71. For formation of collapse mechanism in the following figure, the minimum value of P_u is cm_p /L. m_p and 3 m_p denote the plastic moment capacities of beam sections as shown in this figure. The value of c is________.
    

1. 1. 13.22

   
   
   

   2. 13.25

   
   
   

   3. 13.33

   
   
   

   4. 14

   
   
   

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1. View Hint View Answer Discuss in Forum

   Mechanism I
   3m_p .θ + m_p .(2 θ ) + m_p θ
   

   P u ×	L	× θ
   	4

   
   
   

   ⇒ 6mp .θ = P u ×	L	× θ
   	4

   
   

   ⇒ P u = 24	mp
   	L

   
   Mechanism II
   
   1.Φ = 3θ
   ⇒ Φ = 3θ
   
   

   = 13.33	mp
   	L

   
   ∴ c = 13.33

   Correct Option: C

   Mechanism I
   3m_p .θ + m_p .(2 θ ) + m_p θ
   

   P u ×	L	× θ
   	4

   
   
   

   ⇒ 6mp .θ = P u ×	L	× θ
   	4

   
   

   ⇒ P u = 24	mp
   	L

   
   Mechanism II
   
   1.Φ = 3θ
   ⇒ Φ = 3θ
   
   

   = 13.33	mp
   	L

   
   ∴ c = 13.33

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72. Two beams are connected by a linear spring as shown in the following figure. For a load P as shown in the figure, the percentage of the applied load P carried by the spring is ________.
    

1. 1. 33.33

   
   
   

   2. 22.22

   
   
   

   3. 22

   
   
   

   4. 12

   
   
   

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1. View Hint View Answer Discuss in Forum

   ∆ =	R	=	R	× 2L3
   	K		3EI

   
   

   ∆ =		K =	3EI
   			2L3

   
   

   ∆ =	2RL3
   	3EI

   
   
   

   ⇒	P	= R
   	3

   
   ∴ % of applied load carried by spring
   

   =	1	× 100 = = 33.3%
   	3

   Correct Option: A

   ∆ =	R	=	R	× 2L3
   	K		3EI

   
   

   ∆ =		K =	3EI
   			2L3

   
   

   ∆ =	2RL3
   	3EI

   
   
   

   ⇒	P	= R
   	3

   
   ∴ % of applied load carried by spring
   

   =	1	× 100 = = 33.3%
   	3

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73. For the 2D truss with the applied loads shown below, the strain energy in the member XY is _______ kN-m. For member XY, assume AE=30kN, where A is cross section area and E is the modulus of elasticity.
    

1. 1. 5

   
   
   

   2. 33

   
   
   

   3. 23

   
   
   

   4. 234

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   R_A × 3 + 10 × 9 = 0
   ⇒ R_A = –30 kN
   R_B = 35 kN
   Taking joint A
   
   Taking joint B
   
   Taking joint x
   F_x = 10 kN
   

   U =	F2 × L
   	2AE

   
   

   =	102 × 3	= 5 kNm
   	2 × 3

   
   

   Correct Option: A

   
   R_A × 3 + 10 × 9 = 0
   ⇒ R_A = –30 kN
   R_B = 35 kN
   Taking joint A
   
   Taking joint B
   
   Taking joint x
   F_x = 10 kN
   

   U =	F2 × L
   	2AE

   
   

   =	102 × 3	= 5 kNm
   	2 × 3

   
   

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74. A tapered circular rod of diameter varying from 20 mm to 10 mm is connected to another uniform circular rod of diameter 10 mm as shown in the following figure. Both bars are made of same material with the modulus of elasticity, E = 2 × 10⁵ MPa. When subjected to a load P= 30π kN, the deflection at point A is ________ mm.
    

1. 1. 12

   
   
   

   2. 13

   
   
   

   3. 15

   
   
   

   4. 32

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   

   ∆1 =	PL	=	4PL
   	AE		πd1d2.E

   
   

   =	4 × 30π × 2 × 106	= 6 mm
   	π × 20 × 10 × 2 × 105

   
   

   ∆2 =	PL
   	AE

   
   
   

   =	4 × 30π × 1.5 × 106	= 9 mm
   	π × 10 × 10 × 2 × 105

   
   ∴ ∆ = ∆₁ + ∆₂ = 15 mm

   Correct Option: C

   
   

   ∆1 =	PL	=	4PL
   	AE		πd1d2.E

   
   

   =	4 × 30π × 2 × 106	= 6 mm
   	π × 20 × 10 × 2 × 105

   
   

   ∆2 =	PL
   	AE

   
   
   

   =	4 × 30π × 1.5 × 106	= 9 mm
   	π × 10 × 10 × 2 × 105

   
   ∴ ∆ = ∆₁ + ∆₂ = 15 mm

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75. Two Triangular wedges are glued together as shown in the following figure. The stress acting normal to the interface, σ_n is __ MPa.
    

1. 1. 0

   
   
   

   2. 1

   
   
   

   3. 2

   
   
   

   4. 3

   
   
   

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   Normal stress, σ_n
   

   σn =	σx + σy	+	σx - σy	cos2θ
   	2		2

   
   

   =	100 - 100	+	100 - (-100)	cos(2 × 45)
   	2		2

   
   

   = 0 +	200	× 0 = 0
   	2

   Correct Option: A

   Normal stress, σ_n
   

   σn =	σx + σy	+	σx - σy	cos2θ
   	2		2

   
   

   =	100 - 100	+	100 - (-100)	cos(2 × 45)
   	2		2

   
   

   = 0 +	200	× 0 = 0
   	2

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