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

Transcription

1 A S O N R Y Spring 010 Engineering Notes For Design With Conete Block asonry C H R O N I C L E S Openings in Conete asonry Walls (Part III): Ot-of-Plane Forces Introdction Figre 1 - Ot-of-Plane Loads Arond Openings Previos editions of asonry Chronicles discssed the design of conete asonry arond openings to resist in-plane gravity and lateral loads. This edition will discss the design of asonry arond openings to resist ot-of-plane lateral loads. As shown in Figre 1, there are basically two aspects of the design of asonry to resist otof-plane loads arond openings. The first aspect involves the design of the asonry above the opening (and below the opening for windows). The next step is the design of the jab reinforceent on either side of the opening. Theoretically, the direction of span of the asonry above an opening is deterined by the geoetry of the wall, with the priary span being in the shorter direction. However, for reinforced asonry, the engineer can control the behavior of the asonry and decide which direction the asonry spans. This is becase if sfficient reinforceent is not provided in one direction, the asonry will ack and resist load in the direction with adeqate strength. The engineer can therefore select which direction he or she wants the asonry above the opening to span, and then ensre that the asonry has sfficient strength in that direction. It is generally ore convenient for the asonry to span horizontally, becase all the reinforceent above the opening can then be sed to resist the ot-of-plane forces. The jab reinforceent on either side of the opening st also be designed to spport the reaction fro the asonry above and below the opening. A siplifying approach that is often sed when designing the jabs is to ignore any redction in ot-of-plane loading de to the opening. Then, the jab reinforcing is deterined sing additional load fro a tribtary width eqal to half the width of the opening. This approach is reasonably accrate for wind loading and typically conservative for earthqake loading, since the weight of the door or window in the opening is sally ch less that of the asonry assed in the calclations. A ore rigoros procedre, in which the actal load iposed on the jab by the asonry above the opening is calclated, ay be sed to redce the conservatis of the design. When sing strength design to deterine the jab reinforceent, the design st be based on an analysis that incldes the inflence of acking on eber stiffness, and the effect of deflections on oents and forces ( P- effects).the eqations inclded in TS-0 [1] for incorporating P- effects in the design of wall are valid for the walls with siple spports and niforly distribted otof-plane loads. They wold therefore be appropriate if the siplified approach desibed above is sed. However, when a ore rigoros approach is sed, a different approach is reqired to accont for P- effects when designing the jab reinforceent. This is becase the ot-of-plane loads on the jab are not niforly distribted over the jab height. Conete asonry Association of California and Nevada

2 One approach is to se eqations siilar to those for the oent agnifier procedre desibed in ACI 18 []. The axi oent calclated withot P-Δ effects,, is agnified to accont for P-Δ effects as follows: DL 6 plf LL 80 plf -6 Parapet c P e (1) 9-0 where P is the factored axial load, and P e is the itical bckling load, which is given by: 10-0 P e π EIeff () H 18-0 E is odls of elasticity of the conete asonry and H is the effective height of the wall. The effective oent of inertia, I eff, depends on whether the jab is acked or nacked: I I ; eff g c I I ; > eff c () where is the acking oent, I g is the gross oent of inertia and I is the acked oent of inertia, which is given by: I na ( d c) se + bc The design of conete asonry to resist ot of plane loads arond openings is best illstrated in the following exaple. Exaple Design the conete asonry to resist the ot-ofplane earthqake loads arond the opening shown in Figre. The wall is constrcted with 1-inch thick (noinal), flly-groted asonry with a selfweight of 1 psf and a specified copressive strength of 1500 psi. Type S ortar is sed and reinforcing steel is Grade 60. The spectral acceleration for short periods, S DS, is eqal to 1.6g. The reaction fro roof loads is located is located 9. inches fro the center of the wall. Figre - Exaple Ot of Plane Loads Arond Openings Siplified Soltion In accordance with Section of ASCE 7 [], the ot of-plane force on the wall is given by: Fp 0.SDSIW 0.(1.6)(1.0)(1) 7. psf Conservatively assing siple spports at the jabs, the oent in the asonry above the opening is eqal to: 7.(18).9 kip-ft /ft 8(1000) With two layers of reinforceent we can asse that the effective depth of the reinforceent in the ot-of-plane direction is eqal to 8.5 inches (the horizontal reinforceent is the inner layer). Then, the reqired area of steel can be estiated: A sreq.9(1) φf 0.9d 0.9(60)(8.5) y 0.08 in /ft Try two layers of #5 bars at inches (A s 0.15 in /ft). Noting that the copression steel is ignored, the noinal oent capacity is eqal to: fa y s n fyas d 1.6 f ' b 60(0.15) 1 (60)(0.15) (1.5)1 1

3 6.1 kip-ft /ft φ n 0.9(6.1) 5.5 kip-ft /ft...ok The oent capacity st be greater than 1. ties the acking oent. Fro Table of TS 0-08 (flly-groted wall with type S ortar, tensile stresses parallel to bed joints) the odls of rptre is eqal to 00 psi. Therefore: 1.(1)(11.6) Snfr kip-ft /ft < n...ok Note that the reinforceent above the opening st be checked to ensre that it can transfer the in-plane drag/collector forces between the walls on each side of the opening. Additional reinforcing steel st be placed above the opening for the lintel as desibed in the Winter edition of asonry Chronicles. Since the distribted roof loads are above the apex of the assed triangle arch, they do not contribte to the loads on the lintel. In addition, the weight of asonry otside the arch is assed to be distribted to the sides of the opening by arch action. Therefore, the weight of wall spported by the lintel is: 1 L W 1 L lbs And the axi oent and shear on the bea are given by: WL 100(18) 0.1 kip-ft 6 6(1000) W 100 V 5.0 kips (1000) And the factored loads are eqal to: 1.(0.1) 6.1 kip-ft V 1.(5.0) 6.0 kips Assing the depth of the lintel to the reinforceent is eqal to half the span (108 in, d~10 in) we can try -#7 bars (A s 1. in ). Then: fa y s φn φfyas d 1.6 f ' b 60(1.) 1 0.9(60)(1.) (1.5) kip-ft >...OK The oent strength of the oss-section st be copared with the acking oent. Cracking is deterined by the odls of rptre of the asonry, which is eqal to 00 psi. Then: S f n r (11.6)(108) kip-ft 1. 1.(77) 90 kip-in <...OK Fro Section...5 of the SJC code and coentary, the axi reinforceent ratio is eqal to: ρ ax f ' ε 0.6 f f y y ε Es (60) A s 1. ρ < ρ ax...ok bd 11.6(10) Check the axi shear strength: Vn,ax An f ' (11.6)(108) kips > V...OK n

4 The shear strength provided by the asonry is given by: φ V 0.8(.5) An. f ' 0.8(.5)( ) kips > V The shear strength provided by the asonry is sfficient to resist the deand and no shear reinforceent is reqired. When designing the jab reinforceent, the width of the jab that resists the load arond the opening st be selected. Using an approach siilar to the deterination of the effective flange width in shear walls, it is reasonable to asse that the effective jab width shold not exceed 6 ties the noinal wall thickness. Ths, an effective jab width of 8 inches can conservatively be sed and all the steel that resists the ot-of-plane forces arond the opening st be placed within this width. With the siplified soltion, the effect of the opening is ignored. Therefore, the ot-of-plane loading de to the tribtary width of the opening and the jab selfweight is given by: ( ) 91. lbs /ft And since the jab is assed to be 8 inches wide, the load per foot is eqal to: psi For brevity, only one load cobination will be considered (0.9D + E). For a coplete soltion, the procedre desibed here shold be repeated for all applicable load cobinations. The vertical coponent of earthqake load is given by 0.S DS. Therefore the factored axial load fro the roof dead load id-height, which is where axi oent occrs, is eqal to: P f [ (1.6) ](6) (8) lbs 16.9 lbs /ft The total factored axial load, inclding the selfweight of the wall is given by; f + w lbs 06 lbs /ft psi 0.05 f ' A g 1(11.6)...OK Fro Table of TS 0-08 flly-groted asonry wall with type S ortar and tensile stresses parallel to bed joints has a odls of rptre of 16 psi. Therefore, the acking oent is given by: P S fr + An 1(11.6) (11.6) 5,0 lbs-in/ft 70 lbs-ft /ft If we try 6-#7 bars (d 9. inches) in the 8-inch wide jab: 6(0.60) A s 0.9 in /ft The depth of the copression block, a, netral axis, c and effective area of steel A se are calclated as follows: + Asfy a 0.8 f ' b (60000).05 in 0.8(1500)1 a.05 c 5.06 in Asfy Ase f y (60000) in /ft Then the acked of oent of inertia, I, can be calclated:

5 Es 9,000,000 9,000,000 n 1.5 E 900(1500) 1,50,000 a t n ( Asfy + ) d d I na ( d c) se in /ft bc 1.5(0.97)( ) 1(5.06) While the gross oent of inertia is eqal to: bt 1(11.6) I g in /ft The wall deflection, inclding P-Δ effects, can be calclated with a closed-for eqation, assing that the wall is acked: wh Pe f I I g δ 8EI ( w + f ) 5H ( ) (9.) (1) 1 8(1) 157 8(150000)(875.7) in ( ) Ths the oent deand at the id-height of the wall is given by: wh Pe f + + ( P + P ) δ 8 f w 5.(9) lbs-ft /ft The oent deand is larger than the acking oent, so the assption of a acked wall is correct. The flexral strength with the reinforceent closer to one face of the wall is given by:.05 1 ( ) lbs-ft /ft φ n 0.9 n 08 lbs-ft /ft > OK Figre shows the jab reinforceent for the siplified design. Effective Jab Width -0 Jab Reinf 1-#7 Figre Jab Reinforceent for Siplified Design Alternative Soltion If we asse a 6-inch effective width of the jab, the ot-of-plane load fro the asonry above the opening is given by: lbs /ft And the ot-of-plane load de to the self-weight of the jab is eqal to: 7.() 17. lbs /ft Figre shows the loading and oent diagra on the jab, taking into accont the effect of the opening.

6 1. ft A se + A f f y s y (60000).65 in lbs/ft 17. lbs/ft 75.8 kip-ft By inspection the wall is acked and the acked oent of inertia, I, is eqal to: I na ( d c) se in /ft bc 1.5(.65)(9..6) 6(.6) Figre Loads and oents on Jab The itical bckling load is obtained fro Eqation (): For the load cobination 0.9D+E, The factored axial loads at that location of axi oent, which occrs 1. feet fro the roof level, are given by: P e π E I H eff P f [ (1.6) ](6) (768) 68.5 lbs π (150)(7) 61 kips (9 1) And the aplified oent is calclated fro Eqation (1): f + w ( ) lbs c kip-ft P 0.75(61) e If we try -#7 (A s. in ) in the jab, the depth of the netral axis, c, and effective area of steel A se are given by: + Asfy a 0.8 f ' b (60000).68 in 0.8(1500)6.68 c.6 in 0.8 a t n ( Asfy + ) d d.68 1 ( ) lbs-ft /ft φ n 0.9 n 8.9 kip-ft > c OK Figre 5 shows the jab reinforceent for the alternative design and Figre 6 shows an elevation of the wall with the reinforceent arond the opening.

7 Effective Jab Width -0 Jab Reinf 8-#7 Figre 5 Jab Reinforceent for Alternative Design CHORD REINF 8 - #7 JAB REINF HORIZ. E.F. 16 VERT. E.F. - # PARAPET 10-0 Figre 6 Wall Reinforceent Arond Opening Conclsions As expected, a design sing a ore rigoros design approach reslts in significantly lower reinforceent reqireents than an approxiate approach that ignores the redction in ot-of-plane earthqake loads de to the presence of openings in the wall. It shold be noted that the oent agnification procedre sed with the alternative design approach ay be applied to any load distribtion or bondary conditions on a eber. It is also generally reslts in a larger inease of oents de P-Δ effects than the code eqations that are only valid for niforly distribted loads on siply spported ebers. This edition of asonry Chronicles was written by Chkwa Ekwee, PhD., S.E. of Weidlinger Associates, Inc., arina Del Rey, California. 9-0 Noenclatre A s area of reinforcing steel A se effective area of reinforcing steel inclding the effect of axial load a b c d depth of eqivalent copression stress block width of oss-section distance fro fiber with axi copressive strain to the netral axis distance fro fiber of axi copressive strain to centroid of tension reinforceent E odls of elasticity of asonry in copression E odls of elasticity of steel H effective height of wall I acked oent of inertia I eff effective oent of inertia I g gross oent of inertia c factored oent deand agnified to accont for P-Δ effects factored oent deand n noinal oent strength n odlar ratio P e itical bckling load P factored axial load P f factored axial load fro floor or roof P w factored axial load fro wall self weight t φ thickness of wall strength redction factor References 1. asonry Standards Joint Coittee (SJC), Bilding Code Reqireents for asonry Strctres (TS 0-08/ACI 50-08/ASCE 5-08), The asonry Society, Bolder, Colorado, ACI Coittee 18, Bilding Code Reqireents for Strctral Conete (ACI 18-08) and Coentary, Aerican Conete Institte, Farington Hills, I, ASCE, ini Design Loads for Bildings and Other Strctres (ASCE/SEI 7-05), Inclding Sppleent 1, Aerican Society of Civil Engineers (ASCE), Reston Virginia, 006.

8 Conete asonry Association of California and Nevada 6060 Snrise Vista Drive, Site 1990 Citrs Heights, CA (916) Presort Standard U.S. Postage PAID Preit No. 60 Saaento, CA CHANGE SERVICE REQUESTED Conete asonry is Safe & Sond. Contact CACN with Reqests for Design Seinars at (916) or Available 011: 009 Design of Reinforced asonry Strctres, CD09 Copter Progra, Typical asonry Details CD incldes AtoCAD and PDF forats Conete asonry Association of California and Nevada (CACN) is pleased to introdce pdated prodcts for practicing engineers. Universities please call to inqire abot discont pricing on stdent text books. Orders can be placed on line at (all cards accepted) or by calling (916) (Visa and astercard only). CACN PRODUCER EBERS Prodcer ebers are an individal, partnership, or corporation, which is actively engaged in the anfactre and sale of conete asonry nits. Air Vol Block, Inc. Angels Block Copany, Inc. Basalite Conete Prodcts, LLC Blocklite (a sbsidiary of Basalite Conete Prodcts LLC) Calstone Copany, Inc. CEEX Cind-R-Lite Block Copany, Inc. Desert Block Copany, Inc. Oldcastle APG West, Inc. ORCO Block Copany, Inc. RCP Block & Brick, Inc. Tri Delta (a division of Oldcastle APG West, Inc.)