Structural Analysis-II — Winter 2022

State and explain Castigliano’s second theorem with example.

Derive slope-deflection equations from first principles.

Using Castigliano’s 1st theorem, calculate the deflection at point Cfor the beam shown in Figure - 1. Take EI = 10 x 1013 Nmm2

Explain causes of side-sway in plane frame with illustrations.

Calculate deflection at free end Cfor a cantilever beam ABC having length 6m shown in figure - 2 using energy principle. EI = 10 x 1013 N mm2

Draw the bending moment diagrams for the beam shown in figure 3. Use Slope Deflection Method.

Find the matrices: [DQ], [DQL], [F] and [Q] with usual notations for the beam shown in figure 4. Use Flexibility method assuming vertical support reaction at B (RB) and vertical support reaction C (RC) as redundant.

Define: Stiffness, Distribution factor, Carry over factor

Analyze the beam shown in Figure – 3 by Moment Distribution method. Also draw the Bending Moment Diagram.

Analyze the portal frame shown in Figure – 5 by Moment Distribution method. Also draw the Shear force and Bending Moment Diagram.

State and explain the Muller-Breslau’s Principle.

For cantilever of span Ldraw ILD for support reactions and shear force and bending moment at center.

For a propped cantilever beam AB, fixed at Aand having roller support at B, of span 7m, draw ILD for RB. Calculate ordinates of ILD at every 1m interval.

Calculate slope-deflection equations for the portal frame as shown in figure – 6.

Find the fixed end moment and distribution factors for the beam shown in figure – 4.

Figure-7 shows the beam AB having varying moment of inertia. It is subjected to an eccentric load. Calculate the moment under the load using Castigliano’s 2nd theorem.

Enlist the properties of Stiffness matrix.

Write only the Stiffness matrix [S] for the beam shown in Figure – 4. (Take AE and EI = Constant).

Analysis the beam shown in Figure – 8 by Flexibility method. Take EI=constant. (Take MB as Q1 and MC as Q2 as redundant).

Explain with illustrations the characteristics of flexibility matrices.

For a 5 m span propped cantilever beam AB, fixed at Aand having roller support at B, Draw ILD for RB showing ordinates of ILD at every 1m interval.

Draw bending moment diagram for the frame shown in fig. 6 using Slope Deflection Method.

For two span continuous beam having span AB = 3m and BC = 3m, draw qualitative ILD for support reactions. (all supports are simply support)

Differentiate the influence line diagram for BM at any section and normal BM diagram. Explain this with taking simple example.

Find the matrices: [AD], [ADL], [S] and [D] with usual notations for the beam shown in figure - 8, using Stiffness method.