Problem with exercise - Indeterminate Structure

[Chicca96]

Hello,
I hope there is someone who can help me with the problem I am trying to solve. I have a structure composed of a beam, located at the centre and connected to two plates. Each plate is supported by a torsional spring. Since the stiffness of the plate is higher than the one of the beam, the plate can be considered as a rigid body. When the plates are loaded with a force "Fe", they rotate downwards due to the torsional springs.

The spring constants and all geometrical parameters are known. In particular:

a= distance between the point of application of the force and the torsional spring;
b= plate length;
c= beam length;

Since the structure is hyperstatic, I have tried to solve using the method of superposition. The redundant reaction forces are the moment at the torsional springs.

The "primary" associated isostatic structure is:

where the rotation (computed using the known solutions for beams) is:

Then, I computed the rotation due to the moment of torsional springs:

For the torsional spring:

I compute the moment M from the compatibility equation:

If the moment M is known, solve the structure is easy.

I do not know if this procedure is correct or if I am doing something wrong. Thank you for your time and help.

Kindest,
Chi

 

[GregLocock]

The problem description seems rather lacking. Draw an FBD for just one of the plates, and the beam.


Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

http://eng-tips.com/market.cfm?

 

[BAretired]

If the supports are pinned, and the torsional springs are removed, the problem boils down to a three-link chain. Each link is stressed in tension. Only the plates are stressed in bending.

The tension in the beam is M/s where s is the sag at midspan. M = F[sub]e[/sub]*a and s is a function of the axial strain in each link of the chain.

When the plates are said to be "rigid", it may be concluded that the bending of the plate may be neglected. Does it also mean the axial strain of the plate can be neglected? What about the axial strain of the beam? The only stress felt by the beam is axial, as it has a moment of zero. EI of the beam has no bearing on the solution, only A (area).

When torsional springs are added to the problem, EI of the beam still has no bearing on the problem because there will be no bending in the beam. So your solution, which includes the value EI cannot be correct.

Edit: The solution can be found by equating internal and external work. Internal work is the work done by the rotational springs plus the axial strain in the plates and beam. External work is the force times travel distance of the applied loads.

BA

 

[BAretired]

It is customary for the OP to respond to those who have taken the trouble to respond to the question. Failing to do so is just plain rude.

BA

 

[Chicca96]

Dear BAretired,
thank you a lot for your answer. I am so sorry for being rude. It was not my intention, I don’t check the forum often. I am so sorry for that.

Your edit helped me a lot. I think this is the correct way to proceed.

Thank you again for your time and help.

Chi

 

[BAretired]

Dear Chicca96,
Thank you for your response today. I'm pleased to hear that I was of some help.

BA