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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
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B
67.5
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C
200.0
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D
225.0
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Solution

The correct option is B 67.5


RA+RB=6000N
Taking moment about A
600×3RC×4=0
Rc=4500N
RA=1500N

Taking any section x m from A.
Shear force =1500300(x2)
and maximum bending moment occurs where shear force = 0
15003000(x2)=0
x=2.5 m
or 2500 mm from A
Maximum bending moment,
(BM)max=1500x30002(x2)2

at x=2.5 m

(BM)max=1500×2.51500(0.5)2

= 3375 N-m

Bending stress,

σ=Mz
where z=16bd2

σ=6×337530×1002×109


=67.5×106N/m2=67.5MPa

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