GATE Civil Engineering (CE) 2027 Test: Methods of Indeterminate Analysis

at left end
To keep rotation at right and zero a moment should be applied in anticlockwise direction. Let the moment in M'

Since the member are firmly fixed at E. It is a rigid joint at which all the members will have same rotation. So from slope deflection equations all the members will have moment.

A -3 , B -4 , C - 1 , D - 2

Taking;
- anticlockwise end moment positive
- anticlockwise rotation at member end positive
- anticlockwise chord rotation positive
FEM_ba = 30 kN-m

Distribution Factors 

The principle of superposition states that the displacements resulting from each of a number of forces may be added to obtain the displacements resulting from the sum of forces. This method depends upon the linearity of the governing relations between the load and deflection, The linearity depends upon two factors.
(i) the linearity between bending moment and curvature which depends upon the linear elastic materials  In non-linear material superposition of curvatures is not possible.
(ii) the linearity between curvatures and deflection depends upon the assumption that the deflections are so small that the approximate curvature can be used in place of true curvature.

The distribution factors for member AB and SC at S will be 0.5 for both.
Thus member end moment at BC is M.
From carry over factor of 1/2, member end moment at C = M/2

This reaction is away from B so axial force in member AB is tensile. This can be found from free body diagram of AB. Similarly axial force in member BC will also be   but compressive.