According to Von-Mises' distortion energy theory, the distortion energy under three dimensional stress state is represented by

1[ 1 + 2 + 3 - 2m( 1 2 + 3 2 + 1 3)]3E

1[ 1 + 2 + 3 - 2m( 1 2 + 3 2 + 1 3)] E

1 - 2 [ 1 + 2 + 3 - 2m( 1 2 + 3 2 + 1 3)]6E

1 + [ 1 + 2 + 3 - 2m( 1 2 + 3 2 + 1 3)]3E

1[ 1 + 2 + 3 - 2m( 1 2 + 3 2 + 1 3)]3E

A simply supported laterally loaded beam was found to deflect more than a specified value. Which of the following measures will reduce deflection?

Increase the area moment of inertia

Select a different material having lesser modulus of elasticity

Magnitude of the load to be increased

An axial residual compressive stress due to a manufacturing process is present on the outer surface of a rotating shaft subjected to bending. Under a given bending load, the fatigue life of the shaft in the presence of the residual compressive stress is

increased or decreased, depending on the external bending load

neither decreased nor increased

A circular rod of length L and area of crosssection A has a modulus of elasticity E and coefficient of thermal expansion . One end of the rod is fixed and other end is free. If the temperature of the rod is increased by T, then

stress developed in the rod is E T and strain developed in the rod is zero

stress developed in the rod is E T and strain developed in the rod is a T

both stress and strain developed in the rod are zero

stress developed in the rod is zero and strain developed in the rod is T

stress developed in the rod is E T and strain developed in the rod is zero

104 + Mcqs in Strength Of Materials Miscellaneous in Strength of Materials Page 1 McqOptions

1.	If the two principal strains at a point are 1000 x 10^-6 and 600 10^-6, then the maximum shear strain is
A.	800 10
B.	500 10
C.	1600 10
D.	200 10
Answer» D. 200 10

Discussion

2.	Two solid circular shafts of radii R₁ and R₂ are subjected to same torque. The maximum shear stresses developed in the two shafts are ₁ and ₂. If R₁/R₂ = 2, then ₂/ ₁ is ______.
A.	8
B.	8.1
C.	7.9
D.	8.2
Answer» B. 8.1

Discussion

3.	A hollow shaft (d₀ = 2d_i where d₀ and d_i are the outer and inner diameters respectively) needs to transmit 20 kW power at 3000 RPM. If the maximum permissible shear stress is 30 MPa, d₀ is
A.	11.29 mm
B.	22.58 mm
C.	33.87 mm
D.	45.16 mm
Answer» C. 33.87 mm

Discussion

4.	In terms of Poisson's ratio ( ) the ratio of Young's modulus (E) to Shear modulus (G) of elastic materials is
A.	2(1 + )
B.	2 (1 )
C.
D.
E.
Answer» B. 2 (1 )

Discussion

5.	If the Young's modulus and Poisson's ratio of the container material' are 100 GPa and 0.3, respectively, the axial strain in the cylinder wall at mid-depth is
A.	2 10
B.
C.	6 10
D.	7 10
E.	1.2 10
Answer» B.

Discussion

6.	A 200 100 50 mm steel block is subjected to a hydro static pressure of 15 MPa. The Young's modulus and Poisson's ratio of the material are 200 GPa and 0.3 respectively. The change in the volume of the block in mm³ is
A.	85
B.	90
C.	100
D.	110
Answer» C. 100

Discussion

7.	A horizontal bar, fixed at one end (x = 0), has a length of 1 m, and cross-sectional area of 100 mm². Its elastic modulus varies along its length as given by E(x) = 100e^x GPa, where x is the length coordinate (in m) along the axis of the bar. An axial tensile load of 10 kN is applied at the free end (x = 1). The axial displacement of the free end is _____ mm.
A.	1.788
B.	0.718
C.	1.718
D.	2.718
Answer» D. 2.718

Discussion

8.	The state of stress at a point is _x = _y = _z = _xz = _zx = _yx = _zy= 0 and _xy = _yx = 50 MPa. The maximum normal stress (in MPa) at that point is ______.
A.	50
B.	52
C.	55
D.	60
Answer» B. 52

Discussion

9.	In a plane stress condition, the components of stress at a point are _x = 20 MPa, _y = 80 MPa and _xy = 40 MPa. The maximum shear stress (in MPa) at the point is
A.	20
B.	25
C.	50
D.	100
Answer» D. 100

Discussion

10.	The principal stresses at a point in a critical - section of a machine component are ₁ = 60 MPa, ₂ = 5 MPa and ₃ = 40 MPa. For the material of the component, the tensile yield strength is _y = 200 MPa. According to the maximum shear stress theory, the factor of safety is
A.	1.67
B.	2.00
C.	3.60
D.	4.00
Answer» C. 3.60

Discussion

11.	The state of stress at a point under plane stress condition is _xx = 40 MPa, _yy = 100 MPa and _xy =40 MPa The radius of Mohr's circle representing the given state of stress in MPa is
A.	40
B.	50
C.	60
D.	100
Answer» C. 60

Discussion

12.	A cylindrical rod of diamet er 10 mm and length 1.0 m fixed at one end. The other end is twisted by angle of 10 by applying a torque. If the maximum shear strain in the rod is p 10^-3, then p is equal to _______ (round off to two decimal places).
A.	0.87
B.	0.86
C.	0.85
D.	0.88
Answer» B. 0.86

Discussion

13.	The cross-sections of two solid bars made of the same material are shown in the figure. The square cross-section has flexural (bending) rigidity I1 while the circular cross-section has flexural rigidity I2. Both sections have the same cross-sectional area. The ratio I₁ /I₂ is
A.	1/
B.	2/
C.	/3
D.	/6
Answer» D. /6

Discussion

14.	A simply supported beam of length L is subjected to a varying distributed load sin (3 x/L) Nm^-1, where the distance x is measured from the left support. The magnitude of the vertical reaction force in N at the left support is
A.	zero
B.	L/3
C.	L/
D.	2 L/
Answer» C. L/

Discussion

15.	The state of stress at a point is given by _x = 6 MPa, _y = 4 MPa, and _xy = 8 MPa. The maximum tensile stress (in MPa) at the point is ______
A.	8
B.	8.43
C.	43
D.	3.4
Answer» C. 43

Discussion

16.	A 200 mm long, stress free rod at room temperature is held between two immovable rigid walls. The temperature of the rod is uniformly raised by 250 C. If the Young's modulus and coefficient of thermal expansion are 200 GPa and 1 10^{-5/ C}, respectively, the magnitude of the longitudinal stress (in MPa) developed in the rod is _______
A.	500 MPa
B.	4990 MPa
C.	501 MPa
D.	350 MPa
Answer» B. 4990 MPa

Discussion

17.	The state of plane-stress at a point is given by _x =200 MPa, _y =100 MPa and _xy = 100 MPa. The maximum shear stress
A.	111.8
B.	150.1
C.	180.3
D.	223.6
Answer» B. 150.1

Discussion

18.	If the principal stresses in a plane stress problem are ₁ = 100 MPa, ₂ = 40 MPa, the magnitude of the maximum shear stress (in MPa) will be
A.	60
B.	50
C.	30
D.	20
Answer» D. 20

Discussion

19.	A solid cube of side 1 m is kept at a room temperature of 32 C. The coefficient of linear thermal expansion of the cube material is 1 10^-5/ and the bulk modulus is 200 GPa. If the cube is constrained all around and heated uniformly t o 42 C, t hen t he magnit ude of volumetric (mean) stress (in MPa) induced due to heating is _____.
A.	60 MPa
B.	59 MPa
C.	58 MPa
D.	61 MPa
Answer» B. 59 MPa

Discussion

20.	A rectangular region in a solid is in a state of plane strain. The (x, y) coordinates of the corners of the undeformed rectangle are given by P(0, 0), Q(4, 3), S(0, 3). The'rectangle is subjected to uniform strain _xx = 0.001, _yy = 0.002, _xy = 0.003. The deformed length of the elongated xy diagonal, upto three decimal places, is _______ units.
A.	5.015 units
B.	15 units
C.	5 units
D.	None of the above
Answer» B. 15 units

Discussion

21.	In a metal forming operation when the material has just started yielding, the principal stresses ₁ = +180 MPa, ₂ = 100 MPa, ₃ = 0. Following von Mises criterion, the yield stress is _____, MPa.
A.	245.76 MPa
B.	244.76 MPa
C.	243.76 MPa
D.	246.76 MPa
Answer» B. 244.76 MPa

Discussion

22.	A solid cube of side 1 m is kept at a room temperature of 32 C. The coefficient of linear thermal expansion of the cube material is 1 10
A.	60 MPa
B.	59 MPa
C.	58 MPa
D.	61 MPa
Answer» B. 59 MPa

Discussion

23.	A steel column of rectangular section (15 mm 10 mm) and length 1.5 m is simply supported at both ends. Assuming modulus of elasticity, E = 200 GPa for steel, the critical axial load (in kN) is _____ (correct to two decimal places)
A.	1.097
B.	1.397
C.	1.297
D.	1.197
Answer» B. 1.397

Discussion

24.	The directions of maximum and minimum principal stresses at the point P from the Mohr's circle are
A.	0,90
B.	90 , 0
C.	45 , 135
D.	All directions
Answer» E.

Discussion

25.	The maximum and minimum principal stresses respectively from the Mohr's circle are
A.	+175 MPa,-175 MPa
B.	+175 MPa,+175 MPa
C.	0,-175 MPa
D.	0, 0
Answer» C. 0,-175 MPa

Discussion

26.	The principal stresses at a point in a critical - section of a machine component are
A.	1.67
B.	2.00
C.	3.60
D.	4.00
Answer» C. 3.60

Discussion

27.	The state of stress at a point under plane stress condition is
A.	40
B.	50
C.	60
D.	100
Answer» C. 60

Discussion

28.	A 200 mm long, stress free rod at room temperature is held between two immovable rigid walls. The temperature of the rod is uniformly raised by 250 C. If the Young's modulus and coefficient of thermal expansion are 200 GPa and 1 10
A.	500 MPa
B.	4990 MPa
C.	501 MPa
D.	350 MPa
Answer» B. 4990 MPa

Discussion

29.	Two solid circular shafts of radii R
A.	8
B.	8.1
C.	7.9
D.	8.2
Answer» B. 8.1

Discussion

30.	According to Von-Mises' distortion energy theory, the distortion energy under three dimensional stress state is represented by
A.	<table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td><td rowspan="2">[ <sub>1</sub> + <sub>2</sub> + <sub>3</sub> - 2m( <sub>1</sub> <sub>2</sub> + <sub>3</sub> <sub>2</sub> + <sub>1</sub> <sub>3</sub>)]</td></tr><tr><td style="text-align: center;"> E</td></tr></table>
B.	<table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1 - 2 </center></td><td rowspan="2">[ <sub>1</sub> + <sub>2</sub> + <sub>3</sub> - 2m( <sub>1</sub> <sub>2</sub> + <sub>3</sub> <sub>2</sub> + <sub>1</sub> <sub>3</sub>)]</td></tr><tr><td style="text-align: center;">6E</td></tr></table>
C.	<table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1 + </center></td><td rowspan="2">[ <sub>1</sub> + <sub>2</sub> + <sub>3</sub> - 2m( <sub>1</sub> <sub>2</sub> + <sub>3</sub> <sub>2</sub> + <sub>1</sub> <sub>3</sub>)]</td></tr><tr><td style="text-align: center;">3E</td></tr></table>
D.	<table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td><td rowspan="2">[ <sub>1</sub> + <sub>2</sub> + <sub>3</sub> - 2m( <sub>1</sub> <sub>2</sub> + <sub>3</sub> <sub>2</sub> + <sub>1</sub> <sub>3</sub>)]</td></tr><tr><td style="text-align: center;">3E</td></tr></table>
Answer» D. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td><td rowspan="2">[ <sub>1</sub> + <sub>2</sub> + <sub>3</sub> - 2m( <sub>1</sub> <sub>2</sub> + <sub>3</sub> <sub>2</sub> + <sub>1</sub> <sub>3</sub>)]</td></tr><tr><td style="text-align: center;">3E</td></tr></table>

Discussion

31.	A steel rod of length L and diameter D, fixed at both ends, is uniformly heated to a temperature rise of T. The Young's modulus is E and the coefficient of linear expansion is . The thermal stress in the rod is
A.	0
B.	T
C.	E T
D.	E TL
Answer» D. E TL

Discussion

32.	A compression spring is made of music wire of 2 mm diameter having a shear strength and shear modulus of 800 MPa and 80 GPa respectively. The mean coil diameter is 20 mm, free length is 40 mm and the number of active coils is 10. If the mean coil diameter is reduced to 10 mm, the stiffness of the spring is approximately
A.	decreased by 8 times
B.	decreases by 2 times
C.	increased by 2 times
D.	increased by 8 times
Answer» E.

Discussion

33.	A simply supported laterally loaded beam was found to deflect more than a specified value. Which of the following measures will reduce deflection?
A.	Increase the area moment of inertia
B.	Increase the span of the beam
C.	Select a different material having lesser modulus of elasticity
D.	Magnitude of the load to be increased
Answer» B. Increase the span of the beam

Discussion

34.	In a metal forming operation when the material has just started yielding, the principal stresses
A.	245.76 MPa
B.	244.76 MPa
C.	243.76 MPa
D.	246.76 MPa
Answer» B. 244.76 MPa

Discussion

35.	A column has a rectangular cross-section of 10 mm 20 mm and a length of 1 m. The slenderness ratio of the column is close to
A.	200
B.	346
C.	477
D.	1000
Answer» C. 477

Discussion

36.	Consider a simply supported beam of length, 50h, with a rectangular cross-section of depth, h, and width, 2h. The beam carries a vertical point load, P, at its mid-point. The ratio of the maximum shear stress to the maximum bending stress in the beam is
A.	0.02
B.	0.10
C.	0.05
D.	0.01
Answer» E.

Discussion

37.	An axial residual compressive stress due to a manufacturing process is present on the outer surface of a rotating shaft subjected to bending. Under a given bending load, the fatigue life of the shaft in the presence of the residual compressive stress is
A.	decreased
B.	increased or decreased, depending on the external bending load
C.	neither decreased nor increased
D.	increased
Answer» E.

Discussion

38.	A wire of circular cross-section of diameter 1.0 mm is bent into a circular arc of radius 1.0 m by application of pure bending moments at its ends. The Young s modulus of the material of the wire is 100 GPa. The maximum tensile stress developed in the wire is ____ MPa.
A.	52 MPa
B.	50 MPa
C.	51 MPa
D.	49 MPa
Answer» C. 51 MPa

Discussion

39.	The homogenous state of stress for a metal part undergoing plastic deformation is
A.	9.50
B.	16.07
C.	28.52
D.	49.41
Answer» C. 28.52

Discussion

40.	Consider a cantilever beam, having negligible mass and uniform flexural rigidity, with length 0.01 m. The frequency of vibration of the beam, with a 0.5 kg mass attached at the free tip, is 100 Hz. The flexural rigidity (in Nm2) of the beam is ______.
A.	0.065
B.	0.650
C.	0.66
D.	0.066
Answer» B. 0.650

Discussion

41.	A hollow circular shaft of inner radius 10 mm outer radius 20 mm and length 1 m is to be used as a torsional spring. If the shear modulus of the material of the shaft is 150 GPa, the torsional stiffness of the shaft (in kN-m/rad) is ______ (correct to two decimal places).
A.	35.34
B.	33.34
C.	34.34
D.	32.34
Answer» B. 33.34

Discussion

42.	Two shafts A and B are made of the same material. The diameter of shaft B is twice that of shaft A. The ratio of power which can be transmitted by shaft A to that of shaft B is (If maximum shear stress remains the same)
A.	1/2
B.	1/4
C.	1/8
D.	1/16
Answer» D. 1/16

Discussion

43.	A hollow shaft (d
A.	11.29 mm
B.	22.58 mm
C.	33.87 mm
D.	45.16 mm
Answer» C. 33.87 mm

Discussion

44.	A steel cube, with all faces free to deform, has Young's modulus, E, Poisson's ratio, v, and coefficient of thermal expansion, a. The pressure (hydrostatic stress) developed within the cube, when it is subjected to a uniform increase in temperature, T, is given by
A.	0
B.	<table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> ( T)E</center></td><td rowspan="2"></td></tr><td align="center">(1 - 2v)</td></table>
C.	<table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> ( T)E</center></td><td rowspan="2"></td></tr><td align="center">(1 - 2v)</td></table>
D.	<table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> ( T)E</center></td><td rowspan="2"></td></tr><td align="center">3(1 - 2v)</td></table>
Answer» B. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> ( T)E</center></td><td rowspan="2"></td></tr><td align="center">(1 - 2v)</td></table>

Discussion

45.	A cylindrical rod of diamet er 10 mm and length 1.0 m fixed at one end. The other end is twisted by angle of 10 by applying a torque. If the maximum shear strain in the rod is p 10
A.	0.87
B.	0.86
C.	0.85
D.	0.88
Answer» B. 0.86

Discussion

46.	The cross-sections of two solid bars made of the same material are shown in the figure. The square cross-section has flexural (bending) rigidity I1 while the circular cross-section has flexural rigidity I2. Both sections have the same cross-sectional area. The ratio I
A.	1/
B.	2/
C.	/3
D.	/6
Answer» D. /6

Discussion

47.	Two threaded bolts A and B of same material and length are subjected to identical tensile load. If the elastic energy stored in bolt A is 4 times that of the bolt S and the mean diameter of bolt A is 12 mm, the mean diameter of bolt B in mm is
A.	16
B.	24
C.	36
D.	48
Answer» C. 36

Discussion

48.	A solid steel cube constrained on all six faces is heated so that the temperature rises uniformly by T. If the thermal coefficient of the material is , Young's modulus is E and the Poisson's ratio is , the thermal stress developed in the cube due to heating is
A.	<table><tr><td rowspan="2">- </td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> ( T)E</center></td><td rowspan="2"></td></tr><td align="center">(1 - 2v)</td></table>
B.	<table><tr><td rowspan="2">- </td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>2 ( T)E</center></td><td rowspan="2"></td></tr><td align="center">(1 - 2v)</td></table>
C.	<table><tr><td rowspan="2">- </td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>3 ( T)E</center></td><td rowspan="2"></td></tr><td align="center">(1 - 2v)</td></table>
D.	<table><tr><td rowspan="2">- </td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> ( T)E</center></td><td rowspan="2"></td></tr><td align="center">3(1 - 2v)</td></table>
Answer» B. <table><tr><td rowspan="2">- </td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>2 ( T)E</center></td><td rowspan="2"></td></tr><td align="center">(1 - 2v)</td></table>

Discussion

49.	A circular rod of length L and area of crosssection A has a modulus of elasticity E and coefficient of thermal expansion . One end of the rod is fixed and other end is free. If the temperature of the rod is increased by T, then
A.	stress developed in the rod is E T and strain developed in the rod is a T
B.	both stress and strain developed in the rod are zero
C.	stress developed in the rod is zero and strain developed in the rod is T
D.	stress developed in the rod is E T and strain developed in the rod is zero
Answer» D. stress developed in the rod is E T and strain developed in the rod is zero

Discussion

50.	A free bar of length/ is uniformly heated from 0 C to a temperature t C, is the coefficient of linear expansion and E the modulus of elasticity. The stress in the bar is
A.	tE
B.	tE/2
C.	Zero
D.	None of these
Answer» D. None of these

Discussion

Explore topic-wise MCQs in Strength of Materials.

If the two principal strains at a point are 1000 x 10-6 and 600 10-6, then the maximum shear strain is

Two solid circular shafts of radii R1 and R2 are subjected to same torque. The maximum shear stresses developed in the two shafts are 1 and 2. If R1/R2 = 2, then 2/ 1 is ______.

A hollow shaft (d0 = 2di where d0 and di are the outer and inner diameters respectively) needs to transmit 20 kW power at 3000 RPM. If the maximum permissible shear stress is 30 MPa, d0 is

In terms of Poisson's ratio ( ) the ratio of Young's modulus (E) to Shear modulus (G) of elastic materials is

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In a plane stress condition, the components of stress at a point are x = 20 MPa, y = 80 MPa and xy = 40 MPa. The maximum shear stress (in MPa) at the point is

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The cross-sections of two solid bars made of the same material are shown in the figure. The square cross-section has flexural (bending) rigidity I1 while the circular cross-section has flexural rigidity I2. Both sections have the same cross-sectional area. The ratio I1 /I2 is

A simply supported beam of length L is subjected to a varying distributed load sin (3 x/L) Nm-1, where the distance x is measured from the left support. The magnitude of the vertical reaction force in N at the left support is

The state of stress at a point is given by x = 6 MPa, y = 4 MPa, and xy = 8 MPa. The maximum tensile stress (in MPa) at the point is ______

The state of plane-stress at a point is given by x =200 MPa, y =100 MPa and xy = 100 MPa. The maximum shear stress

If the principal stresses in a plane stress problem are 1 = 100 MPa, 2 = 40 MPa, the magnitude of the maximum shear stress (in MPa) will be

In a metal forming operation when the material has just started yielding, the principal stresses 1 = +180 MPa, 2 = 100 MPa, 3 = 0. Following von Mises criterion, the yield stress is _____, MPa.

A solid cube of side 1 m is kept at a room temperature of 32 C. The coefficient of linear thermal expansion of the cube material is 1 10

A steel column of rectangular section (15 mm 10 mm) and length 1.5 m is simply supported at both ends. Assuming modulus of elasticity, E = 200 GPa for steel, the critical axial load (in kN) is _____ (correct to two decimal places)

The directions of maximum and minimum principal stresses at the point P from the Mohr's circle are

The maximum and minimum principal stresses respectively from the Mohr's circle are

The principal stresses at a point in a critical - section of a machine component are

The state of stress at a point under plane stress condition is

A 200 mm long, stress free rod at room temperature is held between two immovable rigid walls. The temperature of the rod is uniformly raised by 250 C. If the Young's modulus and coefficient of thermal expansion are 200 GPa and 1 10

Two solid circular shafts of radii R

According to Von-Mises' distortion energy theory, the distortion energy under three dimensional stress state is represented by

A steel rod of length L and diameter D, fixed at both ends, is uniformly heated to a temperature rise of T. The Young's modulus is E and the coefficient of linear expansion is . The thermal stress in the rod is

A simply supported laterally loaded beam was found to deflect more than a specified value. Which of the following measures will reduce deflection?

In a metal forming operation when the material has just started yielding, the principal stresses

A column has a rectangular cross-section of 10 mm 20 mm and a length of 1 m. The slenderness ratio of the column is close to

Consider a simply supported beam of length, 50h, with a rectangular cross-section of depth, h, and width, 2h. The beam carries a vertical point load, P, at its mid-point. The ratio of the maximum shear stress to the maximum bending stress in the beam is

An axial residual compressive stress due to a manufacturing process is present on the outer surface of a rotating shaft subjected to bending. Under a given bending load, the fatigue life of the shaft in the presence of the residual compressive stress is

A wire of circular cross-section of diameter 1.0 mm is bent into a circular arc of radius 1.0 m by application of pure bending moments at its ends. The Young s modulus of the material of the wire is 100 GPa. The maximum tensile stress developed in the wire is ____ MPa.

The homogenous state of stress for a metal part undergoing plastic deformation is

Consider a cantilever beam, having negligible mass and uniform flexural rigidity, with length 0.01 m. The frequency of vibration of the beam, with a 0.5 kg mass attached at the free tip, is 100 Hz. The flexural rigidity (in Nm2) of the beam is ______.

A hollow circular shaft of inner radius 10 mm outer radius 20 mm and length 1 m is to be used as a torsional spring. If the shear modulus of the material of the shaft is 150 GPa, the torsional stiffness of the shaft (in kN-m/rad) is ______ (correct to two decimal places).

Two shafts A and B are made of the same material. The diameter of shaft B is twice that of shaft A. The ratio of power which can be transmitted by shaft A to that of shaft B is (If maximum shear stress remains the same)

A hollow shaft (d

A steel cube, with all faces free to deform, has Young's modulus, E, Poisson's ratio, v, and coefficient of thermal expansion, a. The pressure (hydrostatic stress) developed within the cube, when it is subjected to a uniform increase in temperature, T, is given by

A cylindrical rod of diamet er 10 mm and length 1.0 m fixed at one end. The other end is twisted by angle of 10 by applying a torque. If the maximum shear strain in the rod is p 10

The cross-sections of two solid bars made of the same material are shown in the figure. The square cross-section has flexural (bending) rigidity I1 while the circular cross-section has flexural rigidity I2. Both sections have the same cross-sectional area. The ratio I

Two threaded bolts A and B of same material and length are subjected to identical tensile load. If the elastic energy stored in bolt A is 4 times that of the bolt S and the mean diameter of bolt A is 12 mm, the mean diameter of bolt B in mm is

A solid steel cube constrained on all six faces is heated so that the temperature rises uniformly by T. If the thermal coefficient of the material is , Young's modulus is E and the Poisson's ratio is , the thermal stress developed in the cube due to heating is

A circular rod of length L and area of crosssection A has a modulus of elasticity E and coefficient of thermal expansion . One end of the rod is fixed and other end is free. If the temperature of the rod is increased by T, then

A free bar of length/ is uniformly heated from 0 C to a temperature t C, is the coefficient of linear expansion and E the modulus of elasticity. The stress in the bar is

If the two principal strains at a point are 1000 x 10^-6 and 600 10^-6, then the maximum shear strain is

Two solid circular shafts of radii R₁ and R₂ are subjected to same torque. The maximum shear stresses developed in the two shafts are ₁ and ₂. If R₁/R₂ = 2, then ₂/ ₁ is ______.

A hollow shaft (d₀ = 2d_i where d₀ and d_i are the outer and inner diameters respectively) needs to transmit 20 kW power at 3000 RPM. If the maximum permissible shear stress is 30 MPa, d₀ is

A 200 100 50 mm steel block is subjected to a hydro static pressure of 15 MPa. The Young's modulus and Poisson's ratio of the material are 200 GPa and 0.3 respectively. The change in the volume of the block in mm³ is

The state of stress at a point is _x = _y = _z = _xz = _zx = _yx = _zy= 0 and _xy = _yx = 50 MPa. The maximum normal stress (in MPa) at that point is ______.

In a plane stress condition, the components of stress at a point are _x = 20 MPa, _y = 80 MPa and _xy = 40 MPa. The maximum shear stress (in MPa) at the point is

The principal stresses at a point in a critical - section of a machine component are ₁ = 60 MPa, ₂ = 5 MPa and ₃ = 40 MPa. For the material of the component, the tensile yield strength is _y = 200 MPa. According to the maximum shear stress theory, the factor of safety is

The state of stress at a point under plane stress condition is _xx = 40 MPa, _yy = 100 MPa and _xy =40 MPa The radius of Mohr's circle representing the given state of stress in MPa is

A cylindrical rod of diamet er 10 mm and length 1.0 m fixed at one end. The other end is twisted by angle of 10 by applying a torque. If the maximum shear strain in the rod is p 10^-3, then p is equal to _______ (round off to two decimal places).

The cross-sections of two solid bars made of the same material are shown in the figure. The square cross-section has flexural (bending) rigidity I1 while the circular cross-section has flexural rigidity I2. Both sections have the same cross-sectional area. The ratio I₁ /I₂ is

A simply supported beam of length L is subjected to a varying distributed load sin (3 x/L) Nm^-1, where the distance x is measured from the left support. The magnitude of the vertical reaction force in N at the left support is

The state of stress at a point is given by _x = 6 MPa, _y = 4 MPa, and _xy = 8 MPa. The maximum tensile stress (in MPa) at the point is ______

The state of plane-stress at a point is given by _x =200 MPa, _y =100 MPa and _xy = 100 MPa. The maximum shear stress

If the principal stresses in a plane stress problem are ₁ = 100 MPa, ₂ = 40 MPa, the magnitude of the maximum shear stress (in MPa) will be

In a metal forming operation when the material has just started yielding, the principal stresses ₁ = +180 MPa, ₂ = 100 MPa, ₃ = 0. Following von Mises criterion, the yield stress is _____, MPa.