Theory of Structure II

a) Describe the degree of static indeterminacy and the degree of kinematic indeterminacy of a structural system with suitable expressions and examples. [5] b) Determine the moment at the fixed support of the following loaded beam using Castigliano's theorem. Take EI constant. [6] c) Enuciate Mueller-Breslau principle of influence line and prove it with an example of a continuous beam.

a) Analyse the continuous beam loaded as shown in figure below and draw the bending moment diagrams using slope-deflection method. Support B sinks by 19 mm. [12] Take $EI=10,000{\text{ KN-m}}^2$ b) Define plastic hinge. Also compare plastic and elastic hinges of a structural system.

a) Explain the principle of moment distribution method with a simple example. [6] b) A portal frame of span 4 m and height 4 m is fixed at both supports. The beam of the frame carries a uniform distributed gravity load of intensity 30 KN/m. Use Force method to solve the frame considering the cross-sectional stiffness (EI) to be constant. Draw bending moment, shear force and normal thrust diagrams for the frame.