31. The frame below shows three beam elements OA, OB and OC, with identical length L and flexural rigidity EI, subject to an external moment M applied at the rigid joint O. The correct set of bending moments [M_OX M_OB, M_OC] that develop at O in the three beam elements OA, OB and OC respectively, is
    ,img src="http://images.interviewmania.com/wp-content/uploads/2019/10/63-2.png">
    EI/L is constant for all three members

1. 1. [3M/8, M/ 8, 4M/8]

   
   
   

   2. [3M/11, 4M/11, 4M/11]

   
   
   

   3. [M/3, M/3, M/3]

   
   
   

   4. [3M/7, 0, 4M/7]

   
   
   

---

1. View Hint View Answer Discuss in Forum

   KOA =	3EI
   	l

   
   

   KOC =	4EI
   	l

   
   K_OB = 0
   

   DFOA =	KOA
   	KOA + KOC

   
   

   =	3	=	3			EI	cancels
   	3 + 4		7			l

   
   

   DFOC =	KOC
   	KOC + KOA

   
   

   =	4	=	4
   	4 + 3		7

   
   DF_OB = 0

   Correct Option: D

   KOA =	3EI
   	l

   
   

   KOC =	4EI
   	l

   
   K_OB = 0
   

   DFOA =	KOA
   	KOA + KOC

   
   

   =	3	=	3			EI	cancels
   	3 + 4		7			l

   
   

   DFOC =	KOC
   	KOC + KOA

   
   

   =	4	=	4
   	4 + 3		7

   
   DF_OB = 0

---

32. Consider the following two statements related to reinforced concrete design, and identify whether they are TRUE or FALSE:
    I. Curtailment of bars in the flexural tension zone in beams reduces the shear strength at the cut-off locations.
    II. When a rectangular column section is subject to biaxially eccentric compression, the neutral axis will be parallel to the resultant axis of bending.

1. 1. Both statements I and II are TRUE

   
   
   

   2. Statement I is TRUE, and Statement II is FALSE

   
   
   

   3. Statement I is FALSE, and statement II is TRUE

   
   
   

   4. Both Statements I and II are FALSE.

   
   
   

---

1. View Hint View Answer Discuss in Forum

   Statement I is TRUE, and Statement II is FALSE

   Correct Option: B

   Statement I is TRUE, and Statement II is FALSE

---

---

33. For the loading given in the figure below, two statements (I and II) are made).
    
    I. Member AB carries shear force and bending moment
    II. Member BC carries axial load and shear force.
    Which of the following is true?

1. 1. Statement I is true but II is false

   
   
   

   2. Statement I is false but II is true

   
   
   

   3. Both statements I and II are true

   
   
   

   4. Both statements I and II are false

   
   
   

---

1. View Hint View Answer Discuss in Forum

   Member AB carries shear force and bending moment. Member BC carries only axial load and no shear force

   Correct Option: A

   Member AB carries shear force and bending moment. Member BC carries only axial load and no shear force

---

34. The shear modulus (G), modulus of elasticity (E) and the Poisson's ratio (v) of a material are related as,

1. 1. G = E/ [2 (1 + v)]

   
   
   

   2. E = G/ [2 (1 + v)]

   
   
   

   3. G = E/ [2 (1 – v)]

   
   
   

   4. G = E/ [2 (v – 1)]

   
   
   

---

1. View Hint View Answer Discuss in Forum

   E =2G (1 + v)
   

   ∴ G =	E
   	2(1 + v)

   Correct Option: A

   E =2G (1 + v)
   

   ∴ G =	E
   	2(1 + v)

---

---

35. Identify, from the following, the correct value of the bending moment M_A (in kNm) units) at the fixed end A in the statically determinate beam shown below (with internal hinges at B and D), when a uniformly distributed load of 10 kN/m is placed on all spans.
    (Hint: Sketching the influence line for M_A or applying the Principle of Virtual Displacements makes the solution easy).
    

1. 1. –80

   
   
   

   2. – 40

   
   
   

   3. 0

   
   
   

   4. + 40

   
   
   

---

1. View Hint View Answer Discuss in Forum

   
   (Influence line Diagram, ILD for M_A)
   Ordinate at B, 2/y = 1
   ⇒ y = 2
   Ordinate at D = 2
   BM at A = loading intensity X area under load
   

   = 10.		1	× 4 × 2		+ 10		-	1	× 4 × 2		= 0
   		2						2

   Correct Option: C

   
   (Influence line Diagram, ILD for M_A)
   Ordinate at B, 2/y = 1
   ⇒ y = 2
   Ordinate at D = 2
   BM at A = loading intensity X area under load
   

   = 10.		1	× 4 × 2		+ 10		-	1	× 4 × 2		= 0
   		2						2

---