Question

A floor system (Figure 2) consists of a 3 in. concrete slab supported by continuous T beams with a span L=24 ft, and 47 in. on centers distance between beams. Web dimensions, as determined by the negative-moment requirements at the supports are bw=11 in. and d=20 in. Use concrete clear cover of 2 in. Determine the tensile steel of the T-beam that is required at mid-span to resist a factored positive moment of Mu=530 kip-ft if fc’=3,000 psi and fy=60,000 psi;

* * bf-bin dezoin + CLEAR K COVER 2in * bub= llin 4711 0.C.

Answer 1

solution hf T + to bwy Asi Ass Ast cuse I' 24812 41 4 Case 2 first determining the elective fang width from section (8.3.1) 07 ACI 8.10.2 1) bs span 713) 11) b = 16hs + bw =(16x3) +!! =59 in 117) bs Clear spacing beth, beams + bw =center to center spacing beth beams 47 in The centerline I beam spacing controls in this case, and b = 47 inches : Assumption ? Assuming that shress-block depth equals to the flange thickness of 3 inches ( beam be haves like a rectangular shape) Mu As o fy (d-9722 mu = 5 3Dkip-Ft = 6360 kips-in Page 114 CS Scanned with CamScanner

6360 = 0.9 X60X (20 -3/2) 6360 - 999 As = 6-366 in 2 1) Solve for Asfy Q= 0.85 fcb 6.366 x 60 0.85 X 3 X47 a = 3-187 in 7 hs =3.0 Assumption Incorrect; There fore, the beam will act as T-beams must be designed as 'Tabeam. from Case I given above and section (8.4-1) we have. 0.85 fo hilb-bw) fy 0.85 x 3 Issi ) (3 in) *(47-11), 60 ksi A sf = 275.4 = Asf = 4.59 in o Mai • Asf xfy Cd. h) = 0.9 x4.59 x C6o ksi) x( 20- 3123 4585.41 in-kips Omni Page 2/4 CS Scanned with CamScanner

& Mn 2 = Mud Mn. 6360 4585-41 = 1774.59 in-kips [Q Mna find 'a' value by iteration, Assume intial a = 3-5 inches! Ag - Asf = & Mn 2 ofy (4-9) 1774.59 0.9 % 60 % (20-3-572 1-8.007 in As A SA Find an improve 'a' value (Ag-Asf) fy 0.85 fc bw a 1.8007 X 60 0.85r8x11 108-04 -3.8517 in Iterate with the new a=348$in $ 'Mnz As - Asf & Fyn (d_%) 3-8517 1774.59 0.9 x 60 x (20 1774.59 976-6041 As-Asf = 1.818 in2 eq? Page 3/4 CS Scanned with CamScanner

= a 0.41 in 2 find an improve 'a' value, (As- Asf)fy a 0.85 fc bw 1.1.818 x 60 0-85X3 XII 109.093 0-85x3x11 3.8892, in Moe As - Asf + o fy cd-/2) 1774.59 O'g x 60 X (20 tap. 3-8892) 1774.59 974.99 eg? since there is no change between eq?012 we have arrived at the answer. Therefore. As = Asf + (As.-Asf) = 4.59 +1.82 2A 2 1-82 in2 As Asf mm amound check with ACI requirements for max of sted (Tensio-controlled) 3.8892 =4.575 B. 0.85 4.575 둥 0.228. <0.375 Tensio - controlled .! The T-beam satisfies the ACI provisions for tension failure. Next steps will be select the nein forement and check all the spacing cs sxequirementinand detail the beam. 20 Page 414