Question

A simply supported beam AB of span L = 24 m is subjected to 2 wheel loads acting at a distance d = 5m apart as shown in the figure below. Each wheel transmits a load P = 3 kN and may occupy
any position along the beam. If beam is an I-section having section modulus; S = $16.2c{m}^3$, the Maximum bending stress (in Gpa) due to the wheel load is ________.

• A. 0.1783
• B. 1.783
• C. 1783.33
• D. 17.83

Answer 1

The correct option is B 1.783

Maximum Bending stress will occur on the section having maximum bending moment.
Max. bending moment will occur in the beam when the center of the beam lies midway between the load and C.G of the series of load




Now,


$R_A+R_B=6kN$
$\sum M_A=0$
$\therefore$ $R_B\times 24=3\times 8.25+3\times 13.25$
$R_B=2.6875kN$
$R_A=3.3125kN$


${\sigma }_b=\frac{M}{Z}=\frac{28.89\times {10}^{6}N-mm}{16.2\times {10}^{3}m{m}^3}$
= 1783.33 $N/m{m}^2$
= $1.783\times {10}^3\times {10}^{6}N/m^2$
= 1.783 GPa