what is the relationship between span and deflection in a steel beam?

Question

the beam is supported with 2 knife edges at either end. everything else is constant apart form the span. can anyone help?

Answer 1

If you take two beams of different lengths and apply the same load (uniform or otherwise), the ratio of the deflections will be directly proportional to some cubic or quartic power of the length.

For uniformly loaded beams, the deflection equation has the length to the 4th power; for beams with point load at the center of the beam, the ratio is directly proportional to the cube of the lengths.

There are innumerable loading conditions and their concomitant expressions for deflection. Consult with typical structural analysis texts to see some of them.

Answer 2

If all other variables remain unchanged, deflection is directly proportional to span, where span refers to length. Those other variables include cross-section and the applied force. For a beam in pure bending subject to a force of P and no moment, d = PL^3/(3EI), where L is length (or span), E is modulus of elasticity, and I is the moment of inertia.