Combined Flexure and Axial Load

Transcription

1 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 Noial tregth Noial axial ad lexural tregth Sectio Radiu o gratio Wall deig or out-o-plae load Scope Noial axial ad lexural tregth Noial hear tregth P-delta eect Delectio Cobied Flexural ad Axial Load

2 Cocetric Axial Copreio P h h A A A P 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 = h/r = 99 P /(A ' ) A P h 1 140r 70r P A h h/r Cobied Flexural ad Axial Load 4

3 Radiu o Gratio 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

4 Exaple 8 i. CMU Bearig Wall Give: 1 high CMU bearig wall, Tpe S aor ceet ortar; Grade 60 teel i ceter o wall; 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 Chec to ae ure tre bloc i i ace hell A a 0.8b ' 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 A A A t t h 1 140r P Uig h/r = 50.4 = 40.8 / Cobied Flexural ad Axial Load 9

5 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 T A 0 P M Fid M Cobied Flexural ad Axial Load 11 Exaple 8 i. CMU Bearig Wall Below Balaced: c = 1.5 i i 3.81 i Strai = 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 T A 0 C P -T 6 P M Fid M i i i Cobied Flexural ad Axial Load 13

6 Exaple 8 i. CMU Bearig Wall Above Balaced: c = 3.0 i i 3.81 i Strai = 1.6 i C Stre T a = 0.8c = 0.8(3.0i.) =.4i. web legth =....0 Fid C Fid T Fid i1.5i1 i C 4, ace hell i.40i 1.5i.0 i 3. C 68, web i T E A 9000i P P M Fid M 1.5i i 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 c = d Balaced a = 1.5 i Pure Moet Cobied Flexural ad Axial Load 15

7 Exaple 8 i. CMU Bearig Wall Cobied Flexural ad Axial Load 16 Iteractio Diagra Solid v. Partial Grout Cobied Flexural ad Axial Load 17

8 Iteractio Diagra Below Balaced Teio, T Copreio, C Noial Axial Stregth, P T A C 0. 8 ba P C T 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 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

9 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 = 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 = / = 11.8 i Vertical Spaig Cobied Flexural ad Axial Load 1

10 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 = ip-i Fid a a d d 11.8i Pu d h / i b M u i 15.6i / i15.6i 156 i 1.04i c a / i./ 0.8 Chec c/d d d 11.8i. Teio cotrol Fid A 0.8 ba Pu / 0.8 A.0i15.6i1.04i 6.9 / i 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

11 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 i wl 0.416ip / 4 M u M wl 8 M wl 3.1 i / i 88i 8 (3.1 i) / i88i 0.0 / 143.7i1 /1i. P u Aue idheight oet i ~ M u. Third ter i M u add i 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

12 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