Example 5.2 Determine the support reactions of the fixed beam with internal hinge as shown in Figure 5.3(a).

Solution: The static indeterminacy of the beam is = 4-2-1 =1 Let the shear in the internal hinge be R . The free body diagrams of the two separated portions of the beam are shown in Figure 5.3(b) along with their M/EI diagrams. The unknown R can be obtained with the condition that the vertical deflection of the free ends of the two separated cantilever beams is identical.   

Consider AC : The vertical displacement of C is given by

Consider CB : The vertical displacement of C is given by

Equating the from Eqs. (i) and (ii)

Solving for R will give

The reactions at the supports are given by