66. A simply supported laterally loaded beam was found to deflect more than a specified value. Which of the following measures will reduce deflection?

1. 1. Increase the area moment of inertia

   
   
   

   2. Increase the span of the beam

   
   
   

   3. Select a different material having lesser modulus of elasticity

   
   
   

   4. Magnitude of the load to be increased

   
   
   

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1. View Hint View Answer Discuss in Forum

   From differential equation of elastic curve
   

   EI	d2y	= M
   	dx2

   
   
   where y = deflection of beam.
   As the I = Area moment increases, the deflection will reduce.

   Correct Option: A

   From differential equation of elastic curve
   

   EI	d2y	= M
   	dx2

   
   
   where y = deflection of beam.
   As the I = Area moment increases, the deflection will reduce.

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67. Consider a prismatic straight beam of length L = π m, pinned at the two ends as shown i n t he figure. The beam has a square cross-section of side p = 6 mm. The Young's modulus E = 20 GPa, and the coefficient of thermal expansion α = 3 × 10^{– 6} K ^{– 1}. The minimum temperature rise required to cause Euler buckling of the beam is ______ K.
    

1. 1. 1 K

   
   
   

   2. 3 K

   
   
   

   3. 4 K

   
   
   

   4. 2 K

   
   
   

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1. View Hint View Answer Discuss in Forum

   Length of prismatic beam,
   L = πm
   P_th = P_axial
   

   or αTEA =	π2EI
   	L2

   
   ⇒ 3 × 10^-6 × ∆T × 6 × 6 × 10^-6
   
   ∆T = 1K

   Correct Option: A

   Length of prismatic beam,
   L = πm
   P_th = P_axial
   

   or αTEA =	π2EI
   	L2

   
   ⇒ 3 × 10^-6 × ∆T × 6 × 6 × 10^-6
   
   ∆T = 1K

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68. A column has a rectangular cross-section of 10 mm × 20 mm and a length of 1 m. The slenderness ratio of the column is close to

1. 1. 200

   
   
   

   2. 346

   
   
   

   3. 477

   
   
   

   4. 1000

   
   
   

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1. View Hint View Answer Discuss in Forum

   Slenderness ratio
   

   =	Effective length of column
   	least radius of gyration

   
   

   =	Le
   	K

   
   
   where I_min = minimum area moment of inertia i.e. I_xx or I_yy, whichever is less.
   For given section
   

   Imin	20 × 103	= 1667 mm3
   	12

   
   
   

   and ratio=	1000	= 346
   	2.89

   Correct Option: B

   Slenderness ratio
   

   =	Effective length of column
   	least radius of gyration

   
   

   =	Le
   	K

   
   
   where I_min = minimum area moment of inertia i.e. I_xx or I_yy, whichever is less.
   For given section
   

   Imin	20 × 103	= 1667 mm3
   	12

   
   
   

   and ratio=	1000	= 346
   	2.89

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69. The minimum axial compressive load, P required to initiate buckling for a pinned-pinned slender column with bending stiffness EI and length L is

1. 1. P =	π2EI
      	4L2

   
   
   

   2. P =	π2EI
      	L2

   
   
   

   3. P =	3π2EI
      	4L2

   
   
   

   4. P =	4π2EI
      	L2

   
   
   

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1. View Hint View Answer Discuss in Forum

   P =	π2EI
   	L2

   Correct Option: B

   P =	π2EI
   	L2

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70. A steel column of rectangular section (15 mm × 10 mm) and length 1.5 m is simply supported at both ends. Assuming modulus of elasticity, E = 200 GPa for steel, the critical axial load (in kN) is _____ (correct to two decimal places)

1. 1. 1.097

   
   
   

   2. 1.397

   
   
   

   3. 1.297

   
   
   

   4. 1.197

   
   
   

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1. View Hint View Answer Discuss in Forum

   Steel column supported at both ends = hinged at both ends.
   so for hinged condition:-
   Effective length, L_e = L
   so buckling load
   

   Correct Option: A

   Steel column supported at both ends = hinged at both ends.
   so for hinged condition:-
   Effective length, L_e = L
   so buckling load
   

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