Loaded Beams

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  • #1
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Homework Statement


I need to plot a graph showing the deflection of the beam across its length giving a value of x at every 1m.
The youngs modulus for the beam is 210 GNm^-2 and the moment of inertia is 54 X 10^-7 m^4

Homework Equations


Really unsure where to start on this one.

I have found the equation M/IE= (d^2 y)/(dx^2) but I am unsure where to go from here


The Attempt at a Solution

 

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  • #3
SteamKing
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Homework Statement


I need to plot a graph showing the deflection of the beam across its length giving a value of x at every 1m.
The youngs modulus for the beam is 210 GNm^-2 and the moment of inertia is 54 X 10^-7 m^4

Homework Equations


Really unsure where to start on this one.

I have found the equation M/IE= (d^2 y)/(dx^2) but I am unsure where to go from here


The Attempt at a Solution

Do you know how to calculate M for the beam with the given loading?
 
  • #4
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I have calculated the bending moments at 1m intervals but I am not sure about calculating the internal moment?
 
  • #5
SteamKing
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I have calculated the bending moments at 1m intervals but I am not sure about calculating the internal moment?
It's not clear what you mean by 'internal moment'. The M which determines the deflection of the beam is the bending moment.
 
  • #6
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In that case, to answer your question, yes i know how to calculate the bending moment(s) of the beam.
 
  • #7
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SteamKing, can you please advise where I need to progress to from this?
 
  • #8
haruspex
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SteamKing, can you please advise where I need to progress to from this?
You are asked to plot a graph. Does mean you are expected to do this numerically, rather than by solving a differential equation? I'll assume so.

Starting at the point of support (x=0), you have zero deflection and zero gradient.
You can use the equations you have to find the bending moment there, and hence find (d^2 y)/(dx^2).
If you now step out a distance dx along the beam, what would you estimate y and dy/dx to be there?
 
  • #9
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I have now found the solution. Thanks for the help.
 

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