Maximum deflection of a beam

Question

Imagine having a equation of a beam as follows and we have to solve this for x. Note that the [] square brackets denote terms involving Macaulay's notation.

How do we solve for x when Macaulay's notation is involved.

w/2(x^2) - w/2[x - L/2]^2 - (wL^2)/8 = 0

Answer 1

The equation can be broken up into

w/2(x²) - (wL²)/8 = 0 for x - L/2 < 0, or x < L/2

and

w/2(x²) - w/2*(x - L/2)² - (wL²)/8 = 0 for x - L/2 >= 0, or x >= L/2

So now you have 2 equations you can work with, and when you find the maximum deflection in each zone, make sure the x value make sense for the zone you're in.