why bridges have I shaped beam?

Asked by vipul_p_doshi | 2nd May, 2015, 03:31: PM

Expert Answer:

Bridges should be constructed in such a way that it does not bend too much or break under the load of traffic or its own load.
From the theory of elasticity we know that when a load W is placed at the midpoint of a bar of length l, breadth b and thickness d, then the bar bends at the midpoint by an amount given by:
begin mathsize 12px style straight delta space equals fraction numerator straight W space straight l cubed over denominator 4 space straight Y space straight b space straight d cubed end fraction Where space straight Y space is space the space young apostrophe straight s space modulus space of space the space material space of space the space bar. end style
From the expression stated above we get that to reduce the bending for a given load, we should use a material of large Youngs modulus( δ is inversely proportional to Y). For a given amount of material we should increase the thickness of the bar rather than the breadth (as δ is proportinal to 1/d3 and only to 1/b). But on increasing the thickness too much also the bar may bend . Thus a compromise between the breadth and thickness is made by using I-shaped beam having large load bearing surface for the construction of bridges.

Answered by Jyothi Nair | 4th May, 2015, 10:56: AM

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