Question

An overhanging beam PQR is subjected to uniformly distributed load 20 kN/m as shown in the figure.



The maximum bending stress developed in the beam is ____ MPa [Round off to one decimal place]

• A. 250

Answer 1

The correct option is A 250
$M_D-M_A=\frac{1}{2}\times 15\times 0.75$

$\sum M_A=60\times 1.5-R_B\times 2=0$

$M_D=5.625kN-m\left(s\right)$

$R_B=45kN(\uparrow );R_A=15kN(\uparrow )$

Location of D:

$\frac{15}{x}=\frac{25}{2-x}$

$6-3x=5x$

$=\frac{3}{4}m$

$M_C-M_B=\frac{1}{2}\times 20\times 1$

$M_B=10kN-m$

$M_B=10kN-m$(+1)

Max.B.M. = Larger of ($M_{B}and{M}_D$)

$M_B=10kN-m$ (+1)

$({\sigma }_b{)}_{max}=\frac{M_{max}}{Z_{NA}}=\frac{6\times 10\times {10}^6}{24\times {100}^2}=250MPa$