The exact expression for the mid-span displacement is (Ref. 3)


Comparing the exact (Eq. (v)) and approximate results (Eq. (iv)) we see that the difference is less than 2 per cent. Further, the approximate displacement is less than the exact displacement since, by assuming a displaced shape, we have, in effect, forced the beam into taking that shape by imposing restraint; the beam is therefore stiffer.

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