# Loaded beams! find where the maxinum deflection occurs on the beam

## Homework Statement

calculate the position from A where the maximum deflection occurs. Your answer should be accurate to 3dp. You may assume IE= 100Mn

## Homework Equations

I'm going to go with EI d2y/dx2 = m
(the 2 are meant to be squared)

## The Attempt at a Solution

Is this equation correct and if yes how do I find out where abouts the deflection is?

## The Attempt at a Solution

You need to give details of the span and the loading. If the loads vary, or there are point loads, you need to identify the approximate point of maximum deflection and then develop a function expressing M in terms of x from the left end. Then integrate once to get an expression for the gradient dy/dx

Hi, I have RA= 30 KN POINTING UP.
RB= 50 KN POINTING UP
80KN pointing down, 5m long, overall length 8m

Hi shortshanks, you have a simply supported beam with one point force acting down near the middle. If you imagine the beam in your mind, you should easily be able to see the point where the highest deflection occurs.

If you want to work out what the deflection is at this point, you will need some geometric and material properties of this beam. (modulus of elasticity and second moment of inertia)

if you want a calculator to work out the deflection, I've made one for http://learntoengineer.com/beam" [Broken]

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If EI is constant, you don't need the values in order to work out the position of the maximum deflection. Shortshanks, you need the equation of the bending moment in the portion of the beam where the maximum deflection is thought to be. Integrate once, think about the boundary conditions to get the arbitrary constant, find the point of zero gradient. That is the point you want. For the purpose of this exercise you can let EI be 1.