Strength of Materials

1.11 BARS OF VARYING CROSS SECTIONS

In practice, one may come across with bars of varying cross sections (e.g., circular or rectangular). In such cases, it is usual to assume that the load is distributed over the cross section as inversely proportional to the area.

1.11.1 Bars of Circular Cross Section

A bar of length l tapering uniformly from a diameter D at one end to a diameter d at the other is considered (Figure 1.18).

 

 

Fig. 1.18 Bar with varying circular cross section.

 

A small strip of length dx at a distance x from the small-diameter end is considered. Diameter at this level is

 

 

Extension of this strip due to the load P acting ...