R050210101 Strength Of Materials I

Set No. 1

Code No: R050210101

II B.Tech I Semester Regular Examinations, November 2007 STRENGTH OF MATERIALS-I (Civil Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ⋆⋆⋆⋆⋆ 1. Explain the following : (a) Working stress (b) Factor of safety (c) Volumetric strain (d) Poisson’s ratio.

[4+4+4+4]

2. A weight of 210 kN is supported by three short pillars each of sectional area 500 mm2 . The central pillar is of steel and the outer ones are of copper. The pillars are so adjusted that at a temperature of 150 C each carries equal load. The temperature is then raised to 950C. Find the stress in each pillar at 150 C and 950 C. Take Es = 200 GPa and EC = 80 GPa αs = 12 × 10−6 / 0 C and αc = 18 × 10−6 / 0 C. [16] 3. Construct the S. F. D & B. M. D for the beam with over hangs as shown in Figure 3 [16]

Figure 3 4. For a hollow circular section obtain the section modulus. Hence calculate the maximum bending stresses in a section external radius 300 mm and internal radius 180 cm, subjected to B. M = 50 KNm. [16] 5. Obtain the shear stress distribution for a rectangular cross section 230 × 400 mm subjected to a shear force of 40 KN. Calculate maximum and average shear stress. [16] 6. (a) State the first theorem of the moment area method? (b) State and prove moment area theorem - 2.

[6+10]

7. (a) A water main 600mm diameter contains water at a pressure head of 100m. Find the thickness of the metal required if the permissible stress is 30 N/mm2 . (b) A vessel in the shape of a spherical shell 800mm in diameter, 10mm shell thickness is completely filled with a fluid at atmospheric pressure. Additional

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Set No. 1

Code No: R050210101

fluid is then pumped in, till the pressure increases by 5N/mm2 . Find the volume of this additional fluid. Take E = 2 X 105 N/mm2 , µ = 0.25.

[6+10]

8. Compare the values of max. and minimum hoop stresses for a cast steel cylindrical shell of 600 mm external dia. And 400 mm internal dia. Subjected to a pressure of 30N/mm2 applied (a) Internally and (b) Externally.

[8+8] ⋆⋆⋆⋆⋆

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Set No. 2

Code No: R050210101

II B.Tech I Semester Regular Examinations, November 2007 STRENGTH OF MATERIALS-I (Civil Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ⋆⋆⋆⋆⋆ 1. Explain the following : (a) Working stress (b) Factor of safety (c) Volumetric strain (d) Poisson’s ratio.

[4+4+4+4]

2. A weight of 210 kN is supported by three short pillars each of sectional area 500 mm2 . The central pillar is of steel and the outer ones are of copper. The pillars are so adjusted that at a temperature of 150 C each carries equal load. The temperature is then raised to 950C. Find the stress in each pillar at 150 C and 950 C. Take Es = 200 GPa and EC = 80 GPa αs = 12 × 10−6 / 0 C and αc = 18 × 10−6 / 0 C. [16] 3. (a) Define the “Beam” and the type of action and deformation it undergoes. (b) Draw the S.F. and B.M. diagram for a simply supported beam of span L m loaded with UDL of w KN/m. [6+10] 4. Define Neutral axis. Sketch the bending stress distribution across the cross section of a rectangular beam section 230 × 400 m subjected to 60 KNm moment. [16] 5. An I-section shown in Figure 5 is subjected to the S.F. = 120KN . Sketch the shear stress distribution. Obtain maximum and mean shear stress. [16]

Figure 5 6. A horizontal beam of uniform section is pinned at its ends which are at the same level and is loaded at the left hand pin with an anticlockwise moment M and at 1 of 2

Set No. 2

Code No: R050210101

the right hand pin with a clockwise moment 2m both in the same vertical plane. The length between the pins is L. Find the angles of slope at each end and the deflection of the midpoint of the span in terms of M, L, E and I. [16] 7. Define the terms (a) Circumferential stress (b) Longitudinal stress and derive the expressions for the same in thin cylinders. [16] 8. Derive Lame?s equations for finding the radial and hoop stresses in a thick spherical shell subjected to an internal pressure. [16] ⋆⋆⋆⋆⋆

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Set No. 3

Code No: R050210101

II B.Tech I Semester Regular Examinations, November 2007 STRENGTH OF MATERIALS-I (Civil Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ⋆⋆⋆⋆⋆ 1. Two vertical wires are suspended from a rigid support at top at a horizontal distance of 60cm apart. Both wires are initially 4.5 m long. At their lower ends there is a rigid horizontal bar carrying a load P. The left steel wire is of 1 mm dia. while the right copper wire is of 1.5 mm dia. Find the position of load P, if both wires extend by the same amount. Find the slope of rigid bar if a load of 300 N is hung at the center of bar. Neglect the weight of the bar. Take ES = 130 GN/m2 . [16] 2. Rails of 15 m length were laid on the track when the temperature was 200 C. A gap of 1.8 mm was kept between two consecutive rails. At what max temperature the rails will remain stress free ? If the temperature is raised further by 150 C, what will be the magnitude and nature of stresses induced in the rails? [16] 3. Draw the B. M. D and S. F. D for the beam shown in Figure 3

[16]

Figure 3 4. Define Neutral axis. Sketch the bending stress distribution across the cross section of a rectangular beam section 230 × 400 m subjected to 60 KNm moment. [16] 5. For a T - section with dimensions flange width 100mm, Depth = 200mm and uniform thickness of 40mm. obtain shear stress distribution and calculate maximum and average shear stresses if it is subjected to a S.F. = 100 KN. [16] 6. Determine the maximum deflection and the slope of the beam as shown in (figure6) Using Macaulay’s method. [16]

Figure 6 7. Define the terms (a) Circumferential stress (b) Longitudinal stress and derive the expressions for the same in thin cylinders. [16] 1 of 2

Set No. 3

Code No: R050210101

8. Compare the values of max. and minimum hoop stresses for a cast steel cylindrical shell of 600 mm external dia. And 400 mm internal dia. Subjected to a pressure of 30N/mm2 applied (a) Internally and (b) Externally.

[8+8] ⋆⋆⋆⋆⋆

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Set No. 4

Code No: R050210101

II B.Tech I Semester Regular Examinations, November 2007 STRENGTH OF MATERIALS-I (Civil Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ⋆⋆⋆⋆⋆ 1. Find the Poisson’s ratio and Bulk modulus of a material whose modulus of elasticity is 200 GPa and modulus of rigidity is 80 GPa. A 2 m long rod of 40 mm dia. made with the same material is stretched by 2.5 mm under some axial load. Find the lateral contraction. [16] 2. Rails of 15 m length were laid on the track when the temperature was 200 C. A gap of 1.8 mm was kept between two consecutive rails. At what max temperature the rails will remain stress free ? If the temperature is raised further by 150 C, what will be the magnitude and nature of stresses induced in the rails? [16] 3. Define Bending moment and state of pure bending. Draw the B. M. D and S. F. D and identify the region of zero S.F.(Figure3) [16]

Figure 3 4. For a T-section shown in Figure 4. Obtain section modulus and hence obtain the maximum bending stress if it is subjected to a B. M of 20 KNm. [16]

Figure 4 5. Derive an expression for the distribution of shear stress across the cross section. How is average shear stress defined. Relate maximum shear stress to the average shear stress in a rectangular section. [16]

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Set No. 4

Code No: R050210101

6. (a) Explain the Mohr’s theorems, for finding the slope and deflection of a beam. (b) A simply supported 6m rolled steel joist carries a U.D.L of 10 KN//m length. Determine slope and deflection at a distance of 3m from one end of the beam. [6+10] 7. Define the terms (a) Circumferential stress (b) Longitudinal stress and derive the expressions for the same in thin cylinders. [16] 8. A compound cylinder is formed by shrinking one tube on to another, the final dimensions being, internal diameter 120 mm, external diameter 240 mm, diameter at junction 180 mm. if after shrinking on, the radial pressure at the common surface is 8N/mm2 , calculate the initial hoop stresses across the sections of the inner and outer tubes. If a fluid under a pressure of 60N/mm2 , is admitted inside the compound cylinder, calculate the final stresses set up in the sections of the pipes. [16] ⋆⋆⋆⋆⋆

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