2012 MECHANICS OF SOLIDS

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1 R10 SET - 1 II B.Tech II Semester, Regular Examinations, April 2012 MECHANICS OF SOLIDS (Com. to ME, AME, MM) Time: 3 hours Max. Marks: 75 Answer any FIVE Questions All Questions carry Equal Marks ~~~~~~~~~~~~~~~~~~~~~~ 1. a) Draw a typical stress-strain curve for mild steel, indicate salient point and define them b) Compute the stresses at various sections and the total elongation of the bar shown in Figure1. L 1 = 4.0 m, L 2 = 3.0 m, L 3 = 2.0 m, A 1 = 100 mm 2, A 2 = 400 mm 2 and A 3 = 200 mm 2. E s = 2.05 X 10 5 N/mm Draw the bending moment and shear force diagram for the beam loaded as shown in Figure 2. Mark the values at the salient points. Determine the point of contra flexure also. 3. Compare the moment carrying capacity of the section given in Figure 3 with equivalent section of the same area but i) Square section ii) Rectangular section with depth twice the width and iii) A circular section. 1 of 3

2 R10 SET The unsymmetric I-section shown in Figure 4 is the cross-section of a beam, which is subjected to a shear force of 100 kn. Draw the shear stress variation diagram across the depth. 5. Determine the forces in the members FH, HG and GI in the truss shown in Figure 5. Each load is 10 kn and all triangles are equilateral with sides 4 m.

3 R10 SET A girder rests on two supports 5 m apart, and carries a distributed load of 60 kn, 2 m from one support. Find the ratio of maximum deflection to deflection under load. 7. Calculate the increase in volume of a spherical shell of 1 m diameter 1 cm thick, when it is subjected to internal pressure of 2 N/mm 2, E = 2.1 x 10 6 N/mm 2 and poisons ratio is The maximum stress permitted in a thick cylinder of internal diameter and external radii 20 cm and 30 cm respectively is 15.5 N/mm 2. If the external pressure is 4 N/mm 2, find the internal pressure that can be applied. Plot the curves showing the variation of hoop and radial stresses through the material. What will be the change in thickness of the cylinder? E = 2.1 x 10 5 N/mm 2 and µ = of 3

4 R10 SET - 2 II B.Tech II Semester, Regular Examinations, April 2012 MECHANICS OF SOLIDS (Com. to ME, AME, MM) Time: 3 hours Max. Marks: 75 Answer any FIVE Questions All Questions carry Equal Marks ~~~~~~~~~~~~~~~~~~~~~~ 1. a) The Poisson s ratio of a material as 0.3 and its young s modulus value is 2.1 x 10 5 N/mm 2. What is the value of shear modulus? b) A steel rod of 20 mm diameter passes centrally through a tight copper tube of external diameter 40 mm. The tube is closed with the help of the rigid washers of negligible thickness and nuts threaded on the rod. The nuts are tightened till the compressive load on the tube is 50 kn. Determine the stresses in the rod and the tube, when the temperature of the assembly falls by 50 0 C. Take E s = 200 GN/mm 2, E c = 100 GN/mm 2, s = 12 x 10-6 per 0 C, c = 18 x 10-6 per 0 C. 2. Draw the shear force and bending moment diagram of the beam shown in Figure 1. Mark the values at the salient points. 3. A symmetric I-section of size 200 mm 500 mm, 15 mm thick is strengthened with 300mm 20 mm rectangular plate on top flange as shown is Figure 2. If permissible stress in the material is 150 N/mm 2, determine how much concentrated load the beam of this section can carry at centre of 6 m span. Given ends of beam are simply supported. 1 of 2

5 R10 SET A beam has cross-section as shown in Figure 3. If the shear force acting on this is 50 kn, draw the shear stress distribution diagram across the depth. 5. Find the forces in all the members of the truss shown in Figure 4 suing method of joints. 6. A uniform circular bar of diameter, d, and length, l, extends an amount, e, under tensile pull, P, Show that the maximum deflection of the bar when it is used as beam simply supported at its 2 wel ends and carrying a central load, W, is given by δ =. Find the ratio of /e if l = 75d and 2 3Pd the maximum bending stress due to W is equal to the tensile stress under the pull, P. 7. A thin cylinder, 5 cm internal diameter and 1 mm wall thickness is closed at its end. And subjected to an internal pressure of 1 N/mm 2. Compute the longitudinal and hoop stress in the cylinder. 8. A compound cylinder is formed by shrinkage one cylinder to another. The internal and external radii of the compound cylinder are 15 cm and 24 cm respectively. All the junction radius is 21 cm. If after shrinkage on the radial pressure at the common surface is 5 N/mm 2. Calculate the initial stress across the section of the inner and outer cylinder. If the compound cylinder is subjected to an internal pressure of 80 N/mm 2, calculate the flexural stress induced. 2 of 2

6 R10 SET - 3 II B.Tech II Semester, Regular Examinations, April 2012 MECHANICS OF SOLIDS (Com. to ME, AME, MM) Time: 3 hours Max. Marks: 75 Answer any FIVE Questions All Questions carry Equal Marks ~~~~~~~~~~~~~~~~~~~~~~ 1. a) A bar of uniform thickness t tapers uniformly from a width b1 at one end to b2 at the other end in a length L. Find the expression for its extension under an axial pull P. b) Tension test was conducted on a specimen and the following readings were recorded. Diameter = 25 mm, Gauge length of extensometer = 200 mm Least count of extensometer = mm, at a load of 30 kn, extensometer reading = 60 At a load of 50 kn, extensometer reading = 100, Yield load = 160 kn Maximum load = 205 kn, Diameter neck = 17 mm Final extension over 125 mm original length = 150 mm Find Young s Modulus, yield stress, ultimate stress, percentage elongation and percentage reduction in area. 2. Draw BM and SF diagrams for the beam shown in Fig. 1, indicating the values at all salient points. 3. The cross-section of a cast iron beam is as shown in Figure 2. The top flange is in compression and bottom flange is in tension. Permissible stress in tension is 30 N/mm 2 and its value in compression is 90 N/mm 2. What is the maximum uniformly distributed load the beam can carry over a simply supported span of 5 m? 1 of 2

7 R10 SET Draw the shear stress variation diagram for the I-section shown in Figure 3, if it is subjected to a shear force of 200 kn. 5. Determine the forces in all the members of the truss shown in Figure 4 using method of joints and indicate the magnitude and nature of forces on the diagram of the truss. All inclined members are at 60 to horizontal and length of each member is 3 m. 6. A beam of uniform cross-section and of length, l, carries a uniformly distributed load, w, per unit length. It is simply supported at the left hand end and at a point 1/3 inside the right hand end. Show the deflection of overhanging end is elasticity and movement of inertia of the beam. 4 wl 648EI, where E and I are the modulus of 7. Calculate the increase in volume of a spherical vessel, 1 m diameter and 1 cm thick, when it is subjected to increase in pressure of 2 N/mm 2, E = 2.1 x 10 5 N/mm 2 and µ = A compound tube is made by shrinkage one tube on to another, the final dimensions being internal diameter 10 cm external diameter 20 cm and the diameter at the junction between the tubes is 15 cm. If the radial pressure between the tubes to be 20 N/mm 2 find the stress in the cylinder i) with no internal pressure and ii) with internal pressure of 100 N/mm 2.

8 R10 SET - 4 II B.Tech II Semester, Regular Examinations, April 2012 MECHANICS OF SOLIDS (Com. to ME, AME, MM) Time: 3 hours Max. Marks: 75 Answer any FIVE Questions All Questions carry Equal Marks ~~~~~~~~~~~~~~~~~~~~~~ 1. a) A tapering rod has diameter d 1 at one end and it tapers uniformly to a diameter d2 at the other end in a length L. If the modulus of elasticity is E, find the change in length when subjected to an axial force P. b) Derive the relationship between i) Modulus of elasticity and modulus of rigidity ii) Modulus of elasticity and bulk modulus. 2. Draw the bending moment and shear force diagram for the beam loaded as shown in Figure. 1. Mark the values at the salient points Determine the point of contra flexure also. 3. a) Derive the bending equation. What are the assumptions made while deriving the bending equation? b) Figure 2 shows the cross-section of a cantilever beam of 5 m span. Material used is steel for which maximum permissible stress is 150 N/mm 2. What is the maximum uniformly distributed load carried by the beam? 1 of 2

9 R10 SET A beam has cross-section as shown in Figure 3. If the shear force acting on this is 25 kn, draw the shear stress distribution diagram across the depth. 5. Determine the forces in all the members of the truss shown in Figure 4 using method of joints and indicate the magnitude and nature of forces on the diagram of the truss. All inclined members are at 60 to horizontal and length of each member is 2 m. 6. Find the maximum deflection for the beam loaded as shown in Figure 5 7. Calculate the increase in volume enclosed by a boiler shell, 2.5 m long and 1 m in diameter, when it is subjected to an internal pressure of 1.5 N/mm 2. The wall thickness is such that the maximum tensile stress in the shell is 25 N/mm 2 under pressure. Take µ = The maximum stress permitted in a thick cylinder of internal diameter and external radii 25 cm and 35 cm respectively is 10.5 N/mm 2. If the external pressure is 3 N/mm 2, find the internal pressure that can be applied. Plot the curves showing the variation of hoop and radial stresses through the material. What will be the change in thickness of the cylinder? E = 2.1 x 10 5 N/mm 2 and µ = 0.3.