Determine the tensile reinforcement needed for a 14 in x 33

Determine the tensile reinforcement needed for a 14 in x 33 in rectangular beam with 30 ft span and the loading shown in the figure below. Assume reinforced concrete unit weight is 150 lb/f3 and the self-weight of the beam needs to be added to the dead load. Use f- 4,000 psi and fy = 60,000 psi. Show a sketch of the designed cross section. 2. P.-20k 1.5km 10 ft 10 ft 10 ft 30 ft Figure for Question 2

Solution

dead load on beam = 1.5 kip/ft

maximum moment in beam due to dead load = 1.5*30²/8=168.75 kip-ft

maximum moment in beam due to live load = 20*10=200 kip-ft

both the moments calcultaed above are at midspan

design moment in beam per load combination 1.2D+1.6L = (1.2*168.75)+(1.6*200)=522.5 kip-ft=6270 kip-in

beam cross section = 14inx33in

grade of concrete=4 ksi

grade of rebar = 60 ksi

Effective depth of beam = 31 in (assuming 2\" effective cover to tension steel)

Let area of steel required be A_st and depth of compression zone be \'a\'

0.85*4*14*a=0.9*A_st*60

a=1.13A_st

Moment capacity = 0.75*0.9*60*A_st*(31-0.567A_st)

Or, 6270 = 0.75*0.9*60*A_st*(31-0.567A_st)= 1255.5A_st-22.96A_st²

A_st = 5.56 in²

Provide 4-#11 rebar