126. The Poisson's ratio for a perfectly incompressible linear elastic material is

1. 1. 1

   
   
   

   2. 0.5

   
   
   

   3. 0

   
   
   

   4. infinity

   
   
   

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   NA

   Correct Option: B

   NA

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127. A square plate of dimension L × L is subjected to a uniform pressure load p = 250 MPa on its edges as shown in the figure. Assume plane stress conditions. The Young's modulus E= 200 GPa.
     
     The deformed shape is a square of dimension L – 2δ. If L = 2 m and δ = 0.001 m, the Poisson's ratio of the piate material is ________.

1. 1. 0.2

   
   
   

   2. 7

   
   
   

   3. 9

   
   
   

   4. 0.8

   
   
   

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   ΔV	=	σ	(1 − v)
   V		E

   
   ε_v = ε_x + ε_y ε_z
   

   εv =

   σ

   −

   μσ

   +

   σ

   −

   μσ

   −

   μ(σ + σ)

   E

   E

   E

   E

   E

   
   Due to plane stress condition ε_z = 0
   

   εv =	σ	× 2 × (1 − μ)
   	E

   
   

   (2 − 2 × 0.001)2	= −	P	× 2(1 − μ)
   22		E

   
   

   − 2 × 10−3 =	250	× 2 × (1 − μ)
   	200 × 103

   
   

   250	= 1 − μ
   200

   
   0.8 = 1 − μ
   ∴  μ = 0.2

   Correct Option: A

   ΔV	=	σ	(1 − v)
   V		E

   
   ε_v = ε_x + ε_y ε_z
   

   εv =

   σ

   −

   μσ

   +

   σ

   −

   μσ

   −

   μ(σ + σ)

   E

   E

   E

   E

   E

   
   Due to plane stress condition ε_z = 0
   

   εv =	σ	× 2 × (1 − μ)
   	E

   
   

   (2 − 2 × 0.001)2	= −	P	× 2(1 − μ)
   22		E

   
   

   − 2 × 10−3 =	250	× 2 × (1 − μ)
   	200 × 103

   
   

   250	= 1 − μ
   200

   
   0.8 = 1 − μ
   ∴  μ = 0.2

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128. If the Poisson's ratio of an elastic material is 0.4, the ratio of modulus of rigidity to Young's modulus is ______

1. 1. 57

   
   
   

   2. 0.357

   
   
   

   3. 0.57

   
   
   

   4. None of the above

   
   
   

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   From E = 2G(1 + μ)
   

   G	=	1
   E		2(1 + μ)

   
   

   =	l	= 0.357
   	2(1 + 0.4)

   Correct Option: B

   From E = 2G(1 + μ)
   

   G	=	1
   E		2(1 + μ)

   
   

   =	l	= 0.357
   	2(1 + 0.4)

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129. A metallic rod of 500 mm length and 50 mm diameter, when subjected to a tensile force of 100 kN at the ends, experiences an increase in its length by 0.5 mm and a reduction in its diameter by 0.015 mm. The Poisson's ratio of the rod material is _______

1. 1. 0.3

   
   
   

   2. 0.8

   
   
   

   3. 10

   
   
   

   4. 1

   
   
   

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1. View Hint View Answer Discuss in Forum

   l = 500 mm, d = 50 mm, p = 100 KN
   δl = 0.5 mm, δd = 0.015
   Poission’s Ratio
   

   	l		=	Lateral strain
   	m			longitudinal strain

   
   

   δd/d	=	0.015/50	= 0.3.
   δl/l		0.5/500

   Correct Option: A

   l = 500 mm, d = 50 mm, p = 100 KN
   δl = 0.5 mm, δd = 0.015
   Poission’s Ratio
   

   	l		=	Lateral strain
   	m			longitudinal strain

   
   

   δd/d	=	0.015/50	= 0.3.
   δl/l		0.5/500

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130. Consider the stress-strain curve for an ideal elastic-plastic strain hardening metal as shown in the figure. The metal was loaded in uniaxial tension starting from O. Upon loading, the stress-strain curve passes through initial yield point at P, and then strain hardens to point Q, where the loading was stopped. From point Q, the specimen was unloaded to point R, where the stress is zero. I f the same specimen is reloaded in tension from point R, the value of stress τ which the material yields again is _____MPa
     

1. 1. In this case material with start yielding from point ‘P’ instead of ‘P’

   
   
   

   2. In this case material with start yielding from point ‘P’ instead of ‘R’

   
   
   

   3. material with start yielding from point ‘R’ instead of ‘P’

   
   
   

   4. None of these

   
   
   

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1. View Hint View Answer Discuss in Forum

   As the point loaded beyond the yield point is unloaded completely and reloaded then because of strain hardening (residual strain remains in body) increase the yield strength.
   In this case material with start yielding from point ‘R’ instead of ‘P’.

   Correct Option: C

   As the point loaded beyond the yield point is unloaded completely and reloaded then because of strain hardening (residual strain remains in body) increase the yield strength.
   In this case material with start yielding from point ‘R’ instead of ‘P’.

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