Question Details

Railway lines and girders for buildings, are I shaped, because

Options

A

The bending of a girder is inversely proportional to depth, hence high girder bends less

B

The coefficient of rigidity increases by this shape

C

Less volume strain is caused

D

This keeps the surface smooth

Correct Answer :

The bending of a girder is inversely proportional to depth, hence high girder bends less

Solution :

The correct option is: The bending of a girder is inversely proportional to depth, hence high girder bends less

When a beam or girder of length L, breadth b, and depth d is supported at its ends and loaded at the center with a load W, it undergoes a vertical depression (bending) δ at its midpoint. The formula for this depression is given by:

δ = W L 3 4 Y b d 3

where Y represents the Young's modulus of the material.

From this relation, it is clear that the depression δ is inversely proportional to the cube of the depth (d) of the girder:
δ 1 d 3
This indicates that the depth of the girder has a very strong influence on reducing bending. By designing the girder to be deeper (higher), the bending decreases significantly.

An I-shape provides a large depth (d) while minimizing the cross-sectional area and weight of the beam. The flange portions at the top and bottom handle the bending stress, while the central web maintains the depth of the girder. Therefore, making girders I-shaped ensures high structural strength and minimal bending with optimal material usage.

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