61. A simply supported beam of uniform rectangular cross section of width b and depth h is subjected to linear temperature gradient, 0° at the top and T° at the bottom, as shown in the figure. The coefficient of linear expansion of the beam material is a. The resulting vertical deflection at the mid-span of the beam is
    

1. 1. 	αTh2	upward
      	8L

   
   
   

   2. 	αTL2	upward
      	8h

   
   
   

   3. 	αTh2	downward
      	8L

   
   
   

   4. 	αTL2	downward
      	8h

   
   
   

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1. View Hint View Answer Discuss in Forum

   Average change in temp = T/2
   Max strain at extreme fibre
   

   ε = α		T
   		2

   
   

   	M	=	f	=	E
   	I		y		R

   
   

   ∴ R =	Ey
   	y

   
   

   ε =	F
   	y

   
   
   

   =	h
   	αT

   
   

   Deflection, δ =	L2	=	L2	×	αT	=	αTL2
   	8R		8		h		8h

   Correct Option: D

   Average change in temp = T/2
   Max strain at extreme fibre
   

   ε = α		T
   		2

   
   

   	M	=	f	=	E
   	I		y		R

   
   

   ∴ R =	Ey
   	y

   
   

   ε =	F
   	y

   
   
   

   =	h
   	αT

   
   

   Deflection, δ =	L2	=	L2	×	αT	=	αTL2
   	8R		8		h		8h

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62. Group I gives the shear force diagrams and Group II gives the diagrams of beams with supports and loading. Match the Group I with Group II.
    

1. 1. P-3, Q-1, R-2, S-4

   
   
   

   2. P-3, Q-4, R-2, S-1

   
   
   

   3. P-2, Q-1, R-4, S-3

   
   
   

   4. P-2, Q-4, R-3, S-1

   
   
   

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   P-3, Q-1, R-2, S-4

   Correct Option: A

   P-3, Q-1, R-2, S-4

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63. Consider a simply supported beam with a uniformly distributed load having a neutral axis (NA) as shown. For points P (on the neutral axis) and Q (at the bottom of the beam) the state of stress is best represented by which of the following pairs?
    

1. 1. 

   
   
   

   2. 

   
   
   

   3. 

   
   
   

   4. 

   
   
   

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   Correct Option: A

   

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64. The Poisson’s ratio is defined as

1. 1. 	axial stress
      	lateral stress

   
   
   

   2. 	lateral strain
      	axial strain

   
   
   

   3. 	lateral stress
      	axial stress

   
   
   

   4. 	axial strain
      	lateral strain

   
   
   

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   	lateral strain
   	axial strain

   Correct Option: B

   	lateral strain
   	axial strain

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65. The following statements are related to bending of beams:
    I. The slope of the bending moment diagram is equal to the shear force.
    II. The slope of the shear force diagram is equal to the load intensity.
    III. The slope of the curvature is equal to the flexural rotation.
    IV. The second derivative of the deflection is equal to the curvature.
    The only FALSE statement is

1. 1. I

   
   
   

   2. II

   
   
   

   3. III

   
   
   

   4. IV

   
   
   

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1. View Hint View Answer Discuss in Forum

   The slope of the curvature is equal to the flexural rotation.

   Correct Option: C

   The slope of the curvature is equal to the flexural rotation.

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