24 in 27 in 4 9 bars 3 in 15 in Figure 4 Problem VII Questio

24 in. 27 in. 4 #9 bars 3 in, 15 in. Figure 4 Problem VII- Questions 31 and 36 refer to the problem below A rectangular beam is shown in Figure 4. The beam is made with normal weight concrete (NwO)·The concrete compressive strength and the rebars yield strength are fc-6ksi and fy-60 ksi, respectively 31) The depth of the neutral axis (c) for the cracked inelastic range at ultimate conditions is: A. 5.54 in B. 5.9 in C. 3.80 in D. 3.69 in 32) Given than the depth of the neutral axis can be computed as c = api, the value of is: A. 0.65 B. 0.8 C. 0.85 D. 0.9 33) The minimum reinforcement ratio (Pmin) is: A. 0.33% B. 1.39 in2 C. 0.39% D. 1.2 in2

Solution

Solution:-

(31) Answer(B) 5.9 inch

X_u = 0.87 fy *A_st/(0.36*f_ck*b)

     = 0.87*60000 * /4*(1.128)²*4/(0.36*6000*15)

    = 6.46 inch

X_umax/d =0.48

X_umax = 0.48* 24 = 11.52 inch

Section is under reinforced so neutral axis =6.46 inch but this is not given in option so we have to choose near value

then neutral axis of section =5.9 inch

(32) Answer( B) 0.8

(33) Answer (A) 0.33%

Minimum reinforcement ratio =0.85/f_y =0.85/415 =0.2%

This is not given in option so we have to choose near value 0.33%

Where fy = 60000 psi =415 N/mm²