Mechanics Of Solids Nov2003 Rr 211402 & Nr 210302

Code No: RR-211402/ NR-210302 II B.Tech. I-Semester RegularExaminations, November-2003

Set No.

MECHANICS OF SOLIDS [RR] (Common to Mechatronics, Metallurgical and Material Technology and Aeronautical Engineering)

1

MECHANICS OF SOLIDS [NR] (Common to Mechanical Engineering, Production Engineering, Mechatronics, Metallurgical and Material Technology and Aeronautical Engineering) Time: 3 hours

1.a) b)

Max. Marks: 80

Answer any FIVE questions All questions carry equal marks --Distinguish between : stress and strain, normal stress and shear stress, working stress and yield stress. An aluminium bar 60 mm diameter when subjected to an axial tensile load 100 kN elongates 0.20 mm in a gage length 300 mm and the diameter is decreased by 0.012 mm. Calculate the modulus of elasticity and the Poisson's ratio of the material.

2.

Prove that Poisson’s ratio for the material of a body is 0.5, if its volume does not change when stressed. Prove also that Poisson’s ratio is zero when there is no lateral deformation when a member is axially stressed.

3.

A ladder 4m long and weighing 150 N/m is resting against a smooth vertical wall and the bottom end is resting on rough ground. If a man weighing 800N stands midway on the ladder, draw the SF and BM diagrams and determine the maximum BM in the ladder. The ladder is inclined at 45 to the horizontal.

4.a) b)

Discuss the assumptions in the theory of simple bending. Compare the weight of two beams of the same material and equal strength. One beam is of solid circular cross section while other beam is of hollow circular section, the internal diameter being 0.78 times the external diameter.

5.a)

A beam AB of span l carries a distributed load of varying intensity from Zero at A to w per unit length at B. Measuring x from the end A, establish the equation for the deflection curve of the beam.

b)

A 3.5 meters long cantilever carries a uniformly distributed load over the entire length. If the slope at the free end is one degree, what is the deflection at the free end.

Code No. RR-211402/NR-210302 6.a) b)

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Contd…2 Set No.1

Distinguish between circumferential stress and longitudinal stress in a cylindrical shell, when subjected to an internal pressure. The diameter of a cylindrical shell made of steel is 3.5 m. The sheet is subjected to an internal pressure of 1.5M N/m2 gauge. Find out the thickness of the sheet plate oif ultimate tensile stress of the mild steel is 480 MN/m2. Longitudinal joint efficiency of the shell is 80% and factor of safely is 6.

7. a) b) c)

Define slenderness ratio. State the limitations of Euler’s formula. Derive an expression for the Rankine’s crippling load for a column How will you justify the Rankine’s formula is applicable for all lengths of columns, ranging from short to long columns.

8.

A steel shaft of diameter 200 mm runs at 300 rpm. This steel shaft has a 30 mm thick bronze bushing shrunk over its entire length of 8 meters. If the maximum shearing stress in the steel shaft is not to exceed 12 MPa, find a) power of the engine b) torsional rigidity of the shaft. Take Gsteel = 84000 N/mm²; Gbronze = 42000 N/mm². ^^^

Code No: RR-211402/ NR-210302 II B.Tech. I-Semester Regular Examinations, November-2003

Set No.

MECHANICS OF SOLIDS [RR] (Common to Mechatronics, Metallurgical and Material Technology and Aeronautical Engineering)

2

MECHANICS OF SOLIDS [NR] (Common to Mechanical Engineering, Production Engineering, Mechatronics, Metallurgical and Material Technology and Aeronautical Engineering) Time: 3 hours

Max. Marks: 80 Answer any FIVE questions All questions carry equal marks ---

1.a) b)

2.a) b)

Define the terms i) proportional limit ii) Poisson's ratio iii) proof stress iv) strain energy. A compound bar 1 metre long is 40 mm diameter for 300 mm length, 30 mm diameter for the next 350 mm length. Determine the diameter of the remaining length so that its elongation under an axial load of 100 KN does not exceed 1mm. Take E = 2X105 N/mm2. State Hooke’s law. Draw stress-strain diagram for mild steel specimen tested under uni-axial tension till fracture and mark all the salient points. A metallic rod of 1 cm diameter, when tested under an axial pull of 10 KN was found to reduce its diameter by 0.0003 cm. The modulus of rigidity for the rod is 51 KN/mm2. Find the Poisson’s ratio, modulus of elasticity and Bulk Modulus.

3.

A beam of length 6m is simply supported at its ends. It is loaded with a gradually varying load of 750 N/m from left end to 1500 N/m to the right end. Construct the SF and BM diagrams and find the magnitude and position of the maximum BM.

4.a) b)

What is elastic section modulus? A beam resting freely on supports 5.8m apart carries a u.d.l of 12 kN/m and also a point load of 15 kN at 2m from the left support. If the permissible stress in timber is 5 MPa, design a suitable section by making the depth equal to 1.8 times the width.

5.a)

What is Macaulay’s method for finding out the slope and deflection? of a beam? Discuss the cases, where it is of a particular use. A 3 meters long cantilever is loaded with a point load of 450 N at the free end. If the section is rectangular 80 mm ( wide) x 160 mm (deep), and E = 10 GN/m2, calculate slope and deflection. (i) at the free end of the cantilever, (ii) at a distance of 0.55 m from the free end.

b)

Code No. RR-211402/NR-210302

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Contd…2 Set No.2

6.a) Explain horizontal and hoop stresses as applied to thin cylinders. b) What thickness of metal would be required for cast-iron water pipe 90 cm in diameter under a head of 100m? Assume the permissible tensile stress for cast iron as 20 MN/m2. 7.

Derive an expression for the Euler’s crippling load for a long column with following end conditions: (i) both ends are hinged (ii) both ends are fixed 8. The stiffness of a close-coiled helical spring is 1.5 N/mm of compression under a maximum load of 60 N. The maximum shearing stress produced in the wire of the spring 125 MPa. The solid length of the spring is given as 5 cm. Find : (i) diameter of wire (ii) mean diameter of the coils (iii) number of coils required. Take G = 4.5 x 104 N/mm².

^^^

Code No: RR-211402/ NR-210302 II B.Tech. I-Semester Regular Examinations, November-2003

Set No.

MECHANICS OF SOLIDS [RR] (Common to Mechatronics, Metallurgical and Material Technology and Aeronautical Engineering)

3

MECHANICS OF SOLIDS [NR] (Common to Mechanical Engineering, Production Engineering, Mechatronics, Metallurgical and Material Technology and Aeronautical Engineering) Time: 3 hours

Max. Marks: 80 Answer any FIVE questions All questions carry equal marks ---

1.a) b)

Define the terms (i) Complementary shear (ii) Poisson's ratio (iii) Volumetric strain If the Young's Modulus of elasticity of a material is twice its modulus of rigidity, then compute the Poisson's ratio of material.

2.a) b)

Derive the relationship between the three moduli of elasticity. Show that in a prismatic bar, the maximum stress intensity due to a suddenly applied load is twice the stress intensity produced by the same load applied gradually.

3.

An overhanging beam of length 7m is supported centrally at two points 5m apart. It carries a uniformly increasing load of 400 N/m from the left end to 800 N/m at the midspan. It also carries a point load of 1000N at the right end. Draw the SF and BM diagrams and locate the point(s) of contra flexure.

4.a)

A cantilever of length 2.8 m fails when a load of 4.7 kN is applied at the free end. If the section of the beam is 65 mm x 105 mm find the stress at failure. A T-beam having flange 210 mm x 20 mm is simply supported over a span of 5m. It carries a u.d.l of 8.8 kN/m over its entire span. Calculate the maximum compressive and tensile stress occurring in the section. What is the magnitude of flexural stress at the junction of flange and web? Draw the variation of stress across the section.

b)

5.a) b)

Explain the procedure for finding the deflection of a beam of composite section. A cantilever 3 m long is of rectangular section 120 mm wide 240mm deep. It carries a uniformly distributed load of 2.5 kN per meter length for a length of 1.5 meters from the fixed end and a point load of 1 kN at the free end. Find the deflection at the free end. Take E = 10 GN/ m2.

Code No. RR-211402/NR-210302

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Contd…2 Set No.3

6.a) Derive a formula fore the hoop stress in a thin spherical shell subjected to an internal pressure. b) A cylindrical shell 13 m long and 60 cm in diameter an 1.25cm thick is at atmospheric pressure. What would be its dimensions when it is subjected to an internal pressure of 2 MN/m2? E = 200 GN/m2 and m = 4. 7.a) b)

Derive an expression for the maximum shear stress induced in the wire and stiffness of spring in case of close coiled helical springs. What are the functions of springs?

8. A close coiled spring has a stiffness of 10 N/mm. Its length when fully compressed, with adjacent coils touching each other is 40cm. Take G = 0.8 x 105 N/mm². (i) Determine the wire diameter and mean coil diameter if their ratio is 1:10 (ii) If the gap between any two adjacent coils is 0.2cm, what maximum load can be applied before the spring becomes solid, i.e. adjacent coils touch ? (iii) What is the corresponding maximum shear stress in the spring ? ^^^

Code No: RR-211402/ NR-210302 II B.Tech. I-Semester Regular Examinations, November-2003

Set No.

MECHANICS OF SOLIDS [RR] (Common to Mechatronics, Metallurgical and Material Technology and Aeronautical Engineering)

4

MECHANICS OF SOLIDS [NR] (Common to Mechanical Engineering, Production Engineering, Mechatronics, Metallurgical and Material Technology and Aeronautical Engineering) Time: 3 hours

1.a) b)

Max. Marks: 80

Answer any FIVE questions All questions carry equal marks --Derive relation between three elastic moduli. Draw stress - strain diagram for mild steel. Indicate salient points and define them.

2.

A bar of mild steel 20 mm diameter is subjected to an axial pull of 50 kN. The increase in length over a gauge length of 200 mm is measured to be 0.16 mm. The decrease in diameter was 0.0048 mm. From the above data determine the modulus of Elasticity and Poisson's ratio of mild steel.

3.

A horizontal beam AB of length 6m is height at A and supported on rollers at B. The beam carries inclined loads on 75 kN, 100 kN, 125 kN and 100 kN inclined towards the hinged support at 30 , 45 , 50 and 60 Respectively to the vertical. The points of application of the loads are 1m, 2.5m, 4m and 5m respectively form A. Draw the SFD and BMD.

4.a)

A simply supported beam of span 6m has a cross section 180 mm x 300 mm. If the permissible stress is 9MPa, find the maximum concentrated load that can be applied at 2m from left end. A rolled steel joist of I section has top and bottom flanges 185 mm x 25 mm and web of size 300 mm x 15 mm. It is used as a simply supported beam over a span 5m to carry an uniformly distributed load of 75 kN/m over its entire span. Draw

b)

bending stress across a section at (

1 5

)th the span.

5.a)

A girder of uniform section and constant depth is freely supported over a span of 2.5 meters. Calculate the central deflection and slopes at the ends of the beam under a central load of 25 KN. Given: I XX = 7.807x 10-6 m4 and E = 200 GN/m2 .

b)

A simply supported 6 meters long rolled steel joist carries a uniformly distributed load of 9.5 kN/meter length. Determine slope and deflection at a distance of 3 meters from one end of the beam.

Code No. RR-211402/NR-210302

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Contd…2 Set No.4

6.a) A thin cylindrical steel shell of diameter 225 mm and wall thickness 4.5 mm has spherical ends. Determine the thickness of hemisphere ends if there is no distortion of the junction under the pressure. b) A 2000 mm diameter cast iron pipe has thickness of 10 mm and is closely wound with a layer of 5 mm diameter steel wire under a tensile stress of 60 MN/m 2. If now water under a pressure of 3.5 MN/m2 is admitted in to the pipe, find the stresses induced in the pipe and steel wire. 7.

Derive an expression for the shear stress produced in a circular shaft which is subjected to torsion. What are the assumptions made in the above derivation?

8.

A solid shaft transmits 2000 kW at the 200 rpm. The maximum torque developed in the shaft is 1.8 times the mean torque. The distance between the bearings is 1.8 meters with a flywheel weighing 50 kN midway between the bearings. Determine the shaft diameter if (a) the maximum permissible tensile stress is 60 MPa (b) the maximum permissible shearing stress is 40 MPa. ^^^