# Mid Span Deflection : Transposing Equations and Solving by Substitution

The equation for the mid-span deflection of a simply supported beam carring a uniformly distributed load can be determined from.

M=5WL^3 / 384EI AND I=bd^3 / 12

where: M = mid-span deflection

W = total load

L = span

E = Young's modulus of elasticity

I = second moment of area

1. Transpose this equation to make L the subject.

2. Taking care with units, use this transposed equation to find the maximum length of beam that can be used if the midspan deflection is to be limited to 7 mm.

W= 12kN

E= 10,000 N/mm2

b= 75mm

d= 200mm

https://brainmass.com/math/discrete-math/mid-span-deflection-transposing-equations-and-solving-by-substitution-40319

#### Solution Preview

The ^ will signify an exponent. Therefore, the equation can be written as:

M=5WL^3 / 384 EI

Make sense?

Therefore, we need to rearrange this so that we have L = something.

Here's what we do.

First, we cross-multiply. Therefore, we get:

384 MEI = 5 WL^3

Next, we divide each side of the equation by 5W. That gives:

384 MEI / 5W = L^3

Now, flip it around, so it looks ...

#### Solution Summary

Transposing Equations and Solving by Substitution is applied to solving a Mid Span Deflection problem. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.