Determine the reactions and draw the shear and bending moment diagrams for the structure...

Degrees of indeterminacy:

Total number of reactions of the given beam is, but we have only three equilibrium equations,

Therefore degree of indeterminacy of the beam is given by

Primary beam:

Obtained by removing the interior support B from the given indeterminate beam

Primary beam subjected to external loading

Where, denotes the deflection at B due to external loading

Therefore from virtual work method, deflection at B is obtained by

Primary beam subjected to unit value of the redundant

Where, denotes the deflection at B due to unit value of the redundant

Therefore from virtual work method, deflection at B is obtained by

Compatibility equation:

The compatibility equation can be expressed as

By substituting the values of and into the compatibility equation (1), we determine the redundantas

Therefore remaining reactions obtained by

From the equilibrium equations:

Sum of forces in X- direction is zero.

Sum of forces in Y- direction is zero.

Shear and bending moment diagrams