5003 Lectures - Faculty of Engineering and Applied Science

E5003 - Ship Structures I 124
© C.G. Daley
Example 1 of Betti-Maxwell
For a simple cantilever, the deflection at x2 caused by
a force F at x1 should be the same as the deflection at
x1 when F is applied at x2 :
Solution:
The beam deflection tables (see Appendix) can be
used to find ∆12 and ∆21 .
To find ∆21 we first find the deflection at x1 . The
beam to the right of x1 has no shear or bending.
Consequently it is perfectly straight. It slopes
downward at the same angle as the slop at x1 , which
is θ11 . The addition deflection past is just equal to
the slope angle times the distance. The total
deflection at x2 found as follows: