Example 5.23 Analyze the continuous beam shown in Figure 5.27(a) by the three moment equation. Draw the shear force and bending moment diagram.

Solution: The effect of a fixed support is reproduced by adding an imaginary span as shown in Figure 5.27 (b). The moment of inertia, of the imaginary span is infinity so that it will never deform and the compatibility condition at the end A , that slope should be is zero, is satisfied.

Applying three moment equation to the span and AB :

or                                                 + = – 135                                                                                                                           (i)

Span AB and BC :

or                                                 + = – 225                                                                                                                           (ii)

Solving Eqs. (i) and (ii), = – 45 kNm and = – 45 kNm

The shear force and bending moment diagram are shown in Figures 5.27(d) and (e), respectively.