Problem 1 (40 pts) - Flexural design of beams A wealthy client asked you to desi

Question

Problem 1 (40 pts) - Flexural design of beams A wealthy client asked you to design his new dream house. The house has a large balcony which is supported by identical cantilever beams. Because of aesthetics, the architect set limitations on the beam section, which needs to be exactly as shown in the drawing. Determine the theoretical longitudinal reinforcement needed at the fixed end of each beam. Material properties and loads are given in the following. Beam section Normal Weight Concrete fo 4000 psi Gr. 60 steel As Note: the dead load wo includes self-weight of the beam 26 As 14" Wo=1.4 kipft, wL-2.4 kip/ft 15

Explanation / Answer

grade of concrete = 4000 psi

grade of steel = 60 ksi
total depth of beam = 26:

width of beam =14"

effective depth of beam = 26-4=22"

uniform dead load = 1.4 kip/ft

uniform live load = 2.4 kip/ft

factored load on beam = (1.2*1.4)+(1.6*2.4)=5.52 kip/ft

design moment of beam = 5.52*15*15/2=621 kip-ft=7452000 lb-in

Let the steel required be Ast

let the depth of compression zone in beam be a

0.85*a*14*4000=60000*Ast

a=1.26Ast

lever arm = 22-a/2 = 22-0.63Ast

Nominal moment capacity of beam = 60000*Ast*(22-0.63Ast)

Design moment = 0.9*60000*Ast*(22-0.63Ast)=54000Ast*(22-0.63Ast)=1188000Ast-34020Ast2

1188000Ast-34020Ast2 =7452000

Ast = 8.2 in2

Therefore, required area of steel = 8.2 in2

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