### Anna University - MECHANICS OF SOLIDS - 2011 November / December - Question Paper

B.E./B.Tech. DEGREE EXAMINATION, NOVEMBER / DECEMBER 2011.

B.E. - Civil Engineering

Third Semester
101301 - MECHANICS OF SOLIDS
(Regulation 2010)

Time : Three hours
Maximum: 100 marks
PART A
1. State the principle of superposition.
2. Write the expression for direct and tangential stress if θ is the inclination of the plane.
3. What is meant by statically determinate structure?
4. What is a thin shell? Give Examples.
5. Define point of inflexion?
6. Define the term simple bending.
7. What are the methods to find slope and deflection of a beam?
8. Sketch the stress distribution of a hollow circular section.
9. What are the assumptions made in the calculation of stresses and deformations due to torsion?
10.Define stiffness of a spring.

PART B (5x16=80marks)

11. (a) The following results were obtained in a tensile test of mild steel specimen of original diameter 20mm and a gauge length of 40mm. At the limit of proportionality the load was 80kN and the extension was 0.048mm. The specimen yielded at a load of 85kN and the maximum load withstood was l50kN. When the two broken parts were fitted together the length between the gauge markings was found to be 55.6mm and the minimum diameter at the neck was 15.8mm. Calculate (i) modulus of elasticity (ii) stress at the limit of proportionality (iii yield stress (iv) ultimate stress (v) % elongation in length (vi) % reduction in area.

Or

(b) A concrete cube of 150mm side is subjected to three pairs of axial forces on the three pairs of faces along the three mutually perpendicular axes x, y and z axis. The forces along x and z directions are tensile while the force along the y direction is compressive.If Px =54 kN, Py =72 kN and Pz =36 kN, E=12.5kN/nm2, compute the change in volume of the cube.

12. (a) Find the magnitude and nature of the forces in the given truss carrying loads as shown in Fig. 12(a).

(b).A cylindrical shell 3m long has 1m internal diameter and 1.5cm metal thickness. Calculate the maximum intensity of shear stress induced and the changes in the dimensions of the shell if it is subjected to an
internal pressure of 15kg/cm2.Take E=2.04x10QN/nm2 and µ=O.3.

Or

13. (a) An overhanging beam is loaded as shown in fig. 13(a). Construct the SFD and BMD for the beam. Also, calculate the maximum bending moment and locate the point of contraflexure.

Or

(b) A cast iron test beam 2cm X 2cm in section and 1 long and supported at the ends fails when a central load of 64kg is applied. What uniformly distributed load will break a cantilever of the same material 5cm wide, 10cm deep and 2m long?

14. (a) A cantilever of length L and constant stan flexural rigidity El carries a uniformly distributed load of intensity w unit length on the middle half of its length. Determine the ratio of slope and the ratio of deflection at the centre and freeend of the cantilever.

Or

(b) An I-section has the following dimension and carries a shear force of 16kN. Calculate the shear stress at critical points and plot the shear stress distribution.
Flange dimension in 80mm x 10mm
Web dimension = 100 mm x 10mm.

15. (a) A solid steel shaft has to transmit 100 H.P at 200 rpm. Taking allowable shear stress as N/mm2, find the suitable diameter of the shaft if the maximum transmitted in each revolution exceeds the mean by 30% . Also find the outer diameter of a hollow shaft to replace the solid shaft if the diameter ratio is 0.7.

Or

(b) A carriage spring is built up of 9 plates each 75mm wide and 6.5mm thick Find the length of the spring so that it may carry a central load of 4kN, the stress being limited to 160N/mm2. Also, find the deflection at the centre of the spring. Take E =2xl0N/mm2.