The deformation of the bar of rectangular section under its own weight is equal to ____ the deformation due to a direct load equal to the weight of the body applied at the lower end.

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The deformation of the bar of rectangular section under its own weight is equal to ____ the deformation due to a direct load equal to the weight of the body applied at the lower end.

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JKSSB JE Mechanical 02 Nov 2021 Shift 1 Official Paper

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three times
two times
four times
half

Answer 1

Deformation under own weight

Consider a small strip ‘dx’ at a distance ‘x’ as shown in figure. We shall find change in length for ‘dx’ and then integrate for whole length. Force exerted by weight below strip ‘dx’

Force (P) = Volume below ‘dx’ x specific weight = A × ρ (A = cross – sectional area)

Elongation of the strip

For total elongation integrate and take limits

…..i)

Now elongation due to load (W)

Load = own weight (given)

W = ρlA

……ii)

Now form equation (i) and (ii)

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The deformation of the bar of rectangular section under its own weight is equal to ____ the deformation due to a direct load equal to the weight of the body applied at the lower end.

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