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The beam will only give the vertical reaction. There will not be any horizontal reaction from the beam. Let's draw the moment diagram parts. The reaction at support B gives a triangular moment and the moment M remains the constant.
Section (1) in the diagram shows the region or area due to the moment in a rectangular form while the triangular area (2) is due to the reaction of support B.
Now apply the moment area method. Consider the moment about point B. The distance of the centroid is given by L/2 and 2L/3.
The area due to the moment M (rectangle), A1 = ML
The area due to the support reaction (trinagle), A2 = -1/2 L(ByL)
Now apply moment area method,
The boundary condition is that deflection remains zero at end A and end B.
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