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)

विकल्प

• `("Wl"^3)/(2"bd"^3"Y")`

• `("Wl"^3)/(4"bd"^3"Y")`

• `("Wl"^2)/(2"bd"^3"Y")`

• `("Wl"^3)/(4"bd"^2"Y")`

Answer 1

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)`