Equivalent beams

[mechy20]

Hi all,
I have a basic question from strength of materials.

If I have a beam whose cross section is a trapezium, how would I get an equivalent beam whose csa is a rectangle?

Would the two beams be equated for max. stress, or just moment of inertia ?

Thanks

 

[rb1957]

"equivalent" means so many things ...

equal maximum stress in bending ?
(remember the neutral axis isn't in the middle of the trapezoid section) ... this would be equal section modulus (I/c)

equal csa ? (this is too easy)

 

[mechy20]

Thanks for your response.

I am just trying to approximate the trapezoidal beam with a rectangular beam while not changing its critical functional properties.

Like for instance I know it is not equal csa.

If you had a trapezoidal beam whose main application was achieved by bending, then how would you replace it with a rectangular beam which would still do the same job? That looks like equal max. stress in bending to me.

Thanks again...

 

[rb1957]

that'd be good enough ... depending on your constraints (need to maintain the same beam depth) you could come up with an optium (minium csa) solution

 

[jte]

mechy-

Ok, so its main function is handling some load by bending. But are you stress limited or deflection limited? If stress limited, match the section modulus to get the same result; if its deflection limited, match the moment of inertia.

jt

 

[JStephen]

What exactly are you doing?

If you have some sort of program that accepts rectangular beam cross sections, but not odd shapes- then calculate a rectangle that has equivalent area and moment of inertia. And realize in this case, the moments and forces would work out right, but you would need to calculate the stresses by hand. And this wouldn't necessarily make the weak-axis properties work out right, either.

Also in this case, check if you can just make a custom shape with section properties directly entered, rather than using the rectangle.