Question

If a rectangular beam measuring 10 × 18 × 400 cm carries a uniformly distributed load such that the bending stress developed is 100 kg/cm2. The intensity of the load per metre length, is (a) 240 kg (b) 250 kg (c) 260 kg (d) 270 kg answer: option b

Answer 1

The correct answer is 270 kg.

Bending Stress = f = M/Z (Moment / section Modulus).

100 kg/cm2 = (WL^2/8)/(1/6 bd^3) M = 100/6 x 10 x 18^2.

M = 54,000 Kg.cm - 540 Kg.m.

M = WL^2/8= 540.

W = 8 * M / L^2.

W = 8 * 540 / 4^2.

W = 270 Kg.

Answer 2

Concept:

Bending stress: When an object is subjected to a heavy load at a specific spot, it often experiences bending stress, which causes the object to bend and tyre.

Given:

The dimension of a rectangular beam is $10\times18\times400cm$.

The bending stress developed in the rectangular beam is $100kg/cm^2$.

Find:

The intensity of the load per meter length.

Solution:

A rectangular beam with dimension $10\times18\times400cm$ carries a uniformly distributed load.

The bending stress, $\sigma =100kg/cm^2$.

Now we know,

Bending stress = Moment/Section Modulus

So, $\sigma =\frac{M}{Z}$

$100=\frac{M}{\frac{bd^2}{6} }$

$M=\frac{100}{6}bd^2$

$M=\frac{100}{6}\times10\times18^2$

$M=54000kg.cm=540kg.cm$

Now,

Moment, $M=\frac{WL^2}{8}$

$540=\frac{W\times4^2}{8}$

$W=270kg$

Therefore, the intensity of the load per meter length is $270kg$.

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