Find out ratio of  upper end area to lower end area  of bar of uniform strength

Sol: The figure given to us shows a bar subjected to external tensile load P. If bar had been of uniform cross- section, tensile stress intensity at any section would be constant if the self weight of member is ignored. If weight of the member is considered, the intensity of stress increases for sections at the higher level. It is possible to maintain uniform stress of all the sections by increasing area from lower end to upper end. Let the areas of upper and lower ends be A₁ and A₂. Let A be area at distance x and A + dA at a distance x + dx from lower end. Let weight per unit volume be w Making force balance for the element ABCD.

  
  Assuming w and s to be uniform