What is the Elongation of a Bar by its Self Weight?

A bar suspended freely from a fixed end is subjected to an elongation dlwhich is caused by its own weight. Here, the value of elongation of a freely suspended bar is determined.

 Elongation of a Bar by its Self Weight Consider a bar AB that is freely suspended, with one end fixed. The length of the bar be 'L', area of cross-section be 'A', 'E' be the modulus of elasticity and 'w' is the weight per unit volume of the bar material.
Consider a small strip of thickness'dx' at a distance 'x' from the free end 'B'. Step 1: Weight of the bar of the length 'x'  Let the weight of the bar of length 'x' be P. Then,
P = Specific weight x Volume = Specific weight x area x thickness = w . A.x
This implies, on the strip of length 'x' a weight is acting downwards whose value is P = wAx. Step 2: Stress on the element 'dx' The stress on the element 'dx' is given by  = Weight acting on the element / Area of …

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