CE 4111 Seismic Design of Structures School of Civil and Environmental Engineering Shiraz University of Technology S.M. Dehghan Fall 2015 Steel Seismic Force Resisting Systems Dr. Dehghan 1
Steel SFRS 3 Steel Seismic Force Resisting Systems will be covered in Five Parts: 1. Ductile Design / Structural Steel 2. General Requirements 3. Special Moment Resisting Frame (SMRF) 4. Special Concentrically Braced Frame (SCBF) A. Behavior B. Design 5. Eccentrically Braced Frame (EBF) Steel Seismic Load Resisting Systems Concentrically Braced Frames - Design Dr. Dehghan 2
Concentrically Braced Frames Outline Topics Description and Types of Concentrically Braced Frames Basic Behavior of Concentrically Braced Frames 6 AISC Seismic Provisions for Special Concentrically Braced Frames (SCBF) Dr. Dehghan 3
7 References ASCE 7-10, Minimum Design Loads for Buildings and Other Structures AISC 360-10, Specification for Structural Steel Buildings AISC 341-10, Seismic Provisions for Structural Steel Buildings NIST GCR13-917-24 Seismic Design of Steel special Concentrically Braced Frame Concentrically Braced Frames AISC Seismic Provisions Dr. Dehghan 4
9 AISC Seismic Provisions AISC 341-10 Chapter F Braced-Frame and Shear-Wall Systems F1. Ordinary Concentrically Braced Frames (OCBF) o Have a low R-factor: R=3.25 for OCBF F2. Special Concentrically Braced Frames (SCBF) o Have a moderate R-factor: R=6 for SCBF F3. Eccentrically Braced Frames (EBF) o Have the highest R-factor: R=8 for SMF F4. Buckling-Restrained Braced Frames (BRBF) o Have the highest R-factor: R=8 for BRBF F5. Special Plate Shear Walls (SPSW) o Have a high R-factor: R=7 for SPSW AISC Seismic Provisions Section F2 10 1. Scope 2. Basis of Design 3. Analysis 4. System Requirements 4a. Lateral Force Distribution 4b. V- and Inverted V-Braced Frames 4c. K-Braced Frames 4d. Tension-Only Frames Dr. Dehghan 5
11 AISC Seismic Provisions Section F2 5. Members 5a. Basic Requirements 5b. Diagonal Braces 5c. Protected Zones 6. Connections 6a. Demand Critical Welds 6b. Beam-to-Column Connections 6c. Required Strength of Brace Connections 6d. Column Splices F2.1 Scope 12 SCBF are a type of braced frames in which the centerline of members that meet at a joint intersect at a point, forming a vertical truss system CBFs provide complete truss action with members subjected primarily to axial loads in the elastic range During a moderate to severe earthquake, bracing members and connections are expected to undergo significant inelastic deformations into the post-buckling range Dr. Dehghan 6
13 F2.1 Scope Common types of CBFs are diagonally braced X-braced V-braced (or inverted V-braced) F2.2 Design Basis 14 SCBF are distinguished from OCBF (with R = 3) by requirements for ductility Dr. Dehghan 7
15 F2.2 Design Basis During a severe earthquake, bracing members in a CBF frame are subjected to large deformations in cyclic tension and compression In the compression direction flexural buckling causes the formation of flexural plastic hinges in the brace Braces in a typical CBF frame can be expected to yield and buckle at rather moderate story drifts of about 0.3% to 0.5% In a severe earthquake, the braces could undergo post-buckling axial deformations 10 to 20 times their yield deformation In order to survive such large cyclic deformations without premature failure, the bracing members and their connections must be properly detailed F2.3 Analysis 16 Dr. Dehghan 8
17 F2.3 Analysis F2.3 Analysis 18 SCBF are typically designed based on an elastic analysis Expected behavior includes significant nonlinearity due to brace buckling and yielding, which is anticipated in MCE Braced-frame system ductility can only be achieved if beams and column buckling can be prevented Dr. Dehghan 9
F2.3 Analysis There is a need to supplement the elastic analysis in order to have an adequate design The required strength of braces is typically determined based on the analysis required by ASCE 7 The analysis required by this section is used in determining the required strength of braced-frame beams and columns, and brace connections In AISC 341-10 explicit consideration of the inelastic behavior by requiring a plastic-mechanism analysis It is naturally desirable that engineers performing analyses of ductile systems give some thought to the manner in which they will behave 19 F2.3 Analysis The first-mode of deformation is considered when determining if a brace is in tension or in compression the columns are considered to be inclined in one direction consideration must also be given to the behavior when the columns slope the opposite direction Expected Brace Strength Tension P et = R y F y A g Compression P ec = min (R y F y A g and 1.14 F cr A g ) Use R y F y for computing F cr per Chapter E of Specification Post-Buckling P eresid = 0.3 Pec 20 Dr. Dehghan 10
21 Specification E3 Flexural Buckling of Members Nominal Compressive Strength P n Note use R y F y for computing F cr F2.4 System Requirements F2.4a Lateral Force Distribution 22 Dr. Dehghan 11
23 F2.4a Lateral Force Distribution This provision attempts to balance the tensile and compressive resistance across the width of the building the buckling and post-buckling strength of the bracing members in compression can be substantially less than tension good balance helps prevent the accumulation of inelastic drifts in one direction Ideally, the braces should be arranged so that about half of the applied lateral load is resisted by tension braces, for either direction of loading on the frame NG OK All braces in tension (or compression) 24 F2.4b V and inverted V-Braced Frames V-braced and inverted V-braced (chevron) frames exhibit a special problem The expected behavior of SCBF is that an unbalanced vertical force must be resisted by the intersected beam Dr. Dehghan 12
F2.4b V and inverted V-Braced Frames The effect of this unbalanced load can be mitigated by using V- and inverted V-braces in alternate stories (creating an X-brace over two story) Adequate lateral bracing at the brace-beam is necessary in order to prevent possible LTB of the beam The stability of this connection is influenced by the flexural and axial forces in the beam, and any torsion imposed by brace buckling or post-buckling 25 F2.4b V and inverted V-Braced Frames To avoid hinge formation in the beam, and to avoid the potential for a soft story, the beam must be designed to resist the unbalanced forces from the braces Design beams for unbalanced load that will occur when compression brace buckles and tension brace yields Take force in tension brace R y F y A g Take force in compression brace 0.3 P ec Assume beam has no vertical support between columns 26 Dr. Dehghan 13
F2.4b V and inverted V-Braced Frames The design forces for the beam includes the gravity load on the beam the unbalanced brace forces w gravity = (1.2 + 0.2 S DS ) D + 0.5L L 27 w gravity = (1.2 + 0.2 S DS ) D + 0.5L 0.3 P ec R y F y A g simple framing ( R y F y A g + 0.3 P ec ) cos ( R y F y A g - 0.3 P ec ) sin Unbalanced vertical force on the beam produces bending and shear in the beam Unbalanced horizontal force on the beam produces axial force in the beam The beam must be designed as a member under combined axial force and bending These large unbalanced brace forces will often result in very heavy beams D1.2a Moderately Ductile Members 28 Dr. Dehghan 14
29 D1.2a Moderately Ductile Members Examples of lateral braces in an inverted V-brace F2.4c K-Braced Frames 30 K-bracing is generally not considered desirable in CBFs is prohibited entirely for SCBF because it is considered undesirable to have columns that are subjected to unbalanced lateral forces from the braces these forces may contribute to column failures K-Type Braces are not Permitted for SCBF Dr. Dehghan 15
31 F2.4c K-Braced Frames F2.4d Tension Only Braces SCBF provisions have not been developed for use with braces that only act in tension tension-only braced frames are not allowed for SCBF tension-only bracing is allowed for OCBF 32 F2.5 Members F2.5a Basic Requirements This is to assure that these members can develop their plastic flexural strength, and maintain this strength through large inelastic deformations without excessive strength loss due to local buckling Dr. Dehghan 16
33 F2.5a Basic Requirements An elastic analysis of a braced frame shows that the columns and braces only carry axial force so flexural strength and ductility are not necessary in the elastic range When a braced frame goes inelastic in an earthquake the columns and braces may see very large bending moments, so flexural strength and ductility become important The flexural strength and rotation capacity of the column has been shown to be a significant contributor to the stability of SCBF It has also been demonstrated that SCBF can be subject to significant story drift, requiring columns to undergo inelastic rotation F2.5a Basic Requirements This slide shows why the columns may see significant bending after braces buckle The column moments are not usually explicitly considered in the design of an SCBF the requirement for seismically compact columns is intended to help allow columns to carry large moments in an earthquake 34 Dr. Dehghan 17
F2.5a Basic Requirements Braces will form a plastic flexural hinge in the postbuckling condition, due to P-Δ moments in the member brace members with high b/t ratios will suffer local buckling at these hinge locations high localized strains in the local buckle regions, may result in fracture of the brace member after just a few cycles of loading plastic hinge The requirement for seismically compact brace members is P Δ intended to delay the local buckling, and delay fracture of the brace at the hinge region 35 F2.5a Basic Requirements Photo shows a laboratory cyclic loading test on a braced frame with HSS section Note the plastic flexural hinge that has formed at mid-span of the brace and the local buckle that has formed 36 Dr. Dehghan 18
37 F2.5a Basic Requirements Photo was taken in a braced frame building following the Northridge Earthquake The braces were constructed using HSS members Photo shows a local buckle in the brace, that resulted in fracture of the brace The brace has suffered local buckling at the mid-span hinge which then caused fracture F2.5b Diagonal Braces 38 Dr. Dehghan 19
39 F2.5b Diagonal Braces The slenderness (KL/r) limit is 200 for braces in SCBF An upper limit is provided to prevent dynamic effects associated with extremely slender braces Closer spacing of stitches and higher stitch strength requirements are specified for built-up bracing members in SCBF than those required for typical built-up members this is critical for double-angle and double-channel braces that impose large shear forces on the stitches upon buckling this is intended to restrict individual element bending between the stitch points and premature fracture of bracing Bolted stitches are not permitted within the middle one-fourth of the clear brace length due to formation of plastic hinge F2.5b Diagonal Braces 40 The required strength of bracing members with respect to the limit state of net section rupture is the expected brace strength It should be noted that some steel materials used for braces have expected yield strengths significantly higher than their specified minimum yield strengths Dr. Dehghan 20
41 F2.5b Diagonal Braces A basic goal of SCBF detailing is that tension yielding of the brace gross-sectional area will occur prior to the occurrence of fracture limit states in the brace At the end connections of a brace member, the effective net area of the member is usually less the gross area the reduction in effective cross-sectional area can result from holes in the members (bolts holes or holes made to facilitate welding) and can also result from shear lag Reductions of cross-sectional area can occur along the length of the member if holes are made in the member Although not explicitly stated, this requirement should also be satisfied when checking block shear failure in the bracing member F2.5b Diagonal Braces 42 The bracing members have fractured at bolted connections The effective cross-sectional area is reduced by bolt holes and by shear lag Dr. Dehghan 21
43 F2.5b Diagonal Braces Example - Check double angle bracing member for limit state of net section fracture gusset plate double angle bracing member 44 F2.5b Diagonal Braces Example P u = R y F y A g Required axial tension strength of brace for limit state of fracture of the net section Critical Net Section Ae = U An Ae < Ag Bolt hole An < Ag Shear lag U < 1 Dr. Dehghan 22
F2.5b Diagonal Braces Example 45 P u = R y F y A g P u = R y F y A g Limit state of fracture of net section φ Pn = φ Ae (Rt Fu) φ = 0.75 Having no reduction in the section is deemed sufficient to ensure this behavior Ae Ag (0.75) Ae (Rt Fu) Ry Fy Ag F2.5b Diagonal Braces Example 46 For A36 Angles A A e g 1.5 250MPa 1.04 0.75 1.2 400MPa Calculations show that the effective net area Ae must exceed the gross area Ag Ae Ag Dr. Dehghan 23
47 F2.5b Diagonal Braces Example - Check block shear rupture of bracing member P u = R y F y A g Design strength of the brace member based on a limit state of block shear rupture should also equal or exceed the required strength computed P n = (0.75) U bs A nt R t F u + lesser of 0.6 A nv R t F u 0.6 A gv R y F y 48 F2.5b Diagonal Braces Reinforcing net section of bracing member Satisfying Ae Ag, will generally require reinforcing of the brace member so that its effective net area is at least equal to its gross area This slide shows how the net section of the angles might be increased by welding reinforcing plates to the angles Dr. Dehghan 24
F2.5b Diagonal Braces Example - HSS bracing member for limit state of net section fracture gusset plate rectangular HSS bracing member 49 The end of member is slotted, and then welded to a gusset plate along the slot edges. The slot is made longer than needed, to facilitate fit-up in the field F2.5b Diagonal Braces Example 50 Some examples of slotted HSS brace connections to gusset plates Dr. Dehghan 25
51 F2.5b Diagonal Braces Reinforcing net section of bracing member This slide shows how the net section of the HSS might be increased by welding reinforcing plates to the angles F2.5c Panel Zones 52 Welded or shot-in attachments in areas of inelastic strain may lead to fracture Such areas in SCBF include gusset plates and expected plastic-hinge regions in the brace Note that for the X-braced frame, the half-length of the brace is used and a plastic hinge is anticipated at any of the brace quarter points Dr. Dehghan 26
53 F2.5c Panel Zones F2.5c Panel Zones 54 Dr. Dehghan 27
55 F2.6 Connections F2.6a Demand Critical Welds F2.6a Demand Critical Welds Groove welds at column splices are designated as demand critical for several reasons the consequences of a brittle failure at a column splice are not clearly understood, may endanger safety of the frame the actual forces that will occur at a column splice during an earthquake are very difficult to predict the locations of points of inflection in the columns during an earthquake are constantly moving In order to provide a high degree of protection against brittle failure at column splice groove welds, the use of demand critical welds is specified 56 Dr. Dehghan 28
57 F2.6b Beam-to-Column Connections Braced frames are likely to be subject to significant inelastic drift their connections will undergo significant rotation connections with gusset plates can be vulnerable to rupture if they are not designed to accommodate this rotation F2.6b Beam-to-Column Connections The provision allows engineer to select from two options the first is a simple connection for which the required rotation is defined as 0.025 rad 58 An example of a configuration tested that effectively allowed rotation between the beam and column Dr. Dehghan 29
59 F2.6b Beam-to-Column Connections The provision allows engineer to select from two options the first is a simple connection for which the required rotation is defined as 0.025 rad A connection with rotation capacity outside the gusset plate F2.6b Beam-to-Column Connections 60 Dr. Dehghan 30
61 F2.6b Beam-to-Column Connections The provision allows engineer to select from two options the second option is a fully restrained moment connection for which the maximum moment can be determined from the expected strength of the connecting beam or column Such connections must meet the same requirements for beam-to-column connections in ordinary moment frames, as specified in Section E1.6 Specification - B3.6 Design of Connections Connection Classification The basic assumption made in classifying connections is that the most important behavioral characteristics of the connection can be modeled by a moment-rotation (M-θ) curve Implicit in the moment-rotation curve is the definition of the connection as being a region of the column and beam along with the connecting elements The connection response is defined this way because the rotation of the member in a physical test is generally measured over a length that incorporates the contributions of not only the connecting elements, but also the ends of the members being connected and the column panel zone 62 Dr. Dehghan 31
63 Specification - B3.6 Design of Connections Connection Stiffness The initial stiffness of the connection does not adequately characterize connection response at service levels The secant stiffness, K S, at service loads is taken as an index property of connection stiffness where M S = moment at service loads θ S = rotation at service loads Specification - B3.6 Design of Connections If K S L/EI 20, it is acceptable to consider the connection to be fully restrained FR in other words, able to maintain the angles between members If K S L/EI 2, it is acceptable to consider the connection to be simple in other words, it rotates without developing moment Connections with stiffness between these two limits are partially restrained PR and the stiffness, strength and ductility of the connection must be considered in the design 64 Dr. Dehghan 32
65 Specification - B3.6 Design of Connections F2.6c Required Strength of Brace Connections 66 Many of the failures reported in CBFs due to strong ground motions have been in the connections cyclic testing of specimens designed and detailed in accordance with typical provisions for concentrically braced frames has produced connection failures typical design practice, design connections only for axial loads good connection performance can be expected if the effects of brace member cyclic post-buckling behavior are considered Dr. Dehghan 33
67 F2.6c Required Strength of Brace Connections Certain references suggest limiting the free edge length of gusset plates The committee has reviewed the testing cited and has concluded that such edge stiffeners do not offer any advantages in gusset plate behavior There is therefore no limitation on edge dimensions in these provisions F2.6c(1) Required Tensile Strength 68 The brace connection should be stronger than the brace Note that using the amplified seismic load is not an acceptable method to establish the maximum load effect In general, the braces in an SCBF can be expected to yield in an earthquake, and so the brace connection must be designed for the expected yield strength of the brace Dr. Dehghan 34
69 F2.6c(1) Required Tensile Strength There are a number of ways one can determine the maximum force transferred to the connection, include 1. Perform a pushover analysis to determine the forces acting on the connections when the maximum frame capacity (collapse mechanism) is reached 2. Determine how much force can be resisted before causing uplift of a spread footing (note that the foundation design forces are not required to resist more than the code base shear level) 3. Perform a suite of inelastic time history analyses and envelop the connection demands F2.6c(1) Required Tensile Strength Required axial tensile strength of the brace connection R y F y A g 70 Dr. Dehghan 35
F2.6c(1) Required Tensile Strength Consider load path through connection region P u sin P u = R y F y A g P u cos When designing the brace connection, it is important to consider the load path through the connection This is important not only for seismic design, but also when designing brace connections for any other type of load like wind For the arrangement shown, o the horizontal component of the brace force must be transferred to the beam o the vertical component must be transferred to the column 71 F2.6c(1) Required Tensile Strength Uniform Force Method V uc V ub V ub P u = R y F y A g V uc + V ub = P u sin P u sin P u cos 72 There are many methods for approaching brace connection design One of the more common methods is the Uniform Force Method This slide shows the load path for transferring the vertical component of the brace force to the column o A portion of the vertical component (V uc ) of brace force is transferred directly to the column through the gusset plate o The remaining portion of the vertical component (V ub ) of brace force is transferred to the beam, and then from the beam to the column Dr. Dehghan 36
F2.6c(1) Required Tensile Strength Uniform Force Method H uc H ub H uc P u = R y F y A g H uc + H ub = P u cos P u sin P u cos 73 This slide shows the load path for transferring the horizontal component of the brace force to the beam, as defined by the Uniform Force Method o A portion of the horizontal component (H ub ) of the brace force is transferred directly to the beam through the gusset plate o The remaining portion of the horizontal component (H uc ) of the brace force is transferred to the column, and then from the column to the beam F2.6c(1) Required Tensile Strength Bolts and welds shall not be designed to share force in a joint, or the same force component in a connection (D2.2) P u sin P u = R y F y A g P u cos 74 A portion of the vertical component of the brace force is transferred to the column by the gusset to column welds, and the remainder is transferred to the column through the bolted beam end connection Bolts and welds must share same force component, which is prohibited by D2.2 A portion of the horizontal component of the brace force is transferred to the beam by the gusset to beam welds, and the remainder is transferred to the beam through the bolted beam end connection Bolts and welds again share same force component, which is prohibited by D2.2 Dr. Dehghan 37
75 F2.6c(2) Required Compressive Strength Bracing connections should be designed to withstand the maximum force that the brace can deliver in compression a factor of 1.1 has been adopted here due to the use of conservative column curve equations = 1.1 P ec Expected brace strength in compression in F2.3 P ec = min (R y F y A g and 1.14 F cr A g ) Use R y F y for computing F cr per Chapter E of Specification F2.6c(2) Required Compressive Strength Required axial compression strength of brace connection 1.1 P ec 76 Dr. Dehghan 38
77 F2.6c(2) Required Compressive Strength Required axial compression strength of brace connection 1.1 P ec The required axial compression strength is intended to assure that the brace connection is stronger then the brace in compression The required axial compression strength is used to check limit states such as o buckling of the gusset plate, o web crippling of the beam and column The gusset will often result in a large unsupported length that may be prone to buckling when the brace is in compression Gusset buckling is often checked by assuming the unsupported segment of gusset behaves as a column F2.6c(2) Required Compressive Strength Examples of brace connection elements have buckled Photos of steel braced frame buildings following the 1995 Kobe Earthquake 78 Dr. Dehghan 39
F2.6c(3) Accommodation of Brace Buckling 79 F2.6c(3) Accommodation of Brace Buckling Braces in SCBF are expected to undergo cyclic buckling under severe ground motions, forming plastic hinges at their center and at each end Plastic Hinges 80 To prevent fracture resulting from brace rotations bracing connections must either have sufficient strength to confine inelastic rotation to the bracing member sufficient ductility to accommodate brace end rotations Dr. Dehghan 40
F2.6c(3) Accommodation of Brace Buckling Fixed End braces Connections with stiffness in two directions can be designed and detailed test results indicate that forcing the plastic hinge to occur in the brace rather than the connection plate results in greater energy dissipation capacity brace will impose bending moment on connections and adjoining members M u = 1.1 R y M p = 1.1 R y F y Z brace (for critical buckling direction) Plastic Hinges 81 P M M F2.6c(3) Accommodation of Brace Buckling Photos of buckled braced frame in the 1995 Kobe Earthquake The deformed shape of buckled brace indicates large bending moments that were generated 82 An example of braced frame with heavy wide-flange braces The end connections appear to provide a high degree of rotational restraint 1.1 R y M p-brace Dr. Dehghan 41
F2.6c(3) Accommodation of Brace Buckling Where fixed end connections are used in one axis with pinned connections in the other axis, the effect of the fixity should be considered in determining the critical buckling axis For brace buckling in the plane of the gusset plates the end connections should be designed to resist the expected compressive strength and the expected flexural strength of the brace note that a realistic value of K should be used to represent the connection fixity For brace buckling out of the plane of the gusset plate weak-axis rotation in the gusset is provided (pinned) Satisfactory performance can be ensured by allowing the gusset plate to develop restraint-free plastic rotations 83 F2.6c(3) Accommodation of Brace Buckling Pinned End braces Flexural plastic hinge will form at mid-length only Brace will impose no bending moment on connections and adjoining members must design brace connection to behave like a pin 84 P P Plastic Hinge P P Dr. Dehghan 42
F2.6c(3) Accommodation of Brace Buckling Providing Fold Line The most common strategy provide rotational flexibility at the brace connection is the fold line concept Rotation of the brace end is permitted by allowing a line of rotation (the fold line) in the gusset plate Buckling perpendicular to gusset to plate 85 Line of rotation (fold line) when the brace buckles out-of-plane (thin direction of plate) F2.6c(3) Accommodation of Brace Buckling Providing Fold Line The distance of 2t should be considered the minimum offset In practice, it may be advisable to specify larger distance (2t + 20 mm) for erection tolerance 86 2t 2t A brace with a shallow angle with the beam A brace with a steep angle with the beam Dr. Dehghan 43
F2.6c(3) Accommodation of Brace Buckling Providing Fold Line If a concrete floor slab is present, then the fold line must be located so that the slab does not interfere with out-of-plane bending of the gusset along the fold line 87 2t Concrete floor slab 2t Concrete floor slab Styrofoam F2.6c(3) Accommodation of Brace Buckling Examples of brace connections which are not provided with a fold line If these braces buckle out-of-plane, the brace end rotations will likely tear apart the connections 88 Dr. Dehghan 44
F2.6c(3) Accommodation of Brace Buckling Example of brace connections which are not provided with a fold line This photo is a braced frame building in 1994 Northridge Earthquake When this brace buckled out-of-plane, the absence of rotational flexibility in the connection caused the brace end to fracture 89 F2.6c(3) Accommodation of Brace Buckling Examples of brace connections detailed with fold lines A laboratory cyclic loading test on a braced frame with HSS braces The HSS brace has buckled out-of-plane detailed with a fold line The gusset plate behaved as a pin" for out-of-plane buckling, and permitted the buckling to occur without damage to the connection 90 Dr. Dehghan 45
F2.6c(3) Accommodation of Brace Buckling Examples of brace connections detailed with fold lines 91 > 2t F2.6c(3) Accommodation of Brace Buckling Examples of brace connections detailed with fold lines 92 >2t Dr. Dehghan 46
F2.6d Column Splices 93 F2.6d Column Splices In the event of a major earthquake, columns in CBFs undergo significant bending beyond the elastic range after buckling and yielding of the braces Columns in SCBF are required to have adequate compactness and shear and flexural strength in order to maintain their lateral strength during large cyclic deformations In addition, column splices are required to have sufficient strength to prevent failure under expected post-elastic forces Analytical studies on SCBF that are not part of a dual system have shown that columns can carry as much as 40% of the story shear 94 Dr. Dehghan 47