How do I model an Indeterminately Loaded Beam using theory?

  • Thread starter Thread starter bakoo
  • Start date Start date
  • Tags Tags
    Beam
AI Thread Summary
The discussion focuses on modeling an indeterminately loaded beam, specifically a fixed end beam subjected to loads at 25% and 75% of its length. The user seeks theoretical modeling techniques to understand deflection and stress calculations. Key methods mentioned include using superposition principles for multiple loads and solving simultaneous equations to determine unknown reactions at the supports. The user is particularly interested in how to apply the fixed end theorem to achieve accurate results. Overall, the conversation emphasizes the importance of theoretical understanding in practical beam loading scenarios.
bakoo
Messages
19
Reaction score
0
Hey

This may seem like a homework question, but its actually extending my knowledge...

I attended a lab, and it was for beam bending, here is the setup...

Beam of length was clamped at either end, think this is called "Indeterminately Loaded Beam"? Two loads are then applied to it, one at 25% of the way, and one at 75% of the way.

The delfection was measured, and using a quarter bridge strain gauge the strain was took.

Here is my problem, i want to know how to model this with theory, but i can't seem to figure out how to do it?

This is just to expand my understanding of loading, rather than any homework, but if it comes up in the future I want to know how to do my calculations.

Thanks for any help or light you can shed on this for me.
 
Last edited:
Engineering news on Phys.org
Can you clarify how it is clamped. Is it supported on both ends or is set up as a cantilever? If it is set up in cantilever configuration use this equation to model it.

deflection = Load/(6 * Modulus of Elasticity * Moment of Inertia) * (2 * l^3 - 3 * l^2*x + x^3)

l = length of beam from clamping point to end
x = distance from end that load is placed

For multiple loads you could use superposition principles to figure out the total deflection.
 
Its clamped on both ends

/|...L1...L2...|\
/|____V______V_____|\
/|......|\

The V is where the L load is applied... For clarification __v_____v___ is the beam and |\ is the wall/clamp/fixing as in a cantilever beam. The ..... are just to format, so ignor

Strain gauage is possitioned between L1 and the wall/clamp

Thanks
 
It should still work with superposition. In calculating the stress you would figure out three simultaneous equations for the beam, by breaking loose all the redundant fixtures, until the beam is determinate and replacing them with unknown reactions.

This beam set up is the same as a cantilever with a moment and an upward force acting to the free end.

You solve for the unknown reactions (moment and upward force) in the simultaneous equations. Now that you have solved for the unknown reactions plug them back into the free body diagram and solve for the internal beam stresses.

The part I am not to sure about is how to account for the fixed end theorem for both ends of the beam to get actual results instead of theoretical.

Hope that helps
 
Hey

i will use superpossition to try and solve this, i have the real results so if the theory is close they i will know i have it right.

Thanks again for the advice
 
I have found the name of the beam configuration.

Its related to as a "Fixed end beam" and i think you apply superpossition to it from simply supported and cantilever, but still working on this to find how its done?
 
Thread 'I need a concave mirror with a focal length length of 150 feet'
I need to cut down a 3 year old dead tree from top down so tree causes no damage with small pieces falling. I need a mirror with a focal length of 150 ft. 12" diameter to 36" diameter will work good but I can't think of any easy way to build it. Nothing like this for sale on Ebay. I have a 30" Fresnel lens that I use to burn stumps it works great. Tree service wants $2000.
Hi all, i have some questions about the tesla turbine: is a tesla turbine more efficient than a steam engine or a stirling engine ? about the discs of the tesla turbine warping because of the high speed rotations; does running the engine on a lower speed solve that or will the discs warp anyway after time ? what is the difference in efficiency between the tesla turbine running at high speed and running it at a lower speed ( as fast as possible but low enough to not warp de discs) and: i...
Back
Top