Question

Maximum bending moment at the point P in the simply supported beam, when it is traversed by the moving load from left to right as shown in figure below is:

• A. 120 kNm
• B. 60 kNm
• C. None of these
• D. 240 kNm

Answer 1

The correct option is D 240 kNm

	Average load on AP Average load on PB
20 kN crosses P	$(\frac{30+60+40}{6}=21.67)>(\frac{20}{4}=5)$
40 kN crosses P	$(\frac{30+60}{6}=15)=(\frac{20+40}{4}=15)$
60 kN crosses P	$(\frac{30}{6}=5)<(\frac{20+40+60}{4}=30)$

Place either 40 kN or 60 kN at P to get more $B{M}_P$

Influeuce line for bending moment at P

Bending moment at P , when 60 kN load is at P then
$M_{atp}=30\left(1.6\right)+60\left(2.4\right)+40\left(1.2\right)+20\left(0\right)=240kNm$
Bending moment at P, when 40 kN load is at P then
$M_{atp}=20\times 1.2+40\times 2.4+60\times 1.6+30\times 0.8=225$