Structural Analysis-II — Winter 2023

Explain the characteristics of flexibility matrices.

State and explain Castigliano’s first theorem.

Find the deflection under the 60 kN load for the beam shown in figure.1 by Castigliano’s first theorem. Assume E = 200 GPa, I = 24 x 106 mm4.

Draw qualitative ILD for support reactions of two equal spans continuous beam with all simple supports.

Write and explain Muller Breslau’s principal.

Apropped cantilever beam is having 10 m span. Draw ILD for shear force at section 4 m from the fixed end.

Draw ILD of top chord and bottom chord member for a warren truss shown in figure 2.

Define: (1) Carry over moment. (2) Absolute maximum bending moment (3) Distribution factor.

Atwo span simple support continuous beam ABC having AB=5 m and BC = 6m. The span AB is loaded by a point load at centre by 30kN and span BC is loaded by a UDL of 40 kN/m over entire span. Analyze the beam by moment distribution method and draw BMD.

Analyze the beam shown in figure 3 by slope deflection method and draw bending moment diagrams.

Define: Sway. What are the causes for Sway in portal frames?

Define and explain distribution factor with example.

Draw the bending moment diagram for the beam as shown in figure 4. When support Bsinks by 10 mm. Assume E = 200 GPa, I = 132 x 106 mm4 for all the members. Using moment distribution method.

Generate the stiffness matrix for a prismatic cantilever with coordinates as shown in figure 5.

Differentiate: Stiffness method and Flexibility method.

Find the matrices: [AD], [ADL], [S] and [D] with usual notations for the beam shown in figure 6, using Stiffness method.

Write assumptions made in slope deflection method.

Define Stiffness. Derive relation between stiffness and flexibility.

Analyze the beam ABC using Stiffness method fixed at Aand rollers at Band C. EI of span AB and BC are EI and 3EI respectively. Span AB caring uniformly distributed load of 10 kN/m and span BC caring concentrated load of 16 kN at center. Span AB = BC = 10m.1

For two span continuous beam having span AB = 3m and BC = 4m, draw qualitative ILD for support reactions.

Write slope deflection equation for the beam shown in figure 4. When support Bsinks by 10 mm.

Find the matrices: [DQ], [DQL], [F] and [Q] with usual notations for the beam shown in figure 6. Use Flexibility method assuming Mand A Mas redundant. B

State Castigliano’s second theorem and its usefulness in analysis of structure.

Asimply supported beam AB has span 8 m. Draw ILD for R , R ,Vx, A B Mx for section Xat 3 m from left hand support.

Determine support reactions for propped cantilever beam AB of span 4m. It carries point load of 16 kN at 3m from left support. Fig. 1 Fig 2. Fig. Fig. Fig. Fig. 62