B.Tech. [SEM III (ME)] QUIZ TEST-1 - being...

EME-302 /Mr C.B.Khatri,Krishna kr. Yadav and Harsh Dwivedi Date: 08/09/2012

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SHRI RAMSWAROOP MEMORIAL COLLEGE OF ENGG. & MANAGEMENT

B.Tech. [SEM III (ME)] QUIZ TEST-1 (Session : 2012-13)

Time: 60 min Max. Marks: 30 STRENGTH OF MATERIAL

(EME-302)

Roll No. (To be filled by the Student)

Part – A

(Questions from Tutorial Sheet) [10 Marks]

Q.1. Draw the Mohr’s stresses circle for direct stresses of 65 MN/m2 and 35 MN/m2(compressive) and estimate

the magnitude and direction of the resultant stresses on planes making angle of 200 and 650 with the plane of the

first principal stress. Find also the normal and tangential stresses on these planes Q.3 [2+3]

Q.8. . A mild steel shaft 120 mm diameter is subjected to a maximum torque of 20 KNm and maximum bending

moment of 12 KNm at a particular section. Find the FOS according to the maximum shear stress theory if the

elastic limit in simple tension is 220 MN/m2. Q.12 [2+3]

Part- B [20 Marks]

Q.1. There is a stressed point as shown in fig.(A) , find out the following

(i) Normal and tangential stress on the oblique section. [1+1]

(ii) Principal stresses, maximum shear stresses and their planes. [1+1+1+1]

(iii) Verify it with the use of Mohr circle.(scaling is not necessary) [2]

Q.2. At a point ‘A’ in a body, σxx = 80kN/ cm2 ,σyy = -20kN/cm2 ,σzz = 20kN/cm2 and τxy =τyz = τzx= 20kN/cm2 , determine normal and shearing stresses on a plane which is parallel to the X+Y+Z=1. [3+3] Q.3. Design a steel bolt subjected to compressive load 30 kN along with a shear force of 15 kN. The yield point for the material is 300 Mpa and µ(poison ratio) = 0.3. Calculate the safe diameter by , Maximum shear stress theory and Maximum total strain energy theory. Take FOS= 2.5. [2+4]

Academic/26 Refer/WI/ACAD/18


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(EME-302)


Part – A


Q.1. Direct stresses of 120MN/m2 in tension and 90MN/m2 in compression are applied to an elastic material at a

certain point on planes at a right angle to another. If the maximum principal stress is not exceeding 150 MN/m2

in tension, to what shearing stress can material be subjected? What is the maximum resulting shearing stress in

the material? Also find the magnitude of the other principal stress. Q.4 [2+3]

Q.2 A steel shaft is subjected to an end thrust producing a stress of 90 MPa and minimum shearing stress on the

surface arising from torsion is 60 MPa. The yield point of the material in simple tension was found to be 300

MPa. Calculate the FOS of the shaft according to the maximum distortion energy theory. Q.13 [2+3]

Part- B [20 Marks]





Q.2. At a point ‘A’ in a body, σxx = 80kN/ cm2 ,σyy = -20kN/cm2 ,σzz = 20kN/cm2 and τxy =τyz = τzx= 20kN/cm2 , determine normal and shearing stresses on a plane which is parallel to the X+Y+Z=1. [3+3] Q.3. Design a steel bolt subjected to compressive load 30 kN along with a shear force of 15 kN. The yield point for the material is 300 Mpa and µ(poison ratio) = 0.3. Calculate the safe diameter by , Maximum shear



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stress theory and Maximum total strain energy theory. Take FOS= 2.5. [2+4]


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(EME-302)


Part – A


Q.1. At a point in stressed body the principal stresses are 100 MN/m2(tensile) and 60MN/m2 (compressive).

Determine the normal stress and the shear stress on a plane inclined at 500 to the axis of major principal stress.

Also calculate the maximum shear at the point. Q.1 [3+2]

Q.2. A material is subjected to two mutually perpendicular linear strains together with a shear strain. One of the

linear strain is 0.00025 tensile. Determine the magnitudes of the other linear strain and the shear strain if the

principal strains are 0.0001 compressive and 0.0003 tensile. Q.8 [3+2]

Part- B [20 Marks]





Q.2. At a point ‘A’ in a body, σxx = 80kN/ cm2 ,σyy = -20kN/cm2 ,σzz = 20kN/cm2 and τxy =τyz = τzx= 20kN/cm2 , determine normal and shearing stresses on a plane which is parallel to the X+Y+Z=1. [3+3] Q.3. Design a steel bolt subjected to compressive load 30 kN along with a shear force of 15 kN. The yield point for the material is 300 Mpa and µ(poison ratio) = 0.3. Calculate the safe diameter by , Maximum shear stress theory and Maximum total strain energy theory. Take FOS= 2.5. [2+4]



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(EME-302)


Part – A


Q.1 A block of material is subjected to a tensile strain of 12×10-6 and a compressive strain of 15×10-6 on a

planes at right angles to each other. There is also a shear strain of 12×10-6 and there is no strain on a planes at

right angles to above planes. Calculate the principal strain in magnitude and direction. Q.9 [2+3]

Q.2. . At a point in a material under stress, the intensity of the resultant stress on a certain plane is

50MN/m2 (tensile) inclined at 300 to normal of that plane. The stress on a plane at right angles to this has a

normal tensile component of intensity of 30 MN/m2, Find

(i) Resultant stress on the second plane.

(ii) The principal plane and stresses (iii)The plane of maximum shear and its intensity. Q.6[1+2+2]

Part- B [20 Marks]





Q.2. At a point ‘A’ in a body, σxx = 80kN/ cm2 ,σyy = -20kN/cm2 ,σzz = 20kN/cm2 and τxy =τyz = τzx= 20kN/cm2 , determine normal and shearing stresses on a plane which is parallel to the X+Y+Z=1. [3+3] Q.3. Design a steel bolt subjected to compressive load 30 kN along with a shear force of 15 kN. The yield point



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for the material is 300 Mpa and µ(poison ratio) = 0.3. Calculate the safe diameter by , Maximum shear stress theory and Maximum total strain energy theory. Take FOS= 2.5. [2+4]


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(EME-302)


Part – A


Q.1. Two mutually perpendicular planes of an element of material are subjected to direct stresses of 10.5 MN/m2

(tensile) and 3.5 MN/m2 (compressive) and shear stress of 7 MN/m2.

Find graphically or otherwise:

(i) magnitude and direction of principal stress, and

(ii) The magnitude of the normal and shear stresses on a plane on which the shear stress is maximum.

Q.5 [2+3]

Q.2. Estimate the principal stresses acting on the plate which gave the following results:

Principal strain, e1 = 3.24 ×10-4 ; e2 = 1.28×10-4

Modulus of elasticity, E= 200GN/m2, Poisson’s ratio, 1/m = 0.2 Q.7 [2+3]

Part- B [20 Marks]





Q.2. At a point ‘A’ in a body, σxx = 80kN/ cm2 ,σyy = -20kN/cm2 ,σzz = 20kN/cm2 and τxy =τyz = τzx= 20kN/cm2 , determine normal and shearing stresses on a plane which is parallel to the X+Y+Z=1. [3+3]



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Q.3. Design a steel bolt subjected to compressive load 30 kN along with a shear force of 15 kN. The yield point for the material is 300 Mpa and µ(poison ratio) = 0.3. Calculate the safe diameter by , Maximum shear stress theory and Maximum total strain energy theory. Take FOS= 2.5. [2+4]


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(EME-302)


Part – A


Q.1. A simply supported beam with a span of 4.5 m carries a point load of 30 kN at 3 m from the left support. Take, Ixx= 54.97x 10-6 m4 and E=200GPa, find

(i) The deflection under the load. (ii) The potion of maximum deflection. Q.1 [2+3] Q.2. What must be the length of a 5 mm diameter Al wire so that it can be twisted through one complete revolution without exceeding a shearing stress of 42 MN/m2 ? Take, C = 27 GN/m2. Q.9 [5]

Part- B [20 Marks]

Q.1. A timber beam 100mm wide by 150mm deep is to be strengthened by two plates 100mm X 12mm and 100mmX 6mm. The thicker plate is secured to the top surface and thinner to the lower surface. The maximum permissible stress in steel is 120 MPa and the value of modular ratio is 20. Calculate moment of resistance of strengthened section. Also calculate maximum stress in timber. [4+3]

Q.2. A 100mm diameter shaft is subjected to bending moment ‘M’ and a twisting moment ‘T’. The

magnitude of maximum principal stress due to these moments is 110 MPa. If maximum bending stress due to M is same as the maximum shear stress due to T. Evaluate M and T. [3+3]

Q.3. An I-section beam 340mm X 200mm has a web thickness of 10mm and flange thickness of 20mm. It’s

carries a shearing force of 100kN. Sketch the shear stress distribution across the section. [7]



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(EME-302)


Part – A


Q.1. A cantilever 1.5 m long carries a UDL over the entire length. Find the deflection at the free end if the slope at the free end is 1.50. Q.2 [5] Q.2 . Two shafts are of length l and outside diameter D, the first one is solid while the second one is hollow with inside diameter D/2. What is the ratio of strain energies that two steel shafts can absorb without exceeding the allowable shear stress? Q.13[3+2]

Part- B [20 Marks]

Q.1. A timber beam 100mm wide by 150mm deep is to be strengthened by two plates 100mm X 12mm and

100mmX 6mm. The thicker plate is secured to the top surface and thinner to the lower surface. The maximum permissible stress in steel is 120 MPa and the value of modular ratio is 20. Calculate moment of resistance of strengthened section. Also calculate maximum stress in timber. [4+3]







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(EME-302)


Part – A


Q.1. A girder of uniform section and constant depth is freely supported over a span of 3m. If the point load at the mid span is 30 kN and Ixx = 15.614 x10-6 m4, Take, E = 200 GN/m2 calculate. (i) The central deflection. (ii) The slopes at the ends of the beam.

Q.3 [2+3]

Q.2. A hollow shaft is to transmit 300 kW at 80 rpm. If the shear stress is not to exceed 60 MN/m2 and internal diameter is 0.6 of the external diameter, find the external and internal diameters assuming that the maximum torque is 1.4 times the mean torque. Q.12 [2+3]

Part- B [20 Marks]

Q.1. A timber beam 100mm wide by 150mm deep is to be strengthened by two plates 100mm X 12mm and 100mmX 6mm. The thicker plate is secured to the top surface and thinner to the lower surface. The maximum permissible stress in steel is 120 MPa and the value of modular ratio is 20. Calculate moment of resistance of strengthened section. Also calculate maximum stress in timber. [4+3]







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(EME-302)


Part – A


Q.1. A cantilever 2 meters long, is of rectangular cross section 100 mm wide and 200 mm deep. It carries a UDL of 2 kN / unit meter length for a length of 1.25 meters from the fixed end a point load of 0.8 kN at the free end. Find the deflection at the free end. Take, E = 10GN/m2. Q.4 [5] Q. 2. A solid steel shaft has to transmit 75 kW at 200 rpm. Taking allowable shear stress as 70 MN/m2, find suitable diameter for the shaft, if the maximum torque transmitted on each revolution exceeds the mean by 30%. Q.14 [2+3] Part- B [20 Marks]









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(EME-302)


Part – A


Q.1. A 250 mm long cantilever of rectangular section 40 mm wide and 30 mm deep carries a UDL. Calculate the value of ‘w’, if the maximum deflection in the cantilever is not exceed 0.5 mm. Take, E = 70 GN/m2 . Q.7 [5] Q.2. A solid circular shaft transmits 75 kW power at 200 rpm. Calculate the shaft diameter, if the twist in the shaft is not to exceed 10 in 2 meters length of the shaft, and shear stress is limited to 50 MN/m2. Take C = 100 GN/m2 Q.11 [5] Part- B [20 Marks]









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(EME-302)


Part – A


Q.1. An open coil helical spring of wire diameter 12mm, mean coil radius 84mm, helix angle 200 carries an axial lode of 480N. Determine the shear stress and direct stress developed at the inner radius of coil. Q.5 [3+2] Q.2. Calculate the critical load of a strut, which is made of a bar circular in section and 5 m long and which is pin-jointed at both ends. The same bare when freely supported givens mid-span deflection of 10 mm with a 80N load at the centre. Q.10 [5]

Part- B [20 Marks]

Q.1). An open-coil helical spring is made of a wire of 1 cm diameter. It has 10 coils of 5cm mean diameter. What is the greatest axial load that can be applied to the ends of the spring if the maximum principal stress is not to exceed 10 kN/cm2 and maximum shear stress is not to exceed 6 kN/cm2? Calculate for this load the axial deflection and angular rotation of the spring. [3+2+2] Q.2). Compare the crippling load obtained by Euler’s and Rankine theory for an axially loaded hollow cylindrical cast iron column 150 mm external diameter and 20 mm thick. The column is 6 m long and hinged at both ends. Given σfailure= 550 Mpa, Rankine constant (a) = 1/(1600) and E= 80Mpa. [6] Q.3). Derive the equation to obtain critical or buckling load by Euler’s theory for the column having one end fixed and other free with assumptions which are involved in developing the theory. [6]



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(EME-302)


Part – A


Q.1. A close-coiled helical spring has mean diameter of 75 mm and spring constant of 80 KN/m. It has 8 coils. What is the suitable diameter of spring wire if maximum shear stress is not exceeding 250MN/m2? Modulus of rigidity of spring wire material is 80 GN/m2. What is maximum axial load the spring can carry? Q.1[3+2] Q.2 . A hollow C.I. column whose outside diameter is 200 mm has a thickness of 20 mm. It is 4.5 long and is

fixed at both ends. Calculate the safe load of Rankine-Gordon formula using a factor of safety of 4. Maximum Compressive stress σc = 550Mpa and a = 1/1600. Q.11[5]

Part- B [20 Marks]



EME-302 /Mr C.B.Khatri,Krishna kr. Yadav and Harsh Dwivedi Date: 22 /10/2012

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(EME-302)


Part – A


Q.1.A closely coil helical spring made of wire diameter 5 mm and having an inside diameter of 40mm joints two shafts. The effective no. of coils between the shaft is 15 and 0.735 kW is transmitted through the spring at 1000 rpm. Calculate relative axial twist in degrees between the end of spring and also the intensity of bearing stress in the material E=200 GPa. Q.3[3+2] Q.2. A mild steel hollow column, having 100 mm external diameter and 60 mm internal diameter and 4m length is used as a column. Determine the crippling load by Rankine’s formula, when both ends are hinged. Take σc = 320 N/mm2, a = 1/7500 Q.14 [5] Part- B [20 Marks]




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(EME-302)


Part – A


Q.1. A carriage spring is to be 600mm long and made of 9.5mm thick steel plates and 50mm broad. How many plates are required to carry a load of 4.5kN, without the stress exceeding 230MN/m2? What would be central deflection and initial radius of curvature, if plates straighten under the load? E=200GN/m2. Q.7 [3+2] Q. 2. Determine the maximum compressive stress set up in a 200 m = 60 mm I-section girder carrying load 100 kN with an eccentricity of 6 mm from the critical axis of the section. The ends of the structure are pin-jointed and overall length is 4 m. Q.13 [2+3] Part- B [20 Marks]




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(EME-302)


Part – A


Q.1 A railway wagon weighing 25 kN is moving at speed of 3 kmph. How many springs each of 24 coils will be required in a buffer stop to absorb the energy of, motion during a compression of 200 mm? The mean diameter of coils is 240mm and the diameter of steel rod comprising the coils is 20 mm. G = 0.9 x 105 N/mm2, g = 9.8 m/sec2 . Q.9 [5]

Q.2 A straight steel bar, 1.5 meter long and section 20 mm x 5 mm, is compressed longitudinally until it buckles. Using Euler’s formula, estimate the maximum central defection before the steel passes the yield point at 330 N/mm2. Take E = 200000 N/mm2 Q.12 [5]

Part- B [20 Marks]



(EME-302)/ C.B.Khatri, K.K.Yadav & Harsh Dwivedi Date: 17/112012

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B.Tech. [SEM 3rd(ME)] QUIZ -4

(Session : 2012-13) STRENGTH OF MATERIAL

Time: 1Hour (EME-302) Max. Marks 30

Roll No.

(To be filled by the Student) Note: Attempt all the questions.

Part – A

(Questions from Tutorial Sheet)

[10 Marks] Q1) A cylinder shell 90 cm long and 20 cm internal diameter having a thickness of 8 mm is filled with a fluid at atm. Pressure. If additional 20 cm3 of fluid is pumped into the cylinder, find (i) the pressure exerted by the fluid on the cylinder and (ii) the hoop stress induced. Take µ = 0.3 E= 200Gpa (Q.3) (2.5+2.5)mark Q2) A hollow cylinder of 45 cm internal diameter and 10 cm thickness contains the fluid under pressure of 850 N/cm2. Find the maximum and minimum hoop stress across the section. (Q.16) (2.5+2.5)mark

Part – B

[20 Marks] Q1) A thick cylinder of external and internal diameters of 300mm and 180mm is subjected to an internal

pressure of 42 N/mm2 and external pressure 6 N/mm2 .Determine the stresses in the material. Now if the external pressure is doubled, what internal pressure can be maintained without exceeding the previously determined maximum stress? (7)mark

Q2) A boiler shell is to be made of 15mm thick plate having limiting tensile stress of 120 N/mm2 . If then ηl

= 70% & ηc = 30% respectively determine ;(a) The max. permissible diameter of the shell for an internal pressure of 2 N/mm2 .(b) Permissible intensity of internal pressure when the shell diameter is 1.5m (3+3)mark

Q3) A compound cylinder is to be formed with inner dia. 300mm, diameter at the junction 400mm and outer diameter 500mm.If initial difference in the diameter is 0.2mm, find the radial stress developed at junction.Take E=2 × 105 N/mm2. (7)mark

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Roll No.


Part – A


[10 Marks] Q1) A copper cylinder, 90 cm long, 40 cm external diameter and wall thickness of 6mm has its both ends closed by rigid blank flanges. It is initially full of oil at atm. Pressure. Calculate the additional volume of oil which must be pumped into in order to raise the oil pressure 5 MN/m2 above atm. Pressure. For copper, assume E=100GPa, µ = 0.33, and K = 2.6 GPa. (Q.5) (5)mark Q2) A thick cylinder with closed ends has 100 mm internal radius and 150 mm external radius. It is subjected to an internal pressure to 60 MN/m2 and external pressure of 30 MN/m2. Determine the hoop and radial stresses at the inside and outside of the cylinder together with longitudinal stress. (Q.15) (1+1+1+1+1)mark

Part – B






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Roll No.


Part – A


[10 Marks] Q1) A thin spherical shell 1 m in diameter with its wall of 1.2 cm thickness is filled with a fluid at atm. Pressure . What intensities of pressure will be developed in it if 175 cm3 more of fluid is pumped into it ? Also calculate the circumferential stress at that pressure and increase in diameter.Take E= 200 GPa, and µ= 0.3.

(Q.6) (2+1.5+1.5)mark Q2) A pipe has internal diameter and external diameter of 150 mm and 250 mm respectively. If the fluid pressure is 140 bars, then calculate the radial stress and hoop stress at radius of 90 mm. (Q.12) (2.5+2.5)mark

Part – B

[20 Marks]

Q1) A thick cylinder of external and internal diameters of 300mm and 180mm is subjected to an internal pressure of 42 N/mm2 and external pressure 6 N/mm2 .Determine the stresses in the material. Now if the external pressure is doubled, what internal pressure can be maintained without exceeding the previously determined maximum stress? (7)mark




__________X__________



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Roll No.


Part – A


[10 Marks] Q1) A cylindrical shell 3 m long which is closed at the ends has an internal diameter of 1 m and a wall thickness of 15 mm. Calculate the circumferential and longitudinal stresses induced and also change in the dimensions of the shell, if it is subjected to an internal pressure of 1.5 MN/m2. Take E = 200 GN/m2 and μ =0.3.

(Q.10)(1+1+1+1+1)mark Q2) Find the thickness of the metal for a thick steel cylindrical shell of internal diameter 250 mm to withstand an internal pressure of 60 N/mm2. The maximum hoop stress in the section is not to exceed 200 N/mm2

(Q.13) (5)mark

Part – B



Q2) A boiler shell is to be made of 15mm thick plate having limiting tensile stress of 120 N/mm2 . If then ηl = 70% & ηc = 30% respectively determine ;(a) The max. permissible diameter of the shell for an internal pressure of 2 N/mm2 .(b) Permissible intensity of internal pressure when the shell diameter is 1.5m (3+3)mark

Q3) A compound cylinder is to be formed with inner dia. 300mm, diameter at the junction 400mm and outer diameter 500mm.If initial difference in the diameter is 0.2mm, find the radial stress developed at

junction.Take E=2 × 105 N/mm2. (7)mark



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Roll No.


Part – A


[10 Marks] Q1) A boiler drum consists of a cylindrical portion 2 m long, 1 m diameter and 25 mm thick, closed by hemispherical ends. In a hydraulic test to 10 N/mm2, how much additional water will be pumped in, after initial filling at atmospheric pressure? Assume the circumferential strain at the junction of cylinder and hemisphere is the same for both. For the drum material, E = 207000 GN/mm2, μ = 0.3. For water K = 2100 N/mm2. (Q.9) (5)mark Q2) The cylinder of a hydraulic ram is of 6 cm internal diameter. Find the thickness required to withstand an internal pressure of 40 N/mm2, if the maximum tensile stress is limited to 60 N/mm2 and the maximum shear stress to 50 N/mm2. (Q.11) (5)mark

Part – B

[20 Marks] _Q1) A thick cylinder of external and internal diameters of 300mm and 180mm is subjected to an internal


Q2) A boiler shell is to be made of 15mm thick plate having limiting tensile stress of 120 N/mm2 . If then ηl =

70% & ηc = 30% respectively determine ;(a) The max. permissible diameter of the shell for an internal pressure of 2 N/mm2 .(b) Permissible intensity of internal pressure when the shell diameter is 1.5m (3+3)mark


_________X__________


(EME-302)/ C.B.Khatri, K.K.Yadav & Harsh Dwivedi Date: /12/2012

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B.Tech. [SEM 3rd(ME)] SPECIAL QUIZ TEST


Time: 1Hour (EME-302) Max. Marks: 30

Roll No.

(To be filled by the Student) Note: Attempt all the questions. Q.1) At a point in a beam the normal stress along the length is 80 N/mm2. The shear stress at that point is positive of magnitude 35 N/mm2. Find the stresses on a plane whose normal is inclined at 30° to the longitudinal axis. Also find the principal stresses and planes on which they act. [3+2] Q.2) At a point in a stresses material, the three principal stresses are 90Mpa (tensile), 60 Mpa (tensile) and 30 Mpa (compressive). Find the factor of safety if yield stress is 230 Mpa and µ= 0.3 maximum principal and maximum shear stress theory. [2+3] Q.3) A timber beam has to carry a load of 2 kN/m over a span of 3m. The permissible stress is 8 Mpa (tensile). Design the rectangular section beam if the width is half of the depth. [5] Q.4) A cantilever carries a concentrated load at free end. Derive the general expression for slope and deflection at the free end. [5] Q.5) A solid circular shaft has a diameter of 80mm. Find the maximum shear stress and the angle of twist in a length of 2m when the shaft is subjected to a torque of 10 kNm. Take C= 85 Gpa. [3+2]


(EME-302)/ C.B.Khatri, K.K.Yadav & Harsh Dwivedi Date: /12/2012

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B.Tech. [SEM 3rd(ME)] SPECIAL QUIZ TEST



Roll No.

(To be filled by the Student)

Note: Attempt all the questions.

Q.1) The strains at a point in a stresses body are as follows, εxx= -640 X 10-6 and εyy= 300 X 10-6 and γxy=160 x 10-6. Determine the strains along the directions inclined at 25° to the X-axis. Find the principal strains and their directions. [3+2] Q.2) Design a steel bolt subjected to a tensile load of 20kN along with a shear stress of 10 kN. The yield point for the material is 300 Mpa and µ=0.3. Calculate the safe diameter by maximum shear stress theory. [5] Q.3) A rectangular section, 200mm X 400mm spans a distance of 2m. Find what uniformly distributed load the beam section can carry on this span. Permissible stress is 7 Mpa. [5] Q.4) A simply supported beam carries a concentrated load at mid-spam. Derive the general expression for slope and deflection at centre of beam. [5] Q.5) A circular shaft is subjected to a torque of 20,000 Nm. If the maximum permissible shear stress is 50 Mpa, find a suitable minimum diameter for the shaft. [5]


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