Example

Determine, using the unit load method, the deflection at C of a simple beam of constant cross-section loaded as shown in Figure 2.68a.

Solution

The bending moment diagram for the beam due to the applied loading is shown in Figure 2.68b. A unit load is applied at C where it is required to determine the deflection as shown in Figure 2.68c and the corresponding bending moment diagram is shown in Figure 2.68d. Now, using Equation 2.128, we have fL Mm dx dC = 1 ~eT

1 n4, J3 \ , 1 r3L'4fWL\ 1, = — (WxU -x dx + — - - (L - x) dx

EI J o ( \4 J EIJl/4 W/4( ) 1 fL 1 + -ei J W (L - x) 4(L - x) dx

Further details on energy methods in structural analysis may be found in Borg and Gennaro (1959).

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