同济大学：《建筑结构抗震》课程教学资源（课件讲稿）Chapter 6 Seismic Design of Reinforced Concrete Buildings（2/2）

Chapter 6 Chapter 6 Seismic Design of Reinforced Concrete Buildings 6.6 Detaiing 2 meaoora0ebe0nmce38r26rSwiins(网 Seismic grading for reinforced concrete buildings able6.12inGB50011-2010) 120 the heieht in 0 is the value listed in GB 50011-2008 be continued (Table6.1.2inGB50011-2010) 6.4 Seismic design of RC frames 用

1 Chapter 6 Seismic Design of Reinforced Concrete Buildings Chapter 6 6.1 Introduction 6.2 Earthquake Damage in Reinforce Concrete Buildings 6.3 Structural System and Seismic Grading for Structures 6.4 Seismic design of RC frames 6.5 Seismic design of RC walls 6.6 Detailing 6.7 Dual system * 6.8 Case Study The appropriate maximum height for R/C buildings (m) (Table 6.1.1 in GB50011-2010) Notes: the height in () is the value listed in GB 50011-2008 Structure Types System Seismic Fortification Intensity 6 7 8 (0.2g) 8 (0.3g) 9 Frame System 60 50 (55) 40 (45) 35 24 (25) Frame-Wall System 130 120 100 80 50 Structural Wall System 140 120 100 80 60 Frame supported Wall System 120 100 80 50 N.A Frame- Tube System 150 130 100 90 70 Tube in Tube System 180 150 120 100 80 Slab-Column and Wall System 80(40) 70(35) 55(30) 40 N.A Seismic grading for reinforced concrete buildings (Table 6.1.2 in GB50011-2010) Types of structure Seismic fortification intensity 6 7 8 9 Fram structure Height (m) ≤24 >24 ≤24 >24 ≤24 >24 ≤24 Frames 4th 3rd 3rd 2nd 2nd 1st 1st Large span frames 3rd 2nd 1st 1st Wall￾Frame structure Height (m) ≤60 >60 ≤24 25~60 >60 ≤24 25~60 >60 ≤24 25~60 Frames 4th 3rd 4th 3rd 2nd 3rd 2nd 1st 2nd 1st Structural walls 3rd 3rd 2nd 2nd 1st 1st Structural wall structure Height (m) ≤80 >80 ≤24 25~80 >80 ≤24 25~80 >80 ≤24 25~60 Structural walls 4th 3rd 4th 3rd 2nd 3rd 2nd 1st 2nd 1st be continued Types of structure Seismic fortification intensity 6 7 8 9 Frame - supported wall structure Height (m) ≤80 >80 ≤24 25~ 80 >80 ≤24 25~ 80 Struc￾tural walls General 4th 3rd 4th 3rd 2nd 3rd 2nd Streng￾thening 3rd 2nd 3rd 2nd 1stI 2nd 1st Frames that supporting walls 2nd 2nd 1st 1st Framed-tube structure Frame 3rd 2nd 1st 1st Tube 2nd 2nd 1st 1st Tube in tube structure Exterior tube 3rd 2nd 1st 1st Interior tube 3rd 2nd 1st 1st Slab-column￾wall structure Height (m) ≤35 >35 ≤35 >35 ≤35 >35 Columns 3rd 2nd 2nd 2nd 1st Walls 2nd 2nd 2nd 1st 2nd 1st (Table 6.1.2 in GB50011-2010) Flow Chart of seismic design simplified m4 m3 m2 m1 K4 K3 K2 K1 Calculation of Eq. Action Floor 1 Floor 2 Floor 3 Floor 4 I-Point D value Shear force distribution Response Eq. Action Unfavorable Combinations of Some Responses 6.4 Seismic design of RC frames Three Methods to calculate the Eq. Action

Flow Chart of seismic design megatnobeamcolumoinssprinmsrily (1)Schematic Diagram (2)Design vahe of shear foree v,-c+T--“+“- ，- (642 -15,1.35,1.2 coeresponding to grade 1.2 and 3 for frame structure gu2-别 6,4 (3)Seismic shear strength checking of joint core 85aaa2nchntorcod Structural wall system (6.39 -,Aa5竖4学）a0 64) 2

2 Design of Element Flexural Strength Shear Strength Flexural Strength Shear Strength The strength of Shear shall be stronger than flexural columns shall be stronger than beams Joint shear strength joint shall be stronger than connected beams and columns Mc,up Mc,low Mb,r Mb,l Vc,up Vb,l Vb,r Nc,up Nc,low Vc,low Vc,low Vc,low Beam Column The strength of Shear shall be stronger than fexual Flow Chart of seismic design 6.4.5 Design of beam-column joints Principle: strong joints-weak members  The design of beam-column joints is primarily aimed at: (i) preserving the integrity of the joint so that the strength and deformation capacity of the connected beams and columns can be developed and substantially maintained. (ii) preventing significant degradation of the joint stiffness due to cracking of the joint and loss of bond between concrete and the longitudinal column and beam reinforcement or anchorage failure of beam reinforcement. (1)Schematic Diagram                c b bo s b s b jb j H h h a h a M V / / 0 1 (5.41)               c b bo s b s bua j H h h a h a M V / / 0 1 1.15 (5.42) (2) Design value of shear force =1.5,1.35, 1.2 corresponding to grade 1, 2 and 3 for frame structure  j (6.42) (6.43) For Grade 1 frame structure at Intensity 9 area, it should also comply with: strong joints - weak members             s h a f A b b V f b h N b s yv svj c j j t j j j RE j 0 1.1 0.5 1    (3) Seismic shear strength checking of joint core          s h a V f b h f A b s j t j j yv svj RE j 0 0.9 1   ( .3 ) j c c j j RE 1 V 0 f b h     (6.39) (6.40) (6.41) For Grade 1 frame structure at Intensity 9 area, it should also comply with: 6.5 Seismic design of reinforced concrete structural walls Structural wall system • Reinforced-concrete structural walls (commonly referred to as shear walls) are being used more and more for resisting earthquake forces, either alone or in conjunction with ductile moment resisting frames. • The reason is that shear walls stiffen a building, and this reduces nonstructural damage

6.5.1 Structural wall system 回回 estertowi 6.5.2 StructuralAnalysis Boundary elements wide sta 6.5.3 Seismic design of structural wall 6.5.3Seismic design of structural walls a.Walls under vertical load Nsap(Af.+A) b.ga,acmyi8eabgationofsenmc 69 697a 225V≤015明hk)697 FK) 6,9

3 • When walls are situated in advantageous position in building, they can form an efficient lateral-force-resisting system, while simultaneously fulfilling other functional requirements. • The extent to which a wall will contribute to the resistance of overturning moments, story shear forces, and story torsion depends on its geometric configuration, orientation, and location within the plane of the building. 6.5.1 Structural wall system Construction of RC-Shear Wall Colum Slab Beam Beam Colum Main reinforcement of the colum Stirrup Main reinforcement of the beam Longitudinal reinforcement of the wall horizontal reinforcement of the wall Strengthening rebar of the opening • Boundary elements (边缘约束构件) are often present to allow effective anchorage of transverse beams. • Boundary elements are often provided • to accommodate the principal flexural reinforcement, • to provide stability against lateral buckling of a thin￾walled section and, • to enable more effective confinement of the compressed concrete in potential plastic hinges. Boundary elements 6.5.2 Structural Analysis Equivalent stiffness of member • a cantilever model is used for simplicity, to derive the equivalent flexure stiffness of structural walls. • For structural walls with regular and uniform stiffness along the vertical direction, the equivalent flexure stiffness E c Ieq can be obtained. single wall Wall with small openings Coupled wall a. Walls under vertical load Where is the coefficient considering construction error allowance, is the coefficient considering out-plane buckling.   6.5.3 Seismic design of structural walls ( ) / c s y N   Af  A f (5.67) (6.93) b. Walls under combination of seismic and gravity loading 6.5.3 Seismic design of structural walls 2.5 (0.2 ) (6.97a) 1 c c w w RE V  f b h   (5.68)   (0.15 ) 1 c c w w RE V  f b h   (5.69) = /( ) (6.98) c c  M V h0 Where the shear-span-ratio is : (6.97b)

65.3 Seimic design ofstructural walk 6.5.4 Shear Capacity checking of wall section The desig ctionnsregheedegos y=功 nder -a成+成 6.105 V-1I (M) a学-心 6.106 V-n(M+M)ll.+Va Where is 13,1.2,1.I for Girade 1,2,3 6.5.4 Shear Capacity checking of wall section 口 cofscwallsder 是) 6.19 口ner .s04-aw斯，】6 当-4 46.121) 7.) (6.124 6.5.5 Design of Structural Wall 10.6,A+0.8N) ction joirt fails to satisty thi at the bo ement of tle beam 4

4 • The design shear force at bottom section in strengthened regions （底部加强区）of a structural wall For structure walls in grade 1,2,3 frames, is 1.6, 1.4 and 1.2. For those with Grade 1 at Intensity 9, • Design shear force at end section of a coupling beam （连梁） with a span depth ratio greater than 2.5 • Where is 1.3, 1.2, 1.1 for Grade 1, 2, 3 V vwVw n Gb r b l V vb (Mb  M )/l V vw 6.5.3 Seismic design of structural walls 1.1 ( / ) V M M V  wua w w vw  Load carrying capacity of normal cross section of wall under eccentric axial loading Walls under eccentric compressive force ( ) 1 / / s y s s sw c RE N  A f  A   N  N  (5.74)               ) 2 ) ( 2 ( 1 / 0 / / w f sw c f s y w RE h h M M N h M A f h  (5.75) (6.105) (6.106) 6.5.4 Shear Capacity checking of wall section  Walls with a rectangular section, subjected to a large eccentric tensile force           wu u RE M e N N 0 0 1  (5.88) 2 / 2 ) 2 ( / 0 / 0 w f sw yw f wu s y w h h A f h M A f h     (5.90) (6.119) (6.121) 6.5.4 Shear Capacity checking of wall section  Diagonal shear resistance of structural walls under eccentric compressive loading  Diagonal shear resistance of structural walls under eccentric tensile loading  Seismic shear resistance of coupling beams           0 0 (0.4 0.1 ) 0.8 0.5 1 1 w sh yh w t w w RE h s A f A A V f b h N   (5.91)             0 0 (0.4 0.1 ) 0.8 0.5 1 1 w sh yh w t w w RE w h s A f A A V f b h N (5.92)        0  0 0.05 0.7 1 b sv c b b yv RE b h s A V f b h f  (5.93) (6.122) (6.123) (6.124)  Shear strength check on the construction joints （施工缝） of structural walls Horizontal construction joints （水平施工缝） are potential planes of weakness for structural walls.  If shear resistance of a construction joint fails to satisfy this requirement, additional steel reinforced bars are needed perpendicular to the horizontal joint, with sufficient anchorage length each side of the joint. V  f A N y s RE wj 0.6 0.8 1    (5.94) 6.5.5 Design of Structural Wall  Plane layout  Vertical layout  Axial-force ratio  Boundary element  Strengthening region at the bottom  Minimum ratio of reinforcement of wall  Construction requirement of tie beam

Plane Layout Vertical Layout T kymdedanaome · Bottom Strengthening Region Limit of Axial-Load Ratio 口Purpose principle, When 150m.1/10 I(degree)Il (7,degree)l WkcA0.40.50.6 Boundary Member Restraining Boundary Membe 口ength of wall:k Restraining boundary membe member ·&61a2x2m8 no0 0.20 0.20 0.20 025 mn at the

5 Plane Layout  Principle：  Increase the integral lateral stiffness, but not too high;  Try to make the stiffness center superpose upon the centric to reduce eccentricity and avoid torsion;  Avoid short-width wall;  The length of wall should be shorter than 8m and the height-to-width should be lager than 2;  Wall should be arranged in two ways along the main axis and the axis of wall should align to the axis of frame.  It’s inappropriate to set the frame beam onto the tie beam. Vertical Layout  Principle：  The shear wall should be arranged continuously from bottom to top;  Openings should be lined up in the same place. Irregular openings should be strengthened;  Pay attention to the situation that the shear wall is set upon beams. These beams are frame-supported beams, so their seismic intensity should be upgraded. ;  Try to avoid weak layer. The shear force of weak layer should multiply the amplification coefficient 1.15;  The out-of-plane stiffness should be controlled. Bottom Strengthening Region  Purpose： To ensure draw ability after plastic hinges appear in the shear walls, the strengthening region at the bottom should be reinforced.  Principle：  1/8 of the total height of shear wall， When H>150m, 1/10  Or reinforce the two stories at the bottom Limit of Axial-Load Ratio  principle：  Increase wall’s drawability to make the shear walls at the bottom form plastic hingles when facing rare earthquake, avoiding brittle failure.  Axial pressure N based on representative value of gravity load. (different from colums) Axial-load ratio Ⅰ（9 degree）Ⅱ（7,8 degree） Ⅱ N/fcA 0.4 0.5 0.6 Boundary Member  Restraining boundary member  Constructing boundary member  Principle  Restraining boundary member：the ends of Grade 1 and 2’s shear wall’ bottom￾strengthening region and the first story above;  Constructing boundary member：the rest ends of Ⅰ,Ⅱ shear wall. The ends of Ⅲ,Ⅳ shear wall and non-seismic design wall. Restraining Boundary Member  Length of wall: lc  Volume stirrup ratio:  Characteristic value of stirrup: v Item Ⅰ（9 degree） Ⅰ（7,8 degree） Ⅱ  v 0.20 0.20 0.20 lc (embedded column) 0.25hw 0.20hw 0.20hw lc (flanking column or column at the end of wall) 0.20hw 0.15hw 0.15hw c v v yv f f   

Restraining Boundary Member Diamncter of:28mm Diameter:616,614; Constructing boundary member Constructing boundary member Length of wall,minimum of stirrup,maximum stirrup 图51剪力速的物造边棕构件 Minimum Dimension of Shear Wall Minimum Dimension of Shear Wall ≤025pfbh Non- 0./) O1AA人， 6

6  Diameter of stirrup: 8mm;  Stirrup spacing value: 100mm（Ⅰ） 150mm（Ⅱ）  Longitudinal reinforcement: range—shaded area A; Area—1.4%， 1.2%， 1.0%； （ special Ⅰ,Ⅰ,Ⅱ shear wall respectively ）  Diameter：  616, 614; Restraining Boundary Member 约束边缘构件 约束 边 缘 构 件 截 面 及 配 筋 Constructing boundary member  Length of wall, minimum of stirrup, maximum stirrup spacing Strengthening portion at the bottom Other locations Seismic Stirrups or tie bar Stirrups or tie bar grade of structure s Minimum amount of longitudinal reinforcements (the greater value should be used) Minimu m diameter (mm) Max. spacing (mm) Minimum amount of longitudinal reinforcements (the greater value should be used) Minimu m diameter (mm) Max. spacing (mm) 1 0.010Ac , 616 8 100 0.008Ac , 614 8 150 2 0.008Ac , 614 8 150 0.006Ac , 612 8 200 3 0.006Ac , 612 （0.005Ac , 412） 6 150 0.005Ac , 412 6 200 4 0.005Ac , 412 6 200 （150） 0.004Ac , 412 6 250 （200） Constructing boundary member Minimum Dimension of Shear Wall  Strength of concrete ≥C20；  Thickness of shear wall Seismic intensity region Embedded column Non-embedded column Ⅰ,Ⅱ Strengthening region at the bottom H/16 200 h/12 200 The rest H/20 160 h/15 180 Ⅲ, Ⅳ Strengthening region at the bottom H/20 160 H/20 160 The rest H/25 160 H/25 180 Non￾seismic design all H/25 160 H/25 180 1. Non-seismic action： 2）Seismic action： Shear-span ratio>2.5： Shear-span ratio≤2.5： . V 0 25 f b h w c c w w0   ( . ) w c c w w0 RE 1 V 0 20 f b h    ( . ) w c c w w0 RE 1 V 0 15 f b h    c c w0 M V h   Minimum Dimension of Shear Wall

Distributing reinforcements Design of Tie Beam Lateral and vertical reinforcemens. hould 100 025% M≤fA,(ho-a) Design of Tie Beam---Shear Capacity 1.non-seismicaction: Design of Tie Beam Ks0.7fho+人nw V≤0.25Bfhh s名0Pe+人子w 2.seismis action Span-to-depth ratio2.5: 1(0.20B.f.b.h.o 5≤名a8AM+09.女w Shear-span ratio2.5.≤(0.15.fhh.o YRE Design of Tie Beam Reinforcement of tie beams Strong-shear-weak-bending 1,,M,seismic 5=+证+a =1a+M@+2

7 Distributing reinforcements  Lateral and vertical reinforcemens： sw sw w A b s   Shear wall Seismic intensity Minimum ratio of reinforcement Maximum spacing value Minimum diameter Normal height Ⅰ, Ⅱ, Ⅲ 0.25% 300 8 Normal height Ⅳ, non-seismic design 0.20% 300 8 B height Special Ⅰ Strengthening region: 0.40% The rest: 0.35% 300 8 Temperature -stress￾increase region Seismic and non-seismic 0.25% 200 —— Design of Tie Beam  principle：  Similar to the design of RC beam;  According to the design of double-tendon section beam;  Moment and shear force should be adjusted： Ideal elastic：6,7 degree： ×0.8， 8,9 degree： ×0.5，  Not consider the function of tie beams when meeting rare earthquake.  Flexure capacity： ' ( ) M f A h a   y s b0 1. non-seismic action： 2. seismic action： Span-to depth ratio>2.5: Span-to-depth ratio2.5： Shear-span ratio≤2.5： . V 0 25 f b h w c c w w0   ( . ) w c c w w0 RE 1 V 0 20 f b h    ( . ) w c c w w0 RE 1 V 0 15 f b h    Design of Tie Beam  Strong-shear-weak-bending Ⅰ,Ⅱ,Ⅲ,Ⅳ seismic： 9 degree： l r b b b vb Gb n M M V V l     . l r bua bua b Gb n M M V 1 1 V l    Design of Tie Beam Reinforcement of tie beams

Exercises Please,Please and Please Giver:A 12-storey office building wil be bul in the area,which sesmic fortification is 7.The building is designed to use concrete (C35,f= 16.7N/m).The kngth of the plane of the bulding is 48m,wth the spacng of columns is 8.0m,the width is 24m,with spacing of colums s Review this chapter！ 6.0m,mearwhil,the height for ground for is 5.5m,and for the other floors are all as 3.9m The dead loads and live lods or every storey s 5.5kN/m and Read Carefully! 2.5kN/m respectively. Ask:1.Please use the liitation of axal-force ratio to the section dimersion of colmmn at bottom story. 2.Check the dmersion of colummn according to the minimum requrement for shear resistant 3.According to GB 50011,2010,plase ghve the lmitation value of dritt ratios of column and beam respectiely. 8

8 Exercises Given: A 12-storey office building will be built in the area, which seismic fortification is 7. The building is designed to use concrete (C35, fc＝ 16.7N/mm2）. The length of the plane of the building is 48m, with the spacing of columns is 8.0m, the width is 24m, with spacing of columns is 6.0m, meanwhile, the height for ground floor is 5.5m, and for the other floors are all as 3.9m. The dead loads and live loads for every storey is 5.5kN/m2 and 2.5kN/m2 respectively. Ask: 1. Please use the limitation of axial-force ratio to evaluate the section dimension of column at bottom story. 2. Check the dimension of column according to the minimum requirement for shear resistant. 3. According to GB 50011,2010, please give the limitation value of drift, torsion action, minimum reinforcement ratios and maximum reinforcement ratios of column and beam respectively. Review this chapter ! Read Carefully! Please, Please and Please