A rectangular reinforced concrete beam f c 4000 psi f y 6

A rectangular reinforced concrete beam (f \'c = 4000 psi , f y = 60 ksi) has the following dimensions; b=18\" , H = 24\" and reinforcements are placed 21.5\" from the top. The beam is simply supported and spans 28\'. What uniform load could be supported if the concrete stress is limied to 0.4 f \'c and steel stress is limited to 0.5 f y? Brittle tensile failure is also of concern.

Solution

Solution:-

Given

b = 18”

H = 24”

d= 21.5”

_fc’ = 4000 psi   , f_y = 60 ksi , l = 28 feet = 336 inch

_Xulim/d =0.48

          x_ulim = 0.48 x 21.5 = 10.5 inch

Let section is under reinforced.

Then x_u will be less than x_ulim.

Assume x_u = 9.5 inch

_xu = 0.87 (0.5 f_y) * A_st /( 0.36 * 0.4 *f_c’ * b)

9.5 = 0.87 * 0.5 * 60 * 10⁶* A_st/(0.36 * 0.4 * 4000*18)

A_st = 3.77 inch²

M_u = 0.87 * (0.5 *f_y)* A_st * ( d – 0.42 * x_u)

     = 0.87 * 0.5 * 60 * 10³ * 3.77 * ( 21.5 – 0.42 * 9.5)

  = 1.722931 * 10⁶ pound - inch

M_u = w l²/8 (for uniformly distributed load)

w* (336)²/8 = 1.722931 * 10⁶

w(uniform load) = 122 pound/inch   Answer