146. The shear stress at the neutral axis in a beam of triangular section with a base of 40 mm and height 20 mm, subjected to a shear force of 3 kN is

1. 1. 3 MPa

   
   
   

   2. 6 MPa

   
   
   

   3. 10 MPa

   
   
   

   4. 20 MPa

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   

   b = 40 ×	2	=	80	mm (by symmetry)
   	3		3

   
   ∴ Area of upper triangle
   

   =	1	×	80	×	40
   	2		3		3

   
   

   =	1600	mm2
   	9

   
   

   y =	40	×	1	=	40	mm
   	3		3		9

   
   

   τnetutral axis =	V.Ay
   	l.b

   
   
   = 10 N/mm² = 10 mPa.

   Correct Option: C

   
   

   b = 40 ×	2	=	80	mm (by symmetry)
   	3		3

   
   ∴ Area of upper triangle
   

   =	1	×	80	×	40
   	2		3		3

   
   

   =	1600	mm2
   	9

   
   

   y =	40	×	1	=	40	mm
   	3		3		9

   
   

   τnetutral axis =	V.Ay
   	l.b

   
   
   = 10 N/mm² = 10 mPa.

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147. The maximum and minimum shear stresses in a hollow circular shaft of outer diameter 20 mm and thickness 2 mm, subjected to a torque of 92.7 Nm will be

1. 1. 59 MPa and 47.2 MPa

   
   
   

   2. 100 MPa and 80 MPa

   
   
   

   3. 118 MPa and 160 MPa

   
   
   

   4. 200 MPa and 160 MPa

   
   
   

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1. View Hint View Answer Discuss in Forum

   	τ	=	T
   	r		J

   
   
   

   τmax =	T.rmax
   	J

   
   

   =	92.7 × 10 × 1000
   	(π/32) × (204 - 104)

   
   ≈ 100 N/mm²
   τ_max is at r = 16/2 = 8 mm
   τ_max = (100/10) × r_min = 80 N/mm² = 80 mPa

   Correct Option: B

   	τ	=	T
   	r		J

   
   
   

   τmax =	T.rmax
   	J

   
   

   =	92.7 × 10 × 1000
   	(π/32) × (204 - 104)

   
   ≈ 100 N/mm²
   τ_max is at r = 16/2 = 8 mm
   τ_max = (100/10) × r_min = 80 N/mm² = 80 mPa

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148. A rigid bar is suspended by three rods made of the same material as shown in the figure. The area and length of the central rod are 3A and L, respectively while that of the two outer rods are 2A and 2L, respectively. If a downward force of 50 kN is applied to the rigid bar, the forces in the central and each of the outer rods will be
     

1. 1. 16.67 kN each

   
   
   

   2. 30 kN and 15 kN

   
   
   

   3. 30 kN and 10 kN

   
   
   

   4. 21.4 kN and 14.3 kN

   
   
   

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1. View Hint View Answer Discuss in Forum

   δl is same for 3 bars.
   

   δl =	PL
   	AE

   
   
   ∴ P_C = 3P_s
   ∴ 2P_C + P_s = 50
   ⇒ 2P_C + 3P_s = 50
   ∴ P_s = 10 kN
   ∴ P_C = 30 kN

   Correct Option: C

   δl is same for 3 bars.
   

   δl =	PL
   	AE

   
   
   ∴ P_C = 3P_s
   ∴ 2P_C + P_s = 50
   ⇒ 2P_C + 3P_s = 50
   ∴ P_s = 10 kN
   ∴ P_C = 30 kN

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149. A metal bar of length 100 mm is inserted between two rigid supports and its temperature is increased by 10°C. If the coefficient of thermal expansion is 12 × 10^–6 per °C and the young’s modulus is 2 × 10⁵ MPa, the stress in the bar is

1. 1. zero

   
   
   

   2. 12 MPa

   
   
   

   3. 24 MPa

   
   
   

   4. 2400 MPa

   
   
   

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1. View Hint View Answer Discuss in Forum

   Stress = E × strain
   

   = E ×	δl
   	l

   
   = Eαt
   =2 × 10⁵ × 12 × 10^-6 × 10 =24 mPa

   Correct Option: C

   Stress = E × strain
   

   = E ×	δl
   	l

   
   = Eαt
   =2 × 10⁵ × 12 × 10^-6 × 10 =24 mPa

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150. An axially loaded bar is subjected to a normal stress of 173 MPa. The shear stress in the bar is

1. 1. 75 MPa

   
   
   

   2. 86.5 MPa

   
   
   

   3. 100 MPa

   
   
   

   4. 122.3 MPa

   
   
   

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1. View Hint View Answer Discuss in Forum

   For maximum, θ = 45°
   

   τmax =	σx - σy	.sin2θ
   	2

   
   

   =	173 - 0	× 1 = 86.5 MPa
   	2

   Correct Option: B

   For maximum, θ = 45°
   

   τmax =	σx - σy	.sin2θ
   	2

   
   

   =	173 - 0	× 1 = 86.5 MPa
   	2

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