Structural Analysis-I — Summer 2023

Differentiate Real Beam and Conjugate Beam.

Write advantages and disadvantages of indeterminate structures over determinate structures.

Analyse the frame as shown in fig.-1 and draw AFD, SFD and BMD.

Explain Maxwell’s reciprocal theorem.

Acantilever beam of span 4m is subjected to a UDL of 20 kN/m over entire span. Calculate deflection at free end by Macaulay’s method.

Find slope and deflection at free end Cfor a cantilever beam as shown in fig.-2 by conjugate beam method.

Find slope at Aand deflection at Cfor a simply supported beam AB as shown in fig.-3 by any method. Take EI to be constant.

Explain SI and KI with illustration.

Derive the formula to find dimension of the core for a hollow circular section.

Ashort column has a hollow square section. The external dimensions are 500 mm x 500mm and thickness of section is 100mm. Aload of 1500 kN is acting on Xaxis at an eccentricity of 100mm from center. Find maximum and minimum stress intensities and draw stress distribution diagram.

Explain theorems of moment area method.

Ahollow cast iron column of 250mm external diameter and 150mm internal diameter is 4m long. Find Euler’s crippling load if both the ends are hinged. Take E=120GPa.

Derive Euler’s formula for crippling load for a column having one end fixed and other end free.

Describe types of arches.

Explain actual arch and linear arch.

Athree hinged parabolic arch has a span of 25m and a central rise of 4m. It carries a point load of 70 kN at 10m horizontally from left end hinge. Calculate normal thrust, shear force and B.Munder the load. Also draw BMD.

Write assumptions made in the Euler’s column theory.

Explain how reactions are found out on a guide pulley support and saddle on roller support for suspension cable.1

Acylindrical vessel closed with plane ends is made of a 5mm thick steel plate. Its external diameter is 350mm and its length is 900mm. It is subjected to an internal fluid pressure of 3 N/mm2. Calculate the longitudinal and hoop stresses in the shell plate. Also calculate the change in diameter, length and volume of the cylinder. Take E=2x105 N/mm2, and Poission’s ratio = 0.3.

Athin spherical shell having 800 mm diameter is subjected to an internal pressure of 2.0 N/mm2. Find the thickness of plate needed if permissible tensile stress is 100 N/mm2. Take efficiency of joint to be 80%.

Apropped cantilever beam of 5m span is fixed at Aand roller supported at B. It is acted upon by a point load of 70 kN at 2m from A. Analyse the beam by consistent deformation method. Take EI = constant.

Analyse the fixed beam as shown in fig.4 and draw SFD and BMD.

Define resilience, proof resilience and modulus of resilience.

Derive expression for strain energy stored in a body when the load is applied with impact.

Asimply supported beam AB of span 10m is acted upon by a UDL of 30 kN/m over entire span. Find strain energy stored in the beam. Take I = 106 mm4 and E=200GPa. 30kN 50kN/ m B C 20kN 3m 2m A 40 kN C 2m, 2EI B 2m, EI 2m Fig.-2 A Fig.-1 75kN 25kN 30 kN/m B A B A 2 m 5 m C 5m 5m Fig.-3 Fig.-4