Horizontal Distribution of Forces to Individual Shear Walls

Transcription

1 Horizontal Distribtion of Fores to ndividal Shear Walls nteration of Shear Walls ith Eah Other n the shon figre the slabs at as horizontal diaphragms etending beteen antilever alls and the are epeted to ensre that the positions of the alls, relative to eah other, don't hange dring lateral displaement of the floors. The fleral resistane of retanglar alls ith respet to their eak aes ma be negleted in lateral load analsis. The distribtion of the total seismi load, F or F among all antilever alls ma be approimated b the folloing epressions. F i F i + F i F F + F here: F load inded in all b inter-stor translation onl, in -diretion i F load inded in all b inter-stor translation onl, in -diretion F " i load inded in all b inter-stor torsion onl, in -diretion F load inded in all b inter-stor torsion onl, in -diretion " F i total eternal load to be resisted b a all, in -diretion F total eternal load to be resisted b a all, in -diretion To obtain F i and F', the fores F and F are distribted to the individal shear alls in proportion to their rigidities. 87

2 The fore resisted b all i de to inter-stor translation, in -diretion, is given b F F i The fore resisted b all i de to inter-stor translation, in -diretion, is given b F i F i here: F total eternal load to be resisted b all alls, in -diretion F total eternal load to be resisted b all alls, in -diretion i seond moment of area of a all setion abot ais seond moment of areas of a all setion abot ais i total seond moment of areas of all alls in -diretion total seond moment of area of all alls in -diretion The fore resisted b all i de to inter-stor torsion, in -diretion, is given b ( F e ) i i + i ( ) Fi i The fore resisted b all i de to inter-stor torsion, in -diretion, is given b ( F e ) i i F ( i i + i ) here: i -oordinate of a all ith respet to the enter of rigidit C.R of the lateral load resisting sstem i -oordinate of a all ith respet to the enter of rigidit C.R of the lateral load resisting sstem e eentriit reslting from non-oinidene of enter of gravit C.G and enter of rigidit C.R, in -diretion e eentriit reslting from non-oinidene of enter of gravit C.G and enter of rigidit C.R, in -diretion 88

3 Eample (3): n Eample (), determine the fores ating on shear all G. Negleting moments of inertia abot eak aes, seond moments of area of eah of the shear alls abot -ais are given b 3 0.() 3 A B G H 0.5m Total seond moments of area abot -ais are given b i ( ) m Seond moments of area of eah of the shear alls abot -ais are given b 3 () 3 0. C D E F 0.5m Total seond moments of area abot -ais are given b i ( ) m i To loate the enter of rigidit C.R, the distane from the origin to the C.R in the -diretion is given b i 0.5 ( )( 8) + ( 0.5)(.5) i i.8.5m The distane from the origin to the C.R in the -diretion is given b 89

4 i i ( )( 0.5)( 8) i i i m Ths, the eentriit in -diretion e m And the eentriit in -diretion e m Torsion ased b eentriit e, T.5 F Torsion ased b aidental eentriit, T F ( 0.05)( 8) 0. 9 F Total torsion, T ± T (.5 F ± 0. 9 F ) F F i 0.5F.8 FA FB FG FH 0. 5 ( F e ) i i + i Fi i F A F B ( ) F G F H F (.5 F ± 0.9 F )( 6.75)( 0.5) ( 0.5)( 6.75) + ( 0.5 )( 6.75) + ( 0.5 )( 9) + ( 0.5 )( 9) (.5 F ± 0.9 F ) F The fores ating on shear all G are given b the folloing epression 0.5 F F 0.9 F Using the stor fores evalated in Eample (), the fores ating on shear all G at eah of floor level are shon in the net figre. Distribtion of fores at eah floor level (Shear all G) 90

5 Classifiation of Strtral Walls Aording To Seismi Risk Aording to Chapters and of AC 38-08, strtral alls are defined as being alls proportioned to resist ombinations of shears, moments, and aial fores inded b earthqake motions. A shear all is a strtral all. Reinfored onrete strtral alls are ategorized as follos: - Ordinar reinfored onrete strtral alls: The are alls ompling ith the reqirements of Chapters throgh 8. - Speial reinfored onrete strtral alls: The are ast-in-plae alls ompling ith the reqirements of. and.7 in addition to the reqirements for ordinar reinfored onrete strtral alls. Speial Provisions for Earthqake Resistane Aording to Clase..9. of AC 38-08, the seismi risk level of a region is reglated b the legall adopted general bilding ode of hih AC forms a part, or determined b loal athorit. Correlation beteen Seismi-Related Terminologies n Model Codes Code/ Standard Level of seismi risk as defined in the ode setion Moderate/ntermediate (.. and..8) Lo (..) High (.. throgh..8) and (. throgh.3) nternational Bilding SDC A, B SDC C SDC D, E, F Code 000, 003, 006 Uniform Bilding Code 99, 99, 997 Seismi Zone 0, Seismi Zone Seismi Zone 3, SDC Seismi Design Categor Aording to Clases..9. and...7 of AC 38-08, in regions of lo and intermediate seismi risk, provisions of Chapter are not to be applied. (Chapter throgh 8 are appliable) Aording to AC 38-08, in regions of high seismi risk, speial strtral alls ompling ith.9 are to be sed for resisting fores inded b earthqake motions. 9

6 Classifiation of Shear Walls Aording To Their Height-to-Length Ratios Shear alls are lassified as short or long aording to their aspet ratios (the ratio of its height h to length in the plane of loading l ), as follos: - For h / l <, the are alled short or sqat shear alls. Their design is dominated b shear, rather than flere. Aspet ratios belo mark the transition from slender to short behavior, and alls ith sh dimensions reqire onsiderable are in design if a dtile failre mode is reqired. Withot this attention, shear alls are likel to fail in brittle failre modes sh as diagonal tension or sliding shear rather than ndergoing the more dtile fleral failre possible in slender alls. Short shear alls ma need inreased strength or speial detailing, inlding diagonal steel to overome these problems. - For h / l, the are alled long or slender shear alls. Their design is dominated b flere. Aspet ratios are normall restrited to 7; higher ratios ma reslt in inadeqate stiffness, problems in anhoring the tension side of the shear all and possibl signifiant amplifiations de to P effets. The above stated lassifiation is not epliitl stated in AC Code. 9

7 Design of Ordinar Shear Walls The shear all is designed as a antilever beam fied at the base, to transfer load to the fondation. Shear fores, bending moments and aial loads are maimms at the base of the all. Tpes of Reinforement: To ontrol raking, shear reinforement is reqired in the horizontal and vertial diretions, to resist in plane shear fores. The vertial reinforement in the all serves as fleral reinforement. f large moment apait is reqired, additional reinforement an be plaed at the ends of the all ithin the setion itself, or ithin enlargements at the ends. The heavil reinfored or enlarged setions are alled bondar elements. Shear Strength: Aording to AC.., design of ross setions sbjet to shear are based on Φ Vn V here strength ompted b V is the fatored fore at the setion onsidered and V V + V n s () V n is the nominal shear here V is nominal shear strength provided b onrete and s V is nominal shear strength provided b shear reinforement. () 93

8 Based on AC.9.3, V n, ma at an horizontal setion for shear in plane of the all is not to be taken greater than V f n,ma. 65 hd here h is thikness of all, and d is the effetive depth in the diretion of bending, ma be taken as 0.8l, here l is length of all onsidered in diretion of shear fore, as stated in AC.9.. A larger vale of d, eqal to the distane from etreme ompression fiber to enter of fore of all reinforement in tension, be permitted to be sed hen determined b a strain ompatibilit analsis. (3) Based on AC.9.5, the shear strength provided b onrete V is given b an of the folloing eqations, as appliable. For aial ompression, Eqn. () is appliable V f h d For aial tension, Eqn. (5) is appliable () N V 0.53 f h d A 35 g here A g is the gross area of all setion and in Eqn. (5). (5) N is the fatored aial tension fore AC.9.6 speifies that a more detailed analsis is permitted to evalate V as follos, here V is the lesser of the to vales shon in Eqns. (6) and (7). V N d 0.88 f ' h d + (6) l V 0.6 f ' + l 0. N 0.33 f ' + l h M l V Where negative, Eqn. (7) is not appliable. hd N is positive for ompression and negative for tension. f ( V l / ) (7) M is / 9

9 Shear Reinforement: A- When the fatored shear fore V is less than Φ V /, minimm all reinforement aording to AC.9.9 or in aordane ith Chapter of AC ode. A- Minimm Horizontal Reinforement Ratio: Ratio of horizontal shear reinforement area to gross onrete area of vertial setion, ρ, shall not be less than Spaing of this reinforement t S is not to eeed the smallest of l / 5, 3 h, 5 m. A- Minimm Vertial Reinforement Ratio: Ratio of vertial reinforement area to gross onrete area of horizontal setion, ρ is l not to be taken less than the larger of h ρ l + ( ρt 0.005) l (8) and 0.005, bt need not be greater than ρ t reqired b Eqn. (9). Spaing of this reinforement S is not to eeed the smallest of l / 3, 3 h, 5 m. Chapter Provisions: Minimm ratio of vertial reinforement area to gross onrete area, ρ l, shall be 0.00 for deformed bars p to 6 mm in diameter, ith f not less than 00 kg/m for other deformed bars. Minimm ratio of horizontal reinforement area to gross onrete area, ρ t, shall be for deformed bars p to 6 mm in diameter, ith f not less than 00 kg/m for other deformed bars. B- When the fatored shear fore eeeds Φ V /, minimm all reinforement for resisting shear, aording to AC.9.9, mst be provided. C- Aording to AC.9.9. hen the fatored shear fore V eeeds Φ V, horizontal shear reinforement mst be provided aording to the folloing eqation. Av f d Vs S (9) here A v is area of horizontal shear reinforement ithin a distane S. Vertial shear reinforement is provided sing Eqn. (8), shon above. 95

10 The ritial setion for shear is taken at a distane eqal to half the all length l /, or half the all height h /, hihever is less. Setions beteen the base of the all and the ritial setion are to be designed for the shear at the ritial setion, as speified in AC.9.7. Design for Flere: Shear all Reinforement The all mst be designed to resist the bending moment at the base and the aial fore proded b the all eight or the vertial loads it arries. Ths, it is onsidered as a beam-olmn. For retanglar shear alls ontaining niforml distribted vertial reinforement and sbjeted to an aial load smaller than that proding balaned failre, the folloing eqation, developed b Cardenas and Magra in AC SP-36 in 973, an be sed to determine the approimate moment apait of the all. P Φ + C M 0.5 As f l As f l Where: 96

11 C ω + α l ω β As f ω and α l h f l P h f C distane from the etreme ompression fiber to the netral ais A s total area of vertial reinforement l horizontal length of all P fatored aial ompressive load f ield strength of reinforement Φ strength redtion fator for bending Lateral Ties for Vertial Reinforement: Based on AC.3.6, vertial reinforement need not be enlosed b lateral ties if vertial reinforement is not greater than 0.0 times the gross onrete area, or here vertial reinforement is not reqired as ompression reinforement. Additional Reinforement arond Openings: n addition to the reqired horizontal and vertial reinforement eplained earlier, AC.3.7 states that not less than φ 6mm bars are provided arond all indo and door openings. Sh bars are to be etended to develop f in tension at the orners of the openings. Additional reinforement arond all openings 97