FOOTING DESIGN EXAMPLE

Size: px
Start display at page:

Download "FOOTING DESIGN EXAMPLE"

Transcription

1 County: Any Design: BRG Date: 10/007 Hwy: Any Ck Dsn: BRG Date: 10/007 FOOTING DESIGN EXAMPLE Design: Based on AASHTO LRFD 007 Specifications, TxDOT LRFD Bridge Design Manual, and TxDOT Project ' - 6" x 8' x 6' Footing Rectangular 8' x 5' column, two 4' diameter drilled shafts Limitations: This example will only work when both drilled shafts are in compression (does not encompass drilled shafts in tension). Footing Design- Strut and Tie (AASHTO LRFD 5.6.3) f c the concrete compressive strength, f' c f c 3.6 kip in f y yield strength of the reinforcement f y 60 kip in W col column width W col 8ft D col column depth D col 5ft h depth of footing h 6ft L 1 dimension along the longitudinal axis of the footing L ft L dimension along the transverse axis of the footing L 8ft D DS drilled shaft diameter D DS 4ft EdgeDistance the clear space between the drilled shaft and the end of the footing EdgeDistance 9in s DS the distance between the centroids of the two drilled shafts s DS L 1 EdgeDistance D DS s DS 1 ft 1 of 10

2 Initially assume that 11 ~ #10 bars will be used for the tension tie reinforcement. Size bar the size of the tension reinforcement bars N b number of the tension reinforcement bars Size bar 10 N b 11 A b area of a single tension reinforcement bar A b 1.7in d b diameter of tension reinforcement bar d b 1.7in d stirrup diameter of #6 stirrup d stirrup 0.75in cc bot clear cover for the transverse reinforcement from the bottom of the footing to the edge of the reinforcement bar cc bot 3in cc side clear cover for the transverse reinforcement from the side of the footing to the edge of the reinforcement bar cc side 3in EndCover concrete cover from the EndCover edge on the footing to the end of the reinforcement bar 3in d c thickness of concrete cover measured from extreme tension fiber to center of the closest tension reinforcement bar d b d c cc bot + + d stirrup d c 4.4 in s bar the distance between the centroids of the tension tie reinforcement bars D DS + d c s bar N b 1 s bar 5.7 in Note: The tension tie reinforcement must be close enough to the drilled shaft to be considered in the truss analysis. Therefore, the tension tie reinforcement must be within a θ t 45 degree distribution angle (i.e. no more than d c away from the drilled shaft on either side) per TxDOT LRFD Bridge Design Manual. of 10

3 Step One: Draw Idealized Truss Model and Solve for Member Forces Draw Idealized Truss Model: First, Solve for Reactions: The loads transferred from the column to the footing are: (AASHTO LRFD and TxDOT LRFD Bridge Design Manual) M u P u 3075kip ft 1559kip Note: Design for the worst case created by a positive M u (clockwise) which generates the maximum force in strut BC and node C in the truss model on the following page. Setting the moment about the right column equal to zero: P u R 1 R kip s DS M u s DS Setting the moment about the left column equal to zero: P u R R kip s DS + M u s DS The following truss model is not applicable for footings with drilled shafts in tension. Check if both drilled shafts are in compression: ( ) ( R > 0) if R 1 > 0, "OK", "NG" "OK" 3 of 10

4 Then convert M u and P u into two concentrated loads located a distance of W col /4 in from each side of the column. FA M u P u + FB W col M u W col + P u FA 10.8 kip FB kip Both FA and FB are in compression. If FA were in tension, the below truss model would not work. Next place a node at all loads and reactions. Finally draw the most rational truss model. Assume nodes A and B are located at the concentrated loads, FA and FB, at the top of the footing. Assume nodes C and D are located at the center of the drill shafts and a distance of d c above the top of the Drilled Shafts. Note: Nodes represent the center of compression struts or tension ties. Dashed lines represent compression struts and the solid lines represent tension ties, or reinforcement. How to draw a rational truss model: 1)Draw straight lines from node to node to represent the members, struts and ties. )Try to place the tension ties where reinforcement is normally located (i.e. avoid diagonal tension ties). 3)If the angle, θ, between the tension tie and compression strut is too small the compression force will take another route making the current truss model invalid. Therefore, the angle between the compression strut and the tension tie must be greater than 6 degrees per TxDOT LRFD Bridge Design Manual. 4 of 10

5 In a case where both drilled shafts and column forces are are not in compression see alternate truss models below. One column force in tension One column force and one drilled shaft in tension Solve for Member Forces: Since node C and strut BC have the maximum loads, solve for the forces in BC and CD to design for the worst case. θ atan θ 54.6 deg h d c s DS W col 4 BC BC CD CD R sin( θ) 170 kip BC cos( θ) ( compression) 735 kip ( tension) The figure above shows the boundaries of the compression struts. Strut AB is positioned such that the footing and the column concrete are being utilized. In the case where the column concrete cannot be utilized, nodes A and B should be located at the center of the strut, which will be inside the footing instead of at the top of the footing. Step Two: Choose Tension Tie Reinforcement for Tie CD Assume #10 bars at 5.7in spacing f y 60 ksi ϕ 0.9 (AASHTO LRFD ) A req CD ϕ f y A req 13.6 in A b 1.7in N b 11 A steel A b N b A steel in ( ) "good" if A steel A req, "good", "no good, add more steel" 5 of 10

6 Step Three: Anchorage of Tension Tie (AASHTO LRFD and 5.11.) x the distance from the effective face of the drilled shaft to where the full development of reinforcement is required x x d c tan( θ) 3.1 in The effective face of the drilled shaft is assumed as the side dimension of the equivalent square as defined below. Area Area π*(d DS /) L b ELEVATION NODE C L b π*(d DS /) (TxDOT Project Section 5.5) L b D DS / * π 0.5 L b 0.89*D DS L available L available D DS D DS EdgeDistance x EndCover 54.5 in Check if the required development length can be reduced: L db factors: (AASHTO LRFD ) 1) Check if the clear cover, cc side, is not less than 3in and the reinforcement bar spacing, s bar, is not less than 6in. cc side 3in D DS + d c s bar N b 1 s bar 5.7 in Since s bar is less than 6in, factor factor ) Check ratio of A srequired /A sprovided. Since the footing is being designed, the factor of A srequired /A sprovided is assumed to be 1.0. factor 1.0 3) Check if the reinforcement is enclosed in a spiral. Since the footing reinforcement is not enclosed in a spiral, the factor is taken as 1.0. factor of 10

7 For #11 bars or smaller: L db L db f y in max 1.5 A b, 0.4d b f y, 1in (AASHTO LRFD ) kip f c kip 50. in ( ) 0.5 L d L db factor 1 factor factor 3 L d 50. in ( ) "good" if L available > L d, "good", "hook required" Step Four: Node Geometry (TxDOT Project Section 5.5) CCT Node - a node which is bounded by two struts (C) and one tie (T) CCC Node - a node which is bounded by three struts (C) w s the width of a strut in plane of the truss model w t the width of the tie, or in a CCC node w t is based on the compression force due to bending of the beam which can be conservatively assumed as the height of the compression block. For simplicity in this design example w t is always taken as the width of a tension tie. Using the width of a tension tie instead of the height of the compression block in most cases should not significantly effect the final result. L b the bearing length corresponding to a node Node A & D Geometry: Since the forces at nodes B and C are larger than those at nodes A and D, the controlling nodal or strut failure will not occur at nodes A and D. Node C Geometry: Assume the bearing length as the side face dimension of the equivalent square for the drilled shaft. L b 0.89 D DS L b 4.7 in w t is the smaller of: w t cc bot 6d b 7.3 in w t cos( θ) + d b 7.3 in 15. in 4. in L b sin( θ) w s w s 39 in 34.8 in w t cos( θ) + L b sin( θ) NODE C GEOMETRY (strut BC and tie CD) 7 of 10

8 Node B Geometry Due to the ambiguity of a node as complex as node B (two diagonal struts and one horizontal strut), this design example only focuses on strut BC. Node B (strut BC) Geometry: The overall bearing length of node B is W col /, but since there is more than one strut at node B the bearing length will be divided into individual bearing lengths for each strut. The bearing lengths are proportional to the amount of load in each strut. In this example, for simplicity, the bearing length of Node B is divided into two equal sections to accommodate the two diagonal struts. L b W col 4 L b 4.0 in For simplicity w t is taken as the height of the tension tie instead of the height of the compression block. The height of the tension tie at Node B is assumed to be the same as Node C, w t. w t w t w t 7.3 in ELEVATION NODE B (strut BC) w t cos( θ) L b sin( θ) 4. in 19.6 in w s w t cos( θ) + L b sin( θ) w s 3.8 in 8 of 10

9 Step Five: Check Capacity of Diagonal Struts (TxDOT LRFD Bridge Design Manual and TxDOT Project Section A..1) Strut BC will control, because of the high compressive force. The interface at Node B will control, because it has the smallest cross-sectional area. ν min ν kip tan( θ) L b in 0.5 f c ws sin( θ) b BC Effective width of strut BC at node B 0.85 L b,, 0.85 w s sin( θ) (TxDOT Project Section A..1 Eq. A-7 and TxDOT LRFD Bridge Design Manual) W col b BC 4 b BC 4.0 in ϕ 0.70 ϕp n ϕν f c w s b BC (TxDOT Project Section A..1 Eq. A-9 and TxDOT LRFD Bridge Design Manual) ϕp n 1 kip R 1036 kip ( ) "good" if ϕp n > R, "good", "no good" Step Six: Crack Control Reinforcement in Struts (TxDOT LRFD Bridge Design Manual and TxDOT Project Section A..) Strut BC will control, because it deals with the largest applied stresses: L strut length of strut h d c L strut sin( θ) L strut b min b min 8.9 in min( w s, w s ) 4 in b ef maximum effective strut width b ef max L strut, b 3 min + L strut 6 (TxDOT Project Section A.. and TxDOT LRFD Bridge Design Manual) b ef 37.6 in 9 of 10

10 m slope of the dispersion of compression m b ef (TxDOT Project Section A.. and TxDOT b ef b min LRFD Bridge Design Manual) m 5.44 b the average width of the strut measured perpendicular to the plane of the truss b 0.89 D DS + D col b 51.4 in ρ min BC/(*fy*b*Lstrut*m) but not less than BC ρ min max0.003, f y b L strut m ρ min (TxDOT Project Section A.. Eq. A-15 and TxDOT LRFD Bridge Design Manual) Horizontal (Skin) Reinforcement: Assuming size #7 bars and 9" spacing s bar_h 9in A b_h 0.60in ***This check requires that both side faces of the footing be reinforced with the specified bar size at the spacing shown. Vertical Reinforcement (Two Legs - Stirrups): Assuming size #7 bars and 9" spacing s bar_v 9in A b_v 0.60in For the transverse direction of the strut, conservatively use the width of the larger node: ρ ρ A b_h max D col, 0.89 D DS ( ) s bar_h + A b_v max D col, 0.89 D DS ( ) s bar_v 0.5 (TxDOT Project Section A.. Eq. A-14 and TxDOT LRFD Bridge Design Manual) ( ) "Good" if ρ > ρ min, "Good", "NG, add more reinforcement" **Use the same bars and spacing throughout the footing Step Seven: Check Nodal Zone Stress Limits (AASHTO LRFD , TxDOT LRFD Bridge Design Manual and TXDOT Project Section A.3.3.) The nodes are all significantly large. By inspection, nodal failure will not occur. 10 of 10

Page 1 of 18 28.4.2008 Sven Alexander Last revised 1.3.2010. SB-Produksjon STATICAL CALCULATIONS FOR BCC 250

Page 1 of 18 28.4.2008 Sven Alexander Last revised 1.3.2010. SB-Produksjon STATICAL CALCULATIONS FOR BCC 250 Page 1 of 18 CONTENT PART 1 BASIC ASSUMPTIONS PAGE 1.1 General 1. Standards 1.3 Loads 1. Qualities PART ANCHORAGE OF THE UNITS.1 Beam unit equilibrium 3. Beam unit anchorage in front..1 Check of capacity..

More information

Design of reinforced concrete columns. Type of columns. Failure of reinforced concrete columns. Short column. Long column

Design of reinforced concrete columns. Type of columns. Failure of reinforced concrete columns. Short column. Long column Design of reinforced concrete columns Type of columns Failure of reinforced concrete columns Short column Column fails in concrete crushed and bursting. Outward pressure break horizontal ties and bend

More information

A transverse strip of the deck is assumed to support the truck axle loads. Shear and fatigue of the reinforcement need not be investigated.

A transverse strip of the deck is assumed to support the truck axle loads. Shear and fatigue of the reinforcement need not be investigated. Design Step 4 Design Step 4.1 DECK SLAB DESIGN In addition to designing the deck for dead and live loads at the strength limit state, the AASHTO-LRFD specifications require checking the deck for vehicular

More information

SEISMIC DESIGN. Various building codes consider the following categories for the analysis and design for earthquake loading:

SEISMIC DESIGN. Various building codes consider the following categories for the analysis and design for earthquake loading: SEISMIC DESIGN Various building codes consider the following categories for the analysis and design for earthquake loading: 1. Seismic Performance Category (SPC), varies from A to E, depending on how the

More information

SLAB DESIGN EXAMPLE. Deck Design (AASHTO LRFD 9.7.1) TYPICAL SECTION. County: Any Hwy: Any Design: BRG Date: 7/2010

SLAB DESIGN EXAMPLE. Deck Design (AASHTO LRFD 9.7.1) TYPICAL SECTION. County: Any Hwy: Any Design: BRG Date: 7/2010 County: Any Hwy: Any Design: BRG Date: 7/2010 SLAB DESIGN EXAMPLE Design example is in accordance with the AASHTO LRFD Bridge Design Specifications, 5th Ed. (2010) as prescribed by TxDOT Bridge Design

More information

FOUNDATION DESIGN. Instructional Materials Complementing FEMA 451, Design Examples

FOUNDATION DESIGN. Instructional Materials Complementing FEMA 451, Design Examples FOUNDATION DESIGN Proportioning elements for: Transfer of seismic forces Strength and stiffness Shallow and deep foundations Elastic and plastic analysis Foundation Design 14-1 Load Path and Transfer to

More information

Technical Notes 3B - Brick Masonry Section Properties May 1993

Technical Notes 3B - Brick Masonry Section Properties May 1993 Technical Notes 3B - Brick Masonry Section Properties May 1993 Abstract: This Technical Notes is a design aid for the Building Code Requirements for Masonry Structures (ACI 530/ASCE 5/TMS 402-92) and Specifications

More information

Design of Steel Structures Prof. S.R.Satish Kumar and Prof. A.R.Santha Kumar. Fig. 7.21 some of the trusses that are used in steel bridges

Design of Steel Structures Prof. S.R.Satish Kumar and Prof. A.R.Santha Kumar. Fig. 7.21 some of the trusses that are used in steel bridges 7.7 Truss bridges Fig. 7.21 some of the trusses that are used in steel bridges Truss Girders, lattice girders or open web girders are efficient and economical structural systems, since the members experience

More information

Detailing of Reinforcment in Concrete Structures

Detailing of Reinforcment in Concrete Structures Chapter 8 Detailing of Reinforcment in Concrete Structures 8.1 Scope Provisions of Sec. 8.1 and 8.2 of Chapter 8 shall apply for detailing of reinforcement in reinforced concrete members, in general. For

More information

IMPROVING THE STRUT AND TIE METHOD BY INCLUDING THE CONCRETE SOFTENING EFFECT

IMPROVING THE STRUT AND TIE METHOD BY INCLUDING THE CONCRETE SOFTENING EFFECT International Journal of Civil Engineering and Technology (IJCIET) Volume 7, Issue 2, March-April 2016, pp. 117 127, Article ID: IJCIET_07_02_009 Available online at http://www.iaeme.com/ijciet/issues.asp?jtype=ijciet&vtype=7&itype=2

More information

Copyright. Eulalio Fernandez Gomez

Copyright. Eulalio Fernandez Gomez Copyright by Eulalio Fernandez Gomez 2012 The Dissertation Committee for Eulalio Fernandez Gomez Certifies that this is the approved version of the following dissertation: Design Criteria for Strength

More information

REINFORCED CONCRETE. Reinforced Concrete Design. A Fundamental Approach - Fifth Edition. Walls are generally used to provide lateral support for:

REINFORCED CONCRETE. Reinforced Concrete Design. A Fundamental Approach - Fifth Edition. Walls are generally used to provide lateral support for: HANDOUT REINFORCED CONCRETE Reinforced Concrete Design A Fundamental Approach - Fifth Edition RETAINING WALLS Fifth Edition A. J. Clark School of Engineering Department of Civil and Environmental Engineering

More information

INTRODUCTION TO BEAMS

INTRODUCTION TO BEAMS CHAPTER Structural Steel Design LRFD Method INTRODUCTION TO BEAMS Third Edition A. J. Clark School of Engineering Department of Civil and Environmental Engineering Part II Structural Steel Design and Analysis

More information

Draft Table of Contents. Building Code Requirements for Structural Concrete and Commentary ACI 318-14

Draft Table of Contents. Building Code Requirements for Structural Concrete and Commentary ACI 318-14 Draft Table of Contents Building Code Requirements for Structural Concrete and Commentary ACI 318-14 BUILDING CODE REQUIREMENTS FOR STRUCTURAL CONCRETE (ACI 318 14) Chapter 1 General 1.1 Scope of ACI 318

More information

Design MEMO 54a Reinforcement design for RVK 41

Design MEMO 54a Reinforcement design for RVK 41 Page of 5 CONTENTS PART BASIC ASSUMTIONS... 2 GENERAL... 2 STANDARDS... 2 QUALITIES... 3 DIMENSIONS... 3 LOADS... 3 PART 2 REINFORCEMENT... 4 EQUILIBRIUM... 4 Page 2 of 5 PART BASIC ASSUMTIONS GENERAL

More information

Index 20010 Series Prestressed Florida-I Beams (Rev. 07/12)

Index 20010 Series Prestressed Florida-I Beams (Rev. 07/12) Index 20010 Series Prestressed Florida-I Beams (Rev. 07/12) Design Criteria AASHTO LRFD Bridge Design Specifications, 6th Edition; Structures Detailing Manual (SDM); Structures Design Guidelines (SDG)

More information

ETABS. Integrated Building Design Software. Concrete Shear Wall Design Manual. Computers and Structures, Inc. Berkeley, California, USA

ETABS. Integrated Building Design Software. Concrete Shear Wall Design Manual. Computers and Structures, Inc. Berkeley, California, USA ETABS Integrated Building Design Software Concrete Shear Wall Design Manual Computers and Structures, Inc. Berkeley, California, USA Version 8 January 2002 Copyright The computer program ETABS and all

More information

MECHANICS OF SOLIDS - BEAMS TUTORIAL 2 SHEAR FORCE AND BENDING MOMENTS IN BEAMS

MECHANICS OF SOLIDS - BEAMS TUTORIAL 2 SHEAR FORCE AND BENDING MOMENTS IN BEAMS MECHANICS OF SOLIDS - BEAMS TUTORIAL 2 SHEAR FORCE AND BENDING MOMENTS IN BEAMS This is the second tutorial on bending of beams. You should judge your progress by completing the self assessment exercises.

More information

S03: Tier 1 Assessment of Shear in Concrete Short Span Bridges to AS 5100 and AS 3600

S03: Tier 1 Assessment of Shear in Concrete Short Span Bridges to AS 5100 and AS 3600 Annexure S03: Tier 1 Assessment of Shear in Concrete Short Span Bridges to AS 5100 and AS 3600 April 2014 Copyright http://creativecommons.org/licenses/by/3.0/au/ State of Queensland (Department of Transport

More information

Detailing of Reinforcement in Concrete Structures

Detailing of Reinforcement in Concrete Structures THE CIVIL & STRUCTURAL ENGINEERING PANEL ENGINEERS AUSTRALIA SYDNEY DIVISION 28 August 2012 Detailing of Reinforcement in Concrete Structures R.I. Gilbert Introduction: Detailing is often considered to

More information

Torsion Tests. Subjects of interest

Torsion Tests. Subjects of interest Chapter 10 Torsion Tests Subjects of interest Introduction/Objectives Mechanical properties in torsion Torsional stresses for large plastic strains Type of torsion failures Torsion test vs.tension test

More information

Reinforced Concrete Design Project Five Story Office Building

Reinforced Concrete Design Project Five Story Office Building Reinforced Concrete Design Project Five Story Office Building Andrew Bartolini December 7, 2012 Designer 1 Partner: Shannon Warchol CE 40270: Reinforced Concrete Design Bartolini 2 Table of Contents Abstract...3

More information

Basics of Reinforced Concrete Design

Basics of Reinforced Concrete Design Basics of Reinforced Concrete Design Presented by: Ronald Thornton, P.E. Define several terms related to reinforced concrete design Learn the basic theory behind structural analysis and reinforced concrete

More information

COMPLEX STRESS TUTORIAL 3 COMPLEX STRESS AND STRAIN

COMPLEX STRESS TUTORIAL 3 COMPLEX STRESS AND STRAIN COMPLX STRSS TUTORIAL COMPLX STRSS AND STRAIN This tutorial is not part of the decel unit mechanical Principles but covers elements of the following sllabi. o Parts of the ngineering Council eam subject

More information

Structural Axial, Shear and Bending Moments

Structural Axial, Shear and Bending Moments Structural Axial, Shear and Bending Moments Positive Internal Forces Acting Recall from mechanics of materials that the internal forces P (generic axial), V (shear) and M (moment) represent resultants

More information

16. Beam-and-Slab Design

16. Beam-and-Slab Design ENDP311 Structural Concrete Design 16. Beam-and-Slab Design Beam-and-Slab System How does the slab work? L- beams and T- beams Holding beam and slab together University of Western Australia School of Civil

More information

ENGINEERING SCIENCE H1 OUTCOME 1 - TUTORIAL 3 BENDING MOMENTS EDEXCEL HNC/D ENGINEERING SCIENCE LEVEL 4 H1 FORMERLY UNIT 21718P

ENGINEERING SCIENCE H1 OUTCOME 1 - TUTORIAL 3 BENDING MOMENTS EDEXCEL HNC/D ENGINEERING SCIENCE LEVEL 4 H1 FORMERLY UNIT 21718P ENGINEERING SCIENCE H1 OUTCOME 1 - TUTORIAL 3 BENDING MOMENTS EDEXCEL HNC/D ENGINEERING SCIENCE LEVEL 4 H1 FORMERLY UNIT 21718P This material is duplicated in the Mechanical Principles module H2 and those

More information

HUS-V Screw anchor. HUS-V Screw anchor. Basic loading data (for a single anchor) Mean ultimate resistance

HUS-V Screw anchor. HUS-V Screw anchor. Basic loading data (for a single anchor) Mean ultimate resistance HUS-V Screw anchor Anchor version HUS-V 8 / 10 Carbon steel concrete screw with hexagonal head Benefits - High productivity less drilling and fewer operations than with conventional anchors - Technical

More information

Seismic design of beam-column joints in RC moment resisting frames Review of codes

Seismic design of beam-column joints in RC moment resisting frames Review of codes Structural Engineering and Mechanics, Vol. 23, No. 5 (2006) 579-597 579 Technical Report Seismic design of beam-column joints in RC moment resisting frames Review of codes S. R. Uma Department of Civil

More information

DESIGN OF SLABS. 3) Based on support or boundary condition: Simply supported, Cantilever slab,

DESIGN OF SLABS. 3) Based on support or boundary condition: Simply supported, Cantilever slab, DESIGN OF SLABS Dr. G. P. Chandradhara Professor of Civil Engineering S. J. College of Engineering Mysore 1. GENERAL A slab is a flat two dimensional planar structural element having thickness small compared

More information

Stresses in Beam (Basic Topics)

Stresses in Beam (Basic Topics) Chapter 5 Stresses in Beam (Basic Topics) 5.1 Introduction Beam : loads acting transversely to the longitudinal axis the loads create shear forces and bending moments, stresses and strains due to V and

More information

Tension Development and Lap Splice Lengths of Reinforcing Bars under ACI 318-02

Tension Development and Lap Splice Lengths of Reinforcing Bars under ACI 318-02 ENGINEERING DATA REPORT NUMBER 51 Tension Development and Lap Splice Lengths of Reinforcing Bars under ACI 318-02 A SERVICE OF THE CONCRETE REINFORCING STEEL INSTITUTE Introduction Section 1.2.1 in the

More information

Design MEMO 60 Reinforcement design for TSS 102

Design MEMO 60 Reinforcement design for TSS 102 Date: 04.0.0 sss Page of 5 CONTENTS PART BASIC ASSUMTIONS... GENERAL... STANDARDS... QUALITIES... 3 DIMENSIONS... 3 LOADS... 3 PART REINFORCEMENT... 4 EQUILIBRIUM... 4 Date: 04.0.0 sss Page of 5 PART BASIC

More information

MATERIALS AND MECHANICS OF BENDING

MATERIALS AND MECHANICS OF BENDING HAPTER Reinforced oncrete Design Fifth Edition MATERIALS AND MEHANIS OF BENDING A. J. lark School of Engineering Department of ivil and Environmental Engineering Part I oncrete Design and Analysis b FALL

More information

CHAPTER 29 VOLUMES AND SURFACE AREAS OF COMMON SOLIDS

CHAPTER 29 VOLUMES AND SURFACE AREAS OF COMMON SOLIDS CHAPTER 9 VOLUMES AND SURFACE AREAS OF COMMON EXERCISE 14 Page 9 SOLIDS 1. Change a volume of 1 00 000 cm to cubic metres. 1m = 10 cm or 1cm = 10 6m 6 Hence, 1 00 000 cm = 1 00 000 10 6m = 1. m. Change

More information

Prestressed Concrete I-Beam and TxGirder Haunch Design Guide

Prestressed Concrete I-Beam and TxGirder Haunch Design Guide Prestressed Concrete I-Beam and TxGirder Haunch Design Guide Components of the Haunch Camber: Camber is the upward deflection in the beam after release of the prestressing strands due to the eccentricity

More information

www.sakshieducation.com

www.sakshieducation.com LENGTH OF THE PERPENDICULAR FROM A POINT TO A STRAIGHT LINE AND DISTANCE BETWEEN TWO PAPALLEL LINES THEOREM The perpendicular distance from a point P(x 1, y 1 ) to the line ax + by + c 0 is ax1+ by1+ c

More information

Design Manual to BS8110

Design Manual to BS8110 Design Manual to BS8110 February 2010 195 195 195 280 280 195 195 195 195 195 195 280 280 195 195 195 The specialist team at LinkStudPSR Limited have created this comprehensive Design Manual, to assist

More information

Structural welding is a process by which the parts that are to be connected are heated and

Structural welding is a process by which the parts that are to be connected are heated and CHAPTER 6. WELDED CONNECTIONS 6.1 INTRODUCTORY CONCEPTS Structural welding is a process by which the parts that are to be connected are heated and fused, with supplementary molten metal at the joint. A

More information

EFFECTS ON NUMBER OF CABLES FOR MODAL ANALYSIS OF CABLE-STAYED BRIDGES

EFFECTS ON NUMBER OF CABLES FOR MODAL ANALYSIS OF CABLE-STAYED BRIDGES EFFECTS ON NUMBER OF CABLES FOR MODAL ANALYSIS OF CABLE-STAYED BRIDGES Yang-Cheng Wang Associate Professor & Chairman Department of Civil Engineering Chinese Military Academy Feng-Shan 83000,Taiwan Republic

More information

SECTION 5 ANALYSIS OF CONTINUOUS SPANS DEVELOPED BY THE PTI EDC-130 EDUCATION COMMITTEE LEAD AUTHOR: BRYAN ALLRED

SECTION 5 ANALYSIS OF CONTINUOUS SPANS DEVELOPED BY THE PTI EDC-130 EDUCATION COMMITTEE LEAD AUTHOR: BRYAN ALLRED SECTION 5 ANALYSIS OF CONTINUOUS SPANS DEVELOPED BY THE PTI EDC-130 EDUCATION COMMITTEE LEAD AUTHOR: BRYAN ALLRED NOTE: MOMENT DIAGRAM CONVENTION In PT design, it is preferable to draw moment diagrams

More information

The elements used in commercial codes can be classified in two basic categories:

The elements used in commercial codes can be classified in two basic categories: CHAPTER 3 Truss Element 3.1 Introduction The single most important concept in understanding FEA, is the basic understanding of various finite elements that we employ in an analysis. Elements are used for

More information

Type of Force 1 Axial (tension / compression) Shear. 3 Bending 4 Torsion 5 Images 6 Symbol (+ -)

Type of Force 1 Axial (tension / compression) Shear. 3 Bending 4 Torsion 5 Images 6 Symbol (+ -) Cause: external force P Force vs. Stress Effect: internal stress f 05 Force vs. Stress Copyright G G Schierle, 2001-05 press Esc to end, for next, for previous slide 1 Type of Force 1 Axial (tension /

More information

Joist. Reinforcement. Draft 12/7/02

Joist. Reinforcement. Draft 12/7/02 Joist Reinforcement Draft 12/7/02 1 JOIST REINFORCING The purpose of this CSD Design Aid is to provide procedures and suggested details for the reinforcement of open web steel joists. There are three basic

More information

Section 16: Neutral Axis and Parallel Axis Theorem 16-1

Section 16: Neutral Axis and Parallel Axis Theorem 16-1 Section 16: Neutral Axis and Parallel Axis Theorem 16-1 Geometry of deformation We will consider the deformation of an ideal, isotropic prismatic beam the cross section is symmetric about y-axis All parts

More information

Chapter 8. Flexural Analysis of T-Beams

Chapter 8. Flexural Analysis of T-Beams Chapter 8. Flexural Analysis of T-s 8.1. Reading Assignments Text Chapter 3.7; ACI 318, Section 8.10. 8.2. Occurrence and Configuration of T-s Common construction type.- used in conjunction with either

More information

RC Detailing to Eurocode 2

RC Detailing to Eurocode 2 RC Detailing to Eurocode 2 Jenny Burridge MA CEng MICE MIStructE Head of Structural Engineering Structural Eurocodes BS EN 1990 (EC0): BS EN 1991 (EC1): Basis of structural design Actions on Structures

More information

Solid Mechanics. Stress. What you ll learn: Motivation

Solid Mechanics. Stress. What you ll learn: Motivation Solid Mechanics Stress What you ll learn: What is stress? Why stress is important? What are normal and shear stresses? What is strain? Hooke s law (relationship between stress and strain) Stress strain

More information

Sandia High School Geometry Second Semester FINAL EXAM. Mark the letter to the single, correct (or most accurate) answer to each problem.

Sandia High School Geometry Second Semester FINAL EXAM. Mark the letter to the single, correct (or most accurate) answer to each problem. Sandia High School Geometry Second Semester FINL EXM Name: Mark the letter to the single, correct (or most accurate) answer to each problem.. What is the value of in the triangle on the right?.. 6. D.

More information

Report on. Wind Resistance of Signs supported by. Glass Fiber Reinforced Concrete (GFRC) Pillars

Report on. Wind Resistance of Signs supported by. Glass Fiber Reinforced Concrete (GFRC) Pillars Report on Wind Resistance of Signs supported by Glass Fiber Reinforced Concrete (GFRC) Pillars Prepared for US Sign and Fabrication Corporation January, 2006 SUMMARY This study found the attachment of

More information

USE OF MICROPILES IN TEXAS BRIDGES. by John G. Delphia, P.E. TxDOT Bridge Division Geotechnical Branch

USE OF MICROPILES IN TEXAS BRIDGES. by John G. Delphia, P.E. TxDOT Bridge Division Geotechnical Branch USE OF MICROPILES IN TEXAS BRIDGES by John G. Delphia, P.E. TxDOT Bridge Division Geotechnical Branch DEFINITION OF A MICROPILE A micropile is a small diameter (typically less than 12 in.), drilled and

More information

Optimum proportions for the design of suspension bridge

Optimum proportions for the design of suspension bridge Journal of Civil Engineering (IEB), 34 (1) (26) 1-14 Optimum proportions for the design of suspension bridge Tanvir Manzur and Alamgir Habib Department of Civil Engineering Bangladesh University of Engineering

More information

US 51 Ohio River Bridge Engineering and Environmental Study

US 51 Ohio River Bridge Engineering and Environmental Study US 51 Ohio River Bridge Engineering and Environmental Study ITEM NOS. 1-100.00 & 1-1140.00 Prepared by: Michael Baker Jr., Inc. 9750 Ormsby Station Rd Louisville, KY 40223 August 16, 2013 Table of Contents

More information

Reinforced Concrete Design

Reinforced Concrete Design FALL 2013 C C Reinforced Concrete Design CIVL 4135 ii 1 Chapter 1. Introduction 1.1. Reading Assignment Chapter 1 Sections 1.1 through 1.8 of text. 1.2. Introduction In the design and analysis of reinforced

More information

Long-term serviceability of the structure Minimal maintenance requirements Economical construction Improved aesthetics and safety considerations

Long-term serviceability of the structure Minimal maintenance requirements Economical construction Improved aesthetics and safety considerations Design Step 7.1 INTEGRAL ABUTMENT DESIGN General considerations and common practices Integral abutments are used to eliminate expansion joints at the end of a bridge. They often result in Jointless Bridges

More information

Chapter 5 Bridge Deck Slabs. Bridge Engineering 1

Chapter 5 Bridge Deck Slabs. Bridge Engineering 1 Chapter 5 Bridge Deck Slabs Bridge Engineering 1 Basic types of bridge decks In-situ reinforced concrete deck- (most common type) Pre-cast concrete deck (minimize the use of local labor) Open steel grid

More information

Analysis of Stresses and Strains

Analysis of Stresses and Strains Chapter 7 Analysis of Stresses and Strains 7.1 Introduction axial load = P / A torsional load in circular shaft = T / I p bending moment and shear force in beam = M y / I = V Q / I b in this chapter, we

More information

1997 Uniform Administrative Code Amendment for Earthen Material and Straw Bale Structures Tucson/Pima County, Arizona

1997 Uniform Administrative Code Amendment for Earthen Material and Straw Bale Structures Tucson/Pima County, Arizona for Earthen Material and Straw Bale Structures SECTION 70 - GENERAL "APPENDIX CHAPTER 7 - EARTHEN MATERIAL STRUCTURES 70. Purpose. The purpose of this chapter is to establish minimum standards of safety

More information

The following sketches show the plans of the two cases of one-way slabs. The spanning direction in each case is shown by the double headed arrow.

The following sketches show the plans of the two cases of one-way slabs. The spanning direction in each case is shown by the double headed arrow. 9.2 One-way Slabs This section covers the following topics. Introduction Analysis and Design 9.2.1 Introduction Slabs are an important structural component where prestressing is applied. With increase

More information

CivilBay Anchor Bolt Design Software Using ACI 318-14 and CSA A23.3-14 Code

CivilBay Anchor Bolt Design Software Using ACI 318-14 and CSA A23.3-14 Code CivilBay Anchor Bolt Design Software Using ACI 318-14 and CSA A23.3-14 Code http://asp.civilbay.com CivilBay anchor bolt design software http://asp.civilbay.com is a complete anchorage design software

More information

APPENDIX H DESIGN CRITERIA FOR NCHRP 12-79 PROJECT NEW BRIDGE DESIGNS

APPENDIX H DESIGN CRITERIA FOR NCHRP 12-79 PROJECT NEW BRIDGE DESIGNS APPENDIX H DESIGN CRITERIA FOR NCHRP 12-79 PROJECT NEW BRIDGE DESIGNS This appendix summarizes the criteria applied for the design of new hypothetical bridges considered in NCHRP 12-79 s Task 7 parametric

More information

SLAB DESIGN. Introduction ACI318 Code provides two design procedures for slab systems:

SLAB DESIGN. Introduction ACI318 Code provides two design procedures for slab systems: Reading Assignment SLAB DESIGN Chapter 9 of Text and, Chapter 13 of ACI318-02 Introduction ACI318 Code provides two design procedures for slab systems: 13.6.1 Direct Design Method (DDM) For slab systems

More information

Performance of Existing Reinforced Concrete Columns under Bidirectional Shear & Axial Loading

Performance of Existing Reinforced Concrete Columns under Bidirectional Shear & Axial Loading Performance of Existing Reinforced Concrete Columns under Bidirectional Shear & Axial Loading Laura M. Flores University of California, San Diego REU Institution: University of California, Berkeley REU

More information

Hilti HIT-HY 150 MAX with rebar

Hilti HIT-HY 150 MAX with rebar Hilti HIT-HY 150 MAX Injection mortar system Hilti HIT- HY 150 MAX 330 ml foil pack (also available as 500 ml and 1400 ml foil pack) Static mixer rebar BSt 500 S Benefits - suitable for non-cracked and

More information

Deflections. Question: What are Structural Deflections?

Deflections. Question: What are Structural Deflections? Question: What are Structural Deflections? Answer: The deformations or movements of a structure and its components, such as beams and trusses, from their original positions. It is as important for the

More information

Two-Way Post-Tensioned Design

Two-Way Post-Tensioned Design Page 1 of 9 The following example illustrates the design methods presented in ACI 318-05 and IBC 2003. Unless otherwise noted, all referenced table, figure, and equation numbers are from these books. The

More information

III. Compression Members. Design of Steel Structures. Introduction. Compression Members (cont.)

III. Compression Members. Design of Steel Structures. Introduction. Compression Members (cont.) ENCE 455 Design of Steel Structures III. Compression Members C. C. Fu, Ph.D., P.E. Civil and Environmental Engineering Department University it of Maryland Compression Members Following subjects are covered:

More information

EDEXCEL NATIONAL CERTIFICATE/DIPLOMA MECHANICAL PRINCIPLES OUTCOME 2 ENGINEERING COMPONENTS TUTORIAL 1 STRUCTURAL MEMBERS

EDEXCEL NATIONAL CERTIFICATE/DIPLOMA MECHANICAL PRINCIPLES OUTCOME 2 ENGINEERING COMPONENTS TUTORIAL 1 STRUCTURAL MEMBERS ENGINEERING COMPONENTS EDEXCEL NATIONAL CERTIFICATE/DIPLOMA MECHANICAL PRINCIPLES OUTCOME ENGINEERING COMPONENTS TUTORIAL 1 STRUCTURAL MEMBERS Structural members: struts and ties; direct stress and strain,

More information

Thank you for joining our live webinar today. We will begin shortly. Please standby. Thank you. Need Help? Call ReadyTalk Support: 800.843.

Thank you for joining our live webinar today. We will begin shortly. Please standby. Thank you. Need Help? Call ReadyTalk Support: 800.843. Thank you for joining our live webinar today. We will begin shortly. Please standby. Thank you. Need Help? Call ReadyTalk Support: 800.843.9166 Today s audio will be broadcast through the internet. Alternatively,

More information

Geometry and Measurement

Geometry and Measurement The student will be able to: Geometry and Measurement 1. Demonstrate an understanding of the principles of geometry and measurement and operations using measurements Use the US system of measurement for

More information

Design of Steel Structures Prof. S.R.Satish Kumar and Prof. A.R.Santha Kumar. The design of any foundation consists of following two parts.

Design of Steel Structures Prof. S.R.Satish Kumar and Prof. A.R.Santha Kumar. The design of any foundation consists of following two parts. 8.7. Design procedure for foundation The design of any foundation consists of following two parts. 8.7.1 Stability analysis Stability analysis aims at removing the possibility of failure of foundation

More information

EDEXCEL NATIONAL CERTIFICATE/DIPLOMA MECHANICAL PRINCIPLES AND APPLICATIONS NQF LEVEL 3 OUTCOME 1 - LOADING SYSTEMS TUTORIAL 3 LOADED COMPONENTS

EDEXCEL NATIONAL CERTIFICATE/DIPLOMA MECHANICAL PRINCIPLES AND APPLICATIONS NQF LEVEL 3 OUTCOME 1 - LOADING SYSTEMS TUTORIAL 3 LOADED COMPONENTS EDEXCEL NATIONAL CERTIICATE/DIPLOMA MECHANICAL PRINCIPLES AND APPLICATIONS NQ LEVEL 3 OUTCOME 1 - LOADING SYSTEMS TUTORIAL 3 LOADED COMPONENTS 1. Be able to determine the effects of loading in static engineering

More information

Lecture 8 Bending & Shear Stresses on Beams

Lecture 8 Bending & Shear Stresses on Beams Lecture 8 Bending & hear tresses on Beams Beams are almost always designed on the asis of ending stress and, to a lesser degree, shear stress. Each of these stresses will e discussed in detail as follows.

More information

SMIP05 Seminar Proceedings VISUALIZATION OF NONLINEAR SEISMIC BEHAVIOR OF THE INTERSTATE 5/14 NORTH CONNECTOR BRIDGE. Robert K.

SMIP05 Seminar Proceedings VISUALIZATION OF NONLINEAR SEISMIC BEHAVIOR OF THE INTERSTATE 5/14 NORTH CONNECTOR BRIDGE. Robert K. VISUALIZATION OF NONLINEAR SEISMIC BEHAVIOR OF THE INTERSTATE 5/14 NORTH CONNECTOR BRIDGE Robert K. Dowell Department of Civil and Environmental Engineering San Diego State University Abstract This paper

More information

TECHNICAL SPECIFICATION SERIES 8000 PRECAST CONCRETE

TECHNICAL SPECIFICATION SERIES 8000 PRECAST CONCRETE TECHNICAL SPECIFICATION SERIES 8000 PRECAST CONCRETE TECHNICAL SPECIFICATION PART 8000 - PRECAST CONCRETE TABLE OF CONTENTS Item Number Page 8100 PRECAST CONCRETE CONSTRUCTION - GENERAL 8-3 8101 General

More information

Aluminium systems profile selection

Aluminium systems profile selection Aluminium systems profile selection The purpose of this document is to summarise the way that aluminium profile selection should be made, based on the strength requirements for each application. Curtain

More information

EDEXCEL NATIONAL CERTIFICATE/DIPLOMA MECHANICAL PRINCIPLES AND APPLICATIONS NQF LEVEL 3 OUTCOME 1 - LOADING SYSTEMS

EDEXCEL NATIONAL CERTIFICATE/DIPLOMA MECHANICAL PRINCIPLES AND APPLICATIONS NQF LEVEL 3 OUTCOME 1 - LOADING SYSTEMS EDEXCEL NATIONAL CERTIFICATE/DIPLOMA MECHANICAL PRINCIPLES AND APPLICATIONS NQF LEVEL 3 OUTCOME 1 - LOADING SYSTEMS TUTORIAL 1 NON-CONCURRENT COPLANAR FORCE SYSTEMS 1. Be able to determine the effects

More information

Geometry Notes PERIMETER AND AREA

Geometry Notes PERIMETER AND AREA Perimeter and Area Page 1 of 57 PERIMETER AND AREA Objectives: After completing this section, you should be able to do the following: Calculate the area of given geometric figures. Calculate the perimeter

More information

Section 5A: Guide to Designing with AAC

Section 5A: Guide to Designing with AAC Section 5A: Guide to Designing with AAC 5A.1 Introduction... 3 5A.3 Hebel Reinforced AAC Panels... 4 5A.4 Hebel AAC Panel Design Properties... 6 5A.5 Hebel AAC Floor and Roof Panel Spans... 6 5A.6 Deflection...

More information

Safe & Sound Bridge Terminology

Safe & Sound Bridge Terminology Safe & Sound Bridge Terminology Abutment A retaining wall supporting the ends of a bridge, and, in general, retaining or supporting the approach embankment. Approach The part of the bridge that carries

More information

Design of Steel Structures Prof. S.R.Satish Kumar and Prof. A.R.Santha Kumar

Design of Steel Structures Prof. S.R.Satish Kumar and Prof. A.R.Santha Kumar Problem 1 Design a hand operated overhead crane, which is provided in a shed, whose details are: Capacity of crane = 50 kn Longitudinal spacing of column = 6m Center to center distance of gantry girder

More information

HSL-3 Heavy duty anchor carbon steel. Anchor Fastening Technology Manual HSL-3. Heavy duty anchor. Version 2015-09 09 / 2015 1

HSL-3 Heavy duty anchor carbon steel. Anchor Fastening Technology Manual HSL-3. Heavy duty anchor. Version 2015-09 09 / 2015 1 Anchor Fastening Technology Manual HSL-3 Heavy duty anchor HSL-3 Heavy duty anchor Version 2015-09 09 / 2015 1 HSL-3 Heavy duty anchor, Anchor version Sizes Benefits HSL-3 Bolt version Threaded rod version

More information

International Nursing and Rehab Center Addition 4815 S. Western Blvd. Chicago, IL

International Nursing and Rehab Center Addition 4815 S. Western Blvd. Chicago, IL PROJECT International Nursing and Rehab Center Addition 4815 S. Western Blvd. Chicago, IL EXP. 11/30/2014 STRUCTURAL CALCULATIONS July 24, 2014 BOWMAN, BARRETT & ASSOCIATES INC. CONSULTING ENGINEERS 312.228.0100

More information

Lab 8: Ballistic Pendulum

Lab 8: Ballistic Pendulum Lab 8: Ballistic Pendulum Equipment: Ballistic pendulum apparatus, 2 meter ruler, 30 cm ruler, blank paper, carbon paper, masking tape, scale. Caution In this experiment a steel ball is projected horizontally

More information

SDNS108 Dynamic response of a reinforced concrete slab leaned on 4 with dimensions subjected to a concentrated loading

SDNS108 Dynamic response of a reinforced concrete slab leaned on 4 with dimensions subjected to a concentrated loading Titre : SDNS108 - Réponse dynamique d'une dalle en béton a[...] Date : 31/05/2012 Page : 1/9 SDNS108 Dynamic response of a reinforced concrete slab leaned on 4 with dimensions subjected to a concentrated

More information

Chapter - 3 Design of Rectangular Beams and One-way Slabs

Chapter - 3 Design of Rectangular Beams and One-way Slabs Rectangular Beams and One-way Slabs Page 1 of 9 Chapter - 3 Design of Rectangular Beams and One-way Slabs 12 h A 12 strip in a simply supported one-way slab h b=12 L Rectangular Beams and One-way Slabs

More information

Residential Deck Safety, Construction, and Repair

Residential Deck Safety, Construction, and Repair Juneau Permit Center, 4 th Floor Marine View Center, (907)586-0770 This handout is designed to help you build your deck to comply with the 2006 International Residential Building code as modified by the

More information

Session 5D: Benefits of Live Load Testing and Finite Element Modeling in Rating Bridges

Session 5D: Benefits of Live Load Testing and Finite Element Modeling in Rating Bridges Session 5D: Benefits of Live Load Testing and Finite Element Modeling in Rating Bridges Douglas R. Heath P.E., Structural Engineer Corey Richard P.E., Project Manager AECOM Overview Bridge Testing/Rating

More information

HUS-HR, CR Screw anchor, stainless steel

HUS-HR, CR Screw anchor, stainless steel HUS-HR, CR Screw anchor, Anchor version HUS-HR 6 / 8 / 10 / 14 Stainless steel concrete Screw with hexagonal head HUS-CR 10 Stainless steel concrete screw with countersunk head Benefits - High productivity

More information

LEGACY REPORT ER-5110. www.icc-es.org. ICC Evaluation Service, Inc. Reissued November 1, 2003. Legacy report on the 1997 Uniform Building Code

LEGACY REPORT ER-5110. www.icc-es.org. ICC Evaluation Service, Inc. Reissued November 1, 2003. Legacy report on the 1997 Uniform Building Code LEGACY REPORT Reissued November 1, 2003 ICC Evaluation Service, Inc. www.icc-es.org Business/Regional Office # 5360 Workman Mill Road, Whittier, California 90601 # (562) 699-0543 Regional Office # 900

More information

Module 5 (Lectures 17 to 19) MAT FOUNDATIONS

Module 5 (Lectures 17 to 19) MAT FOUNDATIONS Module 5 (Lectures 17 to 19) MAT FOUNDATIONS Topics 17.1 INTRODUCTION Rectangular Combined Footing: Trapezoidal Combined Footings: Cantilever Footing: Mat foundation: 17.2 COMMON TYPES OF MAT FOUNDATIONS

More information

Algebra Geometry Glossary. 90 angle

Algebra Geometry Glossary. 90 angle lgebra Geometry Glossary 1) acute angle an angle less than 90 acute angle 90 angle 2) acute triangle a triangle where all angles are less than 90 3) adjacent angles angles that share a common leg Example:

More information

Shear Forces and Bending Moments

Shear Forces and Bending Moments Chapter 4 Shear Forces and Bending Moments 4.1 Introduction Consider a beam subjected to transverse loads as shown in figure, the deflections occur in the plane same as the loading plane, is called the

More information

Design Parameters for Steel Special Moment Frame Connections

Design Parameters for Steel Special Moment Frame Connections SEAOC 2011 CONVENTION PROCEEDINGS Design Parameters for Steel Special Moment Frame Connections Scott M. Adan, Ph.D., S.E., SECB, Chair SEAONC Structural Steel Subcommittee Principal Adan Engineering Oakland,

More information

Design Of Reinforced Concrete Structures ii Two-Way Slabs

Design Of Reinforced Concrete Structures ii Two-Way Slabs 1. Inroduction When the ratio (L/S) is less than 2.0, slab is called two-way slab, as shown in the fig. below. Bending will take place in the two directions in a dish-like form. Accordingly, main reinforcement

More information

SPECIFICATIONS, LOADS, AND METHODS OF DESIGN

SPECIFICATIONS, LOADS, AND METHODS OF DESIGN CHAPTER Structural Steel Design LRFD Method Third Edition SPECIFICATIONS, LOADS, AND METHODS OF DESIGN A. J. Clark School of Engineering Department of Civil and Environmental Engineering Part II Structural

More information

MODULE E: BEAM-COLUMNS

MODULE E: BEAM-COLUMNS MODULE E: BEAM-COLUMNS This module of CIE 428 covers the following subjects P-M interaction formulas Moment amplification Web local buckling Braced and unbraced frames Members in braced frames Members

More information

Solutions to Exercises, Section 5.1

Solutions to Exercises, Section 5.1 Instructor s Solutions Manual, Section 5.1 Exercise 1 Solutions to Exercises, Section 5.1 1. Find all numbers t such that ( 1 3,t) is a point on the unit circle. For ( 1 3,t)to be a point on the unit circle

More information

APE T CFRP Aslan 500

APE T CFRP Aslan 500 Carbon Fiber Reinforced Polymer (CFRP) Tape is used for structural strengthening of concrete, masonry or timber elements using the technique known as Near Surface Mount or NSM strengthening. Use of CFRP

More information