Structural Analysis-I — Summer 2022

i. State assumptions and limitations of Euler’s formula. ii. Draw neat sketch of different end conditions of column and its effective length.

Give equations of Static and Kinematics Indeterminacy for the following structures with meaning of each term used. (i) Beam, (ii ) Plane truss, (iii) Plane Frame ,(iv) Grid

i. Differentiate Conjugate beam and real beam ii. State and explain moment area theorem.

Using moment area method, calculate slope and deflection at free end of a cantilever beam, subjected to UDL of intensity ‘w’ over entire span ‘l’. Take EI = constant.

Find deflection at centre of a simply supported beam of length ‘l’ carrying a concentrated load ‘W’ at centre. Take EI = constant.

i. Define Core of the Section. Derive and locate the same for a Circular cross section. ii. Discuss Stability checks for a dam

Ahollow rectangular column cross section has 200 x 150 mm external dimension with 20 mm thickness. Avertical load of 40 kN acts at an eccentricity of 30 mm on diagonal direction. Find maximum and minimum stress induced.

i. Differentiate between long and short column. ii. Define the following terms. (i) Crippling load (ii) Effective length, (iii) radius of gyration, (iv) slenderness ratio.1

Afixed beam AB of span Lcarried a UDL of w per meter length over entire span. Support Bsettles during application of load. Calculate the settlement, so that there is no fixed end moment at B. Also find FEM at A.

i. Explain Arch and Cable. ii. Define and explain : Anchor cables

i. Enlist the types of framed structures with neat sketch ii. Acylindrical shell 4 m long and 660 mm in diameter with 8 mm thick plates is subjected to an internal pressure of 5 MPa. Calculate (i) circumferential stress (ii) longitudinal stress. Take E = 200 GPa and Poisson’s ratio = 0.3 for the shell material.

i. Explain advantages of three hinged arch over beam. ii. Athin cylindrical shell of internal diameter d, wall thickness t and length I, is subjected to internal pressure p. Derive the expression for change in volume of the cylinder

Athree hinged parabolic arch of span Land central rise “yc” carries a uniformly distributed load of “w: per unit length over the left half of the span. Show that the max positive moment is equal to wl2 /64

i. Define resilience, proof resilience and modulus of resilience. ii. Derive the equation of the strain energy stored in a member due to torsion.

Afixed beam AB of span ‘l’ carries a u.d.l. w kN/m over entire span. The Moment of Inertia of the beam from either end to a distance of l/4 is Iand 2I for the remaining length. Determine the end moments.

i. Find out fixed end moment for a fixed beam subjected to a point load (W) at the center of the span (L). Also draw shear force and bending moment diagrams. ii. Derive an expression for strain energy stored in a body when the load is applied suddenly.

Acantilever beam of span Lcarries Uniformly Distributed Load ‘W’ per unit run. Find the strain energy stored in the beam.