NCMA TEK. TEK 14-20A Structural (2002) POST-TENSIONED CONCRETE MASONRY WALL DESIGN

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1 NCMA TEK Natioal Cocrete Masory Associatio a iormatio series rom the atioal authority o cocrete masory techology POT-TENIONED CONCRETE MAONRY WALL DEIGN TEK 14-0A tructural (00) Keywords: allowale stress desig, desig examples, lexural stregth, post-tesioed masory, prestressed masory, reiorcig tedos, stregth desig INTRODUCTION The 1999 Buildig Code Requiremets or Masory tructures, ACI 530/ACE 5/TM 40 (re. 1), was the irst masory code i the Uited tates to iclude geeral desig provisios or prestressed masory. Prestressig masory is a process wherey iteral compressive stresses are itroduced to couteract tesile stresses resultig rom applied loads. Compressive stresses are developed withi the masory y tesioig a steel tedo, which is achored to the Iteral stresses Top achorage Top achorage lock or od eam Cocrete masory uits (sigle wythe show) Coupler Prestressig tedos (oded or uoded; restred or urestred) Footig achorage Footig Figure 1 chematic o Typical Post-Tesioed Wall top ad ottom o the masory elemet (see Figure 1). Posttesioig is the primary method o prestressig, where the tedos are stressed ater the masory has ee placed. This TEK ocuses o the desig o cocrete masory walls costructed with vertical post-tesioed tedos. Advatages Prestressig has the potetial to icrease the lexural stregth, shear stregth ad stiess o a masory elemet. I additio to icreasig the stregth o a elemet, prestressig orces ca also close or miimize the ormatio o some cracks. Further, while research (res. 14, 15) idicates that ductility ad eergy dissipatio capacity are ehaced with prestressig, Buildig Code Requiremets or Masory tructures (re. 1) coservatively does ot take such perormace ito accout. Post-tesioed masory ca e a ecoomical alterative to covetioally reiorced masory. Oe major advatage o prestressig is that it allows a wall to e reiorced without the eed or grout. Also, the umer o prestressig tedos may e less tha the umer o reiorcig ars required or the same lexural stregth. Post-tesioig masory is primarily applicale to walls, although it ca also e used or eams, piers, ad colums. Vertical post-tesioig is most eective or icreasig the structural capacity o elemets sujected to relatively low axial loads. tructural applicatios iclude loadearig, oloadearig ad shear walls o tall warehouses ad gymasiums, ad commercial uildigs, as well as retig walls ad soud arrier walls. Post-tesioig is also a optio or stregtheig existig walls. MATERIAL Post-tesioed wall costructio uses stadard materials: uits, mortar, grout, ad perhaps steel reiorcemet. I additio, post-tesioig requires tedos, which are steel wires, ars or strads with a higher tesile stregth tha covetioal reiorcemet. Mauacturers o prestressig tedos must supply stress relaxatio characteristics or their material i it is to e used as a prestressig tedo. peciicatios or those materials used speciically or posttesioig are give i Tale 1. Other material speciicatios are covered i reereces 9 through 1. Costructio is TEK 14-0A 00 Natioal Cocrete Masory Associatio (replaces TEK 14-0)

2 Tale 1 Post-Tesioed Material peciicatios Prestressig Tedos ATM A 416 teel trad, Ucoated eve-wire ATM A 41 Ucoated teel Wire ATM A 7 Ucoated High-tregth teel Bar Accessories ATM F 959 covered i Costructio o Post-Tesioed Cocrete Masory Walls, TEK 3-14 (re. 3). CORROION PROTECTION As with covetioally reiorced masory structures, Buildig Code Requiremets or Masory tructures (re. 1) madates that prestressig tedos or post-tesioed masory structures e protected agst corrosio. As a miimum, the prestressig tedos, achors, couplers ad ed ittigs i exterior walls exposed to earth or weather must e protected. All other walls exposed to a mea relative humidity exceedig 75% must also employ some method o corrosio aatemet. Uoded tedos ca e protected with galvzig, epoxy coatig, sheathig or other alterative method that provides a equivalet level o protectio. Boded tedos are protected rom corrosio y the corrugated duct ad prestressig grout i which they are ecased. DEIGN LOAD As or other masory structures, miimum required desig loads are icluded i Miimum Desig Loads or Buildigs ad Other tructures, ACE 7 (re. 5), or the goverig uildig codes. I prestressig orces are iteded to resist lateral loads rom earthquake, a actor o 0.9 should e applied to the stregth level prestress orces (0.6 or allowale stress desig) as is doe with gravity loads. TRUCTURAL DEIGN Washer-Type Direct Tesio Idicators The desig o post-tesioed masory is ased o allowale stress desig procedures, except or laterally restred tedos which use a stregth desig philosophy. Buildig Code Requiremets or Masory tructures (re. 1) prescries allowale stresses or ureiorced masory i compressio, tesio ad shear, which must e checked agst the stresses resultig rom applied loads. The lexural stregth o post-tesioed walls is govered y either the lexural tesile stress o the masory (the lexural stress mius the post-tesioig ad dead load stress), the masory compressive stress, the tesile stress withi the tedo, the shear capacity o the masory or the ucklig capacity o the wall. Masory stresses must e checked at the time o peak loadig (idepedetly accoutig or oth short-term ad log-term losses), at the traser o post-tesioig orces, ad durig the jackig operatio whe earig stresses may e exceeded. Immediately ater traser o the post-tesioig orces, the stresses i the steel are the largest ecause logterm losses have ot occurred. Further, ecause the masory has had little time to cure, the stresses i the masory will e closer to their capacity. Oce log-term losses have traspired, the stresses i oth the masory ad the steel are reduced. The result is a coicidetal reductio i the eective capacity due to the prestressig orce ad a icrease i the stresses the ully cured masory ca resist rom exteral loads. Eective Prestress Over time, the level o prestressig orce decreases due to creep ad shrikage o the masory, relaxatio o the prestressig tedos ad potetial decreases i the amiet temperature. These prestressig losses are i additio to seatig ad elastic shorteig losses witessed durig the prestressig operatio. I additio, the prestressig orce o oded tedos will decrease alog the legth o the tedo due to rictioal losses. ice the eective prestressig orce varies over time, the cotrollig stresses should e checked at several stages ad loadig coditios over the lie o the structure. The total prestress loss i cocrete masory ca e assumed to e approximately 35%. At the time o traser o the prestressig orce, typical losses iclude: 1% seatig loss + 1% elastic shorteig %. Additioal losses at service loads ad momet stregth iclude: relaxatio 3% temperature 10% creep 8% CMU shrikage 7% cotigecy 5% total 33% Prestress losses eed to e estimated accurately or a sae ad ecoomical structural desig. Uderestimatig losses will result i havig less avlale stregth tha assumed. Overestimatig losses may result i overstressig the wall i compressio. Eective Width I theory, a post-tesioig orce uctios similarly to a cocetrated load applied to the top o a wall. Cocetrated loads are distriuted over a eective width as discussed i the commetary o Buildig Code Requiremets or Masory tructures (re. 1). A geeral rule-o-thum is to use six times the wall thickess as the eective width. Elastic shorteig durig post-tesioig ca reduce the stress i adjacet tedos that have already ee stressed. pacig the tedos urther apart tha the eective width theoretically does ot reduce the compressive stress i the eective width due to the post-tesioig o susequet tedos. The applied loads must also e cosolidated ito the eective width so the masory stresses ca e determied. These stresses must e checked i the desig stage to avoid overstressig the masory. Flexure Tesile ad compressive stresses resultig rom edig momets applied to a sectio are determied i accor-

3 dace with covetioal elastic eam theory. This results i a triagular stress distriutio or the masory i oth tesio ad compressio. Maximum edig stress at the extreme iers are determied y dividig the applied momet y the sectio modulus ased o the miimum et sectio. Net Flexural Tesile tress uiciet post-tesioig orce eeds to e provided so the et lexural tesile stress is less tha the allowale values. Flexural crackig should ot occur i post-tesioig orces are kept withi acceptale ouds. Flexural crackig due to susted post-tesioig orces is elieved to e more severe tha crackig due to trasiet loadig. Flexural cracks due to eccetric post-tesioig orces will rem ope throughout the lie o the wall, ad may create prolems related to water peetratio, reeze-thaw or corrosio. For this reaso, Buildig Code Requiremets or Masory tructures (re. 1) requires that the et lexural tesile stress e limited to zero at traser o the post-tesioig orce ad or service loadigs with gravity loads oly. Axial Compressio Compressive stresses are determied y dividig the sum o the post-tesioig ad gravity orces y the et area o the sectio. They must e less tha the code prescried (re. 1) allowale values o axial compressive stress. Walls must also e checked or ucklig due to gravity loads ad post-tesioig orces rom urestred tedos. Laterally restred tedos ca ot cause ucklig; thereore oly gravity compressive orces eed to e checked or ucklig i walls usig laterally restred tedos. Restrig the tedos also esures that the tedos do ot move laterally i the wall whe the masory delects. The maximum compressive orce that ca e applied to the wall ased upo ucklig is 1 /4 P e, per equatio -11 o Buildig Code Requiremets or Masory tructures (re. 1). Comied Axial ad Flexural Compressive tress Axial compressive stresses due to post-tesioig ad gravity orces comie with lexural compressive stresses at the extreme ier to result i maximum compressive stress. Coversely, the axial compressive stresses comie with the lexural tesile stresses to reduce the asolute extreme ier stresses. To esure the comiatio o these stresses does ot exceed code prescried allowale stresses, a uity equatio is checked to veriy compliace. Employig this uity equatio, the sum o the ratios o applied-to-allowale axial ad lexural stresses must e less tha oe. Uless stadards (re. 5) limit its use, a additioal oe-third icrease i allowale stresses is permitted or wid ad earthquake loadigs, as is customary with ureiorced ad reiorced masory. Further, or the stress coditio immediately ater traser o the post-tesioig orce, a 0% icrease i allowale axial ad edig stresses is permitted y Buildig Code Requiremets or Masory tructures (re. 1). hear As with all stresses, shear stresses are resisted y the et area o masory, ad the wall is sized such that the maximum shear stress is less tha the allowale stress. I additio, the compressive stress due to post-tesioig ca e relied o to icrease allowale shear stresses i some circumstaces. Post-Tesioig Tedos The stress i the tedos is limited (re. 1) such that: (a) the stress due to the jackig orce does ot exceed 0.94 py, 0.80 pu, or that recommeded y the mauacturer o the tedos or achorages, () the stress immediately ater traser does ot exceed 0.8 py or 0.74 pu, ad (c) the stress i the tedos at achorages ad couplers does ot exceed 0.78 py or 0.70 pu. DETERMINATION OF POT-TENIONING FORCE Case (a) ater prestress losses ad at peak loadig: Assumig that the momet, M, due to wid or earthquake loadigs is large relative to the eccetric load momet, the critical locatio will e at the mid-height o the wall or simply-supported walls, ad the ollowig equatios apply (racketed umers are the applicale Buildig Code Requiremets or Masory tructures (re. 1) equatio or sectio umers): a [-10] F F where: a d l p a A ad P The 1.33 actor i Equatio [-10] represets the oethird icrease i allowale stress permitted or wid ad earthquake loadigs. I the momet, M, is a result o soil pressures (as is the case or retig walls), the 1.33 actor i Equatio [-10] must e replaced y [-11] P d l p < 1 /4 P e Note that i the tedos are laterally restred, P p should ot e icluded i Equatio [-11]. - a < t [ ] - a < 0 (uder the load comiatio o prestressig orce ad dead load oly) Additioal stregth desig requiremets or laterally restred tedos: [4-3] < φm φ [P p + y du lu ] (d - a/) Equatio 4-3 aove applies to memers with uiorm width, cocetric reiorcemet ad prestressig tedos ad cocetric axial load. The omial momet stregth or other coditios should e determied ased o static momet equilirium equatios. [4-1] P a p + A y s 0.85 ' m ed M + du lu Pe P e l l p + + p

4 a < t [ ] a/d < 0.45 [ ] φ 0.80 Case () at traser o post-tesioig: Assumig that vertical live loads are ot preset durig posttesioig, the ollowig equatios apply. The worst case is at the top o the wall where post-tesioig orces are applied. i [-10] + 1. F F where: A ad: i - < 0 pi i i e d pi e p + M For catilevered walls, these equatios must e modiied to the ase o the wall. I the eccetricity o the live load, P l, is small, eglectig the live load i Equatio [-10] may also gover. Case (c) earig stresses at jackig: Bearig stresses at the prestressig achorage should e checked at the time o jackig. The maximum allowale earig stress at jackig is 0.50' mi per Buildig Code Requiremets or Masory tructures (re. 1) sectio DEIGN EXAMPLE Desig a simply-supported exterior wall 1 t (3.7 m) high or a wid load o 15 ps (0.7 kpa). The wall is costructed o cocrete masory uits complyig with ATM C 90 (re. 6). The uits are ld i a ull ed o Type Portlad cemet lime mortar complyig with ATM C 70 (re. 7). The speciied compressive stregth o the masory (' m ) is 1,500 psi (10.3 MPa). The wall will e post-tesioed with 7 /16 i. (11 mm) diameter laterally restred tedos whe the wall achieves a compressive stregth o 1,50 psi (8.6 MPa). Axial load ad prestress are cocetric. Give: 8 i. (03 mm) CMU t 1.5 i. (3 mm) ' m 1,500 psi (10.3 MPa) ' mi 1,50 psi (8.6 MPa) F t 5 psi (0.17 MPa) (Type Portlad cemet/lime mortar) py 100 ksi (690 MPa) (ars) pu 1 ksi (840 MPa) 0.14 i (9 mm ) E s 9 x 10 6 psi (00 GPa) E m 900 m 1.35 x 10 6 psi (9,300 MPa) E s /E m 1.5 d 7.65/ i i. (97 mm) (tedos placed i the ceter o the wall) uit weight o CMU wall 39 ps (190 kg/m ) (re. 13) Loads: M wh /8 (15)(1) /8 70 t-l (366 N-m) P d at mid-height (39)(1)/ 34 l/oot o wall (3,410 N/m) (P l 0) Maximum tedo stresses: Determie goverig stresses ased o code limits (re. 1): At jackig: 0.94 py 94.0 ksi (648 MPa) 0.80 pu 97.6 ksi (673 MPa) At traser: 0.8 py 8.0 ksi (565 MPa) 0.74 pu 90.3 ksi (63 MPa) At service loads: 0.78 py 78.0 ksi (538 MPa) govers 0.70 pu 85.4 ksi (589 MPa) Because the tedo's speciied tesile stregth is less tha 150 ksi (1,034 MPa), ps se (per re. 1 sectio ). Prestress losses: Assume 35% total loss (as descried i the Eective Prestress sectio aove). Tedo orces: Determie the maximum tedo orce, ased o the goverig tedo stress determied aove or each case o jackig, traser ad service. At traser, iclude % prestress losses. At service, iclude the ull 35% losses. Tedo capacity at jackig 0.94 py 13.3 kips (59 kn) Tedo capacity at traser 0.8 py x kips (51 kn) (icludig traser losses) Tedo capacity at service 0.78 py x kips (3 kn) (icludig total losses) Try tedos at 48 i. (1,19 mm) o ceter (ote that this tedo spacig also correspods to the maximum eective prestressig width o six times the wall thickess). Determie prestressig orce, ased o tedo capacity determied aove: at traser: P pi 11.4 kips/4 t,850 l/t (41.6 kn/m) at service: P p 7. kips/4 t 1,800 l/t (6.3 kn/m) Wall sectio properties: (re. 8) 8 i. (03 mm) CMU with ull mortar eddig: A 41.5 i. /t (87,900 mm /m) I 334 i. 4 /t (456 x 10 6 mm 4 /m) 87.6 i. 3 /t (4.71 x 10 6 mm 3 /m) r.84 i. (7.1 mm) At service loads: At service, the ollowig are checked: comied axial compressio ad lexure usig the uity equatio (equatio - 10); et tesio i the wall; stlity y esurig the compressive load does ot exceed oe-ourth o the ucklig load, P e, ad shear ad momet stregth. Check comied axial compressio ad lexure: a A p psi (0.34 MPa) h/r (1 t)(1 i./t)/.84 i < 99

5 [-1] F a 1 /4 ' m [ 1- ( h/140r ) ] 1 /4 (1,500 psi) [1- ( 50.7/140) ] 36 psi (. MPa) M + ed p ep x 1 i./t psi (0.6 MPa) [-14] F 1 /3 ' m 500 psi (3.4 MPa) F a + a F < 1.33 OK Check tesio or load comiatio o prestress orce ad dead load oly (per re. 1 sectio ): - a psi (-0.08 MPa) < 0 OK Check stlity: Because the tedos are laterally restred, the prestressig orce, P p, is ot cosidered i the determiatio o axial load ( per re. 1 sectio ), ad the wall is ot suject to live load i this case, so equatio -11 reduces to: P P d 34 l/t (3,414 N/m) π h E m [-15] 1 /4 P e 1 /4 ( e ) 3 π 6 ( )( 334) ( 1) 3 ( 1 1) I r 53,653 l (39 kn) [-11] P < 1 /4 P e OK Check momet stregth: Buildig Code Requiremets or Masory tructures sectio icludes the ollowig criteria or momet stregth o walls with laterally restred tedos: a/d < 0.45 < φ M where φ 0.8 ad M [P p + y du ] [d - a/] I additio, the compressio zoe must all withi the masory, so a < t. 1.3 M 1.3 x t-l (476 N. m) P du 1. P d 1. x l (1. kn) where 1.3 ad 1. are load actors or wid ad dead loads, respectively. P a p + F A y s 0.85 ' m du 1, , i. (3.6 mm) ( )( 1) a < t OK a/d 0.14/ < 0.45 OK < φ M φ M 0.8 [P p + y du ] [d - a/] 0.8 [1, ] ( /)/1 i./t 519 t-l (703 N. m) > OK At traser: Check comied axial compressio ad lexure usig the uity equatio (equatio -10) ad et tesio i the wall. pi 34 +, psi (0.51 MPa) A 41.5 h/r (1 t)(1 i./t)/.84 i F 1 /4 ' mi [1- ( h/140r ) ] 1 /4(1,50)[1 -(50.7/140) ] 7 psi (1.9 MPa) M + ed piep i 37 psi (0.6 MPa) /3 ' mi 1 /3(1,50) 417 psi (.9 MPa) F i F + i Fi < 1. OK Check tesio or load comiatio o prestress orce ad dead load oly (per re. 1 sectio ): i psi (-0.6 MPa) < 0 OK Thereore, use 7 /16 i. (11 mm) diameter tedos at 48 i. (1,19 mm) o.c. Note that although wall desig is seldom govered y out-o-plae shear, the shear capacity should also e checked. NOTATION A et cross-sectioal area o masory sectio, i. (mm ) threaded area o post-tesioig tedo, i. (mm ) cross-sectioal area o mild reiorcemet, i. (mm ) a depth o a equivalet compressio zoe at omial stregth, i. (mm) width o sectio, i. (mm) d distace rom extreme compressio ier to cetroid o prestressig tedo, i. (mm) E s modulus o elasticity o prestressig steel, psi (MPa) E m modulus o elasticity o masory, psi (MPa) e d eccetricity o dead load, i. (mm) e l eccetricity o live load, i. (mm) e p eccetricity o post-tesioig load, i. (mm) F a allowale masory axial compressive stress, psi (MPa) F allowale masory axial compressive stress at traser, psi (MPa) F allowale masory lexural compressive stress, psi (MPa) F i allowale masory lexural compressive stress at traser, psi (MPa) F t allowale lexural tesile stregth o masory, psi (MPa) a axial stress ater prestress loss, psi (MPa) axial stress at traser, psi (MPa) lexural stress ater prestress loss, psi (MPa) i lexural stress at traser, psi (MPa) ' m speciied compressive stregth o masory, psi (MPa) ' mi speciied compressive stregth o masory at time o traser o prestress, psi (MPa) ps stress i prestressig tedo at omial stregth, psi (MPa) pu speciied tesile stregth o prestressig tedo, ksi (MPa) py speciied yield stregth o prestressig tedo, ksi (MPa) se eective stress i prestressig tedo ater all prestress losses have occurred, psi (MPa) y speciied yield stregth o steel or reiorcemet ad achors, psi (MPa)

6 h I masory wall height, i. (mm) momet o iertia o et wall sectio o extreme ier tesio or compressio, i. 4 /t(mm 4 /m) M momet due to lateral loads, t-l (N. m) M omial momet stregth, t-l (N. m) actored momet due to lateral loads, t-l (N. m) modular ratio o prestressig steel ad masory (E s /E m ) P d axial dead load, l/t (kn/m) P du actored axial dead load, l/t (kn/m) P e Euler ucklig load, l/t (kn/m) P l axial live load, l/t (kn/m) P lu actored axial live load, l/t (kn/m) P pi prestress orce at traser, l/t (kn/m) P p prestress orce icludig losses, l/t (kn/m) r radius o gyratio or et wall sectio, i. (mm) sectio modulus o et cross-sectioal area o the wall, i. 3 /t (mm 3 /m) t ace shell thickess o cocrete masory, i. (mm) w applied wid pressure, ps (kpa) φ stregth reductio actor 0.8 REFERENCE 1. Buildig Code Requiremets or Masory tructures, ACI 530-0/ACE 5-0/TM Reported y the Masory tadards Joit Committee, 00.. Buildig Code Requiremets or tructural Cocrete, ACI Detroit, MI: America Cocrete Istitute, Revised Costructio o Post-Tesioed Cocrete Masory Walls, TEK Natioal Cocrete Masory Associatio, Iteratioal Buildig Code. Iteratioal Code Coucil, Miimum Desig Loads or Buildigs ad Other tructures, ACE 7-98, America ociety o Civil Egieers, tadard peciicatio or Loadearig Cocrete Masory Uits, ATM C 90-01a. America ociety or Testig ad Materials, tadard peciicatio or Mortar or Uit Masory, ATM C America ociety or Testig ad Materials, ectio Properties o Cocrete Masory Walls, TEK Natioal Cocrete Masory Associatio, ATM peciicatios or Cocrete Masory Uits, TEK 1-1C. Natioal Cocrete Masory Associatio, Mortars or Cocrete Masory, TEK 9-1A. Natioal Cocrete Masory Associatio, Grout or Cocrete Masory, TEK 9-4. Natioal Cocrete Masory Associatio, teel or Cocrete Masory Reiorcemet, TEK 1-4B. Natioal Cocrete Masory Associatio, Cocrete Masory Wall Weights, TEK 14-13A. Natioal Cocrete Masory Associatio, chultz, A.E., ad M.J. coloro, A Overview o Prestressed Masory, TM Joural, Vol. 10, No. 1, August 1991, pp chultz, A.E., ad M.J. coloro, Egieerig Desig Provisios or Prestressed Masory, Part 1: Masory tresses, Part : teel tresses ad Other Cosideratios, TM Joural, Vol. 10, No., Feruary 199, pp tadard peciicatio or teel trad, Ucoated eve- Wire or Prestressed Cocrete, ATM A America ociety or Testig ad Materials, tadard peciicatio or Ucoated tress-relieved teel Wire or Prestressed Cocrete, ATM A 41-98a. America ociety or Testig ad Materials, tadard peciicatio or Ucoated High-tregth teel Bar or Prestressed Cocrete, ATM A America ociety or Testig ad Materials, tadard peciicatio or Compressile-Washer-Type Direct Tesio Idicators or Use with tructural Fasteers, ATM F a. America ociety or Testig ad Materials, 001. NATIONAL CONCRETE MAONRY AOCIATION To order a complete TEK Maual or TEK Idex, urise Valley Drive, Herdo, Virgiia 0171 cotact NCMA Pulicatios (703)