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Posted By: sasi kala Member Level: Diamond Posted Date: 30 May 2008
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2007 Anna University B.E Civil CE 231 — MECHANICS OF SOLIDS Question paper
B.E./B.Tech. DEGREE EXAMINATION,
Third Semester
Civil Engineering
CE 231 — MECHANICS OF SOLIDS
Time : Three hours Maximum : 100 marks
Answer ALL the questions.
PART A — (10 ? 2 = 20 marks)
1. Define Poisson’s ratio.
2. What is the stress developed in a bar of length l, coefficient of linear expansion , modulus of elasticity E when subjected to a rise in temperature of t with the ends clamped.
3. What is an improperly constrained frame?
4. What is the maximum bending moment for a simply supported beam subjected to uniformly distributed load and where it occurs?
5. What is Neutral axis?
6. Draw the variation of shear stress across Rectangular section.
7. What is the torque that can be transmitted by a solid shaft of diameter ‘‘d’’ and allowable shear stress ?
8. Differentiate between a closely coiled helical spring and an open coiled helical spring.
9. Write the expression for longitudinal strain and circumferential strain in the case of thin cylindrical shells.
10. Draw the Mohr’s circle for the state of pure shear and mark the principal stresses.
PART B — (5 ? 16 = 80 marks)
11. A steel bar 3.5 m long is acted upon by forces as shown in fig. 1. Determine the value of P and the total elongation of the bar. Take E = 210 kN/mm2.
Fig. 1
12. (a) Find the forces in all the members of the girder shown in fig. 2 by the method of joints, indicating whether the force is compressive or tensile.
Fig. 2
Or
(b) Find the forces in all the members of the truss shown in fig. 2 by the method of tension coefficients.
13. (a) Draw the BMD and SFD indicating the salient values for the beam load as shown in fig. 3.
Fig. 3
Or
(b) At a section in a beam the shear force is 75 kN. Find the ratio of the maximum shear stress and the average shear stress for the cross section shown in fig. 4.
Fig. 4
14. (a) A hallow steel shaft 24 cm external and 16 cm internal diameter is to be replaced by a solid alloy shaft. If both the shafts should have the same polar modulus, find the diameter of the latter and the ratio of torsional rigidities. Take N for steel = 2.0 * N for alloy.
Or
(b) A closely coiled helical spring made out of a 10 mm diameter steel bar has 12 complete coils, each of mean diameter of 100 mm. Calculate the stress induced in the section of the rod, the deflection under the pull and the amount of energy stored in the spring during the extension if it is subjected to an axial pull of 200 N. Modulus of rigidity is
0.84 ? 105 N/mm2.
15. (a) (i) At appoint in a stressed material, the normal component of the stresses on a plane is 50 N/mm2 tensile and on a perpendicular plane, there is a resultant stress of 100 N/mm2 acting away from the plane at an angle of 30? to the normal to the plane. Find the principal stresses at the point and locate the position of the planes on which they act.
(ii) A thin cylindrical shell 1000 mm long, 200 mm in external diameter, thickness of metal 10 mm is filled with a fluid at atmospheric pressure. If an additional 25 cm3 of the fluid is pumped in to the cylinder, find the pressure exerted by the fluid on the wall. Take
E = 2 ? 105 N/mm2 and Poisson’s ratio = 0.3. Find also the hoop stress induced.
Or
(b) A beam ABC is loaded as shown in fig. 5. If E = 2 ? 105 N/mm2 and
I = 9 ? 107 mm4 determine
(i) Slope at the end ‘‘A’’
(ii) Deflection at the free end ‘‘C’’
(iii) Maximum deflection.
Fig. 5
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