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# residual stress in bent steel4

## residual stress in bent steel

(OP)
I am in process of designing a steel truss that utilizes bent steel shapes as web members.  I would anticipate that bending steel would result in residual stresses that I would need to include in my analysis.

DOES ANYONE KNOW HOW TO FIGURE THE MAGNITUDE OF THE RESIDUAL STRESS?

DO DIFFERENT BENDING PROCEDURES RESULT IN LESS RESIDUAL STRESSES?

### RE: residual stress in bent steel

If you have an accurate stress-strain curve of the actual material (not just something similar) you can ESTIMATE the residual stress by computing the strain, though keep in mind the non-linearity of the curve after yield.

Residual stress can be tested.  Using a special strain gage, you can determine the residual stress in a member after bending.  It is almost non-destructive in that it only requires drilling a small hole.  Not sure where you are located, but some testing labs have that capability.  Otherwise call MicroMeasurements in Raleigh, NC.

### RE: residual stress in bent steel

Why are you required to calculate the residual stress?
As already mentioned by Ron, such a calculation can't give sufficiently realistic figures, simply because the stress patterns will be very different depending on the bending (or forming?) procedure.
Moreover you will inevitably find stresses that are close to yield, if, as I understand, your process is a cold forming process: what usage do you intend to do with them?
If you are assessing the strength of a structure, then you shouldn't worry about residual stress, unless you are in a high fatigue environment.

prex

http://www.xcalcs.com
Online tools for structural design

### RE: residual stress in bent steel

(OP)
Thanks Ron, Thanks Prex,

The bent truss member cannot be tested until it is bent, which is hopefully going to happen after the design.  I was hoping I could somehow estimate the residual stress level and take that in consideration when evaluating the stress level under gravity and wind loads.  The stress level of the bent HSS8x6x3/8 is at 76 % of its allowable stress level under gravity and wind loading, but not considering the impact of bending.

The stresses being close to the yield makes sense in order to have plastic deformation.  Wouldn't that mean that the remaining capacity for additional loads is essentially zero when bent by cold forming process?

The truss will support a roof for a new church, has a 60'-0" span and a 22'6" tribuarty width.  The top chord on each end of the truss pitches at 6:12 over a 15'-0" length.  The center 30'-0" section of the truss has a flat topchord that is approzimately 6'-0" from the bottom chord.  The webing of the center 30'-0" section consists of a single arch member with the crown of the arch pointing upward.  The project, has am I, are located in Asheville/ North Carolina.

### RE: residual stress in bent steel

Residual stresses from bending are normally not included in the design of structures.  Classic example would be tank or pressure vessel design, where all members are formed to a curved shape, then loaded in hoop tension.

You can assume a simplified stress-strain curve (IE, linear up to yield point, constant stress after that) and calculate the residual stresses.  It gets messy pretty quick.  In a bent plate, the residual stress level varies depending on the radius.  As the radius becomes smaller, the plate acts more like a plastic hinge, with yielding across the full face.

Don't give this too much thought or you'll start wondering if beams come out of the mill with residual stresses, and what should be done with them.

### RE: residual stress in bent steel

The theoretical stress/strain curve is straight up to the yeild point at a slope equal to Young's Modulus. After that yeild occurs and you get infinite strain for no increase in stress.
If you remove the load (stress) you have material which is plastically deformed (strain) but has the same material properties as the original material.
Put simply, residual stresses do not exist within the theoretical model. Member design is conducted on the portion of the stress/strain curve which is elastic.

NOW - bending a section does mean that the internal forces have to act around the curve. This generates forces at 90 degrees to the section and these do have to be considered. Their magnitude depends on the survature of the section and on the applied forces

### RE: residual stress in bent steel

(OP)
pba:  Thanks for the info.  Do you know of any guidelines on how to figure the internal forces?

### RE: residual stress in bent steel

Residual stresses are present in nearly all steel shapes and are primarily the result of uneven cooling due to the hot-rolled forming process or welding. Several good sources on this are Salmon and Johnson's "Steel structures, design and behavior", "Guide to stability Design Criteria for metal structures", and "Welding Handbook" These residual stresses are the reason for the non linear portion of the average stress-strain curve (this is explained in Salmon and Johnson's book) They also have a guide for developing column strength curves that incorporate the residual stresses. I haven't done this in the paste as I normally just follow the equations in the green book, but feel free to go for it.

JRC

### RE: residual stress in bent steel

I'm sure there will be good book or paper on the method of calculating the out of plane forces which is relevant to your code.
I work in the UK and our book for this is produced by the Steel Construction Institute and is Publication P281 ' Design of Curved Steel'.

The UK company which specialises in curved steel is 'Angle Ring' they have been a great help in the past with the technical aspects of the design. Is there a similar company in the USA? (I'm assuming you work in the USA).

### RE: residual stress in bent steel

I'm really confused by this string of comments.  Shouldn't cold-formed bent shapes have no residual stresses?  They have experienced stresses to achieve the bent shape, however once the steel material becomes "plastic", the load to bend the shape is released and there are no longer any stresses imposed on the steel.  Also, as long as the steel has not experienced any "strain hardening" during the bending process, the bent portion of the steel, when loaded again, will have the same yield stress as the unbent steel. (If it has experienced strain hardening, then the yield stress will be higher.)  regardless, design requirements keep materials within some percent less than the yield stress.  I agree with 3dboy.

### RE: residual stress in bent steel

Okay, let's say you start bending the part.  The material near the surfaces yields.  At some point closer to the neutral axis, the material never yields, but is stressed elastically.  So a stress diagram across the surface would show yield stress in compression on one side, yield stress in tension on the other side, and a linear transition between these two points, with zero stress at the neutral axis.  As you bend the material more, the depth of the fully-yield area increases.

The material at the surface is stressed to the yield point, and at that point, continues to be stressed to the yield point as the material is bent more.  (Based on the simplified stress-strain curve mentioned above).

When you stop bending the material, it moves back the other way ("springback").  It has a permanent strain near the surfaces.  As it comes to equilibrium, the surface that was stretched in tension will have compressive elastic stresses in it, and vice versa at the far side.  The interior of the piece was stretched in tension will now be balanced by the outer surface in compression (and vice versa at the other face).  So yes, you do have residual stresses.  But as I mentioned above, these are not normally taken into account in the design.

Of course, any type of welding or cutting on the member will induce internal stresses in it, and these are not normally considered, either.

### RE: residual stress in bent steel

In cold bending, the material is deformed through the yield point into the plastic range and becomes work hardened, where the material displays different yield properties.  The increase in strength can even be an advantage.

Within the elastic range the load-bearing properties of the material are effectivelty unchanged, although there will be some loss in ductility.

For normal strength steels the changes are not sufficient to require stress relieving.

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