Anna University, Chennai

**QUESTION BANK**

**ME2254-STRENGTH OF MATERIALS DEPARTMENT OF MECHANICAL ENGINEERING**

**SRINIVASAN ENGINEERING COLLEGE- PERAMBALUR**

**UN****I****T- I**

**STRESS STRAIN DEFORMATION OF SOLIDS**

1. A rod of 150 cm long and diameter 2.0cm is subjected to an axial

pull of 20 KN. If the modulus of elasticity of the material of the rod is 2x

105 N/mm2 Determine 1. Stress 2. Strain 3. the elongation of the rod

(16)

2. The extension in a rectangular steel bar of length 400mm and thickness

10mm is found to 0.21mm .The bar tapers uniformly in width from

100mm to 50mm. If E for the bar is 2x 105 N/mm2 ,Determine the axial

load on the bar (16)

3. Find the young’s modulus of a rod of diameter 30mm and of length

300mm which is subjected to a tensile load of 60 KN and the extension of the rod is equal to 0.4 mm

(16)

4. The extension in a rectangular steel bar of length 400mm and thickness

3mm is found be 0.21mm .The bar tapers uniformly in width from

20mm to 60mm E for the bar is 2x 105 N/mm2 Determine the axial load on the bar. (16)

5. The ultimate stress for a hollow steel column which carries an axial load of 2Mn is 500 N/mm2 .If the external diameter of the column is

250mm, determine the internal diameter .Take the factor of safety as 4.0

(16)

6. A steel rod of 20mm diameter passes through a brass tube of 30 mm inside diameter and 40mm outside diameter . Two nuts one on each side are tightened until a stress of 10 n/mm2 is induced in the rod. F1.2xind the stresses in the rod and the tube if the assembly is heated through 600C. Take

Es = 2x105N/mm2, αs =1.2x10-5/0C

Eb = 0.8x105N/mm2, αb =1.2x10-5/0C

7. A solid steel rod of 5 m length and 10 mm diameter is subjected to an axial load of 5 kN . Find the stress induced in the rod if the load is applied (a) gradually,(b) suddenly and (c) impact after falling from a height of 150 mm. Also find the strain energy stored in the rod under given conditions. Take E= 200 kN/mm2.

8. A rod of diameter 10 mm and length 1.5 mm hangs vertically from the ceiling of a roof. A collar is attached at its lower end on which a load of 250 N falls from a height of 200 mm. Find the strain energy absorbed and the instantaneous deflection of the rod. Take E = 200 kN/ mm2.

**UN****I****T II**

**BEAMS – LOADS AND STRESSES**

1. Three planks of each 50 x200 mm timber are built up to a symmetrical I section for a beam. The maximum shear force over the beam is 4KN. Propose an alternate rectangular section of the same material so that the maximum shear stress developed is same in both sections. Assume then width of the section to be 2/3 of the depth. (16)

2. A beam of uniform section 10 m long carries a udl of KN/m for the entire length and a concentrated load of 10 KN at right end. The beam is freely supported at the left end. Find the position of the second support so that the maximum bending moment in the beam is as minimum as possible. Also compute the maximum bending moment (16)

3. A beam of size 150 mm wide, 250 mm deep carries a uniformly distributed load of w kN/m over entire span of 4 m. A concentrated load 1 kN is acting at a distance of 1.2 m from the left support. If the bending stress at a section 1.8 m from the left support is not to exceed 3.25

N/mm2 find the load w. (16)

4. A cantilever of 2m length carries a point load of 20 KN at 0.8 m from the fixed end and another point of 5 KN at the free end. In addition, a u.d.l. of 15 KN/m is spread over the entire length of the cantilever. Draw the S.F.D, and B.M.D. (16)

5. A Simply supported beam of effective span 6 m carries three point

loads of 30 KN, 25 KN and 40 KN at 1m, 3m and 4.5m respectively from the left support. Draw the SFD and BMD. Indicating values at salient points.

(16

)

6. A Simply supported beam of length 6 metres carries a udl of

20KN/m throughout its length and a point of 30 KN at 2 metres from the right support. Draw the shear force and bending moment diagram.Also find the position and magnitude of maximum Bending moment.

(16)

7. A Simply supported beam 6 metre span carries udl of 20 KN/m for left half of span and two point loads of 25 KN end 35 KN at 4 m and 5 m from left support. Find maximum SF and BM and their location drawing SF and BM diagrams.

(

16)

8. A horizontal beam of 10 m long is carrying a usdl load of 1 kN/m. The beam is supported on two supports 6 m apart. Find thee position of the supports so that the bending moment on the beam is as small as possible. Also draw the shear force and bending moment diagram.

**UN****I****T- III TORSION**

1. Determine the diameter of a solid shaft which will transmit 300 KN at 250 rpm. The maximum shear stress should not exceed 30 N/mm2 and twist should not be more than 10 in a shaft length 2m.

Take modulus of rigidity = 1x 105N/mm2. (16)

2. The stiffness of the closed coil helical spring at mean diameter 20 cm is made of 3 cm diameter rod and has 16 turns. A weight of 3 KN is dropped on this spring. Find the height by which the weight should be dropped before striking the spring so that the spring may be compressed

by 18 cm. Take C= 8x104 N/mm2. (16)

3. It is required to design a closed coiled helical spring which shall deflect 1mm under an axial load of 100 N at a shear stress of 90 Mpa. The spring is to be made of round wire having shear modulus of 0.8 x

105 Mpa. The mean diameter of the coil is 10 times that of the coil wire.

Find the diameter and length of the wire. (16)

4. A steel shaft ABCD having a total length of 2400 mm is contributed by three different sections as follows. The portion AB is hollow having outside and inside diameters 80 mm and 50 mm respectively, BC is solid and 80 mm diameter. CD is also solid and 70 mm diameter. If the angle of twist is same for each section, determine the length of each portion and the total angle of twist. Maximum permissible shear stress is 50 Mpa and shear modulus

0.82 x 105 MPa (16)

5. The stiffness of close coiled helical spring is 1.5 N/mm of compression under a maximum load of 60 N. The maximum shear stress in the wire of the spring is 125 N/mm2. The solid length of the spring (when the coils are touching) is 50 mm. Find the diameter of coil, diameter of wire and number of coils.

C = 4.5 (16)

6. A solid shaft of length 3.5 m and diameter 25 mm rotates at a frequency of

40 Hz. Find the maximum power to be transmitted by the shaft, assuming the maximum shear stress in the shaft is limited to 40 Mpa and angle of twist does not exceed 60. Take G = 80 Gpa

7. Find the maximum torque that can be applied safely to a shaft of diameter

300 mm. The permissible angle of twist is 1.50 in a length of 7.5 m and a maximum shear is limited to 42 Mpa. Take G = 84.4 Gpa.

**8****. **A solid steel shaft has to transmit 100 kW at 160 r.p.m. Taking allowable shear stress as 70 Mpa, find the suitable diameter of the shaft. The maximum torque transmitted in each revolution exceeds the mean by 20%.

**UN****I****T-IV BEAMDEFLECTION**

1. A simply supported beam of 10 m span carries a uniformly distributed load of 1 kN/m over the entire span. Using Castigliano’s theorem, find the slope at the ends. EI = 30,000 kN/m2.

(16)

2. A 2m long cantilever made of steel tube of section 150 mm external diameter and10mm thick is loaded. If E=200 GN/m2 calculate (1) The value of W so that the maximum bending stress is 150 MN/m (2) The maximum deflection for the loading (16)

3. A beam of length of 10 m is simply supported at its ends and carries two point loads of100 kN and 60 kN at a distance of 2 m and 5 m respectively from the left support. Calculate the deflections under each load. Find also the maximum deflection. Take I = 18 X 108 mm4 and E =

2 X 105. (16)

4. i) A column of solid circular section, 12 cm diameter, 3.6 m long is hinged at both ends. Rankine’s constant is 1 / 1600 and σc = 54 KN/cm2. Find the buckling load. ii) If another column of the same length, end conditions and rankine constant but of 12 cm X 12 cm square cross- section, and different material, has the same buckling load, find the value of σc of its material. (16)

5. A beam of length of 6 m is simply supported at its ends. It carries a uniformly distributed load of 10 KN/m as shown in figure. Determine the deflection of the beam at its mid-point and also the position and the maximum deflection. Take EI=4.5 X 108 N/mm2. (16)

6. An overhanging beam ABC is loaded as shown is figure. Determine the deflection of the beam at point C. Take I = 5 X 108 mm4 and E = 2 X

105 N/mm2. (16)

7. A cantilever of length 2 m carries a uniformly distributed load of 2.5

KN/m run for a length of 1.25 m from the fixed end and a point load of 1

KN at the free end. Find the deflection at the free end if the section is rectangular 12 cm wide and 24 cm deep and E=1 X 104 N/mm2

(16)

8. A cantilever of length 2m carries a uniformly distributed load 2 KN/m over a length of 1m from the free end, and a point load of 1 KN at the free end. Find the slope and deflection at the free end if E = 2.1 X 105 N/mm2 and I = 6.667 X 107 mm4 . (16)

9. Determine the section of a hollow C.I. cylindrical column 5 m long with ends firmly built in. The column has to carry an axial compressive load of 588.6 KN. The internal diameter of the column is 0.75 times the

external diameter. Use Rankine’s constants. a = 1 / 1600, σc = 57.58

KN/cm2 and F.O.S = 6. (16)

(10). A cantilever beam of length L carries a udl of intensity w per unit length over its entire span and a point load P at its free end. Find the maximum deflection of the beam using castingliano’s theorem.

**UN****I****T-V**

**ANA****LYSIS OF STRESSES IN TWO DIMENSIONS**

1. A Thin cylindrical shell 3 m long has 1m internal diameter and 15 mm metal thickness. Calculate the circumferential and longitudinal stresses induced and also the change in the dimensions of the shell, if it is subjected to an internal pressure of1.5 N/mm2 Take E = 2x105

N/mm2 and poison’s ratio =0.3. Also calculate change in volume. (16)

2. A closed cylindrical vessel made of steel plates 4 mm thick with plane ends, carries fluid under pressure of 3 N/mm2 The diameter of the cylinder is 25cm and length is 75 cm. Calculate the longitudinal and hoop stresses in the cylinder wall and determine the change in diameter, length and Volume of the cylinder. Take E =2.1x105 N/mm2 and 1/m =

0.286.

(16)

3. A rectangular block of material is subjected to a tensile stress of 110

N/mm2 on one plane and a tensile stress of 47 N/mm2 on the plane at right angle to the former plane and a tensile stress of 47 N/mm2 on the

plane at right angle to the former. Each of the above stress is

accompanied by a shear stress of 63 N/mm2 Find (i) The direction and

magnitude of each of the principal stress (ii) Magnitude of greatest shear stress (16)

4. At a point in a strained material, the principal stresses are100 N/mm2 (T) and 40 N/mm2 (C). Determine the resultant stress in magnitude and

direction in a plane inclined at 600 to the axis of major principal stress. What is the maximum intensity of shear stress in the material at the point? (16)

5. A rectangular block of material is subjected to a tensile stress of 210

N/mm2 on one plane and a tensile stress of 28 N/mm2 on the plane at right angle to the former plane and a tensile stress of 28 N/mm2 on the

plane at right angle to the former. Each of the above stress is

accompanied by a shear stress of 53 N/mm2 Find (i) The direction and

magnitude of each of the principal stress (ii) Magnitude of greatest shear stress (16)

6 .A closed cylindrical vessel made of steel plates 5 mm thick with plane ends, carries fluid under pressure of 6 N/mm2 The diameter of the cylinder is 35cm and length is 85 cm. Calculate the longitudinal and hoop stresses in the cylinder wall and determine the change in diameter, length and Volume of the cylinder. Take E =2.1x105 N/mm2 and 1/m =

0.286.

(16)

7. At a point in a strained material, the principal stresses are 200 N/mm2 (T) and 60 N/mm2 (C) Determine the direction and magnitude in a plane inclined at 600 to the axis of major principal stress. What is the maximum intensity of shear stress in the material at the point

(16)

8. At a point in a strained material, the principal stresses are 100 N/mm2 (T) and 40 N/mm2 (C) Determine the direction and magnitude in a plane inclined at 600 to the axis of major principal stress. What is the maximum intensity of shear stress in the material at the point

(16)

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