Margin of safety for combined loads 1

[franc11]

Here's a question that's been bothering me for some time.

I have a rectangular section in the XY plane. For this section, I have an out of plane tension force, I have one shear force along Y axis, one shear force along Y axis, plus a bending moment around X axis and a bending moment around Y axis.

I need to find the margin of safety for that structure. Normally, I would take the stress ratio for the tension force, then adding the two stress caused by the moment, I would find the stress ratio for bending, then, taking the root square of the summation of the squares of the shear forces, I would calculate de stress ratio. That said, I would have three stress ratio : One for tension (Rt), one for shear(Rs) and one for bending (Rb).

How can I combined those ratios to get a margin of safety? In Bruhn, somewhere, there's a formula giving : MS = (1/((Ra+Rb)^2+Rs^2))-1, but they seem to say that it's only availabe if your axial force is compression and not tension.

Do you guys know if there's another formula for this? Do you think my method is valid to get a margin of safety?

Thank you very much!

 

[civilperson]

Least margin of safety is the applicable number. No combining or averaging should be attempted. Combined stresses may be compared to allowable stress.

 

[rb1957]

i'd apply that formulae for tension or compression axial loads, but that being said i don't think i'd combine the shear forces together, but apply them separately (as their distributions on a rectangular prizzmatic section are quite different.

that being said, you could always calculate the stresses at 8 places on your section (the corners and the mid-sides) and combine your axial stresses (due to axial load and bending) and your shear stresses using your failure criteria of choice (principal stress, von Mises, etc) and compare to the material allowables.

good luck

 

[swearingen]

I second rb1957's suggestion - this looks like it is a principal or von Mises stress failure criteria candidate as long as your material properties are isotropic.

 

[franc11]

It seems fair to me. That's what I've had done. I used Von Mises 3D and compared it to Ftu on 15 points on my section. At some points, it showed that my structure would fail, especially because of the bending. i'm now considering plastic bending to give me better margins. But is there a way to usde Von Mises and taking into account plastic bending at the same time?

in the same order of idea, is there a reason why the interaction formula for a tube and a rectangular section is different. I have for a rectangular section MS = 1/(SQRT((Ra+Rb)^2+Rs^2)-1 and for a tube : MS= 1/(RA+SQRT(Rb^2+Rs^2)) ? It's becoming confusing how to combine all those stresses.

Thanks again!