GATE Papers >> Civil >> 2015 >> Question No 143

Question No. 143 Civil | GATE 2015

A simply supported beam AB of span, L = 24 m is subjected to two wheel loads acting at a distance, d = 5 m apart as shown in the figure below. Each wheel transmits a load, P = 3 kN and may occupy any position along the beam . If the beam is an I-section having section modulus, S = 16.2 cm3, the maximum bending stress (in GPa) due to the wheel loads is_____________.


Answer : 1.78 to 1.79


Solution of Question No 143 of GATE 2015 Civil Paper

Maximum Bending stress will occur on the section having max. 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,

RA + RB = 6 kN

$\sum$MA = 0

$\therefore$ RB $\times$ 24 = 3 $\times$ 8.25 + 3 $\times$ 13.25

RB = 2.6875 kN

RA = 3.3125 kN

${\mathrm\sigma}_\mathrm b=\frac{\mathrm M}{\mathrm Z}=\frac{28.89\times10^6\mathrm N-\mathrm{mm}}{16.2\times10^3\;\mathrm{mm}^3}$

= 1783.33 N/mm2

= 1.783 $\times$ 103 $\times$ 106 N/m2

= 1.783 GPa

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