A S O N R Y Revied Spring 007 Engineering Note For Deign With Concrete Block aonry C H R O N I C L E S To rectify the ituation, the Spring 007 article i being reiued. We apologize for any inconvenience thi may have caued.......... Comparion of the Effect of Axial Load on Out-of-Plane Slender Wall: Allowable Stre Deign Preface Figure 1 - Wall Deflecting Out-of-Plane Pleae note that thi i a revied and updated verion of the Spring 007 article. Due to ome typographical error, the olution to ome of the example were found to be in error. Thee error and omiion include: 1. In Example 3, a roof load of 80 lb/ft wa ued to deign the wall intead of the correct load of 3,000 lb/ft.. The moment on the wall due to the eccentricity of the roof load wa multiplied by an incorrect load factor (1/1.4 intead of.9). 3. In Example 1 and 3, which were baed on the IBC, the code-required check that the axial load component i le than the allowable axial load wa omitted. Note that the aonry Chronicle only highlight ome key iue in the deign of wall to reit out-of-plane load, and doe not repreent a comprehenive decription of all the tep required to deign concrete maonry wall. For brevity, only one load condition i conidered, and wall detailing requirement and in-plane deign procedure are not decribed here (pleae ee other iue of aonry Chronicle for more information at www.cmacn.org). Introduction The deign of maonry wall to reit out-ofplane load i an important apect in the deign of maonry building. In mot large building that ue maonry wall a the lateral load reiting ytem, out-of-plane repone i the critical phae of the deign. Typical layout of common maonry warehoue-type building do not contain an abundance of opening. A a reult, thee type of building can uually reit lateral demand impoed by wind or earthquake load. However, the large tory height inherent in thee tructure may reult in coniderable out-of-plane demand. Figure 1 illutrate how a wall would repond to out-of-plane loading. When thi type of loading occur, the wall are no longer part of the lateral load reiting ytem in the direction of the lateral load being conidered. Intead, they act a tructural element or component in the tructure that upport the load directly impoed on them. The wall deflecting out-of-plane mut pan between upport and tranfer lateral load to the floor or roof diaphragm, which in turn tranfer the load to the wall that form the lateral load reiting ytem. Evaluation of the wall i complicated by the fact that the wall are lender relative to their height. Therefore, deflection induced by lateral Concrete aonry Aociation of California and Nevada
load may, in certain cae, be comparable to the width of the wall. A a reult, econdary deformation effect (P-Δ effect) will need to be conidered in order to accurately determine the wall demand. In allowable tre deign, P-Δ effect are not conidered. A future iue of aonry Chronicle will deal with the deign of lender wall uing trength deign. With thi deign methodology, the effect of diplacement on wall demand i conidered. Example of out-of-plane wall deign will be provided to illutrate the difference between the calculation method permitted in the 1997 Uniform Building Code (UBC) [1] and the 006 International Building Code (IBC) []. For maonry deign, the IBC reference the ACI 530-05/ASCE 5-05/TS40-05 [3], which i alo referred to a the 005 aonry Standard Joint Committee Building Code (SJC). The ame example problem will be worked in two eparate way to demontrate the effect of axial load, the ue of the new code and it implication. Only outof-plane iue will be dealt with in thi iue. In-plane conideration were addreed in the winter 007 iue of aonry Chronicle. Determination of Deign Load Out-of-plane load on maonry wall in building are uually induced by inertial earthquake force or wind preure. In baement wall, out-of-plane load are alo caued by lateral oil preure, but thi will not be pecifically addreed here. Alo, the deign of freetanding fence wall will not be addreed. It hould be noted that while the load on retaining wall and fence wall are calculated in a lightly different matter, their deign follow the principle decribed herein. For additional information regarding out-of-plane deign load, pleae refer to the winter 003-004 iue of aonry Chronicle, which can be found on the Concrete aonry Aociation of California and Nevada (CACN) webite (www.cacn.org). The 1997 UBC and the 006 IBC differ in the way out-ofplane load are calculated. For load calculation pleae reference ection 163 of the 1997 UBC, or the 006 IBC equivalent in ection 1613. Table 1 how the different force determined according to the 1997 UBC and 006 IBC requirement at four different city hall location in California and Nevada. 1997 UBC Out-Of-Plane Load Lo Angele San Francico Sacramento La Vega 35 pf 35 pf 6 pf 19 pf Load hown in Table 1 are imilar for Lo Angele, San Francico, and La Vega, but differ for Sacramento. A dicuion regarding the difference in the way the repective code were developed i beyond the cope of thi article. However, it i obviou that the implication of thee load on deign outcome may be ignificant. For each example problem dicued here, an out-of-plane load of 35 pf will be ued. Out-Of-Plane Analyi of aonry Wall It i a common aumption that maonry wall are retrained by pin upport at the floor and roof level. Thi i a reaonable deign approach, ince the wall to floor connection doe not uually poe ufficient tiffne or trength to tranfer wall moment into the floor. Therefore, a rigid connection cannot be jutified. In addition, ince earthquake and wind repone are dynamic phenomena, the aumption of pinned upport i conitent with the modal repone of the wall ubjected to earthquake and wind load. aonry wall are typically analyzed differently for out-of-plane load, depending on whether working tre or trength deign procedure are ued. Thi article will attempt to invetigate the difference and conequence of allowable tre deign conducted uing the 1997 UBC and the 006 IBC under varying level of axial loading. The 1997 UBC working tre proviion anction the ue of the unity equation (UBC 107..7) for the deign of maonry wall ubjected to axial and flexural load. However, thi technique ha come under crutiny, ince it i not completely accurate and can lead to flawed deign a dicued in the winter 007 iue of aonry Chronicle. In the 006 IBC, the ue of the unity equation for the deign of reinforced concrete element i no longer permitted. Intead, tree for each material are calculated independently. Doing o allow the deigner to take into account the beneficial effect of axial load which i neglected by the unity equation. Example will be provided to illutrate how axial load affect the final deign of lender maonry wall. The ame problem will be worked in eparate way to determine the effect of the code. 1997 UBC precription for allowable tre deign (unity equation), a well a the 006 IBC proviion for allowable tre deign, will be utilized. 006 IBC Out-Of-Plane Load Lo Angele San Francico Sacramento La Vega 35 pf 37 pf 17 pf 17 pf Table 1 Out-of-Plane Load for the 1997 UBC and 006 IBC
Nomenclature The nomenclature ued in thi paper i a follow: b Effective width d Ditance to rebar e Eccentricity of roof load E Steel modulu of elaticity E m aonry modulu of elaticity f b aximum calculated tre in maonry f aximum calculated tre in teel F b aximum allowable tre in maonry F aximum allowable tre in teel F ab aximum compreive tre from combined axial and flexural load h Effective height of wall jd Ditance between the centroid of flexural compreive force and the centroid of the tenile force kd Effective depth of compreion area Total moment at wall mid-height E oment due to out-of-plane load n Ratio of the modulu of elaticity of teel and maonry P D Axial load at mid-height of wall P uf Factored axial load r Radiu of gyration T Actual thickne of maonry ρ Reinforcement ratio Example 1: Deign of a Slender Concrete aonry Wall (Out-of- Plane) Under Low Axial Load Uing 006 IBC Allowable Stre Deign Determine the vertical teel to reit out-of-plane force for the wall with the dead load hown in Figure. The fully grouted wall (78 pf) i contructed with 8-inch medium-weight concrete maonry unit. A 3-foot parapet it on top of the wall, above the roof level. The pecified maonry compreive trength i 1500 pi and Grade 60 teel i ued. Out-of-plane-loading i 35 pf. An axial load of 80 lb/ft i offet 7.3 inche from the wall centerline. Ue the alternative load combination in the 006 IBC (A one-third increae in allowable tree i permitted). Solution: Figure aonry Wall Under Low Axial Load: Front and Side View For brevity, only one load combination (.9DE/1.4) will be ued. For a complete deign, all the combination contained in ection 1605.3. of the IBC hould be evaluated. The maximum out-ofplane bending moment (per unit foot width of wall) at mid-height i equal to: E D wh 35(0) 1, 750 lb ft/ft 8 8 Pe 7.3 (80) 4. 3 lb ft/ft (1). 9 D E 17 lb - ft/ft /1.4.9(4.3) (1750 /1.4) and the axial load (per unit foot width of wall) at midheight where the maximum bending moment occur i: P D 80 78(10) 78(3) 1094 lb/ft Uing the one-third increae in allowable tre deign a permitted by the IBC: 1 F a b f ' m 1.33 667 pi 3 F 4,000 1.33 3,000pi The applied compreive tre at mid-height i: 0.9(1094) f a 10.75 pi 1(7.63) The radiu of gyration i calculated uing the minimum wall thickne. Therefore: r t 7.63. in 1 1 Where the allowable tre due to axial load, F a, i calculated in accordance with SJC Section..3.1: 70(.) Fa.5(1500) 154. 4 pi 0(1) f F O.K. a a
If we try #4 bar at 16 inche on center: 9,000,000 n 1.5 1,500(900) A 0.(1 /16) ρ 0.0033 1(3.81) 0.071 P h d n F 0.9(1094) 1.54pi 1(3.81) 7.65.0 3.81 1.5 0.00067 3,000 Firt, we calculate the allowable moment baed on the maonry compreive tre. The neutral axi for thi cae i given below: k (.071.03) (.071) 0.34 P F P Fa a b b (.071.03) The allowable moment can be calculated from: F a b h k 4d 1.34 667.34 6 k h h 1 1 6 d k d 0 0 100.5 pi If the cro-ection i governed by the teel tenile tre: k F (.071.0145) 0.337 F (.071.0145) F (.071.0145) The allowable moment can be calculated from: P h k F 1 k d 3 n 3 0.9(1094).337 3,000.337 1.0705 1 1(3.81) 3 1.5 3 11.6pi Therefore, the allowable moment for the given axial load i governed by the allowable maonry tre and i equal to: 100.5pi 100.5(1)(3.81) 1459 lb ft/ft (1) The moment demand at mid-height i equal to: 17 lb ft/ft 17 lb ft/ft < 1459 lb ft/ft O.K. Therefore, #4 bar at 16 inche on center i an acceptable olution. Example : Deign of a Slender Concrete aonry Shear Wall (Out-of-Plane) Under Low Axial Load Uing 1997 UBC Unity Equation Determine the teel required to reit out-of-plane loading for the wall in Example 1. Solution: Note that the ue of the unity equation i not recommended by the SJC code for ue with reinforced maonry. However, it ue i illutrated here to compare the traditional allowable tre deign approach with the olution provided in the previou example. The out-of-plane load are the ame a thoe found in the firt example. Initially, we mut determine the allowable compreive tre due to axial load alone. h r 40 109.1 > 99. Therefore per UBC requirement (107..5): F a 70(.) 0.5(1500) 40 154 pi The applied compreive tre at mid-height of the firt tory i equal to (UBC 107.1.6.1): f a 0.9(1094) 10.75 pi 1(7.63) Uing the unity equation in the form contained in 1997 UBC with the one-third increae in allowable tree (UBC 107..7): fa fb 1.33 Fa Fb which mean that the allowable flexural compreive tre conidering the preence of axial load i given by: f b f a Fb 1.33 Fa 10.75 5001.33 630.1 pi 154 If we try #4 bar at 16 inche on center: A 0.( 1 /16) ρ 0.0038 1(3.81) 9,000,000 n 5.8 750(1,500) 0.0846 From 107..15 of the 1997 UBC: ( ) k (.0846) (.0846).0846 0. 335 k.335 j 1 1 0.89 3 3
Now, the compreive tre in the maonry, a well a the tenile tre in the longitudinal reinforcement due to flexural load alone, can be found: f b f 17(1) jk (1)(3.81) 588pi 630 pi O.K. A jd 17(1) (.15)(.89)(3.81).89(.335) 30,010 pi 3, 000 pi O.K. Both compreive and tenile tree are below allowable value. Thu, our initial aumption of one #4 bar at 16 inche on center ha been validated. Example 3: Deign of a Slender Concrete aonry Wall (Outof-Plane) Under High Axial Load Uing 006 IBC Allowable Stre Deign. Determine the vertical teel to reit out-of-plane force for the wall with the dead load a hown in Figure 3. Thi example i identical to the problem tatement in Example 1, except that the loading ha been increaed from 80 lb/ft to 3000 lb/ft. Solution: Figure 3 aonry Wall Under High Axial Load: Front and Side View The maximum out-of-plane bending moment (per unit foot width of wall) at mid-height i equal to (uing the.9d E/1.4 alternate load combination): E D wh 35(0' ) 1, 750 lb ft/ft 8 8 Pe 7.3 (3000) 91. 5 lb ft/ft (1). 9 D E 071 lb - ft/ft /1.4.9(91.5) (1750 /1.4) and the axial load at mid-height (per unit foot width of wall) where the maximum bending moment occur i: P D 3000 78(10) 78(3) 4,014 lb/ft Uing the one-third increae in allowable tre deign a permitted by the IBC: 1 F a b f ' m 1.33 667pi 3 F 4,000 1.33 3,000 pi The applied compreive tre at mid-height i: 0.9(4014) f a 39.5 pi 1(7.63) Where the allowable tre, F a, i calculated in accordance with SJC Section..3.1: 70(.) Fa.5(1500) 154. 4 pi 0(1) f F O.K. a a If we try #6 bar at 16 inche on center: 9,000,000 n 1.5 1,500(900) A 0.44(1 /16) ρ 0.007 1(3.81) 0.155 P h d n F 0.9(4014) 79.0 pi 1(3.81) 7.65.0 3.81 1.5.00067 pi 3,000 Firt, we calculate the allowable moment baed on the maonry compreive tre. The neutral axi for thi cae i given below: k (.155.118) (.155) 0.5 P F P Fa a b b (.155.118) The allowable moment can be calculated from: F a b h k 4d 1.5 667.5 0 0 6 143.4pi k h h 1 1 6 d k d If the cro-ection i governed by the teel tenile tre: k F (.155.053) 0.47 F (.155.053) F (.155.053) The allowable moment can be calculated from: P h k F 1 k d 3 n 3 0.9(4014).47 3,000.47 1.155 1 1(3.81) 3 1.5 3 61 pi
Therefore, the allowable moment for the given axial load i governed by the allowable maonry tre and i equal to: 143.4 pi 143.4(1)(3.81) (1) 08 lb ft/ft 071 lb - ft/ft O.K. Therefore, #6 bar at 16 inche on center i an acceptable olution. Example 4: Deign of a Slender Concrete aonry Wall (Out-of- Plane) Under High Axial Load Uing 1997 UBC Unity Equation. Determine the teel required to reit out-of-plane loading for the wall in Example 3. Solution: The out-of-plane load are the ame a thoe found in the previou example. Initially, we mut determine the allowable compreive tre due to axial load alone. Since the wall i upported laterally at the roof, the effective height for axial load i given by: h r 40 109.1 > 99. Therefore per UBC requirement (107..5): 70(.) F a 0.5(1500) 154 pi 40 The applied compreive tre at mid-height of the firt tory i equal to (UBC 107.1.6.1): 0.9(4014) f a 39.5 pi 1(7.63) Uing the unity equation in the form contained in 1997 UBC with the one-third increae in allowable tree (UBC 107..7): fa fb 1.33 Fa Fb which mean that the allowable flexural compreive tre conidering the preence of axial load i given by: f a f b Fb 1.33 Fa 39.5 5001.33 537 pi 154 Similar to Example, try #6 bar at 16 inche on center: 9,000,000 n 1.5 1,500(900) A 0.44(1 /16) ρ 0.007 1(3.81) 0.155 From 107..15 of the 1997 UBC: ( ) k (.155) (.155).155 0. 4 k.4 j 1 1 0.86 3 3 Now, the compreive tre in the maonry, a well a the tenile tre in the longitudinal reinforcement, can be found: 071(1) f b jk (1)(3.81) (.86)(.4) 789 pi 537 pi N.G. f A jd 071(1) (.33)(.86)(3.81),984 pi 3, 000 pi O.K. Compreive tre in the maonry exceed allowable value. Thu, our initial aumption of one #6 bar at 16 inche on center i inadequate. ore teel i required to reduce the tree in the maonry. Now we will try #9 bar at 8 inche on center: ρ A 0.85 ( 8) 1.0 1 / 0.033 1(3.81) 9,000,000 n 5.8 750(1,500) From 107..15 of the 1997 UBC: ( ) k (.85) (.85).85 0. 706 k.706 j 1 1 0.765 3 3 Now, the compreive tre in the maonry, a well a the tenile tre in the longitudinal reinforcement, can be found: 071(1) f b jk (1)(3.81).765(.706) 58 pi 537 pi O.K. f A jd 071(1) (1.5)(.765)(3.81) 5,684 pi 3, 000 pi O.K. Both compreive and tenile tree are below allowable value. Thu, our aumption of one #9 bar at 8 inche on center ha been validated. Obviouly, the ue of #9 bar at uch a cloe pacing i not practical in real world ituation, and i only preented here for illutration and comparion purpoe. In lieu of uing #9 bar at 8 inche on center, a thicker wall hould be ued. Thi would reduce the tree on the maonry, and allow for the ue of le reinforcing teel. With the current deign, the maonry tree govern the deign; the teel i not being fully utilized, and thi reult in an inefficient deign.
Figure 4 Amount of Vertical Steel Required to Reit Out-of-Plane Load in the 1997 UBC and 006 IBC Concluion From the four example problem it can be een that under different loading condition, varying amount of vertical reinforcing teel are required to meet the code requirement for out-of-plane loading. Note, that for brevity, not all tep required for the complete deign of the wall were included. Furthermore, thee wall were not deigned for in-plane loading condition. Depending on the magnitude of the in-plane lateral load impoed, that deign condition may govern. A a reult, additional teel may be required to atify requirement publihed in the 1997 UBC and the 006 IBC. Figure 4 how the olution obtained by all four example. The unity equation permitted by the 1997 UBC doe not take into account the beneficial effect of axial load on flexural capacity, but conider the axial and flexural load independently. Conequently, under high axial load, the unity equation provide more conervative reult. However, under low axial load, the unity equation provide the ame olution a the 006 IBC (ee Figure 4). The 006 IBC proviion reult in deign that require ignificantly le vertical reinforcement under high axial load. It i able to accomplih thi by more accurately repreenting the mechanic of reinforced concrete maonry under externally applied load. When deign i conducted uing the 1997 UBC unity equation, the amount of teel required i directly proportional to the axial load. A illutrated in Figure 4, more vertical reinforcement wa required when the axial load wa increaed. However, thi i due to the fact that a large eccentric moment wa generated by the offet at the top of the wall. If the load wa concentric, le teel may have been required when uing the IBC, ince concentric axial load contribute to the flexural reitance provided by the wall. Another conideration i that econdary moment effect are neglected in allowable tre deign. Thee effect can be ignificant, epecially under large axial load. The ummer 007 iue will explore thi topic in more depth, and how they are dealt with through trength deign methodologie. For more information regarding the deign of lender wall pleae ee the 006 edition of Deign of Reinforced aonry Structure. Thi publication i publihed by, and will oon be available through, the Concrete aonry Aociation of California and Nevada (CACN). Reference [1] International Conference of Building Official (ICBO), 1997 Uniform Building Code, International Conference of Building Official, Whittier, California, 1997. [] International Code Council (ICC), 006 International Building Code, International Code Council, Inc., Fall Church, Virginia, 006 [3] aonry Standard Joint Committee (SJC), Building Code Requirement for aonry Structure, aonry Standard Joint Committee, Boulder, Colorado, 005 Thi edition of aonry Chronicle wa written by Henry Huang and Chukwuma Ekwueme, PhD. of Weidlinger Aociate, Inc., arina Del Rey, California.
Concrete aonry Aociation of California and Nevada 6060 Sunrie Vita Drive, Suite 1990 Citru Height, CA 95610 (916) 7-1700 Info@cmacn.org www.cmacn.org Preort Standard U.S. Potage PAID Premit No. 604 Sacramento, CA CHANGE SERVICE REQUESTED Pleae go to www.cmacn.org for coure content and regitration information for the Concrete aonry Teting Procedure Certification Coure (LAB TECH) Sponored by Concrete aonry Aociation of California and Nevada National Concrete aonry Aociation Smith-Emery Laboratorie Teting Engineer - U.S. Laboratorie CACN ACTIVE EBERS Active ember are an individual, partnerhip, or corporation, which i actively engaged in the manufacture and ale of concrete maonry unit. Air Vol Block, Inc. Angelu Block Company, Inc. Baalite Concrete Product, LLC Blocklite Cind-R-Lite Block Company, Inc. Caltone Company, Inc. Deert Block Company, Inc. Oldcatle APG Wet, Inc. ORCO Block Company, Inc. RCP Block & Brick, Inc. Rinker aterial