Stress in a Bars due self weight and Varying section

Stress in a Bar due to its own Weight :-

Consider a bar of length(l) and diameter(d) rigidity fixed at the upper end and hanging freely. The stress at any section in a bar due to its own weight is directly proportional to the distance from the free end. Therefore, stress at a distance x from the free end.

 = w.x

and total elongation of the bar,

∂l = w.l2 / 2E                  [w= weight per unit volume of the bar.]

*** When a conocal bar of the length(l) and base diameter(d) is rigidly fixed with its base diameter at the upper end is hanging freely, then the total elongation of the bar due to its own weight is given by,…

∂l = w.l2 / 6E


Stress in Bars of varying section :-

When a bar is made up of different lengths having different cross-section areas, and is subjected to an axial force P,

then the total deformation of the bar,…

∂l = ∂l1+∂l2+∂l3+…….

      = P.l1/A1.E + P.l2/A2.E + P.l3/A3.E +…….

      = P/E{l1/A1 + l2/A2 + l3/A3 + ……..}

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