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Question
Let a steel bar of length l, breadth b and depth d be loaded at the centre by a load W. Then the sag of bending of beam is ______.
(Y = Young's modulus of material of steel)
Options
`("Wl"^3)/(2"bd"^3"Y")`
`("Wl"^3)/(4"bd"^3"Y")`
`("Wl"^2)/(2"bd"^3"Y")`
`("Wl"^3)/(4"bd"^2"Y")`
MCQ
Fill in the Blanks
Solution
Let a steel bar of length l, breadth b and depth d be loaded at the centre by a load W. Then the sag of bending of beam is `underlinebb(("Wl"^3)/(4"bd"^3"Y"))`.
Explanation:
The bending sag of a beam of length l loaded with weight W at the free end is given by
δ = `("WL"^3)/(48"YI")`
I = Moment of inertia of steel bar = `"bd"^3/12`
So, δ = `("WL"^3)/(48"Ybd"^3)xx12`
= `("Wl"^3)/(4"Ybd"^3)`
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