A rod of length l tapers uniformly from a diameter D at one end to diameter d at other end as shown in Figure 12.8. Considering an small element of thickness dx at distance x from the end of diameter d, the diameter of the element is calculated as 
Figure 12.8 Extension in Taper Rod
Example 12.4: A rod tapers uniformly from 50 to 20 mm diameter in a length of 500 mm. If the rod is subjected to an axial load of 10 kN, find the extension in the rod. Assume E = 2 × 105 MPa.
Solution:
Example 12.5: Determine the elongation of a conical bar under the action of its own weight, if the length of the bar is L, the diameter of the base is D, and the weight per unit volume of the material is ρ.
Solution:
Consider a section of small length dx at a height x from the apex cone (as shown in Figure 12.9) where the diameter is 
, and weight of the cone below the section, 
Figure 12.9 Conical Bar
Total elongation of the bar, 
Leave a Reply