21. Match the following:
    Group I
    P. Slope deflection
    Q. Moment distribution
    R. Method of three moments
    S. Castigliano's second theorem
    Group 2
    1. Force method method
    2. Displacement method method

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

   
   
   

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

   
   
   

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

   
   
   

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

   
   
   

---

1. View Hint View Answer Discuss in Forum

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

   Correct Option: C

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

---

22. All members of the frame shown below have the same flexural rigidity EI and length L. If a moment M is applied at joint B, the rotation of the point is
    

1. 1. ML

      12EI

   
   
   

   2. ML

      11EI

   
   
   

   3. ML

      8EI

   
   
   

   4. ML

      7EI

   
   
   

---

1. View Hint View Answer Discuss in Forum

   Stiffness of members,
   

   KBA =	4EI
   	L

   
   

   KBC =	3EI
   	L

   
   

   KBD =	4EI
   	L

   
   Rotational stiffness = Sum of stiffness of all member
   

   ⇒ K =	11EI
   	L

   
   

   Rotation at B, θB =	m	=	ML
   	k		11EL

   Correct Option: B

   Stiffness of members,
   

   KBA =	4EI
   	L

   
   

   KBC =	3EI
   	L

   
   

   KBD =	4EI
   	L

   
   Rotational stiffness = Sum of stiffness of all member
   

   ⇒ K =	11EI
   	L

   
   

   Rotation at B, θB =	m	=	ML
   	k		11EL

---

---

23. Mohr’s circle for the state of stress defined by
    

    		30		0
    		0		30

    
    MPa is a circle with

1. 1. centre at (0, 0) and radius 30 MPa

   
   
   

   2. centre at (0, 0) and radius 60 MPa

   
   
   

   3. centre at (30, 0) and radius 30 MPa

   
   
   

   4. centre at (30, 0) and zero radius

   
   
   

---

1. View Hint View Answer Discuss in Forum

   Principle stress, σ₁₁ = σ₂₂ (both 30)
   ∴ Radius of Mohr circle = σ₁₁ – σ₂₂ = 0
   In centre will be at (30, 0)

   Correct Option: D

   Principle stress, σ₁₁ = σ₂₂ (both 30)
   ∴ Radius of Mohr circle = σ₁₁ – σ₂₂ = 0
   In centre will be at (30, 0)

---

24. A simply supported beam AB has the bending moment diagram as shown in the following figure. The beam is possibly under the action of following loads:
    

1. 1. Couples of M at C and 2M at D

   
   
   

   2. Couples of 2M at C and M at D

   
   
   

   3. Concentrated loads of M/L at C and 2M/L at D

   
   
   

   4. Concentrated loads of M/L at C and couple of 2M at D

   
   
   

---

1. View Hint View Answer Discuss in Forum

   Variation of moment at D = (+m) – (–m) = 2m
   Variation of moment at C = (+m) = m

   Correct Option: A

   Variation of moment at D = (+m) – (–m) = 2m
   Variation of moment at C = (+m) = m

---

---

25. The stiffness coefficient k_ij indicates

1. 1. force at i due to a unit deformation at j

   
   
   

   2. deformation at j due to a unit force at i

   
   
   

   3. deformation at i due to a unit force j

   
   
   

   4. force at j due to a unit deformation i

   
   
   

---

1. View Hint View Answer Discuss in Forum

   force at i due to a unit deformation at j

   Correct Option: A

   force at i due to a unit deformation at j

---