Strength of Materials

3.3 STRAIN ENERGY DUE TO SELF-WEIGHT

A bar of uniform cross section A and of length l in a vertically hung position is considered (Figure 3.4). Further, a strip of d_x at a distance x from the lower end is also considered.

 

 

Fig. 3.4 Bar of uniform cross section.

 

The strip is acted upon by the weight of the bar of length, x.

Let ρ be the density of the material of the bar.

 

Weight acting on the strip	= (A × x) × δ = δAx
Strain in the strip of thickness,

where δx_s is the elongation in dx

 

Stress in the strip, ...