I am designing a steel plate "flag pole" structure. The plate is 2.5"x14" fixed at the base and is 16' tall. The plate will be twisted along its length to create a cork screw shape. The twisting of this plate will induce residual stresses into the plate. Should I consider these residual stresses? How do I calculate these streses and add them to the stresses due to the bending of the pole? Or, should I lower my allowable stress and how do I determine how much to lower it? Any help is appreciated.
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Residual Stress in Structural Steel Design
- Thread starter nmason78
- Start date
On how to measure residual stresses:
It seems there are also nondestructive ways of measure these by polarization at low distortion levels.
Respect the impact in structural behaviour of residual stresses, for a rehearsal of influence in compression member design see for example section 4.6 of
Design of Steel Structures, 3d. edition
Gaylord, Gaylord, Stallmeyer
McGraw Hill 1992
where the use of different axial stiffness moduluses (reduced from Young's) is examined.
For common shapes the influence of this aspect of material nonlinearity is covered by the design formulas. For particularized shapes a process such in the example in the book needs to be followed to ascertain the influence in the buckling behaviour.
It is clear that such kind of process consists mainly in following the standing stresses at the sections at every stage, so in this sense rewsidual stresses "need" to be added step by step to the bending stresses. Provided you have the initial set residual stresses (where one would expect two opposite corners in tension and the other two in compression) you might follow such kind of procedure to any limit value of the stress you may deem proper (following LRFD or ASD ways).
From the analysis viewpoint, just considering a helical shape a straight member is theoretical excess.
Practically, however, since standing compression seems to be weak only the bending stiffness reduction required to contemplate material nonlinearity as input for second order effects giving also geometrical nonlinearity may be needed to be taken unto account; for ordinary shapes given in appendix 7.3 of AISC 360-05. Ascertaining if the reduction is enough for your particular case involves measuring/estimating adequately the residual stresses and following the ways of the referred example in the quoted book.
It seems there are also nondestructive ways of measure these by polarization at low distortion levels.
Respect the impact in structural behaviour of residual stresses, for a rehearsal of influence in compression member design see for example section 4.6 of
Design of Steel Structures, 3d. edition
Gaylord, Gaylord, Stallmeyer
McGraw Hill 1992
where the use of different axial stiffness moduluses (reduced from Young's) is examined.
For common shapes the influence of this aspect of material nonlinearity is covered by the design formulas. For particularized shapes a process such in the example in the book needs to be followed to ascertain the influence in the buckling behaviour.
It is clear that such kind of process consists mainly in following the standing stresses at the sections at every stage, so in this sense rewsidual stresses "need" to be added step by step to the bending stresses. Provided you have the initial set residual stresses (where one would expect two opposite corners in tension and the other two in compression) you might follow such kind of procedure to any limit value of the stress you may deem proper (following LRFD or ASD ways).
From the analysis viewpoint, just considering a helical shape a straight member is theoretical excess.
Practically, however, since standing compression seems to be weak only the bending stiffness reduction required to contemplate material nonlinearity as input for second order effects giving also geometrical nonlinearity may be needed to be taken unto account; for ordinary shapes given in appendix 7.3 of AISC 360-05. Ascertaining if the reduction is enough for your particular case involves measuring/estimating adequately the residual stresses and following the ways of the referred example in the quoted book.
Nmason78:
The residual stress will be the yield stress in shear. You get the final shape by twisting the bar sufficiently to yield it, and their will be some spring back, if the exact number of twists is critical. This will probably be done, or certainly could be done, on a heated bar to facilitate the twisting with minimal effort. In which case I would immediately go back to the furnace and stress relieve the bar, you’re already half way there, except for furnace and cooling holding times. You might want to hold the bar in position while heat treating. People with hollow induction heating equip. could treat this without a furnace. And, if I could treat the bottom 6' or so, I wouldn’t worry about the rest, since from the base plate up a foot or so, or to the point of 180° twist is really going to be your design problem.
You can calc. the torsional stress, primarily a shear stress for that 2.5"x14" bar, per degree of twist. This is akin to forming a rectangular shaped coil spring. I’ll have to think a bit about shape/size effect factors. These stresses are slightly different in nature and orientation than the normal bending stresses you will be designing for, although your problem has a shear stress component too. I’d look at combined stresses at various points in the bar to find a max. Note that the critical orientation of the bar is going to be the weak axis of the bar resisting the cantilever moment, and that’s a moving target as you move up the pole. Also, recall that we treat the bending of a flat bar a bit differently than when it is on edge and bending about its strong axis. The normal bending stress on a structure like this will themselves induce a torsional stress. For all my harping against the use of FEA for every design problem, it would be quite appropriate on this problem.
There might be some advantage to working with a steel that doesn’t have a well defined yield point, or a long flat plateau; so your design problem is actually working in a stress/strain region on the curve, where increased strain does cause increased stress. That’s a tough problem, and I’ve just shot all six bullets straight from the hip. I’ll have to think about this one a little more.
The residual stress will be the yield stress in shear. You get the final shape by twisting the bar sufficiently to yield it, and their will be some spring back, if the exact number of twists is critical. This will probably be done, or certainly could be done, on a heated bar to facilitate the twisting with minimal effort. In which case I would immediately go back to the furnace and stress relieve the bar, you’re already half way there, except for furnace and cooling holding times. You might want to hold the bar in position while heat treating. People with hollow induction heating equip. could treat this without a furnace. And, if I could treat the bottom 6' or so, I wouldn’t worry about the rest, since from the base plate up a foot or so, or to the point of 180° twist is really going to be your design problem.
You can calc. the torsional stress, primarily a shear stress for that 2.5"x14" bar, per degree of twist. This is akin to forming a rectangular shaped coil spring. I’ll have to think a bit about shape/size effect factors. These stresses are slightly different in nature and orientation than the normal bending stresses you will be designing for, although your problem has a shear stress component too. I’d look at combined stresses at various points in the bar to find a max. Note that the critical orientation of the bar is going to be the weak axis of the bar resisting the cantilever moment, and that’s a moving target as you move up the pole. Also, recall that we treat the bending of a flat bar a bit differently than when it is on edge and bending about its strong axis. The normal bending stress on a structure like this will themselves induce a torsional stress. For all my harping against the use of FEA for every design problem, it would be quite appropriate on this problem.
There might be some advantage to working with a steel that doesn’t have a well defined yield point, or a long flat plateau; so your design problem is actually working in a stress/strain region on the curve, where increased strain does cause increased stress. That’s a tough problem, and I’ve just shot all six bullets straight from the hip. I’ll have to think about this one a little more.
- Thread starter
- #5
See this thread for some informative posts on residual stresses, specifically relating to those inherent in the rolled steel:
Note that in tank and vessel work, where materials are routinely formed to a radius, the residual stresses from those operations are calculable but are not addressed in the design requirements.
Note that in tank and vessel work, where materials are routinely formed to a radius, the residual stresses from those operations are calculable but are not addressed in the design requirements.
paddingtongreen
Structural
We do not reduce the allowable stress when we camber (cold bend) a beam.
Michael.
Timing has a lot to do with the outcome of a rain dance.
Michael.
Timing has a lot to do with the outcome of a rain dance.
gobsmacked
Structural
I think that once the twisting is achieved and the process of twisting is stopped, the stresses go back to zero. What changes is the length of the yield plateau. You have used some up.
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