Cobied Flexure ad Axial Load Iteractio Diagra Partiall grouted bearig wall Bearig Wall: Sleder Wall Deig Procedure Stregth Serviceabilit Delectio Moet Magiicatio Exaple Pilater Bearig ad Cocetrated Load Pretreed Maor Cobied Flexural ad Axial Load 1 Ke Code Sectio 5.3 Colu 5.4 Pilater 9.3. Deig auptio 9.3.4.1 Noial tregth 9.3.4.1.1 Noial axial ad lexural tregth Sectio 4.3.3 Radiu o gratio 9.3.5 Wall deig or out-o-plae load 9.3.5.1 Scope 9.3.5. Noial axial ad lexural tregth 9.3.5.3 Noial hear tregth 9.3.5.4 P-delta eect 9.3.5.5 Delectio Cobied Flexural ad Axial Load
Cocetric Axial Copreio P h h A A A 1 99 0.8 0.80 P 0.80 0.80 t t 140r 70r h A A A 99 t t h r r =0.9 A t = area o laterall tied teel P euler EI h EA r h 900 A r h A 94. r h Equatio above or CMU; or cla (E = 700 ), ter i (83.1r/h) Code equatio actuall derived ro ureiorced aor ad a o-teio aterial, but iilar to Euler buclig Icluio o wall weight Wall weight provide uior axial load over height o wall. Reaoable approxiatio i to ue hal the weight o wall actig at top. Cobied Flexural ad Axial Load 3 Buclig Curve or A t = 0 0.7 0.6 0.5 h/r = 99 P /(A ' ) 0.4 0.3 0. A P 0.8 0.80 h 1 140r 70r P 0.800.80 A h 0.1 0 0 50 100 150 00 h/r Cobied Flexural ad Axial Load 4
Radiu o Gratio 4.3.3 Radiu o gratio Radiu o gratio hall be coputed uig average et cro-ectioal area o the eber coidered. Quetio: I thi a trict average or weighted average? What about dieret tpe o uit (which chage bloc area)? What i the eect o bod bea? NCMA ha tabulated value o average radii o gratio baed o average o ortar bedded area ad bloc area. Beett oe ue / i the exaple ad preadheet. Ureiorced Maor 5 Iteractio Diagra Aue trai/tre ditributio Copute orce i aor ad teel Su orce to get axial orce Su oet about ceterlie to get bedig oet Ke poit Pure axial load Pure bedig Balaced Cobied Flexural ad Axial Load 6
Exaple 8 i. CMU Bearig Wall Give: 1 high CMU bearig wall, Tpe S aor ceet ortar; Grade 60 teel i ceter o wall; #4 @ 48 i.; partial grout; = 000 pi Required: Iteractio diagra i ter o capacit per oot Pure Moet: A Noial oet, M M A d 1 A 0.8b ' Deig oet, M M 0. 0.9 0.934 840 Chec to ae ure tre bloc i i ace hell A a 0.8b ' 0.05 0.8 1 i 60i i.0 i 0.156i Cobied Flexural ad Axial Load 7 Exaple 8 i. CMU Bearig Wall Pure Axial: NCMA TEK 14-1B Sectio Propertie o Cocrete Maor Wall r =.66 i. A = 40.7i / I = 33.0 i 4 / Fid h/r Fid P P 0.8 0.80 A A A t t h 1 140r 44.3 39. P 0.9 9 Uig...86. h/r = 50.4 = 40.8 / Cobied Flexural ad Axial Load 9
Exaple 8 i. CMU Bearig Wall 0.8 = 1.6 i T Balaced: Strai C Stre 3.81 i a = 0.8c = 0.8(.09i.) = 1.67i. web legth = Fid C C, ace hell C, web Fid T Fid P i 60i 0.05 3. T A 0 P M 0.1 5.96 Fid M Cobied Flexural ad Axial Load 11 Exaple 8 i. CMU Bearig Wall Below Balaced: c = 1.5 i. 0.005 1.5 i 3.81 i Strai 0.0051 0.8 = 1.6 i a = 0.8c 1.00 i Stre T Fid C ab 0.8.0i1.00i1 i 19. C 0.8 Fid T Fid i 60i 0.05 3. T A 0 C 0.9 19. 3.0 14. P -T 6 P M 14.6 4.77 Fid M 0.8 1.5i i 0.919. 3.81i 57. 4. 77 Cobied Flexural ad Axial Load 13
Exaple 8 i. CMU Bearig Wall Above Balaced: c = 3.0 i. 0.005 3.0 i 3.81 i Strai 0.00068 0.8 = 1.6 i C Stre T a = 0.8c = 0.8(3.0i.) =.4i. web legth =....0 Fid C Fid T Fid 0.80.0i1.5i1 i C 4, ace hell 0.80.0i.40i 1.5i.0 i 3. C 68, web i 0.00068 0.05 0. T E A 9000i 99 4.0 3.68 0.99 4. P 0.9 0 P M 4.0 6.8 Fid M 1.5i.40 1.5 0.94.0 3.81i 3.68 3.811.5 i 6. 8 Cobied Flexural ad Axial Load 14 Exaple 8 i. CMU Bearig Wall Poit c (i) C, (ip/) C,web (ip/) T (ip/) P (ip/) M (ip-/) a = d 4.76 4.0 8. 0 9.0 6.5 c = d 3.81 4.0 5.8 0 6.8 6.45 3.00 4.0 3.7 1.0 4.0 6.8 Balaced.09 4.0 1.3 3.0 0.1 5.97 a = 1.5 i. 1.56 4.0 0 3.0 18.9 5.73 1.5 19. 0 3.0 14.6 4.77 1.0 15.4 0 3.0 11.1 3.93 0.8 1.3 0 3.0 8.4 3. 0.6 9. 0 3.0 5.6.47 0.4 6.1 0 3.0.8 1.68 Pure Moet 0.195 3.0 0 3.0 0 0.84 Cobied Flexural ad Axial Load 15
Exaple 8 i. CMU Bearig Wall Cobied Flexural ad Axial Load 16 Iteractio Diagra Solid v. Partial Grout Cobied Flexural ad Axial Load 17
Iteractio Diagra Below Balaced Teio, T Copreio, C Noial Axial Stregth, P T A C 0. 8 ba P C T 0. 80 ba A Solve or a Noial Moet Stregth, M a M A P 0.80 b tp a 0.8 ba A t a tp d t p p P A A d Ca olve or M i P i ow Cobied Flexural ad Axial Load 18 Iteractio Diagra Below Balaced φp M u, P u I we could ol ow oe poit o the iteractio diagra, we would wat to ow the poit correpodig to P = P u φm a A P / 0.80 b u M t a p p Pu / A A d t Thee are equatio i 9.3.5. coetar. The igore a teio i a poible ecod laer o teel ear the copreio ace). M For cetered bar: a Pu / A d Cobied Flexural ad Axial Load 19
Deig: Cobied Bedig ad Axial Load a d d Pu d t Calculate p 0.8 b / M u c a 0.8 YES I c c bal? For Grade 60 teel c bal = 0.547 c bal u u d NO A 0.8 ba Pu / d c ue c Copreio cotrol A 0.8 ba Pu / Teio cotrol Cobied Flexural ad Axial Load 0 Exaple: Pilater Deig Give: Noial 16 i. wide x 16 i. deep CMU pilater; =000 pi; Grade 60 bar i each corer, ceter o cell; Eective height = 4 ; Dead load o 9.6 ip ad ow load o 9.6 ip act at a eccetricit o 5.8 i. ( i. iide o ace); Wid load o 6 p (preure ad uctio) ad upli o 8.1 ip (e=5.8 i.); Pilater paced at 16 o ceter; Wall i aued to pa horizotall betwee pilater; No tie. Required: Reiorceet Solutio: e=5.8 i.0 i Load d=11.8 i x Iide Lateral Load w = 6p(16) = 416lb/ d = 15.65 7.65/ = 11.8 i Vertical Spaig Cobied Flexural ad Axial Load 1
Exaple: Pilater Deig Weight o pilater: Weight o ull grouted 8 i wall (lightweight uit) i 75 p. Pilater i lie a double thic wall. Weight i (75p)(16i)(1/1i) = 00 lb/ 1.D + 1.6S Critical locatio i top o pilater. P u = 6.9 ip M u = 156.0 ip-i Fid a a d d 11.8i Pu d h / 0.8 11.8i b M u 6.9 11.8 0.9 i 15.6i / 0.8.0 i15.6i 156 i 1.04i c a / 0.8 1.04i./ 0.8 Chec c/d 0.110 0. 547 d d 11.8i. Teio cotrol Fid A 0.8 ba Pu / 0.8 A.0i15.6i1.04i 6.9 / 0.9 60i 0.066i Cobied Flexural ad Axial Load Exaple: Pilater Deig Wh the egative area o teel? Suiciet area ro jut aor to reit applied orce. Deterie a ro jut copreio. Pu 6.9ip a 1. 08i 0.8 b 0.8.0i 15.6i Fid the oet t a 15.6i 1.08i M P u 6.9ip 195ip i M u = 156 ip-i Suiciet capacit ro jut aor. No teel eeded. Cobied Flexural ad Axial Load 3
Exaple: Pilater Deig 0.9D + 1.0W Chec wid uctio At top o pilater. P u = 0.9(9.6) 1.0(8.1) = 0.54 ip M u = 0.54ip(5.8i) = 3.1 ip-i Locatio o axiu oet, x Maxiu oet, M u Axial orce, P u L M 88i 3.1ip i x 143. 7i wl 0.416ip / 4 M u M wl 8 M wl 3.1 i 0.03467 / i 88i 8 (3.1 i) 0.03467 / i88i 0.0 / 143.7i1 /1i. P u 0.54 0.9 69 Aue idheight oet i ~ M u. Third ter i M u add 0.00 -i. 361.0 i Deig or P u =.7 ip, M u = 361 -i Cobied Flexural ad Axial Load 4 Exaple: Pilater Deig 0.9D + 1.0W 1.D + 1.0W + 0.5S At top: P u =0.5 M u =3 -i x=144 i P u =.7 M u =361 -i a = 1.49 i A = 0.57 i At top: P u =8. M u =48-i x = 139i P u =11.0 M u =384-i a = 1.74 i A = 0.5 i 1.D + 1.6S + 0.5W At top: P u =.8 M u =13-i x=117i P u =5. M u =5-i a = 1.41 i A = 0.1 i Required teel = 0.57 i Ue -#5 each ace, A = 0.6 i Total bar, 4-#5, oe i each cell Cobied Flexural ad Axial Load 5
Exaple: Pilater Deig 1.D+1.6S 1.D+1.6S+0.5W 1.D+1.0W+0.5S 0.9D+1.0W Cobied Flexural ad Axial Load 6