35 Problem 1 A rectangular concrete beam of width b 16 in i

35 Problem 1: A rectangular concrete beam of width b = 16 in, is limited by architectural considerations to a maximum total depth h 22 in. It must carry moment Mu 450 ft-kips. Design the flexural reinforcement for this member. Material strengths are fy = 60,000 psi and f.-4500 psi. Select reinforcement to provide the needed areas, and show a sketch of your final design a total factored load

Solution

Solution:-

Given

Moment (M_u) = 450 kip feet

b = 16 inch

h = 22 inch

Let cover = 2 inch

Effective depth (d ) = 20 inch

F_y   = 60000 psi

F_ck = 4500 psi

We know that

M_u = 0.87 f_y A_st ( d - f_y A_st/( f_ckb))

450 *10³ *12 = 0.87 * 60000 * A_st (20 – 60000*A_st/(4500 * 16))

A_st = 7.54 inch²

Let # 9 rebars are used . Diameter of bars are 1.128 inch

Total number of bars = A_st/(/4 * (1.128)² )

Total number of bars = 7.54/(/4 * (1.128)²)

Total number of bars = 8      Answer

Provide total 8 number of bars @ 1.128 inch diameter