Stress in beam

[AAllbbeerriicc]

Hi Everybody,

I'm working on a beam diagrams and stress in beam.

First question, having a constant bending moment, such as 4 point flexural model, what does it mean on the shape? There is still bending, but does that mean that the area is not changing?

Also if the load is distributed, the curvature of the beam would be different from a point load I assume?

It might be obvious for most of you but just want to clarify some doubts I am having now!

Cheers

 

[IDS]

With a 4 point load the moment is only constant between the two inner loads. Between those two points the shear force is zero, the moment is constant, so the curvature is constant. I don't know which area you are referring to.

If the load was applied as two distributed loads, rather than 4 point loads, the shear and moment over the loaded region would be different (because the shear would be changing rather than constant), but if the constant moment over the central unloaded zone was the same then the curvature would be the same.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[AAllbbeerriicc]

Thanks for your reply

SO what does it mean to have a constant curvature? There is still bending, the beam will not go flat?

 

[klaus.]

curvature and bending belong together
no curvature ==> no bending
no bending ==> no curvature



best regards
Klaus

 

[IDS]

Why would it go flat?

Apply a four point load to a ruler or some other flexible strip and see for yourself what it does.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[klaus.]

maybe you get mixed up
the bending moment is constant between the 2 load point
but constant does not mean Zero !!






best regards
Klaus

 

[AAllbbeerriicc]

So having a constant moment will necessarily induce a constant curvature?

Or a linear deflexion?

 

[JasonMcKee71]

The basic equation for the deformed shape of an elastic beam is:
EIw''=-M,
where: E the elasticity modulus
I: inertia moment
w: elastic line (deflection)
M: moment diagram

So constant moment means constant curvature and a quadratic elastic line.


Jason McKee
proud R&D Manager of
Cross Section Analysis & Design
Software for the structural design of cross sections
Moment Curvature Analysis
Interaction Diagrams
Reinforcement Design etc.

 

[AAllbbeerriicc]

But looking at the deformed shape of the beam, it looks like a U so the curvature is not constant ?

 

[IDS]

But looking at the deformed shape of the beam, it looks like a U so the curvature is not constant ?

Where did you get U shaped deflections from?

Over the region where the moment is constant the deformed shape is a circular arc, that is, it has a constant curvature.

I strongly recommend you have a look at:

https://youtu.be/khuPy_apnsE

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/