M A S O N R Y. Fall Engineering Notes For Design With Concrete Block Masonry

Transcription

1 M A S O N R Y Fall 007 Egieerig Notes For Desig With Cocrete Block Masor C H R O N I C L E S i shear walls will be provided to illustrate the differeces betwee the ethodologies foud i the 1997 Uifor Buildig Code (UBC) [1] ad the 006 Iteratioal Buildig Code (IBC) []. For asor desig, the IBC refereces the ACI /ASCE 5-05/TMS40-05 [3], which is also referred to as the 005 Masor Stadards Joit Coittee Buildig Code (MSJC) Shear Resistace of Cocrete Masor Walls For exaples ivolvig the shear resistace of cocrete asor shear walls we will revisit the exaples iitiall utilized i the Witer 007 issue of Masor Chroicles. Results fro this prior issue will aid i esurig the copliace of our desig with the goverig buildig codes. Past issues of Masor Chroicles are coveietl located o the Cocrete Masor Associatio of Califoria ad Nevada (CMACN) website ( Noeclature The oeclature used i this article is as follows: The Copariso of 006 IBC ad 1997 UBC Provisios for the Shear Resistace of Cocrete Masor Shear Walls Itroductio The desig of the shear resistace provided b shear walls reais a iportat aspect of shear wall desig. Sice shear failure usuall occurs suddel, without warig, deficiecies i the shear stregth of structural ebers should be avoided. To preclude the possibilit of a brittle shear failure, special attetio i the for of ductile detailig, provisios dictatig the aout ad spacig of shear reiforcig, alog with the use of various capacit reductio factors, are iposed b the goverig buildig codes. The Witer 007 issue of Masor Chroicles discussed the flexural ad axial desig of cocrete asor shear walls. This editio will discuss the desig of cocrete asor shear walls to resist i-plae shear loads. Exaples of calculatios illustratig the required aout of horizotal reiforceet A e, A Cross-sectioal area of asor cosidered A v Net area of asor i directio of shear force cosidered A s, A v Cross-sectioal area of shear steel reiforceet b Effective width C d Noial shear stregth coefficiet d Distace to rebar d v Actual depth of asor i directio cosidered f Flexural tesio f Specified copressive stregth of asor F s Allowable shear stress i reiforceet f v Coputed shear stress F v Allowable shear stress i asor f Yield stress of reiforceet h Effective height of wall j Ratio betwee cetroid of flexural copressive forces ad cetroid of tesile forces l Effective legth of wall M Maxiu oet o sectio M E Moet due to earthquake loadig Factored oet M u Cocrete Masor Associatio of Califoria ad Nevada

2 P D P L P Lr S t ductile E s u ρ Axial dead load Axial live load Axial roof live load Sectio Modulus Actual thickess of asor Maxiu shear o sectio Shear dead developed fro correspodig flexural stregth Shear due to earthquake loadig Noial shear stregth of asor + s Noial shear stregth of shear reiforceet Required shear stregth Ratio of distributed shear reiforceet o plae perpedicular to plae of A v. Exaple 1: Shear Resistace of Cocrete Masor Bearig Wall usig the 1997 UBC Allowable Stress Desig Procedures Deterie the horizotal reiforceet ad iiu vertical steel required at the first stor for the wall with the earthquake loads show i Figure 1. The full grouted wall is costructed with 8-ich ediu-weight cocrete asor uits (78 psf) ad is located i a buildig assiged to seisic zoe 4. The specified asor copressive stregth is 1500 psi ad grade 60 steel is used. Use the alterate load cobiatios of Sectio of the UBC (a oe-third icrease i allowable stresses are peritted). E kips M 5(34.5) + 30(4) + 18(13.5) 757 kip ft E Sice the applied shear ust be ultiplied b 1.5 (UBC Sectio ), the earthquake loads for use with allowable stress desig are as follows: 1.5 E 1.5(100) kips M E 757 M 1969 kip ft The gravit loads at the first floor are equal to: P P P D L Lr ( ) 78()(34.5) kips ( ) 44 kips 1000 (500) 11 kips 1000 Assuig the cover to the reiforcig steel is 4 iches: d 1 ( ) 4 60 i ft The average shear stress i the wall is coputed b Equatio 7-37 of the 1997 UBC. Fro the Witer 007 issue of Masor Chroicles, j is equal to 0.94: f v M d bjd 107.1(1000) 58.4psi (7.63)(0.94)(1.67x1) (1.67) 1.7 > 1.0 The allowable shear cosiderig the asor aloe is (UBC Sectio ): 1.33F v 1.33 f ' psi 1.33(35) 46.6 psi govers Sice the shear stress i the wall (58.4 psi) is greater tha that allowed (46.6 psi), shear reiforceet is required. Fro UBC Equatio 7-, the shear stress i the wall ust ot exceed: 1.33F v 1.33(1.5) f ' 77. psi govers < 1.33(75) 99.8 psi Figure 1 Multi-Stor Cocrete Masor Shear Wall Solutio: The i-plae earthquake loads fro the first floor are equal to: The shear dead (58.4 psi) is less tha 77. psi; a thicker wall does ot eed to be used. The horizotal reiforcig is ow desiged to resist all of the shear forces. Assuig #5 bars, the required spacig is obtaied fro UBC Equatio 7-38: Av Fs d s 0.31(3000)(60) 107.1(1000) 4.1 i

3 Therefore, we ca use #5 bars at 4 iches o ceter to fit withi the block odule. Fro the Witer 007 article of Masor Chroicles, the vertical reiforceet was #5 bars at 16 iches o ceter. Sice the buildig has bee assiged to seisic zoe 4, the wall ust copl with detailig provisios dictated i Sectio of the UBC. This eas that the reiforceet placeet ust satisf the followig requireets: A s i 0. i s < 48 i l (1) s < 13 i h 13.5(1) s < 81 i Sectio of the 1997 UBC also states that the iiu area i each directio eeds to be greater tha ties the cross-sectioal area of the wall ad the su of the areas ust exceed 0.00 ties the cross-sectioal area of the wall st hor 4(7.63) st ver 16(7.63) Cosequetl, the use of #5 bars at 4 iches o ceter for horizotal reiforcig, ad #5 bars at 16 iches o ceter for vertical reiforcig, satisfies the spacig requireets. Exaple : Shear Resistace of Cocrete Masor Bearig Wall usig the 006 IBC Allowable Stress Desig Procedures Deterie the horizotal reiforceet ad iiu vertical steel requireets for the 8-ich thick full grouted wall coposed of ediu-weight cocrete asor uits (78 psf) as show i Figure 1. The wall is located i a buildig assiged to seisic desig categor D. Masor copressive stregth is 1500 psi ad the steel is Grade 60. Solutio: The loads are idetical to those defied i exaple 1. Note that as required b the 006 IBC, the shear force is ultiplied b a factor of 1.5 (IBC ), which is idetical to the 1997 UBC requireet. The IBC, b referece to the MSJC, refers to the use of differet equatios for deteriig the allowable shear o a wall, depedig o whether or ot a wall is subjected to flexural tesio. Check flexural tesio occurs usig the load cobiatio with the sallest axial load (.9D+E/1.4): P M E f A S 0.9(35)(1000) (1969x1)(1000)6 7.63(x1) 7.63(x1) 16psi Flexural tesio exists i the wall. The average shear stress i the wall is equal to: f v M d bd 107.1(1000) 54 psi (7.63)(60) (1.67) 1.7 > 1.0 The allowable shear cosiderig the asor aloe is (MSJC Equatio -):.33F v 1.33 f ' psi 1.33(35) 46.6 psi govers 1 Sice the shear stress i the wall (54 psi) is greater tha that allowed (46.6 psi), shear reiforceet is required. Fro MSJC Equatio -5, the shear stress i the wall ust ot exceed: 1.33F v 1.33(1.5) f ' 77. psi govers < 1.33(75) 99.8 psi The shear dead (54 psi) is less tha 77. psi; a thicker wall does ot eed to be used. The horizotal reiforcig is ow desiged to bear all of the shear forces. Assuig #5 bars, the required spacig is obtaied fro MSJC Equatio -6: Av Fs d s 0.31(3000)(60) 107.1(1000) 4.1 i Therefore, we ca use #5 bars at 4 iches o ceter to fit withi the block odule. Fro the Witer 007 article of Masor Chroicles, the vertical reiforceet was #4 at 3 iches o ceter. Sice the buildig has bee assiged to seisic desig categor D, the wall ust copl with the special provisios dictated i Sectios ad of the MSJC. This eas that the reiforceet placeet ust satisf the followig detailig requireets which differ slightl fro those foud i the 1997 UBC:

4 A s i 0. i s < 48 i l (1) s < 88 i 3 3 h 13.5(1) s < 54 i 3 3 Siilar to the 1997 UBC, the iiu area i each directio eeds to be greater tha ties the cross-sectioal area of the wall ad the su of the areas ust exceed 0.00 ties the cross-sectioal area of the wall st hor 4( ) st ver 3( 7.63 ) Ulike the 1997 UBC, the IBC requires the iiu cross-sectioal area of the vertical reiforceet eeds to be at least oe-third of the required shear reiforcig (MSJC Sectio ): As 1 st ver 3 st hor Cosequetl, the use of #5 bars at 4 iches o ceter for horizotal reiforcig ad #4 bars at 3 iches o ceter for vertical reiforcig is satisfactor. Exaple 3: Shear Resistace of Cocrete Masor Bearig Wall usig the 1997 UBC Stregth Desig Procedures The loads ad geoetr reai the sae as show i exaple 1. Solutio: Fro exaple 1, the shear ad oet dead o the wall is 100 kips ad,757 kip-ft, respectivel. The calculatio of shear stregth of a wall usig the 1997 UBC provisios varies depedig o whether the wall is desiged to ield i flexure or if a brittle failure is expected to occur. Whe the shear stregth exceeds the shear that develops fro the correspodig flexural stregth, the wall is expected to ield i flexure, ad ol the shear steel ca be expected to resist the shear forces i the plastic hige zoe. Outside the plastic hige zoe, cotributios fro both the steel ad asor ca be calculated to resist the shear forces. Assuig that the wall will be desiged to ield ad respod i a ductile aer, the shear stregth that develops fro the correspodig oial flexural stregth (3,876 k-ft, as show i the Witer 007 Masor Chroicles article) is as follows: ductile 3876 ( 100) kips 757 Fro Table 1-J of the 1997 UBC, the axiu oial shear stregth is: ax 4Ae f ' 4(7.63)(x1) kips 1500 /1000 Sice the shear dead (140.6 kips) is less tha kips, a thicker wall does ot eed to be used. The plastic hige zoe is defied as the regio fro the base to a distace of L w above the base, where L w is the legth of the wall. However, the plastic hige zoe eed ot exceed half the stor height. I this regio, the wall s shear capacit relies solel o the shear reiforceet used. Note that per Sectio of the 1997 UBC, the φ factor chages fro 0.6 to 0.8 i this regio. Through the use of Equatio 8-38 i the 1997 UBC ad assuig #4 bars at 16 iches o ceter: s Where: ρ A v A s bd Therefore: φ φ ρ f 0.0 (16)(7.63) (60)(7.63)(.0016)(60) 15 kips 15 kips kips The spacig of bars i the first zoe caot exceed 3 ties the thickess of the wall or 4 iches. I the rest of the wall, the shear stregth is calculated b suig the steel ad asor cotributios. The oial shear stregth of the wall ca be foud through Equatios 8-36, 8-37, ad 8-38 i the 1997 UBC (Sectio ): + Where: s Cd Av f ' A ρ f v s The oial shear coefficiet (C d ) is foud i Table 1-K of the 1997 UBC to be equal to 1.. Now, the

5 stregth cotributed b the asor aloe is equal to: φ 1.(x1)(7.63) 0.6(93.6) 56. kips kips Sice the shear dead is greater tha the oial stregth provided b the asor aloe, horizotal shear reiforcig is required. A capacit reductio factor of 0.6 is used i accordace with UBC Sectio At a iiu, the horizotal reiforcig eeds to be desiged to accout for a of the shear force that exceeds the shear capacit of the cocrete asor. The required steel cotributio will be: u φ s req φ s req kips 0.6 s req ρ.001 A f (7.63)(60)(60) v If we use #4 bars at 16 iches o ceter, we have the followig: ρ A s bd 16(7.63) Fro the Witer 007 issue of Masor Chroicles, #4 bars at 16 iches o ceter is sufficiet to resist the iplae flexural deads. Sice the buildig has bee assiged to seisic zoe 4, the wall ust copl with the special provisios dictated i Sectio of the UBC. The spacig for the secod shear regio is used, sice that spacig govers the detailig requireets. This eas that the reiforceet placeet ust satisf the followig requireets: A s i 0. i s < 48 i l 8(1) s < 48 i h 13.5(1) s < 81 i The iiu area i each directio eeds to be greater tha ties the cross-sectioal area of the wall ad the su of the areas ust exceed 0.00 ties the cross-sectioal area of the wall st hor 16(7.63) st ver 16(7.63) Fiall, the iiu cross-sectioal area of the vertical reiforceet eeds to be at least oe-half of the required shear reiforcig, 16 O.C. (UBC Sectio ): st ver st hor.0008 Therefore, the use of #4 bars at 16 iches o ceter for horizotal reiforcig i the plastic hige regio, #4 bars at 3 iches o ceter i the secod shear regio, ad #4 bars at 16 iches o ceter for vertical reiforcig is perissible. Exaple 4: Shear Resistace of Cocrete Masor Bearig Walls usig the 006 IBC Stregth Desig The loads ad geoetr reai the sae as show i exaple. Solutio: Fro exaple, the shear ad oet dead o the wall is 100 kips ad,757 kip-ft, respectivel. Accordig to Sectio of the 005 MSJC, the desig shear stregth is required to be at least 1.5 ties the shear developed b the flexural stregth. This is liited b a upper boud of.5 ties the required shear stregth. The oial flexural stregth of this wall was foud to be 3,071 k-ft i the Witer 007 article of Masor Chroicles. As a result, the shear dead of a ductile wall will be the lesser of: ductile.5 E 3071 (1.5) 139 kips govers kips Fro Sectio of the MSJC the axiu oial shear stregth of the wall is ot to exceed: 4A f ' 4(7.63)(60) kips Sice shear dead (139 kips) is less tha 307 kips, a thicker wall does ot eed to be used. The plastic hige zoe defied b Sectio of the 006 IBC is idetical to provisios foud i the 1997 UBC. I this zoe, the shear stregth is defied as (IBC Equatio 1-1): s A ρ f I the first shear regio, the wall s shear capacit relies solel o the shear reiforceet used: ρ φa f (7.63)(60)(60).0015

6 If we use oe #4 bar at 16 iches o ceter we have the followig: ρ A s bd 7.63(16) The shear stregth of the rest of the wall ca be deteried b suig the idividual shear resistace of the steel ad asor copoets. The oial shear stregth of the wall ca be foud through MSJC Equatios 3-18, 3-1, ad 3-: + s M u A ud v f ' +.5Pu A s 0. 5 s v f d v M where the ter u eed ot be > 1 udv As a result, the shear stregth of the asor aloe ca be show to be: [ (1) ] (60)(7.63) 3 kips φ 0.8(3) 185. kips (35) Sice the shear dead is less tha the stregth provided b the asor aloe, horizotal shear reiforcig is ot required. Nevertheless, ureiforced asor is ot peritted i high seisic regios. As a result, shear reiforcig will be placed i accordace with the detailig requireets foud i Sectios ad of the MSJC. Fro the witer 007 issue of Masor Chroicles, #4 bars at 3 iches o ceter is sufficiet to resist the iplae load deads. With this iforatio, the iiu reiforceet requireets (MSJC Sectios ad ) ca be checked as follows: A s i. i s < 48 i l 8(1) s < 3 i 3 3 h 13.5(1) s < 54 i 3 3 The iiu area i each directio eeds to be greater tha ties the cross-sectioal area of the wall ad the su of the areas ust exceed 0.00 ties the cross-sectioal area of the wall st hor 16(7.63) st ver 3(7.63) Note that if ore vertical steel was required, the use of less steel reiforceet i the secod shear regio would have bee possible. Fiall, the iiu cross-sectioal area of the vertical reiforceet eeds to be at least oe-third of the required shear reiforcig (MSJC Sectio ): st ver st hor.0005 Now, the use of #4 bars at 3 iches for vertical reiforcig, #4 bars at 16 iches o ceter for horizotal reiforcig i the plastic hige regio, ad #4 bars at 16 iches i the secod shear regio is acceptable. Coclusios Provisios for the allowable stress desig of walls to resist i-plae shear forces are siilar i the 1997 UBC ad the 006 IBC. Lookig at the results of exaples 1 ad (also show i Table 1), we see that idetical results are achieved with both buildig codes. Buildig Code ad Desig Methodolog Shear Steel Reiforceet 97 UBC - ASD 4 O.C. 06 IBC - ASD 4 O.C. 97 UBC - Stregth 16 O.C. 06 IBC - Stregth 16 O.C. Table 1 Horizotal Steel Reiforceet Requireets Shear desig, i accordace with stregth desig ethodologies of the 1997 UBC ad 006 IBC, also ielded siilar results (See Table 1). Although requireets regardig the use of the two shear regios are idetical, there were variatios i the desig forces as well as the wa i which the steel cotributio is accouted for. Note that the i-plae flexural desig of the UBC wall, #4 bars at 16 iches were required, whereas the use of #4 bars at 3 iches o ceter were sufficiet for IBC stregth desig. Shear capacit fro the stregth of the asor aloe was sigificatl higher i the IBC, which a result i less steel reiforcig awa fro the plastic hige zoe.

7 Provided that the flexural desigs for the UBC ad IBC were siilar, it is likel that the IBC case would have less shear reiforcig i the d regio. It is curretl show to be #4 at 16 iches o ceter i order to satisf detailig requireets. I allowable stress, as well as stregth desig, the spacig requireets are slightl differet i the IBC. I the UBC, the aout of vertical reiforcig used eeds to be at least half the area of the horizotal reiforcig. However, the IBC stipulates that the aout of vertical reiforcig shall be at least oe third the area of the horizotal reiforcig. Additioall, tighter spacig of rebars is required b the IBC. Accordig to the coetar of the 005 MSJC, these requireets are iposed i order to iprove ductile behavior uder earthquake loadig. For ore iforatio ad detail regardig the coprehesive desig of sleder walls please see the 006 editio of Desig of Reiforced Masor Structures. This publicatio is published b ad ade available through the Cocrete Masor Associatio of Califoria ad Nevada (CMACN). Refereces [1] Iteratioal Coferece of Buildig Officials (ICBO), 1997 Uifor Buildig Code, Iteratioal Coferece of Buildig Officials, Whittier, Califoria, [] Iteratioal Code Coucil (ICC), 006 Iteratioal Buildig Code, Iteratioal Code Coucil, Ic., Falls Church, irgiia, 006 [3] Masor Stadards Joit Coittee (MSJC), Buildig Code Requireets for Masor Structures, Masor Stadards Joit Coittee, Boulder, Colorado, 005 This editio of Masor Chroicles was writte b. Her Huag, P.E. ad Chukwua Ekwuee, PhD, S.E. of Weidliger Associates, Ic., Maria Del Re, Califoria. Itroducig the CMD06 Coputer Progra Cocrete Masor Associatio of Califoria ad Nevada (CMACN), ad its ebers are pleased to itroduce the availabilit of CMD06; a coputer aided desig package for the desig of Reiforced Cocrete ad Cla Masor Eleets. CMD06 is a follow up to the ver popular CMD97. CMD06 is writte b practicig egieers for practicig egieers. CMD06 is a set of odules for the structural desig of reiforced cocrete ad cla asor eleets. Reiforced cocrete ad cla asor eleets ca be desiged utilizig the Stregth Desig Method foud i seve differet buildig codes, icludig: 1997 Uifor Buildig Code (UBC), 001 Califoria Buildig Code (CBC), 00 ACI 530/ASCE 5/TMS 40 (MSJC) Buildig Code Requireets for Masor Structures, reported b The Masor Stadards Joit Coittee (MSJC), 003 Iteratioal Buildig Code (IBC), 005 MSJC, 006 IBC, 007 CBC. Or, the Workig Stress Desig Method foud i eight differet buildig codes, icludig: 1997 Uifor Buildig Code (UBC), 1999 ACI 530/ASCE 5/TMS 40 (MSJC) Buildig Code Requireets for Masor Structures, reported b The Masor Stadards Joit Coittee (MSJC), 001 Califoria Buildig Code (CBC), 00 MSJC, 003 Iteratioal Buildig Code (IBC), 005 MSJC, 006 IBC, 007 CBC. There are six odules based o the Stregth Desig provisios for asor, ad four odules based o the Workig Stress Desig provisios for asor. The odules operate usig a siple eu structure, which allows for the ease of eterig data ad reviewig ad pritig the output. The progras also cotai various 'flags' which war the user whe certai code provisios are ot beig satisfied. The output cotais data required to substatiate the desig of a reiforced cocrete or cla asor eleet i a forat that is suitable for subittal to a buildig departet or other authorit. CMD06 ca be purchased fro CMACN fro the web at: or b callig: We ca also be cotacted at: ifo@cac.org. Please see specific details below. Cost: $60.00 plus sales tax ad shippig for curret CMD97 licese holders through Jauar 31, 008. Please call CMACN at (916) for licese verificatio ad orderig. New purchasers a order olie, b phoe, or b U. S. ail. The cost: $90.00 plus sales tax ad shippig for ew purchasers i Califoria or Nevada; $ plus shippig for ew purchasers outside of Califoria or Nevada. isa ad MasterCard accepted.

8 Cocrete Masor Associatio of Califoria ad Nevada 6060 Surise ista Drive, Suite 1990 Citrus Heights, CA (916) Presort Stadard U.S. Postage PAID Preit No. 604 Sacraeto, CA CHANGE SERICE REQUESTED Itroducig CMD06 Coputer Progra Cocrete Masor Associatio of Califoria ad Nevada (CMACN) is pleased to itroduce the availabilit of CMD06; a coputer aided desig package for the desig of Reiforced Cocrete ad Cla Masor Eleets. CMD06 is a follow-up to the ver popular CMD97. CMD06 is writte b practicig egieers for practicig egieers. Orders ca be placed o lie at or b callig (916) isa ad MasterCard accepted. CMACN ACTIE MEMBERS Active Mebers are a idividual, partership, or corporatio, which is activel egaged i the aufacture ad sale of cocrete asor uits. Air ol Block, Ic. Agelus Block Copa, Ic. Basalite Cocrete Products, LLC Blocklite Cid-R-Lite Block Copa, Ic. Calstoe Copa, Ic. Desert Block Copa, Ic. Oldcastle APG West, Ic. ORCO Block Copa, Ic. RCP Block & Brick, Ic. Riker Materials