Finding yield strength with a load/displacement curve

[Ferdiss]

Hi! I have done a simulation where I got out the load/displacement curve of a steel beam that is simply supported with an equally distributed load across the whole length (10 m). I want to field the point at which the steel yields. I am used to use the 0,2% value on a stress/strain curve, but how do I do it at a load/displacement curve? I have the units N on y-axis and m on x-axis.

Is it correct to say that strain is displacement(in z-direction, in the lateral direction of the beam) / l0(10 meters) ? Even though the displacement is in 'another direction' than the beam length?

So strain = 0,002 * 10 meters = 0,02 m?

Thank you!

 

[Lnewqban]

Welcome, @Ferdiss !

Sorry, I can't understand your description of the task at hand.
Do you have any specification of material and type of that beam?

 

[Ferdiss]

Hi, it is a steel beam S355. A simply supported beam with a uniformly distributed load :)

 

[Lnewqban]

Please, see:
https://mathalino.com/reviewer/mech...tion-to-problem-606-double-integration-method

https://mathalino.com/reviewer/mechanics-and-strength-of-materials/chapter-6-beam-deflections

 

[deajohn]

Hi @Ferdiss

No, you cannot compute strain that way. Unlike a bar in pure tension under axial load, this is a beam bending problem where strain is maximum at the outer fibers of the beam at the beam center location. If you have a plot of load vs displacement z, you can get the 0.002 z yield by drawing ne parallel from .002 z to the linear portion of curve and find the yield load and hence z. load. To convert to strain you need to compute z by the defection equation of the simple support beam (proportional to L^3/EI) and computes tress from the maximum moment (Mc/I) where c is rhe distance neutral axis to outer fiber. Then you compute strain using Hooke Law ( stress = E x strain) and find strain as proportional to zc/L^2 . This max strain at beam center.