Question

A massless beam has a loading pattern as shown in the figure. The beam is of rectangular cross- section with a width of 30 mm and height of 100 mm.

The maximum magnitude of bending stress (in MPa) is given by

• A. 60.0
• B. 67.5
• C. 200.0
• D. 225.0

Answer 1

The correct option is B 67.5



$R_A+R_B=6000N$
Taking moment about A
$600\times 3-R_C\times 4=0$
$\Rightarrow$ $R_c=4500N$
$R_A=1500N$

Taking any section $xm$ from A.
Shear force $=1500-300(x-2)$
and maximum bending moment occurs where shear force = 0
$\Rightarrow 1500-3000(x-2)=0$
$x=2.5m$
or $2500mm$ from A
Maximum bending moment,
$(BM{)}_{max}=1500x-\frac{3000}{2}(x-2{)}^2$

$atx=2.5m$

$(BM{)}_{max}=1500\times 2.5-1500(0.5{)}^2$

= 3375 N-m

Bending stress,

$\sigma =\frac{M}{z}$
$wherez=\frac{1}{6}b{d}^2$

$\therefore \sigma =\frac{6\times 3375}{30\times {100}^2\times {10}^{-9}}$


$=67.5\times {10}^{6}N/m^2=67.5MPa$