Calculated the slope of the cantilever:
Calculated the slope of the cantilever given in Example 6 at its free end.
Solution
To find out rotation in a beam we must have a couple working at that point. Since at the free end, there is no couple, we introduce a fictitious couple M′ as illustrated in Figure
Figure
Now M =- Px - M ′ & ∂M / ∂M ′ = - 1
θA = PL^{2}/ 2EI (Positive sign denoted rotation in the sense of M′, that means clockwise).
Therefore, we see that the tip slope of a cantilever loaded along a concentrated vertical
force P at its free end is PL^{2} /2EL