136. A pin-ended column of length L, modulus of elasticity E and second moment of the crosssectional area I is loaded concentrically by a compressive load P. The critical buckling load (P_cr) is given by
     

1. 1. Pcr =	EI
      	πL2

      
      

   
   
   

   2. Pcr =	π2EI
      	3L2

      
      

   
   
   

   3. Pcr =	πEI
      	L2

      
      

   
   
   

   4. Pcr =	π2EI
      	L2

      
      

   
   
   

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1. View Hint View Answer Discuss in Forum

   The critical buckling load (P_cr) for a column having length L, modulus of elasticity E and second moment of cross sectional area I is loaded centrically. Condition: Both ends are having pin joint. i.e., hinged
   so n = 1
   

   ∴ Pcr = n	π2EI	=	π2EI
   	L2		L2

   Correct Option: D

   The critical buckling load (P_cr) for a column having length L, modulus of elasticity E and second moment of cross sectional area I is loaded centrically. Condition: Both ends are having pin joint. i.e., hinged
   so n = 1
   

   ∴ Pcr = n	π2EI	=	π2EI
   	L2		L2

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137. For the case of a slender column of length l, and flexural rigidity El built in at its base and free at the top, the Euler's critical buckling load is
     

1. 1. 	4π2El
      	l2

      
      

   
   
   

   2. 	2π2El
      	l2

      
      

   
   
   

   3. 	π2El
      	l2

      
      

   
   
   

   4. 	π2El
      	4l2

      
      

   
   
   

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1. View Hint View Answer Discuss in Forum

   P =	π2EI	=	π2EI
   	(2l)2		4le2

   Correct Option: D

   P =	π2EI	=	π2EI
   	(2l)2		4le2

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138. If the length of a column is doubled, the critical load becomes
     

1. 1. 1/2 of the original value
      

   
   
   

   2. 1/4 of the original value
      

   
   
   

   3. 1/8 of the original value
      

   
   
   

   4. 1/16 of the original value

   
   
   

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1. View Hint View Answer Discuss in Forum

   Pe =	π2EI
   	le2

   
   l_e = 2l
   

   P'e =	π2EI
   	4le2

   
   

   P'e =	Pe
   	4

   Correct Option: B

   Pe =	π2EI
   	le2

   
   l_e = 2l
   

   P'e =	π2EI
   	4le2

   
   

   P'e =	Pe
   	4

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139. For a circular shaft of diameter d subjected to torque T, the maximum value of the shear stress is
     

1. 1. 	64T
      	πd3

      
      

   
   
   

   2. 	32T
      	πd3

      
      

   
   
   

   3. 	16T
      	πd3

      
      

   
   
   

   4. 	8T
      	πd3

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let T = torque; d = diameter of shaft and τ = maximum value of shear stress,
   

   ∴ T =	π	d3 × τ or τ =	16T
   	16		πd3

   Correct Option: C

   Let T = torque; d = diameter of shaft and τ = maximum value of shear stress,
   

   ∴ T =	π	d3 × τ or τ =	16T
   	16		πd3

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140. A solid circular shaft of 60 mm diameter transmits a torque of 1600 Nm. The value of maximum shear stress developed is
     

1. 1. 37.72 MPa
      

   
   
   

   2. 47.72 MPa
      

   
   
   

   3. 57.72 MPa
      

   
   
   

   4. 67.72 MPa

   
   
   

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1. View Hint View Answer Discuss in Forum

   fs =	16T	=	16 × 1600	= 37.72 MPa
   	πd3		π × (0.06)3

   Correct Option: A

   fs =	16T	=	16 × 1600	= 37.72 MPa
   	πd3		π × (0.06)3

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