Seismic Design and Detailing of Reinforced Concrete Structures Based on CSA A23.3 - 2004 Murat Saatcioglu PhD,P.Eng. Professor and University Research Chair Department of Civil Engineering The University of Ottawa Ottawa, ON Basic Principles of Design Reinforced concrete structures are designed to dissipate seismic induced energy through inelastic deformations Ve Ve = S(Ta) Mv IE W / (Rd Ro) Ve /Rd Ve /Rd Ro D Basic Principles of Design Inelasticity results softening in the structure, elongating structural period S(T) S1 S2 T1 T2 T Basic Principles of Design Capacity Demand It is a good practice to reduce seismic demands, to the extent possible…. This can be done at the conceptual stage by selecting a suitable structural system. To reduce seismic demands… Select a suitable site with favorable soil conditions Avoid using unnecessary mass Use a simple structural layout with minimum torsional effects Avoid strength and stiffness taper along the height Avoid soft storeys Provide sufficient lateral bracing and drift control by using concrete structural walls Isolate non-structural elements Seismic Amplification due to Soft Soil Liquefaction Liquefaction Liquefaction To reduce seismic demands… Select a suitable site with favorable soil conditions Avoid using unnecessary mass Use a simple structural layout with minimum torsional effects Avoid strength and stiffness taper along the height Avoid soft storeys Provide sufficient lateral bracing and drift control by using concrete structural walls Isolate non-structural elements Use of Unnecessary Mass Use of Unnecessary Mass Use of Unnecessary Mass Use of Unnecessary Mass To reduce seismic demands… Select a suitable site with favorable soil conditions Avoid using unnecessary mass Use a simple structural layout with minimum torsional effects Avoid strength and stiffness taper along the height Avoid soft storeys Provide sufficient lateral bracing and drift control by using concrete structural walls Isolate non-structural elements Effect of Torsion Effect of Torsion Effect of Torsion Effect of Torsion Effect of Torsion Effect of Torsion Effect of Torsion Effect of Torsion To reduce seismic demands… Select a suitable site with favorable soil conditions Avoid using unnecessary mass Use a simple structural layout with minimum torsional effects Avoid strength and stiffness taper along the height Avoid soft storeys Provide sufficient lateral bracing and drift control by using concrete structural walls Isolate non-structural elements Effect of Vertical Discontinuity Effect of Vertical Discontinuity To reduce seismic demands… Select a suitable site with favorable soil conditions Avoid using unnecessary mass Use a simple structural layout with minimum torsional effects Avoid strength and stiffness taper along the height Avoid soft storeys Provide sufficient lateral bracing and drift control by using concrete structural walls Isolate non-structural elements Effect of Soft Storey Effect of Soft Storey Effect of Soft Storey Effect of Soft Storey To reduce seismic demands… Select a suitable site with favorable soil conditions Avoid using unnecessary mass Use a simple structural layout with minimum torsional effects Avoid strength and stiffness taper along the height Avoid soft storeys Provide sufficient lateral bracing and drift control by using concrete structural walls Isolate non-structural elements R/C Frame Buildings without Drift Control Buildings Stiffened by Structural Walls To reduce seismic demands… Select a suitable site with favorable soil conditions Avoid using unnecessary mass Use a simple structural layout with minimum torsional effects Avoid strength and stiffness taper along the height Avoid soft storeys Provide sufficient lateral bracing and drift control by using concrete structural walls Isolate non-structural elements Short Column Effect Short Column Effect Seismic Design Requirements of CSA A23.3 - 2004 Capacity design is employed….. Selected elements are designed to yield while critical elements remain elastic Design for Strength and Deformability Load Combinations Principal loads: 1.0D + 1.0E And either of the following: 1) For storage occupancies, equipment areas and service rooms: 1.0D + 1.0E + 1.0L + 0.25S 2) For other occupancies: 1.0D + 1.0E + 0.5L + 0.25S Stiffness Properties for Analysis Concrete cracks under own weight of structure If concrete is not cracked, then the structure is not reinforced concrete (plain concrete) Hence it is important to account for the softening of structures due to cracking Correct assessment of effective member stiffness is essential for improved accuracy in establishing the distribution of design forces among members, as well as in computing the period of the structure. Flexural Moment Behaviour of R/C Mn My Post-yield rigidity Post-cracking rigidity Mcr Elastic rigidity Actual Idealized Curvature Flexural Behaviour of R/C Moment Mn 0.75Mn Effective elastic rigidity Actual Idealized (bi-linear) y u Curvature Section Properties for Analysis as per CSA A23.3-04 Beams P α 0.5 0.6 Columns f A Coupling Beams c ' c 1.0 s g without diagonal reinforcement with diagonal reinforcement Slab-Frame Element Walls α w 0.6 Ps 1.0 ' fc A g Ie = 0.40 Ig Ie = a cIg Ave = 0.15Ag Ie = 0.40 Ig Ave = 0.45Ag Ie = 0.25 Ig Ie = 0.20 Ig Axe = awAg Ie = aw Ig Seismic Design Requirements of CSA A23.3 - 2004 Chapter 21 covers: Ductile Moment Resisting Frames (MRF) Moderately Ductile MRF Ductile Shear Walls Ductile Coupled Shear Walls Ductile Partially Coupled Shear Walls Moderately Ductile Shear Walls Ductile Moment Resisting Frame Members Subjected to Flexure Rd = 4.0 Pf ≤ Agf’c /10 c2 h d x y bw b w 0.3 h bw c2 x y bw 250mm x 3/4 h n 4 d y 3/4 h Beam Longitudinal Reinforcement - Mr + - - - Mr > 1/4 Mr - Mr > 1/2 Mr Mr + - Mr > 1/2 Mr + Mr > 1/4 Mr Top and Botom 2 bars continuous Top and Bottom: 1.4bwd / fy ≤ r ≤ 0.025 Beam Transverse Reinforcement No lap splicing within this region 2d s1 c1 s2 d / 2 50 mm h Hoops Sirrups with seismic hooks Hoops n s1 d / 4 s 1 8(d b ) long .bar s1 300 mm s 1 24(d b )hoop db Formation of Plastic Hinges Beam Shear Strength Plastic Hinge Wf M+pr M pr ln (Ve )left (Ve ) right - Ve = M pr + M+pr + ln Wf ln 2 Beam Shear Strength The factored shear need not exceed that obtained from structural analysis under factored load combinations with RdRo = 1.0 The values of q = 45o and b = 0 shall be used in shear design within plastic hinge regions The transverse reinforcement shall be seismic hoops Ductile Moment Resisting Frame Members Subjected to Flexure and Significant Axial Load Pf > Agf’c /10 Rd = 4.0 hshort hlong hshort ≥ 300 mm hshort / hlong ≥ 0.4 D D ≥ 300 mm Longitudinal Reinforcement Design for factored axial forces and moments using Interaction Diagrams r min = 1% r max = 6% Strong Beam-Weak Column Design Strong Beam-Weak Column Design Strong Column-Weak Beam Design Manc Nominal moment resistance of columns under factored axial loads M rpb M lpb Probable moment resistance of beams Mbnc M nc Mpb Column Confinement Reinforcement Columns will be confined for improved inelastic deformability lo lo ≥ 1/6 of clear col. height If Pf ≤ 0.5 c f’c Ag ; If Pf > 0.5 c f’c Ag ; lo ≥ 1.5h lo ≥ 2.0h Columns connected to rigid members such as foundations and discontinuous walls, or columns at the base will be confined along the entire height lo Poorly Confined Columns Poorly Confined Columns Well-Confined Column Column Confinement Reinforcement f'c ρ s 0.4kp fyh Circular Spirals fyh 500MPa Pf kp Po Ag f'c ρ s 0.45( 1) Ac fyh Column Confinement Reinforcement A sh Ag f'c 0.2knkp shc Ach fyh A sh f'c 0.09 shc fyh Rectilinear Ties Pf kp P o fyh 500MPa n kn n /(n 2) : No. of laterally supported bars Spacing of Confinement Reinforcement ¼ of minimum member dimension 6 x smallest long. bar diameter sx = 100 + (350 – hx) / 3 Spacing of laterally supported longitudinal bars, hx ≤ 200 mm or 1/3 hc M+pr - M pr a Column Shear Strength Mcol Vcol a M Vcol= lu + M pr - M pr Vcol b M col col b + M col lu Column Shear Strength The factored shear need not exceed that obtained from structural analysis under factored load combinations with RdRo = 1.0 The values of q ≥ 45o and b ≤ 0.10 shall be used in shear design in regions where the confinement reinforcement is needed The transverse reinforcement shall be seismic hoops Shear Deficient Columns Shear Deficient Columns Beam-Column Joints Poor Joint Performance Computation of Joint Shear Ve As T2 = 1. 25 As fy C1 = T1 x C2 = T2 x A's T1 = 1. 25 A's fy Ve Vx-x = Ve - T2 - C1 Vx-x ≤ that obtained from frame analysis using RdRo = 1.0 Shear Resistance of Joints Vj 2.2c f 'c A j Vj 1.6 c f 'c A j Vj 1.3 c f 'c A j Transverse Reinforcement in Joints Continue column confinement reinforcement into the joint If the joint is fully confined by four beams framing from all four sides, then eliminate every other hoop. At these locations sx = 150 mm Design Example Six-Storey Ductile Moment Resisting Frame in Vancouver Chapter 11 By D. Mitchell and P. Paultre Six-Storey Ductile Moment Resisting Frame in Vancouver •Rd = 4.0 and Ro = 1.7 •Site Classification C (Fa & Fv = 1.0) Interior columns: 500 x 500 mm Exterior columns: 450 x 450 mm Slab: 110 mm thick Beams (1-3rd floors): 400 x 600 mm Beams (4-6th floors): 400 x 550 mm Material Properties Concrete: normal density concrete with 30 MPa Reinforcement: 400 MPa Live loads Floor live loads: 2.4 kN/m2 on typical office floors 4.8 kN/m2 on 6 m wide corridor bay Roof load 2.2 kN/m2 snow load, accounting for parapets and equipment projections 1.6 kN/m2 mechanical services loading in 6 m wide strip over corridor bay Dead loads self-weight of reinforced concrete members calculated as 24 kN/m3 1.0 kN/m2 partition loading on all floors 0.5 kN/m2 mechanical services loading on all floors 0.5 kN/m2 roofing Wind loading 1.84 kN/m2 net lateral pressure for top 4 storeys 1.75 kN/m2 net lateral pressure for bottom 2 storeys The fire-resistance rating of the building is assumed to be 1 hour. Gravity Loading Design Spectral Response Acceleration E-W Direction Empirical: Ta = 0.075 (hn)3/4 = 0.76 s Dynamic: T = 1.35 s but not greater than 1.5Ta = 1.14s Design of Ductile Beam Design of Ductile Beam Design of Ductile Beam Design of Ductile Beam Design of Ductile Beam Design of Ductile Beam Design of Ductile Interior Column Design of Ductile Interior Column Design of Ductile Interior Column Design of Ductile Interior Column Design of Ductile Interior Column Design of Ductile Interior Column Design of Interior Beam-Column Joint Design of Interior Beam-Column Joint Design of Interior Beam-Column Joint Ductile Shear Walls Rd = 3.5 or 4.0 if hw / ℓw ≤ 2.0; Rd = 2.0 SFRS without irregularities: Plastic hinge length:1.5 ℓw Flexural and shear reinforcement required for the critical section will be maintained within the hinging region hw Plastic Hinge Length ℓw For elevations above the plastic hinge region, design values will be increased by Mr/Mf at the top of hinging region Ductile Shear Walls Wall thickness in the plastic hinge: tw ≥ ℓu / 14 but may be limited to hw ℓu / 10 in high compression regions ℓu ℓw tw Plastic Hinge Length Because walls are relatively thin members, care must be taken to prevent possible instability in plastic hinge regions Ductile Shear Walls Ductile Shear Walls Ductile Shear Walls Effective flange width: ℓf ℓf ≤ ½ distance to adjacent wall web ℓf ≤ ¼ of wall height above the section Wall Reinforcement Plastic Hinges Other Regions Distributed Reinforcement in Each Direction r ≥ 0.0025 r ≥ 0.0025 Amount Spacing ≤ 300 mm ≤ 450 mm Concentrated Reinforcement Where @ends and corners As ≥ 0.015 bwlw Amount (at least 4 bars) As ≤ 0.06 (A)be @ends Hoops Like nonseismic columns Confine like columns As ≥ 0.001 bwlw As ≤ 0.06 (A)be Ductile Shear Walls Vertical reinforcement outside the plastic hinge region will be tied as specified in 7.6.5 if the area of steel is more than 0.005Ag and the maximum bar size is #20 and smaller Vertical reinforcement in plastic hinge regions will be tied as specified in 21.6.6.9 if the area of steel is more than 0.005Ag and the maximum bar size is #15 and smaller Ductile Shear Walls At least two curtains of reinforcement will be used in plastic hinge regions, if: Vf 0.18c fc' A cv Where; Acv : Net area of concrete section bounded by web thickness and length of section in the direction of lateral force Ductile Shear Walls For buckling prevention, ties shall be provided in the form of hoops, with spacing not to exceed: 6 longitudinal bar diameters 24 tie diameters ½ of the least dimension of of the member Ductility of Ductile Shear Walls Rotational Capacity, qic> Inelastic Demand, qid D f RoRd D f w q id 0.004 w hw 2 hw cu w q ic 0.002 0.025 2c ℓw/2 ℓw y cu Ductility of Ductile Shear Walls D f RoRd D f w q id 0.004 w hw 2 cu w q ic 0.002 0.025 2c Ductility of Ductile Shear Walls Ps Pn Pns a f Af c ' a1 b 1cfcb w ' 1 c c Ductile Coupled Walls Mtotal = M1 + M2 + P x E.Q. If P x 2/3Mtotal Coupled Wall If P x < 2/3Mtotal Partially Coupled Wall M1 P M2 x P Ductility of Ductile Coupled Walls Rotational Capacity, qic> Inelastic Demand, qid D f RoRd q id 0.004 hw cu w q ic 0.002 0.025 2c ℓw: Length of the coupled wall system ℓw: Lengths of the individual wall segments for partially coupled walls Ductility of Coupling Beams Rotational Capacity, qic> Inelastic Demand, qid D f R o R d cg q id hw u qic = 0.04 for coupling beams with diagonal reinforcement as per 21.6.8.7 qic = 0.02 for coupling beams without diagonal reinforcement as per 21.6.8.6 Coupling Beams with Diagonal Reinforcement Wall Capacity @ Ends of Coupling Beams Walls at each end of a coupling beam shall be designed so that the factored wall moment resistance at wall centroid exceeds the moment resulting from the nominal moment resistance of the coupling beam. If the above can not be achieved, the walls develop plastic hinges at beam levels. This requires design and detailing of walls at coupling beam locations as plastic hinge regions. Shear Design of Ductile Walls Design shear forces shall not be less than; Shear corresponding to the development of probable moment capacity of the wall or the wall system Shear resulting from design load combinations with RdRo = 1.0 Shear associated with higher mode effects Shear Design of Ductile Walls Shear design will conform to the requirements of Clause 11. In addition, for plastic hinge regions; If qid ≥ 0.015 Vf ≤ 0.10c f’cbwdv If qid = 0.005 Vf ≤ 0.15c f’cbwdv For qid between the above two values, linear interpolation may be used Shear Design of Ductile Walls For plastic hinge regions: If qid ≥ 0.015 b0 If qid ≤ 0.005 b ≤ 0.18 For qid between the above two values, linear interpolation may be used Shear Design of Ductile Walls For plastic hinge regions: If (Ps + Pp) ≤ 0.1 f’cAg q 45o If (Ps + Pp) ≥ 0.2 f’cAg q ≥ 35o For axial compression between the above two values, linear interpolation may be used Moderately Ductile Moment Resistant Frame Beams (Rd = 2.5) - Mr + - - - Mr > 1/5 Mr - Mr > 1/3 Mr Mr + - Mr > 1/3 Mr + Mr > 1/5 Mr Moderately Ductile Moment Resistant Frame Beams 2h s1 c1 s2 h / 2 50 mm h Stirrups detailed as hoops Stirrups Stirrups detailed as hoops n s1 d / 4 s 1 8(d b ) long .bar s1 300 mm s1 24(d b )hoop db Moderately Ductile Moment Resistant Frame Columns Marc Factored moment resistance of columns M rnb M lnb Column design forces need not exceed those determined from factored load combinations using RdRo = 1.0 Nominal moment resistance of beams b M rc M rc Mnb Moderately Ductile Moment Resistant Frame Columns Columns will be confined for improved inelastic deformability lo lo ≥ 1/6 of clear col. height lo ≥ h lo ≥ 450 mm lo Spacing of Confinement Reinforcement 1/2 of minimum column dimension 8 x long. bar diameter 24 x tie diameters Crossties or legs of overlapping hoops shall not have centre-to-centre spacing exceeding 350 mm Column Confinement Reinforcement f'c ρ s 0.3kp fyh Circular Hoops fyh 500MPa Pf kp Po Ag f'c ρ s 0.45( 1) Ac fyh Column Confinement Reinforcement A sh Ag f'c 0.15knkp shc Ach fyh A sh f'c 0.09 shc fyh Rectilinear Ties Pf kp P o fyh 500MPa n kn n /(n 2) : No. of laterally supported bars Beam Shear Strength Wf M+n - Mn ln (Ve )left Ve = (Ve ) right Mn + ln + Mn + Wf ln 2 Beam Shear Strength The factored shear need not exceed that obtained from structural analysis under factored load combinations with RdRo = 1.0 Computation of Joint Shear Ve As T2 = As fy C1 = T1 x C2 = T2 Joint shear associated with nominal resistance of beams x A's T1 = A's fy Ve Vx-x = Ve - T2 - C1 Joint Shear Joint shear associated with nominal resistances of the beams and the columns will be computed and the smaller of the two values will be used The joint shear need not exceed that obtained from structural analysis under factored load combinations with RdRo = 1.0 Shear Resistance of Joints in Moderately Ductile Frames Vj 2.2c f 'c A j Vj 1.6 c f 'c A j Vj 1.3 c f 'c A j Transverse Reinforcement in Joints Longitudinal reinforcement shall have a centre-to-centre distance not exceeding 300 mm and shall not be cranked within the joint Transverse reinforcement shall be provided with a maximum spacing of 150 mm Moderately Ductile Shear Walls Wall thicknesses will be similar to those of ductile shear walls, except; ℓu / 10 ℓu / 14 ℓu / 14 ℓu / 20 Ductility limitation will be similar to that for ductile walls with minimum rotational demand as 0.003. Moderately Ductile Shear Walls Distributed horizontal reinforcement ratio shall not be less than 0.0025 in the vertical and horizontal directions Concentrated reinforcement in plastic hinge regions shall be the same as that for ductile walls, except the tie requirements are relaxed to those in Chapter 7 Shear Design of Moderately Ductile Walls Design shear forces shall not be less than the smaller of; Shear corresponding to the development of nominal moment capacity of the wall or the wall system Shear resulting from design load combinations with RdRo = 1.0 Shear Design of Moderately Ductile Walls Vf ≤ 0.1 cf’cbwdv b 0.1 q = 45o Design Example Ductile Core-Wall Structure in Montreal Chapter 11 By D. Mitchell and P. Paultre Twelve-Storey Ductile Core Wall Structure in Montreal •E-W: Rd = 4.0 and Ro = 1.7 •N-S: Rd = 3.5 and Ro = 1.6 •Site Classification D (Fa = 1.124 & Fv = 1.360) Design Spectral Response Acceleration N-S Direction Empirical: Ta = 0.05 (hn)3/4 = 0.87 s Dynamic: T = 1.83 s but not greater than 2Ta = 1.74s Torsion of Core Wall Torsional Sensitivity Bx max / ave Max BNS = 1.80 Max BEW = 1.66 Max B > 1.7 irregularity type 7 Seismic and Wind Loading Diagonally Reinforced Coupling Beam Wall Reinforcement Details Factored Moment Resistance E-W Factored Moment Resistance N-S Squat Shear Walls hw / ℓw ≤ 2.0; Rd = 2.0 The foundation and diaphragm components of the SFRS shall have factored resistances greater than the nominal wall capacity. The walls will dissipate energy either; through flexural mechanism, i.e., V @ Mn is less than Vr, or, through shear mechanism, i.e., V @ Mn is more than Vr. In this case: Vr 0.2 f'c b wd v Squat Shear Walls The distributed reinforcement: rh ≥ 0.003 rv ≥ 0.003 Use two curtains of reinforcement if Vf 0.18λφc f'c b wd v At least 4 vertical bars will be tied with seismic hooks and placed at the ends and at junctions of intersecting walls over 300 mm wall length with r ≥ 0.005. Squat Shear Walls Shear Design Vf ≤ 0.15 c f’cbwdv b=0 q = 300 to 450 Vertical reinforcement required for shear: Ps ρ v ρhcot θ φsf y A g 2 where; rh : required horizontal steel Conventional Construction Rd = 1.5 Buildings with Rd = 1.5 can be designed as conventional buildings. However, detailing required for nominally ductile columns will be used unless; Factored resistances of columns are more than those for framing beams Factored resistances of columns are greater than factored loads based on RdRo =1.0 IEFaSa(0.2) < 0.2 Walls of Conventional Construction Walls can be designed as conventional walls. However, the shear resistance will be greater than the smaller of; the shear corresponding to factored moment resistance, the shear computed from factored loads based on RdRo =1.0. Frame Members not Considered Part of the SFRS Frames that are not part of SFRS, but “go for the ride” during an earthquake shall be designed to accommodate forces and deformations resulting from seismic deformations. Thank You….. Questions or Comments?