Problem 1 Design and detail a reinforced concrete beam with

Problem 1: Design and detail a reinforced concrete beam with fixed dimensions ofb-20 inch and h-24 inch with fe -4,500 psi and fy 60,000 psi subjected to the bending moments: (a) Mu .. 250 ft.k, (b) Mu-550 ft.k and Mu-800 ft.k

Solution

Solution:-

Given

b =20 inch ,h = 24 inch

Let cover = 2 inch

Effective depth(d) =22 inch

f_y =60000 psi , f_ck =4500 psi

(1)    M_u = 0.87f_yA_st(d - f_yA_st/(f_ckb))

     250 *12*10³ = 0.87*60000*A_st(22 – 60000A_st/(4500*20))

    A_st = 2.96 inch²

Let 1.28 inch diameter bars are used

Total number of bars = 2.96/(/4*(1.128)²)

                                        = 3

(2)

When M_u = 550*12*10³ lb-inch

550*12*10³ = 0.87*60000*A_st*(22 – 60000A_st/(4500*20))

A_st = 7.848 inch²

Provide 1.128 inch diameter bars

Total number of bars = 7.848/(/4*(1.128)²)

                                       = 8

(3) When M_u = 800 feet- k = 800 *12*10³ lb-inch

A_st = M_u/(0.87f_y(d -0.42x_max)

X_max =0.48*d =0.48 *22 =10.56 inch

A_st = 800 *12*10⁶/(0.87*60000(22 – 0.42*10.56))

A_st = 10.47 inch²

Let 1.128 inch diameter bars are used

Total number of bars = 10.47/(/4*(1.128)²)

                                       = 11