- #1

Jack. C

- 4

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## Homework Statement

Derive an equation for the deflection using Macaulay's method.

Hello all,

New member here, I come across this forum for advice regularly and have decided to register :).

I have been given a problem that is highlighted in the attached picture. I am competent in calculating beam deflections with a simple two support system, with a point load somewhere between, but in this scenario I am thrown off by the 6.5 kN.

I am undecided on where to 'cut' the beam, and more to the point, how to include the 6.5kN load into the equation.

To simplify the derivation I have substituted

R1=2.5kN

P1=11.5kN

R2=15.5kN

P2=6.5kN

a=0.4m

## Homework Equations

EI d^2y/dx^2 = M

## The Attempt at a Solution

I'm really not sure about the 6.5kN. I have searched countless resources for a similar question format to no avail.

My trouble is with with the initial set up of the question, as I feel comfortable with the integration to get y.

Attempt 1) I have attempted to take the moment 'cut' just before P2 which I come to the solution of:

M=R1x - P1<x-a> + R2<x-2a>

I have a feeling this is definitely not right..

Attempt 2) Treat the equation as a simple two support deflection, assuming the bending moment of P2 is absorbed by the reaction at R2. Taking the 'cut' just before R2:

M=R1x - p1<x-a>

Again, probably not..

Attempt 3) Reverse the beam layout as to have P2 at the left hand side. This means that both of the point loads will be included in the equation. 'Cut' just before R1:

M=-P2x + R2<x-a> - P1<x-2a>

This module is self taught so forgive me if there is something blindingly obvious that I have missed.

Am I on the right track with any of these attempts?

Thank you.