Consider a small element of length dx of the plate, at a distance x from the larger end. Then at this section,
Width wx = 100 – (100 – 50) x/400 = (100 -x/8)mm
Cross-section area Ax = thickness × width = 10(100 -x/8)mm2
∴ Elongation of the elementary length,
The total change in length of the plate can be worked out by integrating the above identity between the limits x = 0 and x = 400 mm. That is:
