Question

A rectangular beam of width 230 mm and effective depth 300 mm is proposed to carry a BM and SF of 120 kNm and 270 kN, respectively. If M30 grade of concrete and Fe 415 steel are used for which ${\tau }_{cmax}$ = 3.5 MPa, which one of the following statements is correct?

• A. It can be designed as a singly reinforced, under-reinforced section.
• B. It can be designed as a doubly reinforced section.
• C. The section is unsafe from shear considerations.
• D. It can be designed as a doubly reinforced section but it is unsafe from shear considerations

Answer 1

The correct option is D It can be designed as a doubly reinforced section but it is unsafe from shear considerations



$M_u=1.5\times 120=180kNm$

$V_u=1.5\times 270=405kNm$

${\tau }_v=\frac{V_u}{bd}=\frac{405}{230\times 300}$

$=5.86N/m{m}^2>{\tau }_{cmax}$ (Not safe)

$M_{ulim}=0.36f_{ck}b{x}_{ulim}(d-0.42x_{ulim})$

$=0.36\times 30\times 230\times 0.48\times 300\times (300-0.42\times 0.48\times 300)\times {10}^{-6}$

$=85.67kNm<M_u$

(so design as doubly reinforced beams)