation o actored orces The actored memer orces or each load comination are calculated at each o the previousl deined stations. These memer orces are T or C, 33,,V and V 3 corresponding to actored values o the tensile or compressive axial load, the major moment, the minor moment, the major direction shear, and the minor direction shear, respectivel. Because SAP000 design assumes that the analsis includes P- eects, an magniication o sideswa moments due to the second order eects are alread included, thereore U or oth directions o ending is taken as unit. It is suggested that the P- analsis e done at the actored load level o 1.5 DL plus 1.05 LL. See also White and Hajjar (1991). However, the user can overwrite the values o U or oth major and minor direction ending. In this case in a particular direction is taken as: U, where g t (CISC 8.6.1) U = oment magniication actor or sideswa moments, g = actored moments not causing translation, and t = actored moments causing sideswa. Classiication o Sections 97

106 SAP000 Steel Design anual Description o Section Ratio Checked Class 1 (Plastic) Class (Compact) Class 3 (Noncompact) t I-SHAPE 1100 C h t w C 1700 C C 1900 C C BOX t 40 (rolled) 55 (welded) h t w As or I-shapes As or I-shapes As or I-shapes CHANNEL t Not applicale h t w Not applicale Not applicale Not applicale 00 As or I-shapes T-SHAPE t Not applicale d t w Not applicale Not applicale Not applicale DOUBLE ANGLE t Not applicale Not applicale 00 ANGLE t Not applicale Not applicale 00 PIPE (lexure) D t PIPE (Axial) D t 3000 ROUND BAR Assumed Class RECTAN- GULAR Assumed Class GENERAL Assumed Class 3 Tale VI- Limiting Width-Thickness Ratios or Classiication o Sections ased on CISC Calculation o actored orces

107 Chapter VI Check/Design or CISC94 igure VI-1 CISC 94 Deinition o Geometric Properties Calculation o actored orces 99

108 SAP000 Steel Design anual Calculation o actored Strengths The actored strengths in compression, tension, ending, and shear are computed or Class 1,, and 3 sections in SAP000. The strength reduction actor,, is taken as 0.9 (CISC 13.1). or Class 4 (Slender) sections and an singl smmetric and unsmmetric sections requiring consideration o local uckling, lexural-torsional and torsional uckling, or we uckling, reduced nominal strengths ma e applicale. The user must separatel investigate this reduction i such elements are used. I the user speciies nominal strengths or one or more elements in the Redeine Element Design Data", these values will override all the aove mentioned calculated values or those elements as deined in the ollowing susections. Compression Strength The actored axial compressive strength value, C r, or Class 1,, or 3 sections depends on a actor,, which eventuall depends on the slenderness ratio, Kl r, which is the larger o K l r and K l r, and is deined as = Kl r. E or single angles r Z is used in place o r and r. or memers in compression, i 33 Kl r is greater than 00, a message is printed (CISC 10..1). Then the actored axial strength is evaluated as ollows (CISC ): C r A 1 n - 1 n, where (CISC ) n is an exponent and it takes three possile values to match the strengths related to three SSRC curves. The deault n is 1.34 which is assigned to W-shapes rolled in Canada, aricated oxes and I shapes, and cold-ormed non-stress relieved (Class C) hollow structural sections (HSS) (CISC , CISC C13.3, anual Page 4-1, anual Tale 6-). The WW sections produced in Canada rom plate with lame-cut edges and hot-ormed or cold-relieved (Class H) HSS are assigned to a avorale value o n (CISC , CISC C13.3, anual Page 4-1). or heav sections, a smaller value o n (n ) is considered appropriate (CISC C13.3). SAP000 assumes the value o n as ollows: 100 Calculation o actored Strengths

109 Chapter VI Check/Design or CISC94 n or WW, HS (Class H) and HSS (Class H) sections, or W, L, and L sections and normal HS and HSS sections, or other sections with thickness less than 5.4 mm, or other sections with thickness larger than or equal to 5.4 mm. The HSS sections in the current Canadian Section Dataase o SAP000 are preixed as HS instead o HSS. Also, to consider an HSS section as Class H, it is expected that the user would put a suix to the HS or HSS section names. Tension Strength The actored axial tensile strength value, T r, is taken as A g (CISC 13..(a).(i)). or memers in tension, i lris greater than 300, a message is printed accordingl (CISC 10..). Tr Ag (CISC 13.) Bending Strengths The actored ending strength in the major and minor directions is ased on the geometric shape o the section, the section classiication or compactness, and the unraced length o the memer. The ending strengths are evaluated according to CISC as ollows (CISC 13.5 and 13.6): or laterall supported memers, the moment capacities are considered to e as ollows: or Class 1 and, r Z, and (CISC 13.5) or Class 3, r S. (CISC 13.5) Special considerations are required or laterall unsupported memers. The procedure or the determination o moment capacities or laterall unsupported memers (CISC 13.6) is descried in the ollowing susections. I the capacities ( r and r 33 ) are overwritten the user, the are used in the interaction ratio calculation when strengths are required or actual unraced lengths. None o these overwritten capacities are used or strengths in laterall supported case. Calculation o actored Strengths 101

110 SAP000 Steel Design anual I-shapes and Boxes ajor Axis o Bending or Class 1 and sections o I-shapes and oxes ent aout the major axis, when > u p33, p33 = 1 -, and (CISC 13.6) r3 p33 p33 when u p33, u r 33 = u, where (CISC 13.6) r 33 = actored major ending strength, p33 = ajor plastic moment, Z 33, u = Critical elastic moment, L EI GJ + E L I C w, (CISC 13.6) L = Laterall unraced length, l, C w = Warping constant assumed as 0.0 or oxes, pipes, rectangular and circular ars, and = + a + a. (CISC 13.6) a and are end moments o the unraced segment and a is less than a, eing positive or doule curvature ending and negative or single curvature ending. I an moment within the segment is greater than, is taken as 1.0. The program deaults to 1.0 i the unraced length, l o the memer is overwritten the user (i.e. it is not equal to the length o the memer). should e taken as 1.0 or cantilevers. However, the program is unale to detect whether the memer is a cantilever. The user can overwrite the value o or an memer speciing it. or Class 3 sections o I-shapes, channels, oxes ent aout the major axis, when u 33, 10 Calculation o actored Strengths

111 Chapter VI Check/Design or CISC94 = r , and (CISC 13.6) 33 u when u 33, r 33 u, where (CISC 13.6) r 33 and u are as deined earlier or Class 1 and sections and 33 is the major ield moment, S 33. inor Axis o Bending or Class 1 and sections o I-shapes and oxes ent aout their minor axis, = = Z r p. or Class 3 sections o I-shapes and oxes ent aout their minor axis, = = S r. Rectangular Bar ajor Axis o Bending or Class rectangular ars ent aout their major axis, when > u p33, p33 = 1 -, and (CISC 13.6) r33 p33 p33 when u, p33 u = r33 u. (CISC 13.6) inor Axis o Bending or Class sections o rectangular ars ent aout their minor axis, = = Z r p. Pipes and Circular Rods or pipes and circular rods ent aout an axis Calculation o actored Strengths 103

112 SAP000 Steel Design anual When u>, p33 p33 = 1 -, and (CISC 13.6) r33 p33 p33 when u, p33 u = r33 u. (CISC 13.6) Channel Sections ajor Axis o Bending or Class 3 channel sections ent aout their major axis, when u 33, = r33 33 when u, 33 = r33 u. inor Axis o Bending 33 1, and (CISC 13.6) 33 or Class 3 channel sections ent aout their minor axis, = = S r. T-shapes and doule angles ajor Axis o Bending u or Class 3 sections o T-shapes and doule angles the actored major ending strength is assumed to e (CISC 13.6d), = r33 EI L GJ B+ 1 +B S 33, where B= d L I J. 104 Calculation o actored Strengths

113 Chapter VI Check/Design or CISC94 The positive sign or B applies or tension in the stem o T-sections or the outstanding legs o doule angles (positive moments) and the negative sign applies or compression in stem or legs (negative moments). inor Axis o Bending or Class 3 sections o T-shapes and doule angles the actored minor ending strength is assumed as, = S. r Single Angle and General Sections or Class 3 single angles and or General sections, the actored major and minor direction ending strengths are assumed as, = S, and r33 33 = S. r Shear Strengths The actored shear strength,v r, or major direction shears in I-shapes, oxes and channels is evaluated as ollows (CISC ): or h t w k v, V = A r w. (CISC ) or k v < h t w k v 50, kv V = A r w 90. (CISC ) h t w k or < h v t w k v, V = A r w cri t, where (CISC ) Calculation o actored Strengths 105

114 SAP000 Steel Design anual kv = 90, and cri h t w = t cri 1 1 a/h. Assuming no stiener is used, the value o t is taken as zero. or h t w > k v 61, V = A r w cre t, where (CISC ) kv cre =. ( h/t ) w In the aove equations, k v is the shear uckling coeicient, and it is deined as: k v 4 ( a/ h), a / h 1 k v 4 ( a/ h), a / h 1 and the aspect ratio ahis the ratio o the distance etween the stieners to we depth. Assuming no stiener is used, the value o k v is taken as The actored shear strength or minor direction shears in I-shapes, oxes and channels is assumed as V A r v3. (CISC 13.4.) The actored shear strength or major and minor direction shears or all other sections is assumed as (CISC 13.4.): V V A r v A r3 v3, and (CISC 13.4.). (CISC 13.4.) 106 Calculation o actored Strengths

115 Chapter VI Check/Design or CISC94 Calculation o Capacit Ratios In the calculation o the axial orce/iaxial moment capacit ratios, irst, or each station along the length o the memer, or each load comination, the actual memer orce/moment components are calculated. Then the corresponding capacities are calculated. Then, the capacit ratios are calculated at each station or each memer under the inluence o each o the design load cominations. The controlling compression and/or tension capacit ratio is then otained, along with the associated station and load comination. A capacit ratio greater than 1.0 indicates exceeding a limit state. I the axial, lexural, and shear strengths o a section are overwritten the user, the overwritten values are used in calculating the stress ratios. However, certain strengths can not e overwritten. I the axial and ending capacities are overwritten the user, the are used in the interaction ratio calculation when strengths are required or actual unraced lengths. None o these overwritten capacities are used or strengths in laterall supported case. ore speciic inormation is given in the ollowing susections as needed. During the design, the eect o the presence o olts or welds is not considered. Also, the joints are not designed. Axial and Bending Stresses rom the actored axial loads and ending moments at each station and the actored strengths or axial tension and compression and major and minor ending, an interaction capacit ratio is produced or each o the load cominations as ollows: Compressive Axial Load I the axial load is compressive, the capacit ratio is given : C C + U r r U r, or all ut Class 1 I-shaped sections (13.8.1) C C + U r r33 + U 1 r, or Class 1 I-shaped sections (13.8.) The aove ratios are calculated or each o the ollowing conditions and the largest ratio is reported: Calculation o Capacit Ratios 107

116 SAP000 Steel Design anual Cross-sectional Strength: The axial compression capacit is ased on 0. C r A (CISC ) The and are calculated assuming that the memer is laterall r33 r ull supported ( l 0 and l 33 0) irrespective o its actual lateral racing length (CISC 13.5), and U 1 and U 13 are taken as 1. U U. (CISC , 13.8.) 13 1 I the capacities (C r, r and r 33 ) are overwritten the user, the are assumed not to appl to this case and are ignored. Overall emer Strength: The axial compression capacit is ased on oth major and minor direction uckling using oth K l and K l as descried in an earlier section r r 33 (CISC ). and are calculated assuming that the memer is laterall ull r33 r supported ( l 0 and l 33 0) irrespective o its actual lateral racing length (CISC 13.5), and U 1 and U 13 are calculated using the expression given elow oru 1. In this equation speciic values or major and minor directions are to e used to calculate values o U 1 and U 13 (CISC ). I the capacities (C r, r, and r 33 ) are overwritten the user, the onl overwritten capacit used in this case is C r. Lateral-Torsional Buckling Strength: The axial compression capacit is ased on weak-axis uckling onl ased on K l (CISC ), r and are calculated ased on actual unraced length (CISC r33 r 13.6), and 108 Calculation o Capacit Ratios

117 Chapter VI Check/Design or CISC94 U 1 and U 13 are calculated using the expression given elow oru 1. In this equation speciic values or major and minor directions are to e used to calculate values o U 1 and U 13 (CISC ). oreover, U 13 1 is enorced. (CISC , 13.8.) I the capacities (C r, r, and r 33 ) are overwritten the user, all three overwritten capacities are used in this case. In addition, or Class 1 I-shapes, the ollowing ratio is also checked: 33 r 33 r. (CISC 13.8.) I the capacities ( r and r 33 ) are overwritten the user, all these overwritten capacities are used in this case. In the aove expressions, 1 U = 1 1 -C /C e, (CISC ) C e L EI, 1 -. a 04, and a is the ratio o the smaller to the larger moment at the ends o the memer, a eing positive or doule curvature ending and negative or single curvature ending. is assumed as 1.0 or eams with transverse load and when 1 is zero. The program deaults to 1.0 i the unraced length, l, o the memer is redeined 1 the user (i.e. it is not equal to the length o the memer). The user can overwrite the value o or an memer speciing it. The actor U must e a positive 1 1 numer. Thereore C must e less than C e. I this is not true, a ailure condition is declared. Tensile Axial Load I the axial load is tensile the capacit ratio is given the larger o two ratios. In the irst case, the ratio is calculated as Calculation o Capacit Ratios 109

118 SAP000 Steel Design anual T T r + 33 r 33 + r, (CISC 13.9) assuming are calculated ased on ull supported memer ( l 0 r33 r and l 33 0). I the capacities (T r, r and r 33 ) are overwritten the user, the onl overwritten capacit used in this case is T r. r and r 33 overwrites are assumed not to appl to this case and are ignored. In the second case the ratio is calculated as 33 r33 + r T Z r33 33 A (or Class 1 and ), or (CISC 13.9) 33 r33 + r T S r33 33 A (or Class 3). (CISC 13.9) I the capacities ( r and r 33 ) are overwritten the user, oth o these overwritten capacities are used in this case. or circular sections an SRSS comination is irst made o the two ending components eore adding the axial load component instead o the simple algeraic addition implied the aove interaction ormulas. Shear Stresses rom the actored shear orce values and the actored shear strength values at each station, or each o the load cominations, shear capacit ratios or major and minor directions are produced as ollows: V V r and V V 3 r Calculation o Capacit Ratios

119 Chapter VII Check/Design or BS 5950 This chapter descries the details o the structural steel design and stress check algorithms that are used SAP000 when the user selects the BS 5950 design code (BSI 1990). Various notations used in this chapter are descried in Tale VII-1. The design is ased on user-speciied loading cominations. But the program provides a set o deault load cominations that should satis requirements or the design o most uilding tpe structures. In the evaluation o the axial orce/iaxial moment capacit ratios at a station along the length o the memer, irst the actual memer orce/moment components and the corresponding capacities are calculated or each load comination. Then the capacit ratios are evaluated at each station under the inluence o all load cominations using the corresponding equations that are deined in this section. The controlling capacit ratio is then otained. A capacit ratio greater than 1.0 indicates exceeding a limit state. Similarl, a shear capacit ratio is also calculated separatel. English as well as SI and KS metric units can e used or input. But the code is ased on Newton-illimeter-Second units. or simplicit, all equations and descriptions presented in this chapter correspond to Newton-illimeter-Second units unless otherwise noted. 111

120 SAP000 Steel Design anual A = Cross-sectional area, mm A g = Gross cross-sectional area, mm Av, Av3 = ajor and minor shear areas, mm B = Breadth, mm D = Depth o section, mm or outside diameter o pipes, mm E = odulus o elasticit, Pa c = Axial compression, N t = Axial tension, N v, v3 = ajor and minor shear loads, N G = Shear modulus, Pa H = Warping constant, mm 6 I 33 = ajor moment o inertia, mm 4 I = inor moment o inertia, mm 4 J = Torsional constant or the section, mm 4 K = Eective length actor K 33, K = ajor and minor eective length actors = Applied moment, N-mm 33 = Applied moment aout major axis, N-mm = Applied moment aout minor axis, N-mm a 33 = ajor maximum ending moment, N-mm a = inor maximum ending moment, N-mm = Buckling resistance moment, N-mm c = oment capacit, N-mm c33 = ajor moment capacit, N-mm c = inor moment capacit, N-mm E = Elastic critical moment, N-mm P c = Compression resistance, N Pc33, Pc = ajor and minor compression resistance, N P t = Tension capacit, N Pv, Pv3 = ajor and minor shear capacities, N S 33, S = ajor and minor plastic section moduli, mm 3 T = Thickness o lange or leg, mm Y s = Speciied ield strength, Pa Z, Z = ajor and minor elastic section moduli, mm 3 33 Tale VII-1 BS 5950 Notations 11

121 Chapter VII Check/Design or BS 5950 a = Roertson constant = Outstand width, mm d = Depth o we, mm h = Stor height, mm k = Distance rom outer ace o lange to we toe o illet, mm l = Unraced length o memer, mm l33, l = ajor and minor direction unraced memer lengths, mm le33, le = ajor and minor eective lengths, mm ( K 33l33, K l ) m = Equivalent uniorm moment actor n = Slenderness correction actor q e = Elastic critical shear strength o we panel, Pa q cr = Critical shear strength o we panel, Pa r33, r = ajor and minor radii o gration, mm r z = inimum radius o gration or angles, mm t = Thickness, mm t = lange thickness, mm t w = Thickness o we, mm u = Buckling parameter v = Slenderness actor = Ratio o smaller to larger end moments = Constant 75 = Slenderness parameter o = Limiting slenderness LT = Equivalent slenderness Lo = Limiting equivalent slenderness = Perr actor LT = Perr coeicient c = Compressive strength, Pa E = Euler strength, Pa = Yield strength, Pa = onosmmetr index 1 Tale VII-1 BS 5950 Notations (cont.) 113

122 SAP000 Steel Design anual Design Loading Cominations The design load cominations are the various cominations o the load cases or which the structure needs to e checked. According to the BS 5950 code, i a structure is sujected to dead load (DL), live load (LL), wind load (WL), and earthquake load (EL), and considering that wind and earthquake orces are reversile, then the ollowing load cominations ma have to e considered (BS.4): 1.4 DL 1.4 DL LL (BS.4.1.1) 1.0 DL 1.4 WL 1.4 DL 1.4 WL 1. DL + 1. LL 1. WL (BS.4.1.1) 1.0 DL 1.4 EL 1.4 DL 1.4 EL 1. DL + 1. LL 1. EL These are also the deault design load cominations whenever BS 5950 Code is used. The user should use other appropriate loading cominations i roo live load is separatel treated, other tpes o loads are present, or i pattern live loads are to e considered. Live load reduction actors can e applied to the memer orces o the live load case on an element--element asis to reduce the contriution o the live load to the actored loading. In addition to the aove load cominations, the code requires that all uildings should e capale o resisting a notional design horizontal load applied at each loor or roo level. The notional load should e equal to the maximum o 0.01 times the actored dead load and times the actored dead plus live loads (BS.4..3). The notional orces should e assumed to act in an one direction at a time and should e taken as acting simultaneousl with the actored dead plus vertical imposed live loads. The should not e comined with an other horizontal load cases (BS ). It is recommended that the user should deine additional load cases or considering the notional load in SAP000 and deine the appropriate design cominations. When using the BS 5950 code, SAP000 design assumes that a P- analsis has alread een perormed, so that moment magniication actors or the moments causing side-swa can e taken as unit. It is suggested that the P- analsis e 114 Design Loading Cominations

123 Chapter VII Check/Design or BS 5950 done at the actored load level corresponding to 1. dead load plus 1. live load. See also White and Hajjar (1991). Classiication o Sections The nominal strengths or axial compression and lexure are dependent on the classiication o the section as Plastic, Compact, Semi-compact, or Slender. SAP000 checks the sections according to Tale VII- (BS 3.5.). The parameters R, c and along with the slenderness ratios are the major actors in classiication o section. R is the ratio o mean longitudinal stress in the we to in a section. This implies that or a section in pure ending R is zero. In calculating R, compression is taken as positive and tension is taken as negative. R is calculated as ollows: R A g P is given as c d, where c is the distance rom the plastic neutral axis to the edge o the we connected to the compression lange. or, the section is treated as having compression throughout. c d c D P T, or I and Channel section t D P T, or Box and Doule Channel section 4 t In calculating c, compression is taken as negative and tension is taken as positive. is deined as ollows: 75 1 / The section is classiied as either Class 1 (Plastic), Class (Compact), or Class 3 (Semi-compact) as applicale. I a section ails to satis the limits or Class 3 (Semi-compact) sections, the section is classiied as Class 4 (Slender). Currentl SAP000 does not check stresses or Slender sections. Classiication o Sections 115

124 SAP000 Steel Design anual Description o Section Ratio Checked Class 1 (Plastic) Class (Compact) Class 3 (Semi-compact) T (Rolled) T (welded) I-SHAPE d t wes ( ) d t wes ( ) (rolled) d t wes ( ) (welded) or R 0 : R and 41 R (welded) 1 + R and 41 R (rolled) or R 0 :, and or R 0 : 1 +R and. T (Rolled) BOX T (welded) d t As or I-shapes As or I-shapes As or I-shapes CHANNEL d T t As or I-shapes As or I-shapes As or I-shapes T-SHAPE d T t DOUBLE ANGLE (separated) d t ( +d) t Tale VII- Limiting Width-Thickness Ratios or Classiication o Sections ased on BS Classiication o Sections

125 Chapter VII Check/Design or BS 5950 Description o Section Ratio Checked Class 1 (Plastic) Class (Compact) Class 3 (Semi-compact) ANGLE t ( +d) t PIPE D t SOLID CIRCLE Assumed Compact SOLID RECTANGLE Assumed Compact GENERAL Assumed Semi-compact Tale VII- (cont.) Limiting Width-Thickness Ratios or Classiication o Sections ased on BS 5950 Calculation o actored orces The actored memer loads that are calculated or each load comination are t or c, 33,, v, and v 3 corresponding to actored values o the tensile or compressive axial load, the major moment, the minor moment, the major direction shear load, and the minor direction shear load, respectivel. These actored loads are calculated at each o the previousl deined stations. The moment magniication or non-sideswa moments is included in the overall uckling interaction equations. 1 = g s,max s, where (BS 5.6.3) s,max = aximum stor-drit divided the stor-height, g = actored moments not causing translation, and s = actored moments causing sideswa. 117

126 SAP000 Steel Design anual igure VII-1 BS 5950 Deinition o Geometric Properties 118 Calculation o actored orces

127 Chapter VII Check/Design or BS 5950 The moment magniication actor or moments causing sideswa can e taken as unit i a P- analsis is carried out. SAP000 design assumes a P- analsis has een done and, thereore, smax, or oth major and minor direction ending is taken as 0. It is suggested that the P- analsis e done at the actored load level o 1. DL plus 1. LL. See also White and Hajjar (1991). Calculation o Section Capacities The nominal strengths in compression, tension, ending, and shear are computed or Class 1,, and 3 sections according to the ollowing susections. B deault, SAP000 takes the design strength,, to e 1.0 times the minimum ield strength o steel, Y s, as speciied the user. In inputting values o the ield strength, the user should ensure that the thickness and the ultimate strength limitations given in the code are satisied (BS 3.1.1). Y s (BS 3.1.1) or Class 4 (Slender) sections and an singl smmetric and unsmmetric sections requiring special treatment, such as the consideration o local uckling, lexuraltorsional and torsional uckling, or we uckling, reduced section capacities ma e applicale. The user must separatel investigate this reduction i such elements are used. I the user speciies nominal strengths or one or more elements in the Redeine Element Design Data, these values will override all aove the mentioned calculated values or those elements as deined in the ollowing susections. Compression Resistance The compression resistance or plastic, compact, or semi-compact sections is evaluated as ollows: P c = Ag c, (BS 4.7.4) where c is the compressive strength given c E 1, where (BS C.1) E E, (BS C.1) Calculation o Section Capacities 119

128 SAP000 Steel Design anual Description o Section Thickness (mm) ajor Axis o Bending inor I-SHAPE (rolled) an H-SHAPE (rolled) I-SHAPE (welded) BOX or Pipe (Rolled) an.0.0 BOX (welded) CHANNEL, T-SHAPE, ANGLE an RECTANGULAR or CIRCLE GENERAL an Tale VII-3 Roertson Constant in BS 5950 = Euler strength, E, E = Perr actor, a ) 0, (BS C.) 0 a = Roertson constant rom Tale VII-3, (BS C, BS Tale 5) 0 = Limiting slenderness, E 1, and (BS C.) = the slenderness ratio in either the major, l r,or 33 e33 33 in the minor, l r direction (BS ). e The larger o the two values is used in the aove equations to calculate P c. 10 Calculation o Section Capacities

129 Chapter VII Check/Design or BS 5950 or single angles r z is used instead o r 33 and r. or memers in compression, i is greater than 180, a message to that eect is printed (BS ). Tension Capacit The tension capacit o a memer is given P = A t g. (BS 4.6.1) It should e noted that no net section checks are made. or main memers in tension, the slenderness,, should not e greater than 50 (BS ). I is greater than 50, a message is displaed accordingl. The user ma have to separatel investigate the memers which are connected eccentricall to the axis o the memer, or example angle sections. oment Capacit The moment capacities in the major and minor directions, and are ased c33 c on the design strength and the section modulus, the co-existent shear and the possiilit o local uckling o the cross-section. Local uckling is avoided appling a limitation to the width/thickness ratios o elements o the cross-section. The moment capacities are calculated as ollows: Plastic and Compact Sections or plastic and compact sections, the moment capacities aout the major and the minor axes o ending depend on the shear orce, v, and the shear capacit, P v. or I, Box, Channel, and Doule-Channel sections ending aout the 3-3 axis the moment capacities considering the eects o shear orce are computed as c = S Z, v Pv, (BS 4..5) c = ( S S v ) Z, v P 1 v, (BS 4..6) where S = Plastic modulus o the gross section aout the relevant axis, Z = Elastic modulus o the gross section aout the relevant axis, Calculation o Section Capacities 11

130 SAP000 Steel Design anual S v = Plastic modulus o the gross section aout the relevant axis less the plastic modulus o that part o the section remaining ater deduction o shear area i.e. plastic modulus o shear area. or example, or rolled I-shapes S v is taken to e td 4 and or welded I-shapes it is taken as td 4, P v = The shear capacit descried later in this chapter, 1 = P v v. The comined eect o shear and axial orces is not eing considered ecause practical situations do not warrant this. In rare cases, however, the user ma have to investigate this independentl, and i necessar, overwrite values o the section moduli. or all other cases, the reduction o moment capacities or the presence o shear orce is not considered. The user should investigate the reduced moment capacit separatel. The moment capacit or these cases is computed in SAP000 as = S Z c. (BS 4..5) Semi-compact Sections Reduction o moment capacit due to coexistent shear does not appl or semicompact sections. c Z (BS 4..5) Lateral-Torsional Buckling oment Capacit The lateral torsional uckling resistance moment,, o a memer is calculated rom the ollowing equations. The program assumes the memers to e uniorm (o constant properties) throughout their lengths. urthermore memers are assumed to e smmetrical aout at least one axis. or I, Box, T, Channel, and Doule-Channel sections is otained rom = S 33 E S B B 33 E, where (BS B.1) 1 ) / 1 Calculation o Section Capacities

131 Chapter VII Check/Design or BS 5950 B S 33 LT E, E = LT = The elastic critical moment, The Perr coeicient. The Perr coeicient, LT or rolled sections S 33 LT E, and (BS B.3), or rolled and welded sections is taken as ollows: LT LT L 0, and (BS B.3) or welded sections, with ( ) ( ).(BS B.) LT L 0 LT L0 LT LT L0 In the aove deinition o, and are the limiting equivalent slenderness LT L 0 LT and the equivalent slenderness, respectivel, and is a constant. is taken as (BS.3). or langed memers smmetrical aout at least one axis and uniorm throughout their length, is deined as ollows: L 0 L 0 E, (BS B.4) or I, Channel, Doule-Channel, and T sections LT is deined as LT nuv, (BS B.5) and or Box sections LT is deined as LT.5 n 1, where (BS B.5) is the slenderness and is equivalent to l r e. n is the slenderness correction actor. or langed memers in general, not loaded etween adjacent lateral restraints, and or cantilevers without intermediate lateral restraints, n is taken as 1.0. or memers with equal langes loaded etween adjacent lateral restraints, the value o n is conservativel taken as given the ollowing ormula. This, however, can e overwritten the user or an memer speciing it (BS Tale 13). n 1 C 1.0, where Calculation o Section Capacities 13

132 SAP000 Steel Design anual C = max max A B C, and max,,, and are asolute values o maximum moment, 1/4 A B C point, center o span and 3/4 point major moments respectivel, in the memer. The program also deaults C to 1.0 i the unraced length, l,o the memer is redeined the user (i.e. it is not equal to the length o the memer). C should e taken as 1.0 or cantilevers. However, the program is unale to detect whether the memer is a cantilever. The user can overwrite the value o C or an memer. u is the uckling parameter. It is conservativel taken as 0.9 or rolled I-shapes and channels. or an other section, u is taken as 1.0 (BS ). or I, Channel, and Doule-Channel sections, u S 4 33 A ( D T) 14, or I, Channel, and Doule-Channel, (BS B.5) u I S 33 AH 14, or T section, where (BS B.5) I 1 I 33. (BS B.5) v is the slenderness actor. or I, Channel, Doule-Channel, and T sections, it is given the ollowing ormula. v 1 4N( N 1) + 0 x 1 1, where (BS B.5d) N 0.5, or I, Channel, Doule - Channel sections, 1.0, or T sections with lange in compression, 0.0, or T sections with lange in tension, and 0.0, or I, Channel, Doule - Channel sections, 0.8, or T sections with lange in compression, and -1.0, or T sections with lange in tension. (BS B.5d) (BS B.5d) 14 Calculation o Section Capacities

133 Chapter VII Check/Design or BS 5950 is the uckling index or ox section actor. It is given the ollowing ormula. (BS B.6.1). S 33 AJ 1, where (BS B.6.1) I 1 1 I J.6I (BS B.6.1) or all other sections, lateral torsional uckling is not considered. The user should investigate moment capacit considering lateral-torsional uckling separatel. Shear Capacities The shear capacities or oth the major and minor direction shears in I-shapes, oxes or channels are evaluated as ollows: P = A v, and v (BS 4..3) P = A v. 3 v3 (BS 4..3) The shear areas A v 3 and A v are given in Tale VII-4. oreover, the shear capacit computed aove is valid onl i dt 63, strictl speaking. or dt 63, the shear uckling o the thin memers should e checked independentl the user in accordance with the code (BS 4.4.5). Calculation o Capacit Ratios In the calculation o the axial orce/iaxial moment capacit ratios, irst, or each station along the length o the memer, or each load comination, the actual memer orce/moment components are calculated. Then the corresponding capacities are calculated. Then, the capacit ratios are calculated at each station or each memer under the inluence o each o the design load cominations. The controlling compression and/or tension capacit ratio is then otained, along with the associated station and load comination. A capacit ratio greater than 1.0 indicates exceeding a limit state. During the design, the eect o the presence o olts or welds is not considered. Also, the joints are not designed. Calculation o Capacit Ratios 15

134 SAP000 Steel Design anual Description o Section Condition ajor Axis o Bending inor I-SHAPE Rolled Welded td td 0.9 4T 0.9 4T CHANNEL Rolled Welded td td 0.9 T 0.9 T DOUBLE CHANNEL Rolled Welded.0 td.0 td.0 * 0.9 T.0 * 0.9 T BOX D D B A B D B A T-SHAPE Rolled Welded td t d T 0.9 T 0.9 T DOUBLE ANGLE td t ANGLE td t RECTANGULAR 0.9 A 0.9 A CIRCLE 0.9 A 0.9 A PIPE 0.6 A 0.6 A GENERAL 0.9 A 0.9 A Tale VII-4 Shear Area in BS Calculation o Capacit Ratios

135 Chapter VII Check/Design or BS 5950 Local Capacit Check or memers under axial load and moments, local capacit ratios are calculated as ollows: Under Axial Tension A simpliied approach allowed the code is used to check the local capacit or plastic and compact sections. A t g c33 c (BS 4.8.) Under Axial Compression Similarl, the same simpliied approach is used or axial compression. A c g c33 c (BS ) Overall Buckling Check In addition to local capacit checks, which are carried out at section level, a compression memer with ending moments is also checked or overall uckling in accordance with the ollowing interaction ratio: A c m + m Z g c (BS ) The equivalent uniorm moment actor, m, or memers o uniorm section and with langes, not loaded etween adjacent lateral restraints, is deined as m= +. (BS Tale 18) or other memers, the value o m is taken as 1.0. The program deaults m to 1.0 i the unraced length, l, o the memer is overwritten the user (i.e. i it is not equal to the length o the memer). The user can overwrite the value o m or an memer speciing it. is the ratio o the smaller end moment to the larger end moment on a span equal to the unrestrained length, eing positive or single curvature ending and negative or doule curvature ending. Calculation o Capacit Ratios 17

136 SAP000 Steel Design anual Shear Capacit Check rom the actored shear orce values and the shear capacit values at each station, shear capacit ratios or major and minor directions are produced or each o the load cominations as ollows: P P v v v 3 v 3, and. 18 Calculation o Capacit Ratios

137 Chapter VIII Check/Design or EUROCODE 3 This chapter descries the details o the structural steel design and stress check algorithms that are used SAP000 when the user selects the Eurocode 3 design code (CEN 199). The program investigates the limiting states o strength and stailit ut does not address the serviceailit limit states. Various notations used in this chapter are descried in Tale VIII-1. The design is ased on user-speciied loading cominations. But the program provides a set o deault load cominations that should satis requirements or the design o most uilding tpe structures. In the evaluation o the axial orce/iaxial moment capacit ratios at a station along the length o the memer, irst the actual memer orce/moment components and the corresponding capacities are calculated or each load comination. Then the capacit ratios are evaluated at each station under the inluence o all load cominations using the corresponding equations that are deined in this section. The controlling capacit ratio is then otained. A capacit ratio greater than 1.0 indicates exceeding a limit state. Similarl, a shear capacit ratio is calculated separatel. English as well as SI and KS metric units can e used or input. But the code is ased on Newton-illimeter-Second units. or simplicit, all equations and descriptions presented in this chapter correspond to Newton-illimeter-Second units unless otherwise noted. 19

138 SAP000 Steel Design anual A = Gross cross-sectional area, mm Av, Av3 = Areas or shear in the - and 3-directions, mm C 1 = Bending coeicient E = odulus o elasticit, Pa G = Shear modulus, Pa I t = Torsion constant, mm 4 I w = Warping constant, mm 6 I 33 = ajor moment o inertia, mm 4 I = inor moment o inertia, mm 4 K = Eective length actor L = Length, span, mm K 33, K = ajor and minor eective length actors Rd. = Design uckling resistance moment, N-mm cr = Elastic critical moment or lateral-torsional uckling, N-mm gsd. = Design moments not causing sideswa, N-mm ssd. = Design moments causing sideswa, N-mm VSd. = Design moment resistance ater considering shear, N-mm 33. Sd = Design value o moment aout the major axis, N-mm. Sd = Design value o moment aout the minor axis, N-mm 33. Rd = Design moment resistance aout the major axis, N-mm. Rd = Design moment resistance aout the minor axis, N-mm N Rd. = Design uckling resistance o a compression memer, N N 33. Rd = Design uckling resistance o a compression memer aout the major axis, N N. Rd = Design uckling resistance o a compression memer aout the minor axis, N N csd. = Design value o compressive orce, N N crd. = Design compression resistance, N N tsd. = Design value o tensile orce, N N trd. = Design tension resistance, N N pl. Rd = Design plastic shear resistance, N V. Sd = Design value o shear orce in the major direction, N V 3. Sd = Design value o shear orce in the minor direction, N V. Rd = Design shear resistance in the major direction, N Tale VIII-1 Eurocode 3 Notations 130

139 Chapter VIII Check/Design or EUROCODE 3 V 3. Rd = Design shear resistance in the minor direction, N Wel. 33, Wel. = ajor and minor elastic section moduli, mm 3 Wpl. 33, Wpl. = ajor and minor plastic section moduli, mm 3 = Width, mm c = Distance, mm d = Depth o we, mm = Nominal ield strength o steel, Pa h = Overall depth, mm l33, l = ajor and minor direction unraced memer lengths, mm i33, i = ajor and minor radii o gration, mm i z = inimum radius o gration or angles, mm k33, k = actors applied to the major and minor design moments in the interaction equations k LT = actor applied to the major design moments in the interaction equation checking or ailure due to lateral-torsional uckling t = Thickness, mm t = lange thickness, mm t w = We thickness, mm = Ratio used in classiication o sections, 0 1 = aterial partial saet actors = 1 35 ( in Pa) = Reduction actor a = Post-critical shear strength, Pa 33, = Reduction actors or uckling aout the 3-3 and - axes LT = Reduction actor or lateral-torsional uckling = Ratio o smaller to larger end moment o unraced segment s = Ampliication actor or swa moments Tale VIII-1 Eurocode 3 Notations (cont.) 131

140 SAP000 Steel Design anual Design Loading Cominations The design loading cominations deine the various actored cominations o the load cases or which the structure is to e checked. The design loading cominations are otained multipling the characteristic loads with appropriate partial actors o saet. I a structure is sujected to dead load (DL) and live load (LL) onl, the design will need onl one loading comination, namel 1.35 DL LL. However, in addition to the dead load and live load, i the structure is sujected to wind (WL) or earthquake induced orces (EL), and considering that wind and earthquake orces are suject to reversals, the ollowing load cominations ma have to e considered (EC3.3.3): 1.35 DL 1.35 DL LL (EC3.3.3) 1.35 DL 1.50 WL 1.00 DL 1.50 WL 1.35 DL LL 1.35 WL (EC3.3.3) 1.00 DL 1.00 EL 1.00 DL + 1.5*0.3 LL 1.0 EL (EC3.3.3) In act, these are the deault load cominations which can e used or overwritten the user to produce other critical design conditions. These deault loading cominations are produced or persistent and transient design situations (EC3.3..) comining orces due to dead, live, wind, and earthquake loads or ultimate limit states. See also section 9.4 o Eurocode 1 (CEN 1994) and Tale 1, 3, and 4 and section 4 o United Kingdom National Application Document (NAD). The deault load cominations will usuall suice or most uilding design. The user should use other appropriate loading cominations i roo live load is separatel treated, other tpes o loads are present, or i pattern live loads are to e considered. Live load reduction actors can e applied to the memer orces o the live load case on an element--element asis to reduce the contriution o the live load to the actored loading. In addition to the loads descried earlier, equivalent lateral load cases or geometric imperection should e considered the user. This equivalent load is similar to the notional load o the British code, and depends on the numer o stories and numer o columns in an loor (EC ). Additional load cominations are also needed or these load cases. 13 Design Loading Cominations

141 Chapter VIII Check/Design or EUROCODE 3 When using Eurocode 3, SAP000 design assumes that a P- analsis has een perormed so that moment magniication actors or moments causing sideswa can e taken as unit. It is suggested that the P- analsis should e done at the actored load level corresponding to 1.35 dead load plus 1.35 live load. See also White and Hajjar (1991). Classiication o Sections The design strength o a cross-section suject to compression due to moment and/or axial load depends on its classiication as Class 1 (Plastic), Class (Compact), Class 3 (Semi-compact), or Class 4 (Slender). According to Eurocode 3, the classiication o sections depends on the classiication o lange and we elements. The classiication also depends on whether the compression elements are in pure compression, pure ending, or under the inluence o comined axial orce and ending (EC3 5.3.). SAP000 conservativel classiies the compression elements according to Tale VIII- and Tale VIII-3. Tale VIII- is used when the section is under the inluence o axial compression orce onl or comined axial compression orce and ending. Tale VIII-3 is used when the section is in pure ending or under the inluence o comined axial tensile orce and ending. The section dimensions used in the tales are given in igure VIII-1. I the section dimensions satis the limits shown in the tales, the section is classiied as Class 1, Class, or Class 3 as applicale. A cross-section is classiied reporting the highest (least avorale) class o its compression elements. I a section ails to satis the limits or Class 3 sections, the section is classiied as Class 4. Currentl SAP000 does not check stresses or Class 4 sections. One o the major actors in determining the limiting width-thickness ratio is. This parameter is used to relect the inluence o ield stress on the section classiication. 35 (EC3 5.3.) In classiing I, Box, Channel, Doule-Channel, and T sections, two other actors, are deined as ollows: Classiication o Sections 133

142 SAP000 Steel Design anual Section Element Ratio Checked Class 1 Class Class 3 I-SHAPE we dt w I 0.5, , else i 0.5, 36. I 0.5, , else i 0.5, I 1, , else i 1, 6 1 lange ct (rolled) ct (welded) we dt w Same as I-Shape Same as I-Shape Same as I-Shape BOX lange ( 3t ) t (rolled) t (welded) CHANNEL we dt w Same as I-Shape Same as I-Shape Same as I-Shape lange t we dt w T-SHAPE lange t (rolled) t (welded) DOUBLE ANGLES ht ( h) max( t, ) Not applicale Not applicale 15ε 11.5ε ANGLE ht ( h) max( t, ) Not applicale Not applicale 15ε 11.5ε PIPE dt 50ε 70ε 90ε ROUND BAR None Assumed Class 1 RECTANGLE None Assumed Class Tale VIII- Limiting Width-Thickness Ratios or Classiication o Sections ased on Eurocode 3 (Compression and Bending) 134 Classiication o Sections

143 Chapter VIII Check/Design or EUROCODE 3 Section Element Ratio Checked Class 1 Class Class 3 we dt w I-SHAPE lange ct (rolled) ct (welded) we dt w BOX CHANNEL lange we ( 3 t ) t (rolled) t (welded) dt w (ajor axis) dt w (inor axis) lange t we dt w T-SHAPE lange t (rolled) t (welded) DOUBLE ANGLES ht ( h) max t, Not applicale Not applicale 15.0 ε 11.5 ε ANGLE ht ( h) max t, Not applicale Not applicale 15.0ε 11.5ε PIPE dt 50ε 70ε 90ε ROUND BAR None Assumed Class 1 RECTANGLE None Assumed Class GENERAL None Assumed Class 3 Tale VIII-3 Limiting Width-Thickness Ratios or Classiication o Sections ased on Eurocode 3 (Bending Onl) Classiication o Sections 135

144 SAP000 Steel Design anual igure VIII-1 Eurocode 3 Deinition o Geometric Properties 136 Classiication o Sections

145 Chapter VIII Check/Design or EUROCODE N c, Sd htw, or I, Channel, and T sections, 1 Nc, Sd ht, or Box and Doule - Channel sections, and w 1 N, A c Sd, 0 1.0, In the aove expression, N c, Sd is taken as positive or tension and negative or compression. equals 0.0 or ull tension, 0.5 or pure ending and 1.0 or ull compression. equals -3.0 or ull tension, -1.0 or pure ending and 1.0 or ull compression. Calculation o actored orces The internal design loads which are calculated or each load comination are N tsd. or N csd., 33. Sd,. Sd,V. Sd and V 3. Sd corresponding to design values o the tensile or compressive axial load, the major moment, the minor moment, the major direction shear and the minor direction shear respectivel. These design loads are calculated at each o the previousl deined stations o each rame element. The design moments and orces need to e corrected or second order eects. This correction is dierent or the so called swa and nonswa components o the moments. The code requires that the additional swa moments introduced the horizontal delection o the top o a stor relative to the ottom must e taken into account in the elastic analsis o the rame in one o the ollowing was (EC ): Directl carring out the gloal rame analsis using P- analsis. emer design can e carried out using in-plane uckling lengths or nonswa mode. Indirectl modiing the results o a linear elastic analsis using an approximate method which makes allowance or the second order eects. There are two alternative was to do this ampliied swa moment method or swa mode in-plane uckling method. Calculation o actored orces 137

146 SAP000 Steel Design anual The advantage o the direct second order elastic analsis is that this method avoids uncertaint in approximating the uckling length and also avoids splitting up moments into their swa and nonswa components. SAP000 design assumes that P- eects are included in the analsis. Thereore an magniication o sideswa moments due to second order eects is alread accounted or, i. e. s in the ollowing equation is taken as 1.0. Itis suggested that the P- analsis e done at the actored load level o 1.35 DL plus 1.35 LL. See also White and Hajjar (1991). However, the user can overwrite the values o or oth major and minor direction ending in which case in a s Sd particular direction is taken as: = + Sd g.sd s, where (EC ) s.sd gsd ssd. = Design moments not causing translation, and. = Design moments causing sideswa. oment magniication or non-sideswa moments is included in the overall uckling interaction equations. Swa moments are produced in a rame the action o an load which results in swa displacements. The horizontal loads can e expected alwas to produce swa moments. However, the are also produced vertical loads i either the load or the rame are unsmmetrical. In the case o a smmetrical rame with smmetrical vertical loads, the swa moments are simpl the internal moments in the rames due to the horizontal loads (EC ). Calculation o Section Resistances The nominal strengths in compression, tension, ending, and shear are computed or Class 1,, and 3 sections according to the ollowing susections. The material partial saet actors used the program are:, and (EC ) 0. (EC ) 1 or Class 4 (Slender) sections and an singl smmetric and unsmmetric sections requiring special treatment, such as the consideration o local uckling, lexuraltorsional and torsional uckling, or we uckling, reduced section capacities ma e applicale. The user must separatel investigate this reduction i such elements are used. 138 Calculation o Section Resistances

147 Chapter VIII Check/Design or EUROCODE 3 I the user speciies nominal capailities or one or more elements in the Redeine Element Design Data, these values are will override all the aove mentioned calculated values or those elements as deined in the ollowing susections. Tension Capacit The design tension resistance or all classes o sections is evaluated in SAP000 as ollows: N = A t.rd (EC ) 0 It should e noted that the design ultimate resistance o the net cross-section at the holes or asteners is not computed and checked. The user is expected to investigate this independentl. Compression Resistance The design compressive resistance o the cross-section is taken as the smaller o the design plastic resistance o the gross cross-section (N pl. Rd ) and the design local uckling resistance o the gross cross-section (N Rd. ). N min ( N N ) (EC ) crd. plrd., Rd. The plastic resistance o Class 1, Class, and Class 3 sections is given N = A pl.rd 0. (EC ) The design uckling resistance o a compression memer is taken as N = A.Rd, where (EC ) min A 1 = 1, or Class 1, or 3 cross-sections. A χ is the reduction actor or the relevant uckling mode. This actor is calculated elow ased on the assumption that all memers are o uniorm crosssection. 1, in which (EC ), Calculation o Section Resistances 139

148 SAP000 Steel Design anual Section Limits α (major axis) α (minor axis) I-SHAPE (rolled) h 1. I-SHAPE (rolled) h 1. t 40 mm t 40 mm t 100 mm t 100 mm I-SHAPE (welded) BOX t 40 mm t 40 mm Rolled welded CHANNEL an T-SHAPE an DOUBLE ANGLES an ANGLE an PIPE an ROUND BAR an RECTANGLE an GENERAL an The Tale VIII-4 actor or dierent sections and dierent axes o uckling 140 Calculation o Section Resistances

149 Chapter VIII Check/Design or EUROCODE , A K i l K i l the lesser o the two.. The two values o give 3 and. min is K l L 1. K is conservativel taken as 1 in SAP000 design (EC ). The user can, however, override this deault option i it is deemed necessar. An accurate estimate o K can e otained rom the Annex E o the code. See also EC (). l is the uckling length, L is the length o the column, i is the radius o gration aout the neutral axis, and is determined using the properties o the gross cross-section, 1 E, and 1 is an imperection actor and is otained rom Tale VIII-4. Values o this actor or dierent tpes o sections, axes o uckling, and thickness o materials are otained rom Tales and o the code. Angle, Channel, and T-sections in compression are sujected to an additional moment due to the shit o the centroidal axis o the eective cross-section (EC ). SAP000 does not currentl considers this eccentricit. The user is expected to investigate this issue separatel. Shear Capacit The design shear resistance o a section is the minimum o the plastic shear capacit and the uckling shear capacit. or all tpes o sections, the plastic shear resistance is computed as V = V = A v Rd pl.rd 3 0, (EC ) Calculation o Section Resistances 141

150 SAP000 Steel Design anual where A v is the eective shear area or the section and the appropriate axis o ending. The uckling shear capacities are onl computed or the I, Box, and Channel sections i the width-thickness ratio is large (d t w 69 ). The capacities are computed as V = V = d t, (or d Rd a.rd w 69 ) (EC ) a 1 t w where, is the simple post-critical shear strength which is determined as ollows: a a a a w 3, or w, (EC ) w w 3, or w, and (EC ) w w 3, or w. (EC ) in which w is the we slenderness ratio, w d t w k t, and (EC ) k t is the uckling actor or shear. or wes with transverse stieners at the supports ut no intermediate transverse stieners, k t. (EC ) oment Resistance The moment resistance in the major and minor directions is ased on the section classiication. oment capacit is also inluenced the presence o shear orce and axial orce at the cross section. I the shear orce is less than hal o the shear capacit, the moment capacit is almost unaected the presence o shear orce. I the shear orce is greater than hal o the shear capacit, additional actors need to e considered. I V V Sd pl.rd or Class 1 and Class Sections = W crd. plrd. pl. (EC ) 0 14 Calculation o Section Resistances

151 Chapter VIII Check/Design or EUROCODE 3 or Class 3 Sections = = W crd. elrd. el. 0 (EC ) I V > V Sd pl.rd or I, Box, and Channel sections ending aout the 3-3 axis the moment capacities considering the eects o shear orce are computed as = W - A V. Rd pl v crd. 4tw 0, where (EC ) V V Sd pl.rd -1. or all other cases, the reduction o moment capacities or the presence o shear orce is not considered. The user should investigate the reduced moment capacit separatel. Lateral-torsional Buckling or the determination o lateral-torsional uckling resistance, it is assumed that the section is uniorm, doul smmetric, and loaded through its shear center. The lateral-torsional uckling resistance o I, Box, and Doule Channel sections is evaluated as, = W.Rd LT w pl., where (EC3 5.5.) 33 1 w =, or Class 1 and Class sections, w = W W pl. el , or Class 3 sections, LT LT LT LT 1, in which LT LT LT LT, where LT, or rolled sections, LT, or welded sections, and Calculation o Section Resistances 143

152 SAP000 Steel Design anual LT W w pl. 33 cr 05., where cr = C 1 EI L I I w + L GI EI t 0. 5, (EC3 1.1) I t I w = The torsion constant, = The warping constant, L = Laterall unraced length or uckling aout the minor axis. It is taken as l, C = - 1, and = The ratio o smaller to larger end moment o unraced segment, a. varies etween -1 and 1 ( 1 1). A negative value implies doule curvature. a and are end moments o the unraced segment and a is less a than, eing negative or doule curvature ending and positive or single curvature ending. I an moment within the segment is greater than, C 1 is taken as 1.0. The program deaults C 1 to 1.0 i the unraced length, l o the memer is overwritten the user (i.e. it is not equal to the length o the memer). C 1 should e taken as 1.0 or cantilevers. However, the program is unale to detect whether the memer is a cantilever. The user can overwrite the value o C 1 or an memer speciing it. I LT, no special consideration or lateral torsional uckling is made in the design. The lateral-torsional uckling resistance o a Channel, T, Angle, Doule-Angle and General sections is evaluated as, =W,.Rd el,33 1 and the lateral-torsional uckling resistance o Rectangle, Circle and Pipe sections is evaluated as, =W..Rd pl, Calculation o Section Resistances

153 Chapter VIII Check/Design or EUROCODE 3 Currentl SAP000 does not consider other special considerations or computing uckling resistance o Rectangle, Circle, Pipe, Channel, T, Angle, Doule Angle and General sections. Calculation o Capacit Ratios In the calculation o the axial orce/iaxial moment capacit ratios, irst, or each station along the length o the memer, or each load comination, the actual memer orce/moment components are calculated. Then the corresponding capacities are calculated. Then, the capacit ratios are calculated at each station or each memer under the inluence o each o the design load cominations. The controlling compression and/or tension capacit ratio is then otained, along with the associated station and load comination. A capacit ratio greater than 1.0 indicates exceeding a limit state. During the design, the eect o the presence o olts or welds is not considered. Also, the joints are not designed. Bending, Axial Compression, and Low Shear When the design value o the coexisting shear, V Sd, is less than hal o the corresponding capacities or plastic resistance, V pl. Rd and uckling resistance, V a. Rd, i.e. V V, and (EC ) Sd pl. Rd V V, (EC ) Sd a. Rd the capacit ratios are computed or dierent tpes o sections as ollows: or Class 1 and Class sections, the capacit ratio is conservativel taken as N N c.sd pl.rd + 33.Sd +.Sd pl. 33. Rd pl.. Rd. (EC ) or Class 3 sections, the capacit ratio is conservativel taken as N A c.sd d + W 33.Sd el. 33 d + W.Sd el. d, where (EC ) d 0. Calculation o Capacit Ratios 145

154 SAP000 Steel Design anual Bending, Axial Compression, and High Shear When the design value o the coexisting shear, V Sd, is more than hal the corresponding capacities or plastic resistance, V pl. Rd or uckling resistance, V a. Rd, the shear is considered to e high, i.e. the shear is high i V V, or (EC ) Sd pl. Rd V V. (EC ) Sd a. Rd Under these conditions, the capacit ratios are computed or dierent tpes o sections as ollows (EC ): or Class 1,, and 3 sections, the capacit ratio is conservativel taken as N N c.sd pl.rd + 33.Sd V. 33.Rd +.Sd V..Rd, where (EC ) V. 33.Rd and V..Rd are the design moment resistances aout the major and the minor axes, respectivel, considering the eect o high shear (see page 14). Bending, Compression, and lexural Buckling or all memers o Class 1,, and 3 sections suject to axial compression, N Sd, major axis ending, 33. Sd, and minor axis ending,. Sd, the capacit ratio is given N N c.sd.min.rd + k Sd c. 33.Rd + k.sd c..rd N min N, N,. min. Rd. 33. Rd.. Rd, where (EC ) 0 1, N 33 c.sd k = 1 -, 33 A 33 N c.sd k = 1 -, A 146 Calculation o Capacit Ratios

155 Chapter VIII Check/Design or EUROCODE 3 33 el. 33 ( 4) pl. - + W -W W el. 33, (Class 1 and Class ), W -W pl. el. ( ), (Class 1 and Class ), W. el ), (or Class 3 sections), - 4 ), (or Class 3 sections),. = Equivalent uniorm moment actor or lexural uckling aout the (major) axis etween points raced in - direction, and = Equivalent uniorm moment actor or lexural uckling aout the. - (minor) axis etween points raced in 3-3 direction. The equivalent uniorm moment actors, and, are determined rom.33. = + Q, and Q = Asolute maximum moment due to lateral load onl assuming simple support at the ends, ψ = = = Asolute value o the ratio o smaller to larger end moment. varies etween -1 and 1 ( 1 1). A negative value implies doule curvature. Asolute maximum value o moment or moment diagram without change o sign, and Sum o asolute maximum and asolute minimum value o moments or moment diagram with change o sign. Bending, Compression, and Lateral-Torsional Buckling or all memers o Class 1,, and 3 sections suject to axial compression, N Sd, major axis ending, 33. Sd, and minor axis ending,. Sd, the capacit ratio is given N N c.sd + k LT + k 33.Sd.Sd.. Rd Rd. c..rd, where (EC ) Calculation o Capacit Ratios 147

156 SAP000 Steel Design anual k and are as deined in the previous susection Bending, Compression, and lexural Buckling, N LT c.sd k = 1-1, where LT A LT.LT = -, and.lt = Equivalent uniorm moment actor or lateral-torsional uckling. It is determined or ending aout the - axis and etween two points raced in the - direction. Bending, Axial Tension, and Low Shear When the design value o the coexisting shear, V Sd, is less than hal o the corresponding capacities or plastic resistance, V pl. Rd and uckling resistance, V a. Rd, i.e. V V, and (EC ) Sd pl. Rd V V, (EC ) Sd a. Rd the capacit ratios are computed or dierent tpes o sections as ollows: or Class 1 and Class sections, the capacit ratio is conservativel taken as N N t.sd t.rd + 33.Sd +.Sd pl. 33. Rd pl.. Rd. (EC ) or Class 3 sections, the capacit ratio is conservativel taken as N A t.sd d + W 33.Sd el. 33 d + W.Sd el. d. (EC ) Bending, Axial Tension, and High Shear When the design values o the coexisting shear, V Sd, is more than hal the corresponding capacities or plastic resistance, V pl. Rd or uckling resistance, V a. Rd, the shear is considered to e high, i.e. the shear is high i V V Sd Sd V, or pl. Rd (EC ) V. a. Rd (EC ) 148 Calculation o Capacit Ratios

157 Chapter VIII Check/Design or EUROCODE 3 Under these conditions, the capacit ratios are computed or dierent tpes o sections as ollows (EC ): or Class 1,, and 3 sections, the capacit ratio is conservativel taken as N N t.sd t.rd + 33.Sd V. 33.Rd +.Sd V..Rd. (EC ) Bending, Axial Tension, and Lateral-Torsional Buckling The axial tensile orce has a eneicial eect or lateral-torsional uckling. In order to check whether the memer ails under lateral-torsional uckling, the eective internal moment aout the 3-3 axis is calculated as ollows: e. 33. Sd 33. Sd vec N W tsd. com. A 33, where (EC ) vec (according to the EC3 ox value), and W com.33 is the elastic section modulus or the extreme compression ier. or all memers o Class 1,, and 3 sections suject to axial tension, N tsd., major axis ending, 33. Sd, and minor axis ending,. Sd, the capacit ratio is taken as N N t.sd t.rd + k LT + k 33.Sd.Sd.Rd c..rd vec k LT N W tsd. com. A Rd. 33, (EC ) where k LT, k and are as deined in the previous susections. Shear rom the design values o shear orce at each station, or each o the load cominations and the shear resistance values, shear capacit ratios or major and minor directions are produced as ollows: V V.Sd.Rd and V V 3.Sd 3.Rd. Calculation o Capacit Ratios 149

158

159 Chapter IX Design Output Overview SAP000 creates design output in three dierent major ormats: graphical displa, taular output, and memer speciic detailed design inormation. The graphical displa o steel design output includes input and output design inormation. Input design inormation includes design section laels, K-actors, live load reduction actors, and other design parameters. The output design inormation includes axial and ending interaction ratios and shear stress ratios. All graphical output can e printed. The taular output can e saved in a ile or printed. The taular output includes most o the inormation which can e displaed. This is generated or added convenience to the designer. The memer-speciic detailed design inormation shows details o the calculation rom the designer s point o view. It shows the design section dimensions, material properties, design and allowale stresses or actored and nominal strengths, and some intermediate results or all the load cominations at all the design sections o a speciic rame memer. Overview 151

160 SAP000 Steel Design anual In the ollowing sections, some o the tpical graphical displa, taular output, and memer-speciic detailed design inormation are descried. Some o the design inormation is speciic to the chosen steel design codes which are availale in the program and is onl descried where required. The AISC-ASD89 design code is descried in the latter part o this chapter. or all other codes, the design outputs are similar. Graphical Displa o Design Output The graphical output can e produced either as color screen displa or in grascaled printed orm. oreover, the active screen displa can e sent directl to the printer. The graphical displa o design output includes input and output design inormation. Input design inormation, or the AISC-ASD89 code, includes Design section laels, K-actors or major and minor direction o uckling, Unraced Length Ratios, C m -actors, C -actors, Live Load Reduction actors, -actors, s -actors, design tpe, allowale stresses in axial, ending, and shear. The output design inormation which can e displaed is Color coded P- interaction ratios with or without values, and Color coded shear stress ratios. The graphical displas can e accessed rom the Design menu. or example, the color coded P- interaction ratios with values can e displaed selecting the Displa Design Ino... rom the Design menu. This will pop up a dialog ox called Displa Design Results. Then the user should switch on the Design Output option utton (deault) and select P- Ratios Colors & Values in the drop-down ox. Then clicking the OK utton will show the interaction ratios in the active window. 15 Graphical Displa o Design Output

161 Chapter IX Design Output The graphics can e displaed in either 3D or D mode. The SAP000 standard view transormations are availale or all steel design input and output displas. or switching etween 3D or D view o graphical displas, there are several uttons on the main toolar. Alternativel, the view can e set choosing Set 3D View... rom the View menu. The graphical displa in an active window can e printed in gra scaled lack and white rom the SAP000 program. To send the graphical output directl to the printer, click on the Print Graphics utton in the ile menu. A screen capture o the active window can also e made ollowing the standard procedure provided the Windows operating sstem. Taular Displa o Design Output The taular design output can e sent directl either to a printer or to a ile. The printed orm o taular output is the same as that produced or the ile output with the exception that or the printed output ont size is adjusted. The taular design output includes input and output design inormation which depends on the design code o choice. or the AISC-ASD89 code, the taular output includes the ollowing. All tales have ormal headings and are sel-explanator, so urther description o these tales is not given. Input design inormation includes the ollowing: Load Comination ultipliers Comination name, Load tpes, and Load actors. Steel Stress Check Element Inormation (code dependent) rame ID, Design Section ID, K-actors or major and minor direction o uckling, Unraced Length Ratios, C m -actors, C -actors, and Live Load Reduction actors. Taular Displa o Design Output 153

162 SAP000 Steel Design anual Steel oment agniication actors (code dependent) rame ID, Section ID, raming Tpe, -actors, and -actors. s The output design inormation includes the ollowing: Steel Stress Check Output (code dependent) rame ID, Section location, Controlling load comination ID or P- interaction, Tension or compression indication, Axial and ending interaction ratio, Controlling load comination ID or major and minor shear orces, and Shear stress ratios. The taular output can e accessed selecting Print Design Tales... rom the ile menu. This will pop up a dialog ox. Then the user can speci the design quantities or which the results are to e taulated. B deault, the output will e sent to the printer. I the user wants the output stream to e redirected to a ile, he/she can check the Print to ile ox. This will provide a deault ilename. The deault ilename can e edited. Alternativel, a ile list can e otained clicking the ile Name utton to chose a ile rom. Then clicking the OK utton will direct the taular output to the requested stream the ile or the printer. emer Speciic Inormation The memer speciic design inormation shows the details o the calculation rom the designer s point o view. It provides an access to the geometr and material data, other input data, design section dimensions, design and allowale stresses, reinorcement details, and some o the intermediate results or a memer. The design detail inormation can e displaed or a speciic load comination and or a speciic station o a rame memer. 154 emer Speciic Inormation

163 Chapter IX Design Output The detailed design inormation can e accessed right clicking on the desired rame memer. This will pop up a dialog ox called Steel Stress Check Inormation which includes the ollowing taulated inormation or the speciic memer. rame ID, Section ID, Load comination ID, Station location, Axial and ending interaction ratio, and Shear stress ratio along two axes. Additional inormation can e accessed clicking on the ReDesign and Details uttons in the dialog ox. Additional inormation that is availale clicking on the ReDesign utton is as ollows: Design actors (code dependent) Eective length actors, K, or major and minor direction o uckling, Unraced Length Ratios, C m -actors, C -actors, Live Load Reduction actors, s-actors, and -actors. Element Section ID Element raming Tpe Overwriting allowale stresses Additional inormation that is availale clicking on the Details utton is given elow. rame, Section, Station, and Load Comination IDs, Section geometric inormation and graphical representation, aterial properties o steel, oment actors, Design and allowale stresses or axial orce and iaxial moments, and Design and allowale stresses or shear. emer Speciic Inormation 155

164

165 Reerences AASHTO, 1997 AASHTO LRD Bridge Design Speciications U.S. Units, 1997 Interim Edition, American Association o State Highwa and Transportation Oicials, AISC, 1989 anual o Steel Construction, Allowale Stress Design, 9th Edition, American Institute o Steel Construction, Chicago, Ill, AISC, 1994 anual o Steel Construction, Load & Resistance actor Design, nd Edition, American Institute o Steel Construction, Chicago, Ill, BSI, 1990 Structural Use o Steelwork in Building, Part 1, Code o Practice or Design in Simple and Continuous Construction: Hot Rolled Sections, BS 5950 : Part 1 : 1990, British Standards Institution, London, UK, CEN, 199 Design o Steel Structures, Part 1.1 : General Rules and Rules or Buildings, ENV : 199, European Committee or Standardization, Brussels, Belgium,

166 SAP000 Steel Design anual CISC, 1995 Handook o Steel Construction, CAN/CSA-S , 6th Edition, Canadian Institute o Steel Construction, Willowdale, Ontario, Canada, CSI, 1998a SAP000 Getting Started, Computers and Structures, Inc., Berkele, Caliornia, CSI, 1998 SAP000 Quick Tutorial, Computers and Structures, Inc., Berkele, Caliornia, CSI, 1997 SAP000 Analsis Reerence, Vols. I and II, Computers and Structures, Inc., Berkele, Caliornia, ICBO, 1997 Uniorm Building Code, 1997, International Conerence o Building Oicials, Whittier, Caliornia, D. W. White and J.. Hajjar, 1991 Application o Second-Order Elastic Analsis in LRD: Research to Practice, Engineering Journal, American Institute o Steel Construction, Inc., Vol. 8, No. 4,

167 Index Bending strength AASHTO, 84 ASD (allowale), 30 BS, 11 CISC, 101 Eurocode, 14 LRD, 61 Braced rames, 8 AASHTO, 79 BS, 119 CISC, 97 Eurocode, 137 LRD, 5 Capacit ratio,, 8 AASHTO, 75, 91 ASD, 15, 40 BS, 111, 15 CISC, 93, 107 Eurocode, 19, 145 LRD, 45, 73 Check stations, 7 Classiication o sections AASHTO, 79 ASD, 18 BS, 115 CISC, 97 Eurocode, 133 LRD, 48 Compact section See Classiication o sections Compressive strength AASHTO, 83 ASD, 3 ASD (allowale), 3 BS, 119 CISC, 100 Eurocode, 139 LRD, 54 Design codes, 1 See Also "Supported design codes" Design load cominations, 6 Design output, 151 graphical, 15 memer speciic, 154 taular, 153 Design stations, 7 Eective length actor, 10 Euler uckling load AASHTO, 8 ASD, 4 159

168 SAP000 Steel Design anual BS, 119 CISC, 100 Eurocode, 139 LRD, 5 actored orces and moments AASHTO, 79 BS, 117 CISC, 97 Eurocode, 137 LRD, 5 lexural uckling AASHTO, 83 ASD, 3 BS, 119 CISC, 100 Eurocode, 139 LRD, 3, 54 Graphical output, 15 Interaction equations See Capacit ratio Interactive environment, 1 Lateral drit eect, 8 See Also P-Delta analsis Lateral-torsional uckling AASHTO, 88 ASD, 30 BS, 1 CISC, 101 Eurocode, 143 LRD, 61, 66, 69 Live load reduction actor, 7, 18, 48, 79, 96, 114, 13 Loading cominations, AASHTO, 78 ASD, 18 BS, 114 CISC, 96 Eurocode, 13 LRD, 48 emer speciic output, 154 emer stailit eect, 8 See Also P-Delta analsis oment magniication AASHTO, 8 BS, 117 CISC, 97 Eurocode, 138 LRD, 5 Noncompact section See Classiication o sections Nonswa, 8 AASHTO, 79 BS, 119 CISC, 97 Eurocode, 137 LRD, 5 Notional load BS, 114 CISC, 96 Eurocode, 13 Output, details, 155 graphical, 151 taular, 151 P-Delta analsis, 8 AASHTO, 79, 8 BS, 114, 119 CISC, Eurocode, 133, 138 LRD, 48, 53 P-Delta eects, 8 Perr actor, 119 Plastic section See Classiication o sections 160

169 Index Redesign, 155 Roertson constant, 119 Second order eects See P-Delta eects Shear strength AASHTO, 90 ASD (allowale), 39 BS, 15 CISC, 105 Eurocode, 141 LRD, 7 Slender section See Classiication o sections Strength reduction actors AASHTO, 8 BS (partial actors), 119 CISC, 100 Euro (partial actors), 138 LRD, 54 Supported design codes, 1 AASHTO, 5, 75 ASD, 5, 15 BS, 5, 111 CISC, 5, 93 Eurocode, 5, 19 LRD, 5, 45 Swa, 8 AASHTO, 79 BS, 119 CISC, 97 Eurocode, 137 LRD, 5 Taular output, 153 Tensile strength AASHTO, 84 ASD (allowale), 3 BS, 11 CISC, 101 Eurocode, 139 LRD, 60 Unraced rames, 8 AASHTO, 79 BS, 119 CISC, 97 Eurocode, 137 LRD, 5 Units,, 13 AASHTO, 78 ASD, 18 BS, 111 CISC, 93 Eurocode, 19 LRD, 48 Unsupported length, 9 161