24 in. 27 in. 4 #9 bars 3 in, 15 in. Figure 4 Problem VII- Questions 31 and 36 r

Question

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

Explanation / Answer

Solution:-

(31) Answer(B) 5.9 inch

Xu = 0.87 fy *Ast/(0.36*fck*b)

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

    = 6.46 inch

Xumax/d =0.48

Xumax = 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/fy =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

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