
3.38. A horizontal cantilever beam of length L fixed at its left end is loaded at its right end by a
downward acting force F. Length L is deterministic and force F is a random variable with mean value
µ
F
and standard deviation σ
F
. (a) Find the respective mean values and standard deviations for the
reaction shear force S and resisting moment M. (b) Find the correlation coefficient ρ
SM
between S and
M. Based on your result, what can be concluded about the functional relation between S and M?
Solution: The shear force and the moment at the wall are given by
S = F and M = F L.
(a) The respective mean values and standard deviations are
µ
S
= E {S} = E {F } =