Where did this equation come from? Bent sheet metal Z
Where did this equation come from? Bent sheet metal Z
(OP)
The part in question is a piece of sheet metal bent into a Z with two 90 degree angles. The top part is against a vertical wall and is attached via bolts, the it sticks out from the wall and then bends downward at 90 degrees with a mass hanging off of it.
Someone sent me an analysis of the part with an equation and no explanation where the equation came from and was wondering if anyone would have any idea.
Svm=P/A + 6M/bt2
Svm is the maximum stress
P is the force from the mass hanging off the Z bend
A is the cross sectional area
M is the moment created by the mass
b is the width of the Z bend
t is the thickness of the sheet metal
Also does anyone know of a good reference for bent sheet metal analysis?
Someone sent me an analysis of the part with an equation and no explanation where the equation came from and was wondering if anyone would have any idea.
Svm=P/A + 6M/bt2
Svm is the maximum stress
P is the force from the mass hanging off the Z bend
A is the cross sectional area
M is the moment created by the mass
b is the width of the Z bend
t is the thickness of the sheet metal
Also does anyone know of a good reference for bent sheet metal analysis?





RE: Where did this equation come from? Bent sheet metal Z
The first term is simple direct stress, the second term is stress due to bending. Since bending stresses produce both tensile and compressive stresses, somewhere in the Z part there is a direct tension stress being added to a flexural tension stress (and maybe a corresponding pair of compressive stresses). The analyst that provided you the equation is using a short-hand form that has already been worked out from first principles.
STF
RE: Where did this equation come from? Bent sheet metal Z
You are not a student are you? Anyhow, most strength of materials books will provide you with the required background, but try any book on aircraft structures (Bruhn, Peery (1950), etc.
Andries
RE: Where did this equation come from? Bent sheet metal Z
I'd look at the vertical (loaded) web in shear, and the angles as caps loaded by a couple, and pay particular attention to how it's attached to the support.
First, draw a free body.
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RE: Where did this equation come from? Bent sheet metal Z
I realized this morning what I was looking at was actually the equation for bending in a straight member. I was so use to seeing the S = Mc/I that the 6M/bt2 went right over my head.
Anyway what he was doing was trying to show a finite element model was valid for the maximum stress in the bend by using a straight member equation. Problem really was his FEA model showed less stress than the straight member hand calculation did.
The equation that he used would have been ok if he had used a correction factor for a bent member. Not sure what is wrong with his FEA model yet, that one is for him to figure out.
RE: Where did this equation come from? Bent sheet metal Z
and why have a P/A axial component ? the loading is transverse (ie down on a horizontal beam).
did he draw a free body ?
can you add a sketch of the beam and load, just as we're on the same page ?
I suspect that the flanges of the Zed are not attached to "the rest of the world", that there are some fasteners in the web that react the applied load. so at the base of the beam the flanges are ineffective. it actually makes for an interesting and complicated detailed analysis (as the flange load develops over the length of the beam, and then "shear lags" into the web, into the base fasteners. shear buckling of the web is something that should be checked (or show the shear stresses to be small).
another day in paradise, or is paradise one day closer ?
RE: Where did this equation come from? Bent sheet metal Z
RE: Where did this equation come from? Bent sheet metal Z
if so, then this is much more complicated than first thought. it's easy to easy the loaded leg acting in bending (6M/bt^2) but how does this load get across the web to the other leg which wants to react it ? what would happen is a lot of torsion ... which you can see if you draw a free body diagram. this is something not considered in your equation.
another day in paradise, or is paradise one day closer ?
RE: Where did this equation come from? Bent sheet metal Z
Based on the calculation (which is not uncommon for combined stresses of a lug for example that sees transverse and axial loading), the critical section must be a section that experiences both axial or tension load, as well as a pure bending load and in a lot of real world situations also a shear load. The axial and bending parts must be added for the Rt, and the shear stress for Rs.
In this case however, if a section on the flat portions is considered, then the loading is pure bending. The axial stress is purely in the vertical part of the Z.
Now, since it is pure bending, cozzone plastic bending margin can be used.
In addition, he has to check the fasteners for prying effect.
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RE: Where did this equation come from? Bent sheet metal Z
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Stressing Stresslessly!