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SEISMIC DESIGN OF REINFORCED CONCRETE STRUCTURES Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 1 NEHRP Recommended Provisions Concrete Design Requirements • Context in the NEHRP Recommended Provisions • Concrete behavior • Reference standards • Requirements by Seismic Design Category • Moment resisting frames • Shear walls • Other topics • Summary Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 2 Context in NEHRP Recommended Provisions Design basis: Strength limit state Using NEHRP Recommended Provisions: Structural design criteria: Chap. 4 Structural analysis procedures: Chap. 5 Components and attachments: Chap. 6 Design of concrete structures: Chap. 9 and ACI 318 Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 3 Seismic-Force-Resisting Systems Reinforced Concrete Unbraced frames (with rigid “moment resisting” joints): Three types Ordinary Intermediate Special R/C shear walls: Ordinary Special Precast shear walls: Special Intermediate Ordinary Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 4 NEHRP Recommended Provisions Concrete Design • Context in the Provisions • Concrete behavior Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 5 Unconfined Concrete Stress-Strain Behavior 20000 4500 psi 18000 8800 psi 16000 13,500 psi 14000 17,500 psi Stress, psi 12000 10000 8000 6000 4000 2000 0 0 0.001 0.002 0.003 0.004 Strain, in./in. Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 6 Idealized Stress-Strain Behavior of Unconfined Concrete 6000 5000 4000 Stress, psi 3000 ⎡ 2ε ⎛ ε ⎞2 ⎤ fc = fc' ⎢ c − ⎜ c ⎟ ⎥ ⎢ εo ⎝ εo ⎠ ⎥ ⎣ ⎦ 2000 2fc' εo = 1000 Et Et = 1.8 x106 + 460fc' , psi 0 0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004 Strain Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 7 Confinement by Spirals or Hoops Asp fyhAsp ds fyhAsp Confinement Forces acting Confinement from spiral or on 1/2 spiral or from square circular hoop circular hoop hoop Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 8 Confinement Rectangular hoops Confinement by Confinement by with cross ties transverse bars longitudinal bars Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 9 Opened 90° hook on hoops Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 10 Confined Concrete Stress-Strain Behavior 8000 no confinement 4.75 in. 7000 Pitch of 3.5 in. ¼ in. dia. 6000 2.375 in. spiral 1.75 in. Stress, psi 5000 4000 3000 Tests of 2000 6 in. x 12 in. 1000 cylinders 0 0 0.01 0.02 0.03 0.04 Average strain on 7.9 in. gauge length Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 11 Idealized Stress-Strain Behavior of Confined Concrete Kent and Park Model No Hoops 4500 4 in. 4000 6 in. 9 in. 3500 12 in. 3000 Stress, psi 2500 2000 1500 1000 500 0 0 0.004 0.008 0.012 0.016 Confined Area 12” x 16” Strain, in./in. Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 12 Reinforcing Steel Stress-Strain Behavior 100 Grade 75 80 Stress, ksi Grade 60 60 rupture~10-12% Grade 40 40 strain hardening~ 1-3% E = 29,000 ksi rupture ~18-20% 20 1000 2000 3000 4000 5000 6000 7000 8000 Microstrain Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 13 Reinforced Concrete Behavior steel yields failure Load cracked-inelastic cracked-elastic uncracked Mid-Point Displacement, Δ Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 14 Behavior Up to First Yield of Steel b εc fc c d φ As εsEs < fy εs Strain Stress Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 15 Behavior at Concrete Crushing b ε c,max f'c c C d φ jd As fy Asfy εs >εy Strain Stress Forces Mn = Asfyjd Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 16 Typical Moment Curvature Diagram 700 w/ strain hardening 600 f’c = 4 ksi fy = 60 ksi 500 M, in-kip w/o strain hardening b = 8 in 400 d = 10 in 300 ρ = 0.0125 200 100 0 0 100 200 300 φ x 10-5 in-1 Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 17 Influence of Reinforcement Ratio 5000 f’c = 4 ksi 4000 fy = 60 ksi b = 10 in M, in-kip 3000 d = 18 in 2000 ρ = 2.5% 1000 ρ = 1.5% ρ = 0.5% 0 0 100 200 300 400 φ x 10-5 in-1 Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 18 Influence of Compression Reinforcement 1600 Beam ρ ρ' 1 0.0375 0.0250 2 0.0375 0.0125 1 3 0.0375 0 1200 2 4 0.0250 0.0125 3 5 0.0250 0 6 0.0125 0.0125 800 5 4 7 0.0125 0 M lb / in2 bd2 6 400 7 0 0 0.008 0.016 0.024 φ Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 19 Moment-Curvature with Confined Concrete ε c,max f'c c φ As fy εs >εy Strain Stress Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 20 Moment-Curvature with Confined Concrete 35000 30000 25000 Moment, in-k 20000 Beam - 24 in. x 36 in. Tension Steel - 12 ea. #10 15000 Compression Steel - 5 ea. #8 Confining Steel - #4 hoops at 4 in. c-c 10000 5000 without confining with confining 0 0 500 1000 1500 2000 curvature, microstrain/in. Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 21 Plastic Hinging l idealized M φ actual lp plastic rotation φu −φy Mu φu Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 22 Strategies to Improve Ductility • Use low flexural reinforcement ratio • Add compression reinforcement • Add confining reinforcement Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 23 Other Functions of Confining Steel • Acts as shear reinforcement • Prevents buckling of longitudinal reinforcement • Prevents bond splitting failures Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 24 Structural Behavior Frames Story Mechanism Sway Mechanism Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 25 Story Mechanism Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 26 Structural Behavior - Walls Δs H V N V H V V N V C V T Flexural Horizontal Sliding on Sliding on failure tension flexural cracks construction joint Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 27 Structural Behavior Walls Vu Vu Compression Vu 1 2 1 hw 2 45 lw Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 28 Structural Behavior 14 in square Columns 4-#11 bars f' c = 4 ksi f y = 45 ksi Ultimate 1000 yield 800 Axial load, P, kip 600 1.75” bending axis 400 200 0 0 400 800 1200 1600 0.002 0.001 0 Moment, M, in-kip Curvature, φ, rad/in Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 29 Influence of Hoops on Axial Strength Gross column Confined concrete Area = A g Area = A core Before spalling- After spalling- P = Agf’c P = Acore(f’c + 4 flat) After spalling ≥ Before spalling Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 30 Column with Inadequate Ties Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 31 Well Confined Column Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 32 Hysteretic Behavior of Well Confined Column M 1.0 Mu 0.5 -4 4 -0.5 Drift, % -1.0 Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 33 Structural Behavior Columns Δ M1 M1 V V L V M2 M2 P M1 + M2 2Mu V= = L L Range of P M Mo Mu Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 34 Column Shear Failure Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 35 Structural Behavior Joints V fc T ft h Cc Cs Max. shear force Vj = T- V Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 36 Hysteretic Behavior of Joint with Hoops 1.0 M Mu 0.5 -1 5 6 Drift, % -0.5 Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 37 Hysteretic Behavior of Joint with No Hoops 1.0 M Mu 0.5 -1 5 6 Drift, % -0.5 Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 38 Joint Failure – No Shear Reinforcing Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 39 Anchorage Failure in Column/Footing Joint Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 40 Summary of Concrete Behavior • Compressive Ductility – Strong in compression but brittle – Confinement improves ductility by • Maintaining concrete core integrity • Preventing longitudinal bar buckling • Flexural Ductility – Longitudinal steel provides monotonic ductility at low reinforcement ratios – Transverse steel needed to maintain ductility through reverse cycles and at very high strains (hinge development) Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 41 Summary of Concrete Behavior • Damping – Well cracked: moderately high damping – Uncracked (e.g. prestressed): low damping • Potential Problems – Shear failures are brittle and abrupt and must be avoided – Degrading strength/stiffness with repeat cycles • Limit degradation through adequate hinge development Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 42 NEHRP Recommended Provisions Concrete Design • Context in the Provisions • Concrete behavior • Reference standards Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 43 ACI 318-05 Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 44 Use of Reference Standards • ACI 318-05 – Chapter 21, Special Provisions for Seismic Design • NEHRP Chapter 9, Concrete Structures – General design requirements – Modifications to ACI 318 – Seismic Design Category requirements – Special precast structural walls – Untopped precast diaphragms (Appendix to Ch.9) Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 45 Detailed Modifications to ACI 318 • Modified definitions and notations • Scope and material properties • Special moment frames • Special shear walls • Special and intermediate precast walls • Foundations • Anchoring to concrete Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 46 NEHRP Recommended Provisions Concrete Design • Context in the Provisions • Concrete behavior • Reference standards • Requirements by Seismic Design Category Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 47 Design Coefficients - Moment Resisting Frames Seismic Force Response Deflection Resisting Modification Amplification System Coefficient, R Factor, Cd Special R/C 8 5.5 Moment Frame Intermediate R/C 5 4.5 Moment Frame Ordinary R/C 3 2.5 Moment Frame Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 48 Design Coefficients Shear Walls (Bearing Systems) Seismic Force Response Deflection Resisting Modification Amplification System Coefficient, R Factor, Cd Special R/C Shear 5 5 Walls Ordinary R/C 4 4 Shear Walls Intermediate Precast 4 4 Shear Walls Ordinary Precast Walls 3 3 Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 49 Design Coefficients Shear Walls (Frame Systems) Seismic Force Response Deflection Resisting Modification Amplification System Coefficient, R Factor, Cd Special R/C Shear 6 5 Walls Ordinary R/C 5 4.5 Shear Walls Intermediate Precast 5 4.5 Shear Walls Ordinary Precast Walls 4 4 Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 50 Design Coefficients Dual Systems with Special Frames Seismic Force Response Deflection Resisting Modification Amplification System Coefficient, R Factor, Cd Dual System w/ 8 (7) 6.5 (5.5) Special Walls Dual System w/ 6 5 Ordinary Walls (ASCE 7-05 values where different) Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 51 Frames Seismic Minimum ACI 318 Design Frame Type Requirements Category Chapters 1 thru A and B Ordinary 18 and 22 ACI 21.2.1.3 and C Intermediate ACI 21.12 ACI 21.2.1.4 and D, E and F Special ACI 21.2, 21.3, 21.4, and 21.5 Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 52 Reinforced Concrete Shear Walls Seismic Minimum ACI 318 Design Wall Requirements Category Type Chapters 1 thru A, B and C Ordinary 18 and 22 ACI 21.2.1.4 and D, E and F Special ACI 21.2 and 21.7 Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 53 Precast Concrete Shear Walls Seismic Minimum ACI 318 Design Wall Type Requirements Category Chapters 1 thru A and B Ordinary 18 and 22 ACI 21.2.1.3 and C Intermediate ACI 21.13 ACI 21.2.1.4 and D, E and F Special ACI 21.2, 21.8 Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 54 Additional Provisions Requirements • Category C – Discontinuous members – Plain concrete • Walls • Footings • Pedestals (not allowed) Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 55 NEHRP Recommended Provisions Concrete Design • Context in the Provisions • Concrete behavior • Reference standards • Requirements by Seismic Design Category • Moment resisting frames Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 56 Performance Objectives • Strong column – Avoid story mechanism • Hinge development – Confined concrete core – Prevent rebar buckling – Prevent shear failure • Member shear strength • Joint shear strength • Rebar development Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 57 Frame Mechanisms “strong column – weak beam” Story mechanism Sway mechanism Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 58 Required Column Strength ∑ Mnc ≥ 1.2∑ Mnb M nc1 M nb1 M nb2 M nc2 Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 59 Hinge Development • Tightly Spaced Hoops – Provide confinement to increase concrete strength and usable compressive strain – Provide lateral support to compression bars to prevent buckling – Act as shear reinforcement and preclude shear failures – Control splitting cracks from high bar bond stresses Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 60 Hinge Development Before spalling After spalling Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 61 Hinge Development Bidirectional cracking Spalled cover Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 62 ACI 318-05, Overview of Frames: Beam Longitudinal Reinforcement 200 ≤ ρ ≤ 0 .025 fy At least 2 bars continuous top & bottom Joint face Mn+ not less than 50% Mn- Min. Mn+ or Mn- not less than 25% max. Mn at joint face Splice away from hinges and enclose within hoops or spirals Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 63 ACI 318-05, Overview of Frames: Beam Transverse Reinforcement Closed hoops at hinging regions with “seismic” hook 135º hook, 6dh ≥ 3” extension Maximum spacing of hoops: d/4 8db 24dh 12” Longitudinal bars on perimeter tied as if column bars 2d min Stirrups elsewhere, s ≤ d/2 Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 64 ACI 318-05, Overview of Frames: Beam Shear Strength 1.2D + 1.0L + 0.2S Mpr1 Mpr2 Mpr = Mn with fs = 1.25fy , φ = 1 .0 Ve1 ln Ve2 Mpr1 + Mpr 2 w ul n Ve = ± ≥ Ve by analysis ln 2 If earthquake-induced > 1 V e shear force 2 then Vc = 0 ' A f and Pu < g c 20 Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 65 ACI 318-05, Overview of Frames: Beam-Column Joint Vcol Vj = T + C − Vcol T C T = 1.25fy A s, top Vj C = 1.25fy A s, bottom Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 66 ACI 318-05, Overview of Frames: Beam-column Joint ⎧20⎫ ⎪ ⎪ Vn = ⎨15 ⎬ f 'c A j ⎪12 ⎪ ⎩ ⎭ • Vn controls size of columns • Coefficient depends on joint confinement • To reduce shear demand, increase beam depth • Keep column stronger than beam Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 67 ACI 318-05: Overview of Frames: Column Longitudinal Reinforcement M nc1 0.01 ≤ ρ ≤ 0.06 M nb1 M nb2 ∑ Mnc ≥ 1.2∑ Mnb At joints M nc2 (strong column-weak beam) Mnc based on factored axial force, consistent with direction of lateral forces Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 68 ACI 318-05, Overview of Frames: Column Transverse Reinforcement at Potential Hinging Region Spirals Hoops ⎛ Ag ⎞ f 'c ⎛ f 'c ⎞⎛ A g ⎞ ρs = 0.45⎜ − 1⎟ A sh ≥ 0 .3⎜ sbc ⎟⎜ − 1⎟ ⎜A ⎝ ch ⎟f ⎠ yt ⎜ ⎝ fyt ⎟⎜ A ch ⎠⎝ ⎟ ⎠ and and f 'c f 'c ρs ≥ 0.12 A sh ≥ 0.09sbc fyt fyt Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 69 ACI 318-05, Overview of Frames: Column Transverse Reinforcement at Potential Hinging Region hx hx ⎛ 14 − h x ⎞ so = 4 + ⎜ ⎟ ⎝ 3 ⎠ Spacing shall not exceed the smallest of: b/4 or 6 db or so (4” to 6”) Distance between legs of hoops or crossties, hx ≤ 14” Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 70 ACI 318-05, Overview of Frames: Potential Hinge Region • For columns supporting stiff members such as walls, hoops are required over full height of column if f 'c A g Pe > 10 • For shear strength- same rules as beams (concrete shear strength is neglected if axial load is low and earthquake shear is high) • Lap splices are not allowed in potential plastic hinge regions Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 71 Splice in Hinge Region Terminating bars Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 72 ACI 318-05, Overview of Frames: Potential Hinge Region ⎧ d ⎫ ⎪ ⎪ ⎪ ⎪ ⎪ clear height ⎪ ⎪ ⎪ lo ≥ ⎨ 6 ⎬ ⎪ ⎪ ⎪ 18" ⎪ ⎪ ⎪ ⎪ ⎩ ⎪ ⎭ Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 73 Moment Frame Example A A’ B C C’ D N 1 2 7 @ 30’ = 210’ 3 4 5 6 7 8 5 @ 20’ = 100’ Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 74 Frame Elevations A A’ B C C’ D A A’ B C C’ D 11 @ 12.5' 11 @ 12.5' 15' 18' 15' 18' Column Lines 2 and 7 Column Lines 3 to 6 Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 75 Story Shears: Seismic vs Wind seismic E-W seismic N-S wind E-W wind N-S Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 76 Story Shears: E-W Loading frame 1 frame 2 1 frame 3 2 3 includes shearwall 0 Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 77 Story Shears: 25% rule Frame 1 25% Frame 1 w/ walls w/o walls Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 78 Layout of Reinforcement 4 28.6” 29.6” 32” 22.5” 30” Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 79 Bending Moment Envelopes: Frame 1 Beams A A’ B C C L 4708 4515 Seismic 715 Dead 5232 5834 5761 492 Combined: 834 4122 4222 4149 1.42D +0.5 L + E 0.68D - E 1.2D + 1.6L Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 80 Beam Reinforcement: Longitudinal Max negative Mu = 5834 in-kips b = 22.5” d = 29.6” f’c = 4 ksi fy = 60 ksi Mu 5834 φ 0 .9 A s req'd = = = 4.17in2 fy (0.875d) 60 ⋅ 0.875 ⋅ 29.6 Choose: 2 #9 and 3 #8 As = 4.37 in2 ρ = 0.0066 < 0.025 OK φMn = 6580 in-kips OK Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 81 Beam Reinforcement: Longitudinal (continued) Positive Mu at face of column = 4222 in-kips (greater than ½(5834) = 2917) b for negative moment is the sum of the beam width (22.5 in.) plus 1/12 the span length (20 ft x 12 in./ft)/12, b = 42.5 in. Mu 4222 φ 0.9 = 2.94in2 A s req'd = = fy (0.9d) 60 ⋅ 0.9 ⋅ 29.6 Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 82 Beam Reinforcement: Longitudinal (continued) Choose 2 #7 and 3 #8 As = 3.57 in2 φMn = 5564 in-kips OK Run 3 #8s continuous top and bottom φMn = 3669 in-kips This moment is greater than: 25% of max negative Mn = 1459 in-kips Max required Mu = 834 in-kips Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 83 Beam Reinforcement: Preliminary Layout A A' B C C' D 2 #8 2 #9 3 #8 2 #8 2 #9 2 #7 2 #7 3 #8 3 #8 2 #7 Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 84 Moments for Computing Shear Hinging mechanism B C C' 9697 8999 Plastic moments 10085 9.83' 10085 10.5' (in-kips) 20.0' 20.0' 150.4 Girder and 94.2 90.9 column shears (kips) 150.4 Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 85 Joint Shear Force 150.5 kip 355.5 kip 355.5 kip T = 1.25fy A s,top = 355.5 kips 560.5 kip C = 1.25fy A s,bot = 355.5 kips Vj = T + C − Vcol = 560.5 kips v j = 15 f 'c = 949 psi Vn = v j A j = 949 ⋅ 30 ⋅ 30 = 854 kips φVn = 0.85 ⋅ 854 = 726 kips > 560.5 kips Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 86 Beam Shear Force A A’ B C 79.4 82.7 82.7 Seismic shear 75.6 79.4 82.7 29.5 29.5 29.5 Factored gravity shear 29.5 29.5 29.5 108.9 112.2 112.2 49.9 53.2 53.2 Design shear 46.1 49.9 53.2 105.1 108.9 112.2 Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 87 Beam Reinforcement: Transverse Vseismic > 50% Vu therefore take Vc = 0 82.7 kips = 73%(112.2) Use 4 legged #3 stirrups A v fy d Vs = s At ends of beam s = 5.5 in. Near midspan s = 7.0 in. Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 88 Beam Reinforcement: Transverse • Check maximum spacing of hoops within plastic hinge length (2d) – d/4 = 7.4 in. – 8db = 7.0 in. – 24dh = 9.0 in. Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 89 Column Design Moments A A' B 7311 Girder moments (Level 7) 6181 ∑ Mnc = 1.2(7311 + 6181) = 16190 in − k 8095 8095 Column moments (Level 7) Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 90 Column Design Moments f 'c A g if Pu > 10 ∑ Mnc > 1.2∑ Mnb Distribute relative to stiffness of columns above and below: Mnc = 8095 in-kips (above) Mnc = 8095 in-kips (below) Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 91 Design Strengths Design Aspect Strength Used Beam rebar cutoffs Design strength Maximum probable Beam shear reinforcement strength Beam-column joint Maximum probable strength strength Column flexural strength 1.2 times nominal strength Maximum probable Column shear strength strength Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 92 Column Transverse Reinforcement ⎛ f 'c ⎞ ⎡⎛ A g ⎞ ⎤ A sh = 0.3⎜ sbc ⎟ ⎢⎜ ⎜ A ⎟ − 1⎥ ⎜ ⎝ fyt ⎟ ⎢⎝ ch ⎟ ⎥ ⎠⎣ ⎠ ⎦ and f 'c A sh = 0.09sbc fyt Ag = gross area of column Ach = area confined within the hoops bc = transverse dimension of column core measured center to center of outer legs Second equation typically governs for larger columns Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 93 Column Transverse Reinforcement Maximum spacing is smallest of: •One quarter of minimum member dimension •Six times the diameter of the longitudinal bars •so calculated as follows: 14 − h x so = 4 + 3 hx = maximum horizontal center to center spacing of cross-ties or hoop legs on all faces of the column, not allowed to be greater the 14 in. Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 94 Column Transverse Reinforcement For max s = 4 in. ⎛ f 'c ⎞ ⎡⎛ A g ⎞ ⎤ ⎛ 4 ⎞⎛ 900 ⎞ A sh = 0.3⎜ sbc ⎟ ⎢⎜ ⎜A ⎟ ⎟ − 1⎥ = 0.3⎜ 4 ⋅ 26.5 ⋅ ⎟⎜ − 1⎟ ⎜ fyt ⎟ ⎢⎝ ch ⎠ ⎥ ⎝ 60 ⎠⎝ 702 ⎠ ⎝ ⎠⎣ ⎦ A sh = 0.60 in2 and f 'c 4 A sh = 0.09sbc = 0.09 ⋅ 4 ⋅ 26.5 ⋅ = 0.64 in2 fyt 60 Use 4 legs of #4 bar – Ash = 0.80 in2 Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 95 Determine Seismic Shear Mpr,top Mpr,1 Mpr,2 Vseismic ln Vseismic Mpr,3 Mpr,4 Mpr,bottom Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 96 Column Transverse Reinforcement Shear Demand from Mpr of Beams Mpr, 1 = 9000 in-k (2 #9 and 3 #8) Mpr,2 = 7460 in-k (2 #7 and 3 #8) Assume moments are distributed equally above and below joint 8230 ⋅ 2 Vseismic = = 139 kips (12.5 ⋅ 12) − 32 Note Vseismic~100%Vu f 'c Ag Vc = 0, if Pmin < = 180 kips 20 For 30 in. square column Pmin = 266 kips OK Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 97 Column Transverse Reinforcement Shear Demand from Mpr of Beams φVc = φ2λ f 'c bd = 0.75 ⋅ 2 ⋅ 0.85 4000 ⋅ 30 ⋅ 27.5 = 66.5 kips φVs,required = 139 − 66.5 = 72.5 kips A v fy d 4 ⋅ 0.2 ⋅ 60 ⋅ 29.6 φVs,provided = φ = 0.75 = 266.4 kips s 4 Hoops 4 legs #4 s = 4” Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 98 Column Reinforcement A' 7 @ 4" #4 hoops: 5" 8 @ 6" 5" 7 @ 4" 12 #8 bars Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 99 Levels of Seismic Detailing for Frames Issue Ordinary Intermediate Special Hinge development and minor full confinement Bar buckling lesser full Member shear lesser full Joint shear minor minor full Strong column full Rebar development lesser lesser full Load reversal minor lesser full Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 100 NEHRP Recommended Provisions Concrete Design • Context in the Provisions • Concrete behavior • Reference standards • Requirements by Seismic Design Category • Moment resisting frames • Shear walls Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 101 Performance Objectives • Resist axial forces, flexure and shear • Boundary members – Where compression strains are large, maintain capacity • Development of rebar in panel • Discontinuous walls: supporting columns have full confinement Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 102 Design Philosophy • Flexural yielding will occur in predetermined flexural hinging regions • Brittle failure mechanisms will be precluded – Diagonal tension – Sliding hinges – Local buckling Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 103 ACI 318-05, Overview of Walls: General Requirements lw ρt = parallel to shear plane ρl = perpendicular hw to shear plane Shear plane, Acv = web thickness x length of wall Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 104 ACI 318-05, Overview of Walls: General Requirements • ρl and ρt not less than 0.0025 unless Vu < A cv f 'c then as allowed in 14.3 • Spacing not to exceed 18 in. • Reinforcement contributing to Vn shall be continuous and distributed across the shear plane Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 105 ACI 318-05, Overview of Walls: General Requirements • Two curtains of reinforcing required if: Vu > 2A cv f 'c • Design shear force determined from lateral load analysis Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 106 ACI 318-05, Overview of Walls: General Requirements • Shear strength: ( Vn = A cv α c f 'c + ρ t fy ) αc = 3.0 for hw/lw≤1.5 αc = 2.0 for hw/lw≥2.0 Linear interpolation between • Walls must have reinforcement in two orthogonal directions Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 107 ACI 318-05, Overview of Walls: General Requirements • For axial load and flexure, design like a column to determine axial load – moment interaction P M Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 108 ACI 318-05, Overview of Walls: Boundary Elements For walls with a high compression demand at the edges – Boundary Elements are required Widened end with confinement Extra confinement and/or longitudinal bars at end Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 109 ACI 318-05, Overview of Walls: Boundary Elements • Boundary elements are required if: lw c≥ ⎛ δu ⎞ 600⎜ ⎝ hw ⎟ ⎠ δu = Design displacement c = Depth to neutral axis from strain compatibility analysis with loads causing δu Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 110 ACI 318-05, Overview of Walls: Boundary Elements • Where required, boundary elements must extend up the wall from the critical section a distance not less than the larger of: lw or Mu/4Vu Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 111 ACI 318-05: Overview of Walls Boundary Elements • Boundary elements are required where the maximum extreme fiber compressive stress calculated based on factored load effects, linear elastic concrete behavior and gross section properties, exceeds 0.2 f’c • Boundary element can be discontinued where the compressive stress is less than 0.15f’c Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 112 ACI 318-05: Overview of Walls Boundary Elements • Boundary elements must extend horizontally not less than the larger of c/2 or c-0.1lw • In flanged walls, boundary element must include all of the effective flange width and at least 12 in. of the web • Transverse reinforcement must extend into the foundation Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 113 Wall Example A A’ B C C’ D Instructional Material Complementing FEMA 451, Design Examples 11 @ 12.5' 15' 18' Design for Concrete Structures 11 - 114 Wall Cross-Section 17’-6”=210” 30” 30” 30” 30” 12” Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 115 Story Shears E-W Loading frame 1 frame 2 1 frame 3 2 3 includes shearwall 0 Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 116 Boundary Element Check Required if: fc > 0.2 fc' based on gross concrete section Axial load and moment are determined based on factored forces, including earthquake effects At ground Pu = 5550 kip Mu from analysis is 268,187 in-kip The wall has the following gross section properties: A = 4320 in2 S = 261,600 in3 fc = 2.3 ksi = 38% of f’c = 6 ksi ∴ Need boundary element Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 117 Boundary Element Design Determine preliminary reinforcing ratio in boundary elements by assuming only boundary elements take compression M = 268,187 in-k M P = 5550 k P P M B1 = + = 3892 kip B2 B1 2 240 P M B2 = − = 1658 kip 2 240 Need [ 0 . 8Po = 0 . 8 (0 . 7 ) A g 0 . 85 fc' (1 − ρ ) + ρ f y > 3892 kip ] For Ag = 30(30) = 900 in2 For fc’ = 4 ksi ⇒ ρ = 7.06% Too large For fc’ = 6 ksi ⇒ ρ = 4.18% Reasonable; 24 #11 Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 118 Boundary Element Confinement Transverse reinforcement in boundary elements is to be designed essentially like column transverse reinforcement fc' A sh = 0 . 09 sb c = 1 . 08 in at s = 4 " 2 fy 4 legs of #5 Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 119 Shear Panel Reinforcement Vn = A cv ⎛ 2 λ ⎜ fc' + ρ t f y ⎞ ⎟ ⎝ ⎠ Vu = 539 kips (below level 2) ρl Panel ⊥ to Acv φ = 0.6 (per ACI 9.3.4(a)) Acv ρt ρt = 0.0036 for fy = 40 ksi Min ρl (and ρt) = 0.0025 2 curtains if Vu > 2 ' fc A cv Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 120 Shear Panel Reinforcement Select transverse and longitudinal reinforcement: longitudin al : 0 .2 ⋅ 2 # 4 @ 12" ⇒ = 0.0028 > 0.0025 12 ⋅ 12 transverse : 0 .2 ⋅ 2 # 4 @ 9" ⇒ = 0.0037 > 0.0036 12 ⋅ 9 Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 121 Check Wall Design 30000 Nominal 25000 Factored Combinations Axial Load, k 20000 15000 10000 5000 0 0 20000 40000 60000 80000 100000 120000 140000 Moment, k-ft Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 122 Shear Wall Reinforcement B C B C B C R 8 3 24 #10 12 7 2 fc’ = 6 ksi #4@12" ver. E.F. 24 #9 #4@6" hor. E.F. 11 6 12 #9 G 24 #11 10 5 #5 @ 4" #4@18" ver. E.F. B #4@16" hor. E.F. 9 4 #4@12" E.W. E.F. #4 @ 4" 8 3 fc’ = 4 ksi Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 123 NEHRP Recommended Provisions Concrete Design • Context in the Provisions • Concrete behavior • Reference standards • Requirements by Seismic Design Category • Moment resisting frames • Shear walls • Other topics Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 124 Members Not Part of SRS • In frame members not designated as part of the lateral-force-resisting system in regions of high seismic risk: – Must be able to support gravity loads while subjected to the design displacement – Transverse reinforcement increases depending on: Forces induced by drift Axial force in member Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 125 Diaphragms Diaphragm Shear walls Collectors, if req’d to transfer force from diaphragm to shear walls Load from analysis in accordance With design load combinations Check: • Shear strength and reinforcement (min. slab reinf.) • Chords (boundary members) - Force = M/d Reinforced for tension (Usually don’t require boundary members) Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 126 Struts and Trusses performance objectives • All members have axial load (not flexure), so ductility is more difficult to achieve • Full length confinement Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 127 Precast performance objectives Field connections Field connections at points of low must yield stress Strong connections Ductile connections • Configure system so that hinges • Inelastic action at field splice occur in factory cast members away from field splices Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 128 Quality Assurance Rebar Inspection • Continuous – Welding of rebar • Periodic – During and upon completion of placement for special moment frames, intermediate moment frames and shear walls Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 129 Shear panel reinforcement cage Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 130 Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 131 Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 132 Quality Assurance: Reinforcing Inspection - Prestressed • Periodic – Placing of prestressing tendons (inspection required upon completion) • Continuous – Stressing of tendons – Grouting of tendons Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 133 Quality Assurance: Concrete Placement Inspection • Continuous – Prestressed elements – Drilled piers – Caissons • Periodic – Frames – Shear walls Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 134 Quality Assurance: Precast Concrete (plant cast) • Manufacturer may serve as special inspector if plant’s quality control program is approved by regulatory agency • If no approved quality control program, independent special inspector is required Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 135 Quality Assurance: PCI Certification Program • Review of plant operations – Scheduled and surprise visits – Qualified independent inspectors – Observed work of in-plant quality control – Check results of quality control procedures – Periodic – specific approvals requiring renewal Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 136 Quality Assurance: ACI Inspector Certification • Specialized training available for: – Laboratory and in situ testing – Inspection of welding – Handling and placement of concrete – Others Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 137 Quality Assurance: Reinforcement Testing • Rebar – Special and intermediate moment frames – Boundary elements • Prestressing steel • Tests include – Weldability – Elongation – Actual to specified yield strength – Actual to specified ultimate strength Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 138 Quality Assurance: Concrete Testing • Sample and test according to ACI 318-05 – Slump – Air content – 7 and 28 day strengths – Unit weight • Rate – Once per day per class Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 139 NEHRP Recommended Provisions: Concrete Design • Context in the Provisions • Concrete behavior • Reference standards • Requirements by Seismic Design Category • Moment resisting frames • Shear walls • Other topics • Summary Instructional Material Complementing FEMA 451, Design Examples Design for Concrete Structures 11 - 140

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posted: | 11/17/2011 |

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