136. For the truss shown in the figure, the force in the member QR is
     

1. 1. zero

   
   
   

   2. P/√2

   
   
   

   3. P

   
   
   

   4. 2P2

   
   
   

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1. View Hint View Answer Discuss in Forum

   At T,
   M_T = RQ × L = P.L
   ∴ RQ = P
   ∴ RQ =QR = P

   Correct Option: C

   At T,
   M_T = RQ × L = P.L
   ∴ RQ = P
   ∴ RQ =QR = P

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137. Two people weighing W each are sitting on a plank of length L floating on water at L/4 from either end. Neglecting the weight of the plank, the bending moment at the centre of the plank is

1. 1. WL/8

   
   
   

   2. WL/16

   
   
   

   3. WL/32

   
   
   

   4. zero

   
   
   

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1. View Hint View Answer Discuss in Forum

   At centre,
   

   BM =	2ω	×	L	×	L	- ω ×	L	= 0
   	L		2		4		4

   Correct Option: D

   At centre,
   

   BM =	2ω	×	L	×	L	- ω ×	L	= 0
   	L		2		4		4

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138. A hollow circular shaft has an outer diameter of 100 mm and a wall thickness of 25 mm. The allowable shear stress in the shaft is 125 MPa. The maximum torque the shaft can transmit is

1. 1. 46 kN m

   
   
   

   2. 24.5 kN m

   
   
   

   3. 23 kN m

   
   
   

   4. 11.5 kN m

   
   
   

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1. View Hint View Answer Discuss in Forum

   α₁ = 100 - 2t
   = 100 – 2 × 25 = 50 mm
   

   	τ	=	τ
   	R		J

   
   

   J =	π	(1004 - 50)4
   	32

   
   = 9203884.727 mm⁴
   R = d₀/2 = 100/2 = 50 mm
   

   Tmax =	τmax × J
   	k

   
   

   =	125 × 9203884.727	= 23 kNm
   	50

   Correct Option: C

   α₁ = 100 - 2t
   = 100 – 2 × 25 = 50 mm
   

   	τ	=	τ
   	R		J

   
   

   J =	π	(1004 - 50)4
   	32

   
   = 9203884.727 mm⁴
   R = d₀/2 = 100/2 = 50 mm
   

   Tmax =	τmax × J
   	k

   
   

   =	125 × 9203884.727	= 23 kNm
   	50

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139. A thin walled cylindrical pressure vessel having a radius of 0.5 m and wall thickness of 25 mm is subjected to an internal pressure of 700 kPa. The hoop stress developed is

1. 1. 14 MPa

   
   
   

   2. 1.4 MPa

   
   
   

   3. 0.14 MPa

   
   
   

   4. 0.014 MPa

   
   
   

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1. View Hint View Answer Discuss in Forum

   Hoop stress: σ =	pr	(circular sphere)
   	2t

   
   

   σ =	2pr	(Cylindrical section)
   	2t

   
   

   =	700 × 103 × 0.5	= 14 × 106 = 4 MPa
   	25 × 10-3

   Correct Option: A

   Hoop stress: σ =	pr	(circular sphere)
   	2t

   
   

   σ =	2pr	(Cylindrical section)
   	2t

   
   

   =	700 × 103 × 0.5	= 14 × 106 = 4 MPa
   	25 × 10-3

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140. The stepped cantilever is subjected to movements, M as shown in the figure below. The vertical deflection at the free end (neglecting the self-weight) is
     

1. 1. 	ML2
      	8EI

   
   
   

   2. 	ML2
      	4EI

   
   
   

   3. 	ML2
      	2EI

   
   
   

   4. Zero

   
   
   

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1. View Hint View Answer Discuss in Forum

   ∆B =	M	× L ×	L
   	EI		2

   
   

   =	ML2
   	2EI

   Correct Option: C

   ∆B =	M	× L ×	L
   	EI		2

   
   

   =	ML2
   	2EI

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