121. A continuous beam is loaded as shown in the figure below. Assuming a plastic moment capacity equal to MP, the minimum load at which the beam would collapse is
     

1. 1. 	4MP
      	L

   
   
   

   2. 	6MP
      	L

   
   
   

   3. 	8MP
      	L

   
   
   

   4. 	10MP
      	L

   
   
   

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1. View Hint View Answer Discuss in Forum

   For point load max moment occurs under the load Consider IJ
   Max. moment
   

   =	PL	=	3	MP
   	4		2

   
   

   ∴ P =	6MP
   	L

   
   
   Consider HI,
   

   	PL	= 2MP
   	4

   
   

   ∴ P =	8MP
   	L

   
   
   Collapse load = 6M_P/L (Minimum of two.)

   Correct Option: B

   For point load max moment occurs under the load Consider IJ
   Max. moment
   

   =	PL	=	3	MP
   	4		2

   
   

   ∴ P =	6MP
   	L

   
   
   Consider HI,
   

   	PL	= 2MP
   	4

   
   

   ∴ P =	8MP
   	L

   
   
   Collapse load = 6M_P/L (Minimum of two.)

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122. A symmetric frame PQR consists of two inclined members PQ and QR, connected at ‘Q’ with a rigid joint, and hinged at ‘P’ and ‘R’. The horizontal length PR is l. If a weight W is suspended at ‘Q’, the bending moment at ‘Q’ is

1. 1. Wl/2

   
   
   

   2. Wl/4

   
   
   

   3. Wl/8

   
   
   

   4. zero

   
   
   

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1. View Hint View Answer Discuss in Forum

   V_P = V_R = ω/2
   By symmetry,
   

   	y	=	h
   	x		l/2

   
   

   ∴ y =	hx
   	l/2

   
   
   Horizontal reaction for any support,
   

   H =	∫myds
   	∫y2ds

   
   
   

   ⇒ H =	Wl
   	8h

   
   BM at Q = R₁ . x - H.y
   

   	W	×	l	-	Wl	. h
   	2		2		8h

   
   

   =	Wl
   	8

   Correct Option: C

   V_P = V_R = ω/2
   By symmetry,
   

   	y	=	h
   	x		l/2

   
   

   ∴ y =	hx
   	l/2

   
   
   Horizontal reaction for any support,
   

   H =	∫myds
   	∫y2ds

   
   
   

   ⇒ H =	Wl
   	8h

   
   BM at Q = R₁ . x - H.y
   

   	W	×	l	-	Wl	. h
   	2		2		8h

   
   

   =	Wl
   	8

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123. The sketch shows a column with a pin at the base and rollers at the top. It is subjected to an axial force P and a moment M at mid-height. The reaction(s) at R is/are
     

1. 1. a vertical force equal to P

   
   
   

   2. a vertical force equal to P/2

   
   
   

   3. a vertical force equal to P and a horizontal force equal to M/h

   
   
   

   4. a vertical force equal to P/2 and a horizontal force equal to M/h

   
   
   

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1. View Hint View Answer Discuss in Forum

   P will cause direct vertical reaction at R. Take moment about Q.
   R_H .h - M = 0
   ∴ R_H = M/h
   

   Correct Option: C

   P will cause direct vertical reaction at R. Take moment about Q.
   R_H .h - M = 0
   ∴ R_H = M/h
   

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124. A simply supported beam is subjected to a uniformly distributed load of intensity w per unit length, on half of the span from the end. The length of the span and the flexural stiffness are denoted as l and EI, respectively. The deflection at mid-span of the beam is

1. 1. 	5		wl4
      	6144		EI

   
   
   

   2. 	5		wl4
      	786		EI

   
   
   

   3. 	5		wl4
      	384		EI

   
   
   

   4. 	5		wl4
      	192		EI

   
   
   

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1. View Hint View Answer Discuss in Forum

   Apply Maxwell reciprocal theorem.
   
   

   δc =	5ωl4
   	384EI

   
   

   ∴ δc1=	δc	=	5ωl4
   	2		384EI

   Correct Option: B

   Apply Maxwell reciprocal theorem.
   
   

   δc =	5ωl4
   	384EI

   
   

   ∴ δc1=	δc	=	5ωl4
   	2		384EI

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125. The ratio of the theoretical critical buckling load for a column with fixed ends to that of another column with the same dimensions and material, but with pinned ends, is equal to

1. 1. 0.5

   
   
   

   2. 1.0

   
   
   

   3. 2.0

   
   
   

   4. 4.0

   
   
   

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1. View Hint View Answer Discuss in Forum

   p =	π2 EI
   	leff2

   
   For fixed end, l_eff = l/2
   For pinned end, l_eff = l
   

   p ∝	1
   	leff2

   
   

   	p1	=	l22	=	l2	= 4
   	p2		l12		(l/2)2

   Correct Option: D

   p =	π2 EI
   	leff2

   
   For fixed end, l_eff = l/2
   For pinned end, l_eff = l
   

   p ∝	1
   	leff2

   
   

   	p1	=	l22	=	l2	= 4
   	p2		l12		(l/2)2

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