Allowable Stress Design. Flexural Members - Allowable Stress Design. Example - Masonry Beam. Allowable Stress Design. k 3.

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1 Loa Coiatio llowale Stre Deig () D () D + L () D + (L r or S or R) (4) D L (L r or S or R) (5) D + (0.6W or 0.7E) (6a) D L (0.6W) (L r or S or R) (6) D L (0.7E) S (7) 0.6D + 0.6W It hall e peritte to replace 0.6D with 0.9D i coiatio () or the eig o () 0.6D + 0.7E Special Reiorce aory Shear Wall llowale Stre Deig h lexural eer - llowale Stre Deig Grout aory Uit Strai Stree uptio:. lae ectio reai plae. Stre-trai relatiohip or aory i liear i copreio. ll aory i teio i eglecte 4. erect o etwee teel a grout 5. eer i traight priatic ectio j C= ()()/ T= E E llowale Stre Deig = Traore Sectio Notatio: Lower cae: calculate tre, Upper cae: allowale tre, i allowale copreie tre to reit lexure oly. Note ue or allowale copreie tre to reit coiatio o lexure a axial loa. = Traore Sectio Steel tre: aory tre: llowale oet: Steel: j llowale Stre Deig To i eutral axi, equate oet o area aout eutral axi. ( )( ) ( )( ) ( ) j ( )( j) aory: ( ) ( j) j llowale tree (...,..4..) llowale aory tre = 0.45 llowale teel tre: 0 i Grae 40 teel i Grae 60 teel 0 i Wire joit reiorceet llowale Stre Deig Exaple - aory Bea Gie: =40-i; Grae 60 teel, =000pi; i CU; Type S ortar; 4 coure high ea (= i.); #6 rear Require: I ectio aequate? Solutio: = = E = 900 =.0 x 0 6 pi E = 9 x 0 6 pi = E /E = ρ = / = ρ = ( ) j llowale Stre Deig 4

2 Exaple - aory Bea, cot aory Bea - araetric Stuy =0.7 j=0.94 j ( )( j) What i axiu oet ea coul carry? 0.44i i0.94i ip i j pi 564 j 7.65i0.7i 0.94i ip i all = 64 ip-i llowale Stre Deig 6 =0ich =7.65ich llowale Stre Deig Reiorce lexure: SD. SD SD Deig roceure. ue alue o j (or ). Typically j i etwee 0.5 a Deterie a trial alue o. Chooe reiorceet. j. Deterie a j. j / ( ) 4. Deterie teel tre a aory tre. 5. Copare calculate tree to allowale tree. j ( )( j) 6. I aory tre cotrol eig, coier other optio (uch a chage o eer ize, or chage o ). Reiorceet i ot eig ue eicietly. coplete eig proceure will e preete later. 9 llowale Stre Deig 0

3 SD: Deig etho Exaple: Bea Calculate I al? or Grae 60 teel al = 0. YES al ( ) llowale aory copreio tre cotrol NO Iterate. Ue () a ew gue a repeat. llowale reiorceet teio tre cotrol Gie: 0. opeig; uperipoe ea loa o.5 ip/; lie loa o.5 ip/; 4 i. high; Grae 60 teel; Type S aory ceet ortar; i. CU; = 000 pi Require: Deig ea Solutio: 5...: Legth o earig o ea hall e a iiu o 4 i.; typically aue to e i Spa legth o eer ot uilt itegrally with upport hall e tae a the clear pa plu epth o eer, ut ee ot excee itace etwee ceter o upport. Spa = 0 + (4 i.) = Copreio ace o ea hall e laterally upporte at a axiu pacig o: ultiplie y the ea thice. (7.65 i.) = 44 i. = 0. 0 /. 0(7.65 i.) / (0 i.) = 49 i. = 9. Exaple: Bea Exaple: Bea Loa Weight o ully groute oral weight: p oet w D L wl 45. i rea o teel ( ) 0.900i i 9.i7.65i i Deterie ue copreio cotrol 0i 0i i i7.65i 9.i. Ue - #9 ( =.00 i ) Bar place i otto U-hape uit, or ocout o ea uit. Chec i copreio cotrol 9.i i Copreio cotrol Calculate oular ratio, E E E 9000i i 6. 4

4 Deig or DL = /, LL = / Shear at reactio / ro ace o upport Deig hear orce Shear tre llowale aory hear tre Exaple: Bea wl V 0i. 4i i V V i 0i V pi 50.pi pi Sectio..5.4 allow eig or hear at / ro ace o upport. Sugget that e ue, ot..5 5 Chec ax hear tre Req teel tre Deterie or a pacig o i. Exaple: Bea 000 pi 9. 4 pi 59. pi 50.pi. 9 pi pi 0.04i i. 0i. i. 000 pi0i. Ue # tirrup Deterie o that o hear reiorceet woul e require. V i 50.pi..5i. > 59.pi OK Ue a i. eep ea i poile; will lightly icreae ea loa. 6 Dea Loa (/) (uperipoe) Suary: SD. SD Lie Loa (/) Require (i ) SD SD ( =.5 i) ( =.5 i) ( =.5 i) SD: llowale teio cotrol or 0.5 / a / ( =.5 i) ( =.5 i) ( =.5 i) artially Groute Wall - llowale Stre t t t t C j C. Neutral axi i lage; eig a aalyi or oli ectio B. Neutral axi i we = i aory cotrollig = /((-)) i teel cotrollig w j w C t t t Cw ( t ) j t t t j w t t 7 llowale Stre Deig

5 artially Groute Wall - Exaple Gie: i CU wall; high; Grae 60 teel, =000 pi; Lateral wi loa o 4 p (actore) Require: Reiorcig (place i ceter o wall) Solutio: wh 0.64l / 454l / 544l i / t 7.65i 5.44ip i /. i 0.050i j i(0.9)(.i) / Try i (0.050i /) = 0.45(000pi) = 900 pi = 000 pi E =.0 x 0 6 pi E = 9 x 0 6 pi = E /E = 6. Sole a oli ectio = = 0.7 = 0.65 i < t =.5 i OK j = 0.94 = 7 pi OK = 0. i OK lexural a xially Loae Eleet llowale Copreie orce (..4..) a h 40r a t 70r h h r t h r t i area o laterally tie teel Ue 4 iche llowale Stre Deig 9 llowale Stre Deig 0 Iteractio Diagra ue trai/tre itriutio or > al Set aory trai, i teel trai aory trai = /E = or CU or < al Set teel trai, i aory trai Steel trai = /E = or Grae 60 Copute orce i aory a teel Su orce; u oet aout ceterlie al E / E E i i 0. Grae 60 teel Exaple i. CU Bearig Wall Gie: high CU earig wall, Type S aory ceet ortar; Grae 60 teel i ceter o wall; 4 i.; partial grout; = 000 pi Require: Iteractio iagra i ter o capacity per oot ure oet: = 6. ρ = ρ = i i j i i llowale i -i i0.94.i. 5. i i 0.90i 0.7.i 0.94.i j ( ) 0.7 j j i llowale Stre Deig llowale Stre Deig

6 Exaple i. CU Bearig Wall Exaple i. CU Bearig Wall, SD ure xial: 4.. Raiu o gyratio Raiu o gyratio hall e copute uig aerage et cro-ectioal area o the eer coiere. NC TEK 4-B Sectio ropertie o Cocrete aory Wall r =.66 i. = 40.7i / I =.0 i 4 / Balace: i Stre i <.5 i. N.. i ace hell. i Strai i h/r h 44i 54. r.66i 99 i C i a a t h 40r i i i T i i 4.. llowale Stre Deig llowale Stre Deig 4 Exaple i. CU Bearig Wall, SD Exaple i. CU Bearig Wall, SD Below Balace: =.00 i. i C i T i i 00i(0.0009) = i Stre i C 0.704i.00i i 4. i i T C -T i 4. i i i. i Strai oe Balace: =.00 i. ace Shell We Steel i.5 i 0. i.00 i Stre.i0.05 i 0. T 66. i Neutral axi i i we i C.5i i 9. C 0.i i i Strai.00 i i llowale Stre Deig 6 llowale Stre Deig 7

7 Exaple i. CU Bearig Wall, SD Iteractio Diagra: SD 0.5 / 9. / 0.66/ 0.5 i.5 i /=.5i C 7 C-T Cetroi h h x h h h x h.7.5 i.i 0.5i 0.5.i.5i llowale Stre Deig llowale Stre Deig 9 pproxiate Iteractio Diagra llowale Stre - Deig roceure Three oit pproxiatio Three poit approxiatio Zero axial loa; oet capacity = lage thice Zero oet; axial capacity llowale Stre Deig 0 I al? or Grae 60 teel al = 0. Calculate ( ( t / ) ) YES al ( ) Copreio cotrol NO t Teio cotrol llowale Stre Deig Iterate. Ue () a ew gue a repeat.

8 Deriatio o Deig Equatio Su orce: tp tp Su oet: I the aory tre cotrol, et =, a utitute or i oet equatio uig u o orce. t p p ( ( tp / ) ) t Thi i quaratic equatio i, which ca e ole to otai: ( ) llowale Stre Deig i a ratio o trai: Deriatio o Deig Equatio I the teel tre cotrol, et =, a i i ter o. E E E Sutitute ito u o orce, a ole or. E Now utitute ito u o oet a et =. t t p p llowale Stre Deig Deriatio o Deig Equatio Thi i cuic equatio i : 6 t t p p 0 lthough there are aalytical way to ole a cuic equatio, a iteratie olutio ight e the eaiet. Sole or ro: Exaple - ilater Deig Gie: Noial 6 i. wie x 6 i. eep CU pilater; =000 pi; Grae 60 ar i each corer, ceter o cell; Eectie height = 4 ; Dea loa o 9.6 ip a ow loa o 9.6 ip act at a eccetricity o 5. i. ( i. iie o ace); actore wi loa o 6 p (preure a uctio) a upli o. ip (e=5. i.); ilater pace at 6 o ceter; Wall i aue to pa horizotally etwee pilater; No tie. Require: Deterie require reiorcig uig allowale tre eig. Solutio: e=5. i.0 i Loa =. i x Iie E = 00i = 6. Lateral Loa w = 0.6(6p)(6)=50 l/ Vertical Spaig llowale Stre Deig 4 llowale Stre Deig 5

9 0.6D + 0.6W Exaple - ilater Deig Top o pilater. = 0.6(9.6)-0.6(.) = 0.9ip = 0.9(5.i) = 5.ip-i i locatio o axiu oet ax Uually loa coiatio with allet axial loa a larget lateral loa cotrol. Try 0.6D + 0.6W to eterie require reiorceet a the chec other loa coiatio. h x wh i 5.ip i 0.50 i i 4.i wh i 0.00 i 5. (5. i). i wh 0.00 i i i axial orce at thi poit. Iclue weight o pilater (00 l/) i. i. i.i Exaple - ilater Deig ( ( h / ) ).i (.ip. i 5.6i / 0.900i5.6i ip i).00i.00i 0.54 < al Teio cotrol; iterate.i Deig or =., = -i llowale Stre Deig 6 llowale Stre Deig 7 Exaple - ilater Deig Exaple - ilater Deig Equatio / Value Iteratio Iteratio Iteratio h (-i.) (i ) (i.) (i.) (i.) i.00i i i i 0.55i 0.54 i i i i i5.6i Try -#5, 4 total, oe i each cell 0.67i 0.67i.i 0.67i. i llowale Stre Deig D+S = 9. = 9.5- D+0.75(0.6W)+0.75S = 5. = 6.- D+0.6W = 7. = D+0.6W =. =.- llowale Stre Deig 9

10 Exaple Eect o Exaple SD. SD = 000 pi = 500 pi SD 0.6(0.9*SD) llowale Stre Deig 40 llowale Stre Deig 4 Exaple: Wi Loa SD Exaple: Wi Loa SD Gie: i. CU earig wall; Grae 60 teel; Type S aory ceet ortar; =000pi; roo orce act o i. wie earig plate at ege o wall. Require: Reiorceet Solutio: Etiate reiorceet ~ ,req = i / Try 40 i. (0.06 i /) 0.6 Cro-ectio o top o wall Deterie eccetricity e = 7.65i/.0 i. =. i D = 500 l/ L r = 400 l/ W = -60 l/ p Chec 0.6D+0.6W i orce at top o wall i orce at iheight i oet at top o wall i oet at iheight top / i wh top Loa Co. (ip/) (ip/) top (-/) (-/) (i ) 0.6D+0.6W D+0.6W i Ue #4@ 40 i. (0.06 i /) 7% ore teel tha require; with SD #4@40 i. i 4% ore teel tha require. llowale Stre Deig 4 llowale Stre Deig 4

11 Saple Calculatio: 0.6D+0.6W. al = 0.; al =.9i.. ue aory cotrol. Deterie. Sice 0.55 i. <. i. teio cotrol.. Iterate to i. Exaple: Wi Loa SD i i. i 0.55i i i (i.) t p / / (-/) (i / /) (i.) Equatio / Value Iteratio Iteratio (i.) llowale Stre Deig 44 Shear - llowale Stre Deig g V 0. 5 axiu i: g ( / ) 0. 5 g Iterpolate or alue o /(V ) etwee 0.5 a.0 V ( / V ). 0 5 llowale Stre Deig 45 V g Shear Special Shear Wall Exaple V aory allowale hear tre ecreae y a actor o, ro ½ to ¼. ccout or egraatio o aory hear tregth that occur i platic higig regio. Seiic eig loa require to e icreae y.5 or hear Gie: 0 high x 6 log i. CU hear wall; Grae 60 teel, Type S ortar; = 000 pi; uperipoe ea loa o ip/. I-plae eiic loa (ro SCE 7-0) o 00 ip. S DS = 0.4 Require: Deig the hear wall; oriary reiorce hear wall Solutio: Chec uig 0.6D+0.7E loa coiatio. Try #6 i each o lat cell; Weight o wall: [40 p()+()75p]0 = 700l Lightweight uit, grout at 40 i. o.c. 40 p; ull grout 75 p axiu reiorceet: Shear wall haig /(V) a > 0.05 ax y y or itriute reiorceet, ρ i the total area o teio reiorceet iie y. = ( (0.)(S DS ))D = ( (0.)(0.4))(/(6)+7.) =.9 ip ro iteractio iagra OK; tree to 90% o capacity Stregth Deig: -#5 at e; 40 i. llowale Stre Deig 46 llowale Stre Deig 47

12 Exaple Exaple llowale Stre Deig 4 llowale Stre Deig 49 Exaple Exaple Calculate et area,, icluig groute cell..5i9i 9(i)(7.6i.5i) 49i Shear ratio axiu Shear tre V Vh/ V 0i /9i / 5 g V V l 49i pi pi pi OK Top o wall (critical locatio or hear): Deterie Require teel tre Ue #5 ar i o ea. Deterie pacig. = ( (0.S DS ))D = 0.544(/)(6) =.70 ip l pi pi / g.4 pi / pi 4. 4 pi pi 49i V i000 pii 49i 5.9i i{/, 4 i.} = i{94 i., 4 i.} = 4 i. Coe..5.. Ue #5 at 4 i. o.c. llowale Stre Deig 50 Stregth Deig: Req =.0 i. llowale Stre Deig 5

13 Exaple: Special Shear Wall Gie: 0 high x 6 log i. CU hear wall; Grae 60 teel, Type S ortar; = 000 pi; uperipoe ea loa o ip/. I-plae eiic loa (ro SCE 7-0) o 00 ip. S DS = 0.4 Require: Deig the hear wall; pecial reiorce hear wall Solutio: Chec uig 0.6D+0.7E loa coiatio. Deig or.5v, or.5(70 ip) = 05 ip (Sectio ) = (05 ip)/(49i ) =.7 pi But, axiu i. pi ully grout wall Calculate et area,, icluig groute cell. Shear tre Deterie (pecial wall) Require teel tre Exaple: Special Shear Wall V Ue #5 ar i o ea. Deterie pacig.. 9i i i l 464i l pi pi i pi 7. 7 pi pi 0.i000 pii 6. i pi494i Ue 6 i. Stregth Deig: Req = 54.6 i. uig.5 Req =.6 i. uig.5v u llowale Stre Deig 5 llowale Stre Deig 5 Exaple: axiu Reiorcig Sectio...4 axiu Reiorceet No ee to chec axiu reiorceet ice oly ee to chec i: /(V ) a /(V ) = 0.65 > (000pi)(464i ) = 46 ip; =. ip I we eee to chec axiu reiorcig, o a ollow. ax pi y 60000pi y pi 000pi or itriute reiorceet, the reiorceet ratio i otaie a the total area o teio reiorceet iie y. ue 6 ar i teio i i i. OK llowale Stre Deig 54