11. A rigid horizontal rod of length 2L is fixed to a circular cylinder of radius R as shown in the figure. Vertical forces of magnitude P are applied at the two ends as shown in the figure. The shear modulus for the cylinder is G and the Young's modulus is E.
    
    The vertical deflection at point A is

1. 1. PL³
      (πR4G)

   
   
   

   2. 2PL³
      (πR4E)

   
   
   

   3. 2PL³
      (πR4E)

   
   
   

   4. 4PL³
      (πR4G)

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   T = P (2L) = 2PL
   

   θ =	TL	=	1PL(L)
   	GJ		G(π/32)(2R)4

   
   

   θ =	32 × 2PL²	=	4PL²
   	πGR416		πGR4

   
   

   y = Rθ =	L(4PL)²
   	πGR416

   
   

   =	4PL²
   	πGR416

   Correct Option: D

   
   T = P (2L) = 2PL
   

   θ =	TL	=	1PL(L)
   	GJ		G(π/32)(2R)4

   
   

   θ =	32 × 2PL²	=	4PL²
   	πGR416		πGR4

   
   

   y = Rθ =	L(4PL)²
   	πGR416

   
   

   =	4PL²
   	πGR416

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12. For the overhanging beam shown in figure, the magnitude of maximum bending moment (in kNm) is _______.
    

1. 1. 3kNm

   
   
   

   2. 4kNm

   
   
   

   3. 5kNm

   
   
   

   4. 5.5kNm

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   R_A + R_B = 60
   R_B (4) = 20 (6) +10(4)(2)
   R_B = 50CN
   R_A = 10 KN
   SF = R_A – 10x
   SF_x=0 = 10KN
   SF_x=4= –30KN
   Bending moment is maximum where shear force is zero
   ∴ SF = R_A 10x = 0
   R_A = 10x
   

   BMx-x = RAx -	10x²
   	2

   
   

   BMx=1 = 10(1) -	10(1)²	= 5kNm
   	2

   Correct Option: C

   
   R_A + R_B = 60
   R_B (4) = 20 (6) +10(4)(2)
   R_B = 50CN
   R_A = 10 KN
   SF = R_A – 10x
   SF_x=0 = 10KN
   SF_x=4= –30KN
   Bending moment is maximum where shear force is zero
   ∴ SF = R_A 10x = 0
   R_A = 10x
   

   BMx-x = RAx -	10x²
   	2

   
   

   BMx=1 = 10(1) -	10(1)²	= 5kNm
   	2

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13. A simply supported beam of width 100 mm, height 200 mm and length 4 m is carrying a uniformly distributed load of intensity 10 kNm. The maximum bending stress (in MPa) in the beam is _________
    

1. 1. 32 MPa

   
   
   

   2. 30 MPa

   
   
   

   3. 31 MPa

   
   
   

   4. 29MPa

   
   
   

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1. View Hint View Answer Discuss in Forum

   For 0.01 maximum
   Bending moment, M_max
   

   Mmax =	WI²
   	8

   
   and from bending equation:-
   

   σmax =	6Mmax	=	6 × 10 × (4)² × 1000
   	bd²		8(0.1) × (.2)²

   
   
   σ_max = 30 MPa

   Correct Option: B

   For 0.01 maximum
   Bending moment, M_max
   

   Mmax =	WI²
   	8

   
   and from bending equation:-
   

   σmax =	6Mmax	=	6 × 10 × (4)² × 1000
   	bd²		8(0.1) × (.2)²

   
   
   σ_max = 30 MPa

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14. Consider an elastic straight beam of length L = 10 πm, with square cross-section of side a = 5 mm, and Young’s modulus E = 200 GPa. This straight beam was bent in such a way that the two ends meet, to form a circle of mean radius R. Assuming that Euler-Bernoulli beam theory is applicable t o this bending problem, the maximum tensile bending stress in the bent beam is ______ MPa.
    

1. 1. 102 MPa

   
   
   

   2. 100 MPa

   
   
   

   3. 101 MPa

   
   
   

   4. 99 MPa

   
   
   

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1. View Hint View Answer Discuss in Forum

   By bending equation,
   

   σ	=	M	=	E
   y		I		R

   
   

   σ =	Ey
   	R

   
   

   =	200 × 10³ × 2.5 × 10-3	= 100 MPa
   	5

   
   

   Correct Option: B

   By bending equation,
   

   σ	=	M	=	E
   y		I		R

   
   

   σ =	Ey
   	R

   
   

   =	200 × 10³ × 2.5 × 10-3	= 100 MPa
   	5

   
   

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15. The transverse shear stress acting in a beam of rectangular cross-section, subjected to a transverse shear load, is

1. 1. variable with maximum at the bottom of the beam

   
   
   

   2. variable with maximum at the top of the beam

   
   
   

   3. uniform

   
   
   

   4. variable with maximum on the neutral axis

   
   
   

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1. View Hint View Answer Discuss in Forum

   

   Correct Option: D

   

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