Determine the elongation of plate:
Q: A steel bar AB which is having uniform thickness 2 cm, tapers from 1.5 cm to 7.5 cm uniformly in a length of 50 cm. From 1^{st} principles determine the elongation of plate; if axial tensile force of 100 kN is applied on it. [E = 2 x 10^{5} N/mm^{2}]
Sol.: Consider small element of length dx of plate, at a distance x from larger end. Then at this section,
Width w_{x}=
Cross-section area A_{x } = thickness × width =
∴ Elongation of elementary length, The total change in length of plate can be worked out by integrating above identity between the limits x = 0 and x = 400 mm. That is: