The second moment of area of a rectangle through its centroid is given by:

Question

bL3/12
Using the approximation for binomial series valid for small x (+ve or –ve):

(1+x)^n=1+nx/1!+(n(n-1) x^2)/2!+⋯ 1+nx
Determine the approximate change in the second moment of area if b is increased by 1.5% and L is reduced by 2.0%

please help, this is sample question of assessment which I have tomorrow.

Thanks

Answer 1

If M = bL^3/12
replace b by 1.015b
and L by 0.98L
and you have

(1.015b)(0.98L)^3/12
= (1.015*0.98^3)bL^3/12
= 0.955M

so, M has decreased by 4.5%

I see no reason to resort to binomial approximation. But, if you want to try it, and compare results, feel free.