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1) A rod 200 cm long and of diameter 3.0 cm is subjected to an axial pull of 30 kN. If the Young’s modulus of the material

of the rod is 2*105 N

mm2, determine: (i)

stress, (ii) strain and (iii)the elongation of the rod.

2) Find the young’s modulus of diameter 30 mm and length 300 mm which is subjected to a tensile load of 60 kN and the extension of the rod is equal to 0.4 mm.

3) The safe stress, for a hollow steel column which carries an axial load of

2.2 *103kN is 120MN

m2. If the external

diameter of the column is 25 cm, determine the internal diameter.

4) A brass bar, having cross-section area of 900 mm2, is subjected to axial forces as shown in Fig 1.29 in which AB=0.6m, BC=0.8 m and CD=1.0 m.

5) A rectangular bar made of steel is 3m long and 10 mm thick. The rod is subjected to an axial tensile load of 50kN. The width of the rod varies from 70 mm at one end to 28 mm at the other. Find the extension of the rod if

E=2*105 N

mm2.

6) A rod is 3m long at a temperature of

150C. find the expansion of the rod,

when the temperature is raised to 950

C. if this expansion is prevented; find the stress induced in the material of the

rod. Take E=1*105 N

mm2 and

α=0.000012 per degree centigrade.7) A steel rod 5 cm diameter and 6 m long

is connected to two grips and the rod is

maintained at a temperature of 1000C. determine the stress and pull exerted when the temperature falls to 200C if the ends do not yield by 0.15 cm. Take

E=2*105 N

mm2 and ∝=12*10−6/C0.

8) Determine the changes in length, breadth and thickness of a steel bar which is 5 m long, 40 mm wide and 30 mm thick and is subjected to an axial pull of 35 kN in the direction of its

length.Take E=2*105 N

mm2 and

Poisson’s ratio=0.32.9) Determine the value of young’s

modulus and Poisson’s ratio of a metallic bar of length 25 cm, breadth 3 cm and depth 2 cm when the bar is subjected to an axial compressive loas of 240 kN. The decrease in length is given as 0.05 cm and increase in breadth is 0.002.

10) A steel bar 320 mm long, 40 mm wide and 30 mm thick is subjected to a pull of 250 kN in the direction of its length. Determine the change in volume. Take

E=2*105 N

mm2 and m= 4.

11) A metallic bar 250 mm* 80mm*30 is subjected to a force of 20 kN(tensile), 30kN(tensile)and 15 kN(tensile) along x,y and z direction respectively. Determine the change in the volume of

the block. Take E= 2*105 N

mm2 and

Poisson’s ratio=0.1512) For a material, young’s modulus is gives

as 1.4*105 N

mm2 and Poisson’s ratio

0.28. Calculate the bulk modulus.

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13) Determine the Poisson’s ratio and bulk modulus of a material, for which

young’s modulus is 1.2*105 N

mm2and

modulus of rigidity is 4.5*104 N

mm2

14) A bar of cross-section 10 mm*10 mm is subjected to an axial pull of 8000 N. the lateral dimension of the bar is found to be changed to 9.9985 mm. if the modulus of rigidity of the material is 0.8

*105 N

mm2, determine the Poisson’s

ratio and modulus of elastity.15) A rectangular beam 100 mm wide is

subjected to a maximum shear force of 100kN. Foind the depth of beam of if

the maximum shear stress is 6 N

mm2.

16) Atimber beam of rectangular section is simply supported at the ends and carries a point load at the centre of the beam the length of the beam is 6 m and depth of beam is 1 m. determine the maximum bending stress and the maximum shear stress.

17) A circular beam of 105 mm diameter is subjected to a shear force of 5kN. Calculate : (i)average shear stress, and (ii) maximum shear stress. Also sketch the varation of the shear stress along the depth of the beam.

18) The maximum shear stress in a beam of circular section of diameter 150 mm, is

5.28N

mm2. find the shear stress force to

which the beam is subjected.19) The shear force acting on a section of a

beam is 100 kN. The section of the bean is of T-shaped of diamensions 200 mm*250 mm * 50mm. the flage

thickness and web thickness are 50 mm. moment of inertia about the horizontal neutral axis is 1.134*108mm4. Find the shear stress at the neutral axis and at the junction of the web and the flange.

20) A rectangular column of wide 120 mm and of thickness 100 mm carries a point load of 120kN at an eccentricity of 10 mm. determine the maximum and minimum stresses at the base of the column.

21) If in the above problem, the minimum stress at the base of the section is given as zero then find the eccentricity of the point load of 120 kN acting on the rectangular section also calculate the corresponding maximum stress on the section.

22) In a tension specimen 13 mm in a diameter the line of pull is parallel to the axis of the specimen but is displaced form it. Determine the distance of the line of pull form the axis, when the maximum stress is 15% greater than the mean stress on a section normal to the axis.

23) A short column of diameter 40 cm carries an eccentric load 80 kN. Find the greatest eccentricity which the load can have without producing tension on the cross-section.

24) A short column of external diameter 50 cm and internal diameter 30 cm carries an eccentric load of 100kN. Find the greatest eccentricity which the load can have without producing tension on the cross-section.

25) A hollow circular column of 25 cm external and 20 cm internal diameter respectively carries an axial load of 200 kN it also carries a load of 100kN on a

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bracket whose line of action is 20 cm from the axis of the column. Determine the maximum and minimum stress at base section.

26) A column section 30 cm external diameter and 15 cm internal diameter supporteds an axial load of 2.6 MN and an eccentric load of PN at an eccentricity of 40 cm. if the compressive and tensile stresses are

not to exceed 140 N

mm2respectively,

find the magnitude of load p.27) A solid shaft of 20 cm diameter is used

to transmit torque. Find the maximum torque transmitted by the shaft if the maximum shear stress induced in the

shaft is 50N

mm2.

28) The shearing stress in a solid shaft is not

to exceed 45 N

mm2 when the torque

transmited is 40000 N-m. determine the minimum diameter of the shaft.

29) Find the maximum torque transmitted by a hollow circular shaft of external diameter 30 cm and internal diameter 15 cm if the shear stress is not to

exceed 40 N

mm2.

30) Find the max shear stress induced in a solid circular shaft of diameter 20 cm when the shaft transmit 187.5kW at 200 r.p.m.

31) Determine the diameter of a solid stel shaft which will transmit 112.5 kW at 200 r.p.m. also determine the length of the shaft If the twist must not exceed 1.

50 over the entire length. The max

shear stree is limited to 55N

mm2. Take

the value of modulus of rigidity = 8*

104N

mm2.

32) Determine the diameter of a solid shaft which will transmit 337.5 kW at 300 r.p.m. the max shear stress should not

exceed 35N

mm2. And twist should not

be more than 10 in a shaft length of 2.5

m. take modulus of rigidity=9*104 N

mm2

.33) A closely-coiled helical spring is to carry

a load of 1 kN. Its maen coil diameter is to be 10 times that of wire diameter. Calculate these diameters if the max shear stress in the material of the

spring is to be 90 N

mm2.

34) A cylinder of internal diameter 3.0 m and of thickness 6cm contains a gas . if the tensile stress in the material is not

to exceed 70 N

mm2, determine the

internal pressure of the gas.35) A cylinder of internal diameter 0.60 m

contains air at a pressure of 7.5N

mm2

(gauge). If the max permissible stress

induced in the material is 75 N

mm2, find

the thickness of the cylinder.36) The ratio of modulus of rigidity to

modulus of elasticity for a poisson’s ratio of 0.25 would be

a). 0.5 b).0.4 c).0.3 d).1.0.

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37) The ratio of bulk modulus to modulus of elasticity for a poisson’s ratio of 0.25 would be

a)23

b)13

c)43

d) 1.0

38. The relation between modulus of elasticity (E),modulus of rigidity © and bulk modulus (K) is given by

a)E=3KCC+9K b)E=

9KCC+3K c)E=

C+9K3KC

d)E=C+3K9KC

.

39. The ratio of modulus of rigidity to bulk modulus for a poisson’s ratio of 0.25 would be

a)23

b)25

c)35

d) 1.0

40. The thermal stress is given by

a) E∝T b) ET∝

c) E∝T

d)1

E∝T

41. The tensile force at a distances y from support in a vertical hanging bar of length l which carries a load p at the bottom is equal to

a) p b) p + wl c) p + w(l-y) d) p + wy

42. the normal stress on an oblique plane at an angle θ to the cross-section of a body which is subjected to a direct tensile stress(σ) is equal to

a) σ2

sin2θ b)σcosθc)σcos2θ

d) σsin2θ

43. A simply supported beam carries a uniformly distributed load of w N per unit

length over the whole span (l). The shear force at the centre is

a)wl2

b)w l2

8 c)

wl4

d)

zero.

44. A cantilever of length (l) carries a uniformly distributed load w N per unit length for the whole length. The shear force at the free end will be

a) wl b)w l2

2 c)

wl2

d)zero.

45. The torque transmitted, by a solid shaft of diameter 40 mm if the shear stress is not to

exceed 400 N

cm2, would be

a)1.6*π N-m b) 16*π N-m c) 0.8*π N-m d) 0.4*π N-m.

46. The longitudinal or axial stress in a thin cylindrical shell of diameter (D), length (L) and thickness (t), when subjected to an internal pressure (p) is equal to

a) pD4 t

b) pD2 t

c) 2 pDt

d) 4 pDt

.

47. The max shear stress in a thin cylindrical shell, when subjected to an internal pressure (p) is equal to.

a) pD4 t

b)pD8 t

c)pD2 t

d)pDt

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48. The hoop or circumferential stress in a riveted cylindrical shell , when subjected to an internal pressure (p) is equal to

a) pD4 t ηl

b)pD4 t ηc

c)pD2t ηl

d)pD2t ηc

49. the longitudinal stress in a riveted cylindrical shell, when subjected to internal pressure (p)

Is equal to

a) pD4 t ηl

b)pD4 t ηc

c)pD2t ηl

d)pD2t ηc

50. A water maim 1 m in diameter contains a

fluid having pressure 1 12

N/mm2. If the

maximum permissible tensile stress in the metal is 20 N/ mm2 , the thickness of the metal required would be

a) 2 cm b) 2.5 cm c) 1 cm d) 0.5 cm

51. The circumferential strain in case of thin cylindrical shell, when subjected to internal pressure (p), is equal to

a) pd2tE ( 12− 1

m )

b) pd2tE (1− 1

2m )c) pd4 tE (1− 1

m )

d) 3 pd4 tE (1− 1m )

52. The longitudinal strain in case of thin cylinders shell, when subjected to internal pressure (p) , is equal to

a) pd2tE ( 12− 1

m )b) pd2tE (1− 1

2m )c) pd4 tE (1− 1

m )d) 3 pd4 tE (1− 1

m )53. the strain in any direction in case of thin spherical shell, when subjected to internal pressure (P), is equal to

a) pd2tE ( 12− 1

m )b) pd2tE (1− 1

2m )c) pd4 tE (1− 1

m )d) 3 pd4 tE (1− 1m )

54. the volumetric strain in case of thin spherical shell, when subjected to internal pressure (P), is equal to

a) pd2tE ( 12− 1

m )b) pd2tE (1− 1

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c) pd4 tE (1− 1

m )d) 3 pd4 tE (1− 1

m )55. The crippling load, according to Euler’s theory of long columns, when both ends of the column are hinged, is equal to

a) 4 π2 EIl2

b) π 2EIl2

c) π 2EI4 l2

d) 2π2 EIl2

56. The crippling load, according to Euler’s theory of long colomn when one end of the column is fixed and other end is free, is equal to

a) 4 π2 EIl2

b) π 2EIl2

c) π 2EI4 l2

d) 2π2 EIl2

57. The crippling load, according to Euler’s theory of long column when both ends of the column are fixed. Is equal to

a) 4 π2 EIl2

b) π 2EIl2

c) π 2EI4 l2

d) 2π2 EIl2

58. The crippling load, according to Euler’s theory of long column when one end of the column is fixed and the other end is hinged, is equal to

a) 4 π2 EIl2

b) π 2EIl2

c) π 2EI4 l2

d) 2π2 EIl2

59. The ratio of crippling load, for a column of length (l) with both ends fixed to the crippling load of the same column with both ends hinged, is equal to

a) 2.0 b) 4.0 c) 0.25d) 0.50.

60. The ratio of crippling load, for a column of length (l) with both ends fixed to the crippling load of the same column with one end fixed and other end free, is equal to

a) 2.0 b) 4.0 c) 8.0d) 16.0

61. The ratio of crippling load, for a column of length (l) with both ends fixed to the crippling

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load of the same column with one end fixed and other end hinged, is equal to

a) 2.0 b) 4.0 c) 8.0d) 16.0

62. The equivalent length of a given column with given end conditions is the length of a column of the same material and section with hinged ends having crippling load equal to

a) two times that of the given column

b) half that of given column

c) four times that of the given column

d) that of the given column.

63. The equivalent length is equal length of a column with

a) one end fixed and other end free

b) both ends and fixed

c) one end fixed and other end hinged

d) both ends and hinged.

64. The equivalent length is twice the actual length of a column with

a) one end fixed and other end free

b) both ends and fixed

c) one end fixed and other end hinged

d) both ends and hinged.

65. The equivalent length is equal to half of the actual length of a column with

a) one end fixed and other end free

b) both ends and fixed

c) one end fixed and other end hinged

d) both ends and hinged.

66. The equivalent length is equal to actual length divided by √2 for a column with

a) one end fixed and other end free

b) both ends and fixed

c) one end fixed and other end hinged

d) both ends and hinged.

67. The crippling load by Rankine’s formula is

a)

σc A

1+a( lk )2 b)

σc A

1+a( lek )2 c)

σ c A

1−a ( lk )2 d)

σc A

1+a( lek )2

where A=area of cross-section of the column

σ c=crushing stress

A=Rankine’s constant

𝓀= least radius of gyration

l=actual length of column

le= equivalent length of column.

68. The Rankine’s constant(a) in Rankine’s formula is equal to

a) π 2Eσc

b) π2

Eσc c)

Eσcπ2

d) σcπ 2E

69. A cantilever of length (l) carries a load whose intensity varies uniformly from zero at

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the free end to w per unit length at the fixed end, the bending moment diagram will be a

a)straight line curve

b) parabolic curve

c) cubic curve

d) combination of (a) and (b).

70) A simply supported beam is overhanging equally on both sides and carries a uniformly distributed load of w per unit length over the whole length. The length between the supports is (l) and length of overhang to one side ‘a’. if l>2a then the number of points of contraflexure will be

a) zero b)one c) two d) three.

71. A bar 30 mm in diameter was subject to tensile load of 54 kN and the measured extension’s 300 mm gauge length was 0.112 mm and change in diameter was 0.00366 mm. calculator poisson’s ratio and value of three modulii.

72. A rectangular bar of cross-sectional area 12000 mm2is subject to an axial load of 360 N

mm2. Determine the normal and shear stresses

on a section which is included to at angle of 300 with the normal cross-section of bar.

73. Find the diameter of a circular bar which is subjected to an axial pull id 150 kN, id the maximum allowable shear stress on any section

is 60 N

mm2

74. An elemental cube is subjected to tensile

stresses of 60 N

mm2 and 20

N

mm2 acting on two

mutually perpendicular planes and a shear

stress of 20 N

mm2 on these planes. Draw the

Mohr’s circle of stresses and hence or otherwise determine the magnitudes and directions of principal stresses and also the greatest shear stress.

75. Form a circular plate of diameter 100 mm a circular part of diameter 50 mm is cut as shown in Fig 5.46. Find the centroid of the remainder.

76. A cantilever beam of length 4 m carries point loads of 1 kN, 2kN and 3kN at 1,2 and 4 m form the fixed end. Draw the shear force and B.M. diagrams for the cantilever.

77. A cantilever of length 5 m carries a

uniformly distributed load 1 kNm

run over the

whole length and a point load of 4kN at the free end. Drew the. S.F. and B.M diagrams for the cantilever.

78. A simply supported beam of length 8 m carries point loads of 4kN and 6kN at a distance of 2 m and 4m from the end. Draw the S.F and B.M diameters for the beam.

79. A simply supported beam of length 8 m carries point loads of 4 kN,10kN and 7kN at a distance of 1.5 m, 2.5 m and 2 m respectively from left end A. draw the S.F. and B.M. diagrams for the simply supported beam. S.F. and B.M. diagrams for the beam

80. A beam of length 10 m is simply supported and carries point loads of 5 kN each at a distance of 3 m and 7 m from left supported

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and also a uniformly distributed load of 1kNm

between the point loads. Draw S.F and B.M. diagram for the beam.

81. A steel plate of width 60 mm and thickness 10 mm is bent into a circular arc of radius 10m. determine the maximum stress induced and the bending moment which will produce the

maximum stress. Take E=2*105 N

mm2 .

82. A cast iron pipe of external diameter 60 mm, internal diameter of 40 mm, and of length 5 m is supported load of 100 N at its centre.

83. A rectangular beam 300 mm deep is simply supported over a span of 4 m. What uniformly distributed load per metre, the beam may carry

if the bending stress is not to exceed 120 N

mm2

Take I=8*106mm4.

84. A timber beam is 120 mm wide and 200 mm deep and is used on a span of 4 metres. The beam carries a uniformly distributed load of 2.8kNm

run over the entire length. Find the

maximum bending stress induced.

85. A rectangular beam 100 mm wide and 150 mm deep is subjected to a shear force of 30 kN.determine : (i) average shear stress and (ii) maximum shear stress.

86. A thin cylinder of internal diameter 2.0 m contains a fluid at an internal pressure of 3N

mm2 determine the max thickness of the

cylinder if (i) the longitudinal stress is not to

exceed 30N

mm2 and (ii) the circumferential

stress is not exceed 40N

mm2

87. A water main 90 cm diameter contains water at a pressure head of 110 m if the weight

density of water is 9810 N

mm2, find the

thickness of the metal required for the qater

main. Given the permissible stress as 22N

mm2 .

88. A cylinder shell 100 cm long 20 cm internal diameter having thickness of metal as10 mm is filled with fluid at atmospheric pressure. If an additional 20 cm3 of fluid is pumped into cylinder find (i) the pressure exerted by the fluid on the cylinder and (ii) the hoop stress induced.

Take E=2*105 N

mm2∧¿µ=0.3.

89. A cylindrical vessel whose ends are closed by means of rigid flange plates, is made of steel plate 4 mm thick. The length and the internal diameter of the vessel are 100 cm and 30 cm respectively. Determine the longitudinal and hoop stresses in the cylindrical shell due to an

internal fluid pressure of 2N

mm2. Also calculated

the increase in length, diameter and volume

and of the vessel. Take E=2*105 N

mm2 µ=0.3.

90. A solid round bar 4 m long and 6 cm in diameter is used as a strut with both ends hinged. Determine the crippling load. Take E=2*

105N

mm2.

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91. A column of timber section 10 cm * 15 cm is 5 m long both ends being fixed. If the young’s

modulus for timber= 17.5kN

mm2, determine :

92. A hollow mild steel tube 5 m long, 4 cm internal diameter and 5mm thick is used as a strut with both ends hinged. Fine the crippling load and safe load taking factor of safety as 3.

Taking E=2*105 N

mm2

93. A solid circular bar 5 m long and 4 cm in diameter was found to extend 4.5 mm under a tensile load of 48 kN. The bar is used as a strut with both ends hinged. Determine the buckling load for the bar and also the safe load taking factor of safety as 3.0.

94. Calculate the safe compressive load on a hollow cast iron column (one end rigidly fixed and other hinged) of 10 cm external diameter, 7 cm internal and 8 m in length. Use euler’s formula with a factore of safety of 4 and E=95 kN

mm2.

95. Determine euler’s crippling load for an I-section joist 30 cm *15 cm *2 cm and 5m long which is used as a strut with both ends fixed. Take young‘s modulus for the joint as 2*

105N

mm2.

96. Determine the crippling load for a T-section of dimensions 12 cm *2 cm and 5 m long which is used as a strut with both of its ends hinged.

Take E=2*105 N

mm2

97. Determine the ratio of buckling strengths of two columns one hollow and the other solid. Both are made of the same material and have

the same length, cross-section area and end conditions the internal diameter of hollow

column is 23 rd

of its external diameter.

98. A hollow cylindrical cast iron column is 6 m long with both ends fixed. Determine the minimum diameter of the column is 4 m and both of its ends are fixed, determine the crippling load using Rankine’s formula. Take the

value of f c=550N

mm2 and a=

11600

in Rankine’s

formula

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