Question

Q4 (50 pts Extra Credit): Design the doubly reinforced concrete beam shown below if it is subjected to a bending moment of 900 k.ft f'c = 4,800 psi fy= 60 ksi 27" 15"

Answer 1

Complete design of doubly reinforced section is shown below.

1. Moment Mn= 900 k-ft Minnea 900 0.9 = 1000 k-ft = 12000 k-in 2. Find Pre and associated moment P = 0.85 0.05( fc'-) -0185- 0.05 (4.8-4) IB, = 0.81 003 0.003 +0.005 4.5 60 Х s 0.85*0.81 x (3) Gc 0.02066) 0.02066 X 15x2y = 8, 36 Y in As Pre bd = 11 8.2 in • a= Astfy 0.85fcb 8. 367 X 60 0.85x4.5x15 = 8.367 x 60 x (27-8 8.2 2 Ma = Asify Asify (d-a) (Ma = 11.496.26 k-in

3. Additional capacity required Mn' Mr, neq Mn 12000 -11496,26 Ma' 503.74 Kin 4. Find the additional steel for additional moment 8.2 O.SI = 10.12 Fi 0.003x29700x (10.12-31 (10-12 10.12 fs' = 0.003 Es (ed') fs' z 61.24 > 60 compression steel yields 503.74 60x (27-3) Mn' f (d-dl') As' = As! = 0.35 in ² Total tension steal required G.1.24 ) = 0.35 x 60 Asg = Ad () (As2 = 0.357 in)

" As = Asif Asa 8.367+ 0.357 As 8.72 in² There fore, Assoming # 4 bau for compression steel number of bars 0.35 = 1.75 ~2 8.2 As 0.4 in? 2 #4 . Assuming #114 bars for tension sted number of baw 8.72 3.88 @ @ 2.25 As = q in² 4 #14 6. Check moment capacity Mns (As'x fy x(d-d')] + [CAs-As?) « fy* (2-2)] Substituting all values Mn = 12393.12 kin & Mn = 0.9 x 12.393.12 kin = 11153,81 k-in (6mn = 929:48 929.48 k-ft > 900 koft Safe