A beam PQRS is 18 m long and is simply supported at points Q and R 10m apart. Overhangs PQ and RS are 3 m and 5m respectively. A train of two point loads of 150 kN and 100 kN, 5m apart, crosses this beam from left to right with 100 kN load leading.
The maximum sagging moment under the 150 kN load anywhere is

500 kNm

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400 kNm

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450 kNm

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375 kNm

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Solution

The correct option is B 400 kNm

Sagging moment occurs when the load occupies the position in the portion QR of the beam and maximum bending moment occurs under the load when the resultant of loads and the load under which moment is to be calculated,is equidistant from the centre of the beam.

Taking moment about A,
$R . x = 100 \times 5$
x= $\frac{100 \times 5}{250} = 2 m$

Vertical reaction,
$R_{Q} = 150 \times \frac{6}{10} + 100 \times \frac{1}{10}$
= 100 kN
Sagging moment under 150 kN load = $R_{Q} \times 4$
=400 kNm.

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