6. For a linear elastic structural system, minimization of potential energy yields

1. 1. compatibility conditions

   
   
   

   2. constitutive relations

   
   
   

   3. equilibrium equations

   
   
   

   4. strain-displacement relations

   
   
   

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1. View Hint View Answer Discuss in Forum

   compatibility conditions

   Correct Option: A

   compatibility conditions

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7. The plane frame below is analyzed by neglecting axial deformations. Following statements are made with respect to the analysis
   I. Column AB carries axial force only
   II. Vertical deflection at the centre of beam BC is 1 mm
   
   With reference to the above statements, which of the following applies?
   EI = 81380 kN-m²

1. 1. Both the statements are true

   
   
   

   2. Statement I is true but II is false

   
   
   

   3. Statement II is true but I is false

   
   
   

   4. Both the statements are false

   
   
   

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1. View Hint View Answer Discuss in Forum

   Since there are no horizontal loads, the columns are subjected to axial loads only.
   Deflection at centre
   

   =	5WL4	=	5 × 10 × 54	= 1 mm
   	384EI		384.813

   Correct Option: A

   Since there are no horizontal loads, the columns are subjected to axial loads only.
   Deflection at centre
   

   =	5WL4	=	5 × 10 × 54	= 1 mm
   	384EI		384.813

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8. A propped cantilever of span L is carrying a vertical concentrated load acting at mid span. The plastic moment of the section is Mp. The magnitude of the collapse load is

1. 1. 8MP

      L

   
   
   

   2. 6MP

      L

   
   
   

   3. 4MP

      L

   
   
   

   4. 2MP

      L

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   Bending moment diagram.
   
   Let P be the load on the prop at collapse, then equating the numerical value of BM at fixed end and centre.
   

   MP = Wc ×	L	- Pl
   	2

   
   

   p =	Wc
   	2

   
   

   ∴ MP = Wc	L	-	Wc.l
   	z		3

   
   

   =	Wc.L
   	6

   
   

   ∴ Wc =	6Mp
   	L

   Correct Option: B

   
   Bending moment diagram.
   
   Let P be the load on the prop at collapse, then equating the numerical value of BM at fixed end and centre.
   

   MP = Wc ×	L	- Pl
   	2

   
   

   p =	Wc
   	2

   
   

   ∴ MP = Wc	L	-	Wc.l
   	z		3

   
   

   =	Wc.L
   	6

   
   

   ∴ Wc =	6Mp
   	L

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9. The symmetry of stress tensor at a point in the body under equilibrium is obtained from

1. 1. conservation of mass

   
   
   

   2. force equilibrium equations

   
   
   

   3. moment equilibrium equations

   
   
   

   4. conservation of energy

   
   
   

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1. View Hint View Answer Discuss in Forum

   moment equilibrium equations

   Correct Option: C

   moment equilibrium equations

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10. 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

   
   
   

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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

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