A horizontal beam ABC is loaded as shown in the figure below.

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A horizontal beam ABC is loaded as shown in the figure below. The distance of the point of contraflexure from end A (in m) is ____

1. 0.25
2. 0.75
3. 0.24
4. 0.45

Correct Option: A

Take R_C at redundant
By Marshall Reciprocal Theorem
Deflection at C due to load B, ∆_BC

∆_BC =	10 ×(0.75)³	+	10 ×(0.75)³	× 0.25
	3EI		2EI

=	2.11	↓
	EI

Deflection at C due to redundant R_c, ∆_cc

∆_cc =	R_c ×(0.75)³	=	0.141R_c
	3EI		EI

∴ ∆_c = 0

	2.11	-	0.141R_c	= 0
	EI		EI

R_c =	2.11	= 15 KN
	0.141

M_x = 10x – 15 × (x – 0.25) = 0
⇒ = 10x – 15x + 3.75 = 0
⇒ x = 0.75m
∴ Distanced contraflexure from C = 0.75m
⇒ Distanced contraflexure from A = 1 – 0.75 = 0.25m