FK123 said:
i have made a beam with both ends fixed. when I apply load at center then the ultimate load will be 8Mp/L=8fyz/L which came to be 440KN
My question is how to calculate the load at which beam starts yielding?
I have used E=200000N/mm2 and initial yield strength=220N/mm2
We'll need a lot more information than you've given us to figure out what you've done.
First, tell us the length of the beam.
Second, tell us what you mean when you write "8Mp/L=8fyz/L". About all I can guess is that L = length of the beam. Everything else, who knows?
For a fixed-fixed beam with a central load P, the max. bending moment is M
MAX = PL / 8, which occurs at the ends of the beam and in the center.
While the bending stress remains below the yield stress, then the bending stress σ is calculated by
σ = M y / I,
where M = bending moment,
y = distance from the neutral axis of the beam
I = second moment of area of the beam cross section.
shear stress τ is calculated by
τ = VQ / (I * t)
where V = shear force,
I = second moment of area of the beam cross section (same value used above)
Q = first moment of area
t = span of the cross section in way of the shear stress location.
As you can see, you need to know something about the beam cross section in order to calculate the stresses created when the beam is loaded.
Because of the nature in which a fixed-fixed beam is supported, there will be additional shear stresses created at the locations where the maximum bending moment occurs, so these shear stresses must be calculated and combined with the bending stress to give the proper stress value at those locations, so that one can determine the load at which yielding of the material in the beam occurs.
Once the stress in the outer fibers of beam exceeds the yield stress of the material, the formula above no longer applies and a plastic analysis must be performed.