41. For the structure shown below, the vertical deflection at point A is given by
    

1. 1. 	PL3
      	81EI

   
   
   

   2. 	2PL3
      	81EI

   
   
   

   3. Zero

   
   
   

   4. 	PL3
      	72EI

   
   
   

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1. View Hint View Answer Discuss in Forum

   	2PL3
   	81EI

   Correct Option: B

   	2PL3
   	81EI

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42. The degree of static indeterminacy, N_s, and the degree of kinematic indeterminacy, N_k, for the plane frame shown below, assuming axial deformations to be negligible, are given by
    

1. 1. N_s = 6 and N_k = 11

   
   
   

   2. N_s = 6 and N_k = 6

   
   
   

   3. N_s = 4 and N_k = 6

   
   
   

   4. N_s = 4 and N_k = 4

   
   
   

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1. View Hint View Answer Discuss in Forum

   N_S = D_SE + D_SI
   D_SE = 7 – 3 = 4
   D_SI = 0
   ∴ N_S = 4
   N_k = 3 + 3 + 3 + 0 + 1 + 1 = 11
   When we assume negligible axial deformation,
   N_k = 11 – 5 = 6

   Correct Option: C

   N_S = D_SE + D_SI
   D_SE = 7 – 3 = 4
   D_SI = 0
   ∴ N_S = 4
   N_k = 3 + 3 + 3 + 0 + 1 + 1 = 11
   When we assume negligible axial deformation,
   N_k = 11 – 5 = 6

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43. The bending moment (in kNm units) at the mid -span location X in the beam with overhangs shown below is equal
    

1. 1. 0

   
   
   

   2. –10

   
   
   

   3. –15

   
   
   

   4. –20

   
   
   

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1. View Hint View Answer Discuss in Forum

   Taking moment about B.
   M_B = R_A × 2 – 20 × 3 + 10 ×1 = 0
   ⇒ R_A = 25 kN
   Moment about X,
   M_x = R_A × 1 – 20 × 2
   = 25 × 1 – 20 × 2 = – 15 kNm

   Correct Option: C

   Taking moment about B.
   M_B = R_A × 2 – 20 × 3 + 10 ×1 = 0
   ⇒ R_A = 25 kN
   Moment about X,
   M_x = R_A × 1 – 20 × 2
   = 25 × 1 – 20 × 2 = – 15 kNm

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44. The ‘plane section remains plane’ assumption in bending theory implies:

1. 1. strain profile is linear

   
   
   

   2. stress profile is linear

   
   
   

   3. both strain and stress profiles are linear

   
   
   

   4. shear deformations are neglected

   
   
   

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1. View Hint View Answer Discuss in Forum

   strain profile is linear

   Correct Option: A

   strain profile is linear

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45. The end moment (in kNm) units) developed in the roof level beams in the laterally loaded frame shown below (with all columns having identical cross-sections), according to the Cantilever Method of simplified analysis, is
    

1. 1. 7.5

   
   
   

   2. 15

   
   
   

   3. 20

   
   
   

   4. 30

   
   
   

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1. View Hint View Answer Discuss in Forum

   15

   Correct Option: B

   15

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