Using the slope deflection method, compute the end moments and plot the bending moment diagram. Also, sketch the deflected shape of the beam. The beam has constant EI for both the spans.
Treating each span as a fixed beam, the fixed end moments are as follows:. The end rotations q A and q C are zero since the beam is fixed at A and C. Let us assume q B to be positive.
The result will indicate the correct sign. The slope deflection equations are as follows:. For span AB,.
Find deflection and slope of a simply supported beam with a point load (double integration method)
For span BC ,. Since there is only one un known, i.
For the joint B, we have. The plus sign indicates that q B is positive i. Substituting the values of EI q B in Eqa. These are the same as calculated in the previous problem:.
Since end A is freely supported,. The bending moment diagram and the deflected shape of the beam are shown in the Fig. The beam is statically indeterminate to single degree only. This problem has also been solved by the moment distribution method example However, in the4 slope- deflection method, the slope or rotations are taken as unknowns, and due to this the problem involves three unknown rotations q A , q B and q C.
Determine the bending moments at the supports and plot the bending moment diagram. Substituting this values in Eqs. The bending moment diagram and the deflected shape are shown in Figure.
Treating joint B as rigid, analyze the frame and plot the bending moment diagram and the deflected shape of the structure. The slopes q A and q D are zero since ends A and D are fixed.
For span AB. Substituting this value of EI q B in Eqs. The bending moment diagram and. The deflected shapes are shown in Figure.
The column AB is 3m long. The moment of inertia is 2. Plot B. Let the joints B and C move horizontally by d.
At joint B,. Draw the bending moment diagram and deflected shape of the frame. Developed by Therithal info, Chennai. Toggle navigation BrainKart. Related Topics Influence lines.
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