4- Earthquake Resistant Design According To 1994 UBC

Transcription

1 94 4- Earthquake Resstat Desg Accordg To 1994 UBC The Statc Lateral Force Procedure 4-1 Applcablty: The statc lateral force procedure may be used for the followg structures: A. All structures, regular or rregular (see Tables 4.1.a ad 4.1.b), sesmc zoe o. 1 ad stadard occupacystructures sesmc zoe o. 2 (see Table 4.2 for zoe classfcato ad Table 4.4 for occupacy factors). B. Regular structures uder 73 m heght wth lateral force resstace provded by systems gve Tables 4.5.a ad 4.5.b ecept for structures located sol profle type S4 whch have a perod greater tha 0.70 sec. (see Table 4.3 for sol profles). C. Irregular structures ot more tha fve stores or 20 m heght. D. Structures havg a fleble upper porto supported o a rgd lower porto where both portos of the structure cosdered separately ca be classfed as beg regular, the average story stffess of the lower porto s at least te tmes the average stffess of the upper porto ad the perod of the etre structure s ot greater tha 1.10 tmes the perod of the upper porto cosdered as a separate structure fed at the base.

2 95 Regular Structures: Regular structures are structures havg o sgfcat physcal dscotutes pla or vertcal cofgurato or ther lateral force resstg. Irregular Structures: Irregular structures are structures havg sgfcat physcal dscotutes cofgurato or ther lateral force resstg systems (See Table 4.1.a ad 4.1.b for detaled descrpto of such structures). Load Combatos: The total desg forces are calculated from the followg cases of loadg. U = 1.4( D+ L ± E) (4.1) U = 0.9 D ± 1. 4 E (4.2) Where U = Ultmate desg force D = Servce dead load L = Servce lve load E = Servce earthquake load

3 Cocept of Method: The 1994 UBC equvalet statc method cosders oly horzotal movemet ad eglects effects of vertcal groud movemet. Statcally models the ertal effects usg Newto s 2 d Law of Moto gve by Eq. (4.3). F = M a (4.3) Where F = resultg force o structure M = buldg mass a = accelerato of groud W But M = g Ad Eq. (4.3) ca be wrtte as a F = W (4.4) g Mmum Desg Lateral Forces: The desg sesmc forces may be assumed to act ococurretly the drecto of each prcpal as of the structure. The total desg base shear a gve drecto s to be determed from the followg Eq. 96

4 97 Where Z I CW V = (4.5) R w V= total sesmc lateral force at the base of the structure W= total sesmc load - I storage ad warehouse occupaces, a mmum of 25 % of floor lve load s to be cosdered. - Total weght of permaet equpmet s to be cluded. - Where a partto load s used floor desg, a load of ot less tha 50 kg/m 2 to be cluded. Z Z I C R w = sesmc base shear coeffcet, somewhat equvalet to a / g but accouts for addtoal factors that affect buldg respose lke: uderlyg sol, the structural cofgurato, the type of structure, ad occupacy of the buldg. = sesmc zoe factor gve Table (4.2) ad s related to the sesmcty of the zoe. It s the effectve peak groud accelerato wth 10 % probablty of beg eceeded 50 years. I = Buldg mportace factor gve Table (4.4), whch accouts for buldg use ad mportace R w = structural factor, accoutg for buldg ductlty ad dampg, gve Tables (4.5.a) ad (4.5.b). A Larger R w value meas a better sesmc performace.

5 98 Ductlty = ablty to deform the elastc rage pror to fracture Dampg = resstace to moto provded by materal frcto C = dyamc respose value, ad accouts for how the buldg ad sol ca amplfy the basc groud accelerato 1.25 S C= 2.75 C (4.6) ( T) 2 / 3 S = ste Coeffcet depedg o the sol characterstcs gve Table (4.3). T = structural fudametal perod secods the drecto uder cosderato evaluated from the followg equatos. For momet-resstg frames, For shear walls, 3 / 4 ( h ) R w T = (4.7) ( h ) 3 / 4 T = (4.8) Ac For other buldgs, Where 3 / 4 ( h ) T = (4.9) h = total heght of buldg meters A = effectve cross-sectoal area of shear walls c

6 99 2 D e A c = A h D e / h 0. 9 (4.10) A = cross-sectoal area of dvdual shear walls the drecto of loads m 2 D = legth of each shear wall the drecto of loads e Vertcal Dstrbuto of Force: The base shear evaluated from Eq. (4.5) s dstrbuted to the varous stores of the buldg accordg to the followg Eq. F = ( V F ) t w = 1 w h h (4.11) Fg. (4.1) Vertcal Dstrbuto of Force

7 100 Where F =0 for T 0. 7sec. t F t = 0.07TV 0. 25V for T > 0. 7sec. The shear force at each story s gve by Eq. (4.12) Where V = F + F (4.12) t = = umber of stores above the base of the buldg F t = the porto of the base shear, cocetrated at the top of the structure to accout for whplash effects F, F, F= lateral forces appled at levels,, or, respectvely h, h, h= heght above the base to levels,, or, respectvely V = desg shear story Horzotal Dstrbuto of Force: The desg story shear ay drecto V, s dstrbuted to the varous elemets of the lateral force-resstg system proporto to ther rgdtes. Horzotal Torsoal Momet: To accout for the ucertates locatos of loads, the mass at each level s assumed to be dsplaced from the

8 101 calculated ceter of mass each drecto a dstace equal to 5 % of the buldg dmeso at that level perpedcular to the drecto of the force uder cosderato. The torsoal desg momet at a gve story s gve by momet resultg from eccetrctes betwee appled desg lateral forces appled through each story s ceter of mass at levels above the story ad the ceter of stffess of the vertcal elemets of the story, addto to the accdetal torso. Overturg Momets: The overturg momets are to be determed at each level of the structure. The overturg momet (4.13). M = F t ( h h ) + F ( h h ) M at level s gve by Eq. = + 1 (4.13) Overturg momets are dstrbuted to the varous elemets of the vertcal lateral force-resstg system proporto to ther rgdtes. P Effects: The resultg member forces, momets ad story drfts duced by P effects are to be cosdered the evaluato of overall structural frame stablty. P effects are eglected whe the rato gve by Eq. (4.14) s 0.1.

9 102 M M sec odary prmary P = V P = total sesmc weght at level ad above = drft of story V = shear force of story h = heght of story h (4.14) I sesmc zoes o. 3 ad 4, P effects are eglected whe the story drft 0.02/ R tmes the story heght. Desg of Catlevers: w Horzotal catlever compoets are to be desged for a et upward force of 0.2 wp, where w p s the weght of the catlevered elemet. Story Drft Lmtatos: Story drft s the dsplacemet of oe level relatve to the level above or below due to the desg lateral forces. Calculated drft s to clude traslatoal ad torsoal deformatos. Calculated story drft shall ot eceed 0.04/ R w or tmes the story heght for buldgs wth perods < 0. 7 secod. For structures wth perods 0. 7sec., the calculated story drft s ot to eceed 0.03/ Rwor the story heght. Desg of Daphragms: Floor ad roof daphragms are to be desged to resst the forces determed from the followg formula

10 103 F p F = t = + F = w p (4.15) w The force F p eed ot eceed 0.75Z I wp, but shall ot be less tha 0.35Z I Where wp w p = weght of the daphragm at level F = daphragm lateral desg force at level p

11 104 Table (4.1.a) Vertcal Structural Irregulartes Irregularty Type ad Defto How to Deal wth A- Stffess Irregularty- - -Soft Story A soft story s oe whch the lateral stffess s less tha 70 percet of that the story above or less tha 80 percet of the average stffess of the three stores above. B- Mass Irregularty Mass rregularty s cosdered to est where the effectve mass of ay story s more tha 150 percet of the effectve mass of a adjacet story. C- Vertcal Geometrc Irregularty Vertcal geometrc rregularty shall be cosdered to est where the horzotal dmeso of the lateral force-resstg system ay story s more tha 130 percet of that a adjacet story. D- I-Plae Dscotuty Vertcal Lateral Force-resstg Elemet A -plae offset of the lateral loadresstg elemets greater tha the legth of these elemets. E- Dscotuty Capacty-Weak Story A weak story s oe whch the story stregth s less tha 80 percet of that the story above. The story stregth s the total stregth of all sesmc-resstg elemets sharg the story shear for the drecto uder cosderato. Use the dyamc lateral force procedure. Use the dyamc lateral force procedure. Use the dyamc lateral force procedure. The Structure s to be desged to resst the overturg effects caused by sesmc forces, dow to the foudatos level. Structures are ot to be over two stores or 9 m heght where the weak story has calculated stregth of less tha 65 % of the story above.

12 Vertcal Irregulartes 105

13 106 Table (4.1.b) Pla Structural Irregulartes Irregularty Type ad Defto How to Deal wth A- Torsoal Irregularty Torsoal rregularty s to be cosdered to est whe the mamum story drft, computed cludg accdetal torso, at oe ed of the structure trasverse to a as s more tha 1.2 tmes the average of the story drfts of the two eds of the structure. B- Re-etrat Corers Pla cofguratos of a structure ad ts lateral force-resstg system cota reetrat corers, where both projectos of the structure beyod a re-etrat corer are greater tha 15 % of the pla dmeso of the structure the gve drecto. C- Daphragm Dscotuty Daphragms wth abrupt dscotutes or varatos stffess, cludg those havg cutout or ope areas greater tha 50 % of the gross eclosed area of the daphragm, or chages effectve daphragm stffess of more tha 50 % from oe story to the et. D- Out-of-plae Offsets Dscotutes a lateral force path, such as out-of-plae offsets of the vertcal elemets. E- Noparallel Systems The vertcal lateral load-resstg elemets are ot parallel to or symmetrc about the major orthogoal aes of the lateral forceresstg system. The oe-thrd crease usually permtted allowable stresses for elemets resstg earthquake forces s to be dscarded. The oe-thrd crease usually permtted allowable stresses for elemets resstg earthquake forces s to be dscarded. The oe-thrd crease usually permtted allowable stresses for elemets resstg earthquake forces s to be dscarded. Structures are to be desged to resst the overturg effects caused by earthquake forces ad are these effects are to be carred dow to the foudato. The requremet that orthogoal effects be cosdered may be satsfed by desgg such elemets for 100 % of the prescrbed sesmc forces oe drecto plus 30 % of the prescrbed forces the perpedcular drecto. Alterately, the effects of the two orthogoal drectos may be combed o a square root of the sum of the squares bass.

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15 108 Table (4.2) Sesmc Zoe Factor Zoe 1 2A 2B 3 4 Z Table (4.3) Ste Coeffcets Type Descrpto S Factor S1 - Rock-lke materal characterzed by a shear wave 1.0 velocty greater tha 750 m/s or by other meas of classfcato. - Stff or dese sol codto where the sol depth s less tha 60 m. S2 A sol profle wth dese or stff sol codtos, where 1.20 the sol depth eceeds 60 m. S3 A sol profle 20 m or more depth ad cotag 1.50 more tha 6 m of soft to medum stff clay but ot more tha 12 m of soft clay. S4 A sol profle cotag more tha 12 m of soft clay characterzed by a shear wave velocty less tha 150 m/s. 2.0 Table (4.4) Occupacy Importace Factors Occupacy Category Fuctos of Structure Importace Factor I Essetal Facltes Hosptals, fre statos, polce 1.25 statos, water taks, garages, shelters, dsaster cotrol ceters, ad commucatos ceters. Hazardous Facltes Structures cotag toc, atomc, ad eplosve substaces Specal Occupacy Publc assembly, schools, jals, 1.0 power-geeratg statos. Stadard Occupacy Structures ot lsted above. 1.0

16 109 Table (4.5.a) Structural Factors (buldg structures) Basc Structural System Buldg Frame Momet-Resstg Frame Dual Systems Lateral Load-Resstg System Rw Heght (m) Zoes 3 & 4 Shear Walls (wthout vertcal loads) 8 73 Shear Walls (wth vertcal loads) 6 73 SMRF 12 No Lmt IMRF 8 Not Used OMRF 5 Not Used Shear Walls + SMRF Shear Walls + IMRF 12 9 No Lmt 48 Table (4.5.b) Structural Factor (obuldg structures) No. Structure Type R w 1- Taks, vessels or pressurzed spheres o braced or ubraced 3 legs. 2- Cast--place cocrete sols ad chmeys havg walls 5 cotuous to the foudato. 3- Iverted pedulum-type structures Coolg towers. 5

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18 111 Eample 1: A seve-story buldg frame system (resdetal) wth shear walls has the dmesos show the fgure. The total sustaed dead load s 800 kg/m 2. Ths buldg s located Gaza Strp ad les o top of a deep clayey depost. Eght shear walls, each 3 m log ad 0.2 m thck are used as a lateral force resstg system. Determe the sesmc loads at the floor levels of the buldg a drecto perpedcular to as 1-1, 2-2, 3-3, ad 4-4 usg the 1994 UBC. 73 = 21m 1 A 2 3 B 4 C D 4.5m 4.5m 4.5m E G H F 4.5m m 6m 6m

19 112 Soluto: Z = 0.075, I = 1, S = 2.0, R w = 8 Weght of floor = 0.8( 18)( 18) = tos Total sesmc weght = 259.2( 7) = tos Buldg atural perod, T ( h ) 4 T = A c 2 D e A c = A D e / h 9 h 0. A c = = = 1 21 O.K T = ()( 3 0.2) m 4 ( h ) 3/ ( 21) A c = ( 2) 2 / ( 1.002) 3/ 4 = sec , = < S C = = = 2.5sec < / 3 3 ad > 0.075( 8) T The base shear V s gve by ZICW V = R w V = ( )( 2.5)( ) 8 fort > 0.7sec, = 42.52tos = 0.07TV = Ft = 2.97t < 0.25 Vertcal Dstrbuto of Force: ( V Ft ) wh F = 7 F = 1 F t ( )( 42.52) ( 42.52) O. K

20 113 level Story shears: V = F t 7 + = 1 F Overturg momet: M ( h h ) + F ( h h ) = Ft = + 1 Lateral dsplacemet: δ g = 4π T Story drft: P = δ F 9.81 F 2 2 = () 1 2 = 2 w 4π w δ effects: P V h Whe < h, P Lateral force dstrbuto: w 0.03h R w F w effects are to be eglected. h w h F V M δ ( mm) P P V h

21 114 Eample 2: A seve-story reforced cocrete specal momet-resstg frame (SMRF) has the dmesos show the fgure. The total sustaed dead load s 800 kg/m 2 ad the lve load s 250 kg/m 2. The buldg whch s characterzed as a resdetal buldg s located Gaza Cty ad les o top of a deep clayey depost. Evaluate the sesmc loads at the floor levels of the buldg a drecto perpedcular to as 1-1, 2-2, 3-3, ad 4-4 usg the 1994 UBC.

22 115 Soluto: Z = 0.075, I = 1, S = 2.0, R w = 12 Sce the buldg s resdetal, o lve load s to be used sesmc weght calculato = 324 Weght of floor = ( )( ) tos Total sesmc weght = 324 ( 7) = 2268 tos Buldg atural perod, T 3/ 4 T = 0.073( ) T= h ( 21) 3/ 4 = 0.716sec 1.25( 2) 2 / ( 0.716) 1.25S C = = = 3.12 sec > / 3 3 T N.O.K C 2.75 = = > R w 12 O.K The base shear V s gve by Z I C W V = R w = ( 1.0)( 2.75)( 2268) 12 = tos ( 0.716)( 38.98) 1.95 tos T > 0.7 sec, Ft = 0.07TV = 0.07 = < 0.5 V O.K Vertcal Dstrbuto of Force: F ( V F ) t = 7 = 1 w h F

23 116 Lateral force dstrbuto: level w h w h F V M