Bent Rod Minimum Radius

[twils9]

I'm have a rod that I am trying to assess capacity for from an old design where the calculations were either lost or never done. There is an area on the design that consists of a 1-1/4" steel rod bent at a 7/8" bend radius into a full circle then it is welded back on to the rod. I am trying to find a standard or method for calculating the capacity of this eye as it is too tight of a bend but would be best to estimate as it was implemented.

I have analyzed the shear and tension resistance but feel that there would be loss of the strength of the steel in this section which I don't know how to quantify. It is also possible that this cannot be calculated without knowing the fabrication methods.

Any guidance that people may be able to provide would be helpful.

 

[Stress_Eng]

You may want to consider curved beam bending?

 

[dauwerda]

I have analyzed the shear and tension resistance but feel that there would be loss of the strength of the steel in this section which I don't know how to quantify. It is also possible that this cannot be calculated without knowing the fabrication methods.

Are you saying you think there might be a loss in strength due to the bending?
If so, no, at least not exactly.
The steel would actually have an increase in yield strength due to cold working (strain hardening), but this comes at the cost of a loss of ductility and toughness.

The bending process could also introduce cracking in the steel, this obviously would cause strength (and fatigue) issues.

If hot bent, the small radius might be just fine, meaning cracking and loss of ductility is less of a concern.

 

[Stress_Eng]

The comment was based on the fact that any +ve bending (tensile stress) seen at the smaller inner radius will effectively see a geometry based kt influence at the inner radius arising from the nonlinear stress / strain distribution. It would be interesting to see a comparison of the ultimate bending moment allowable (moment of rupture) for a straight rod compared to a curved rod, for the same cross section and material condition.

 

[Stress_Eng]

Just out of curiosity, using Roark's formulas 7th edition (Table 9.1, Case 6 - Solid circular or elliptical section), and the dimensions given, under a bending moment you'll see a stress intensity at the inner radius of 1.458 x a unit stress calculated by an ordinary flexure formula. As long as your rod can take this stress level (in addition to your shear and tension loading), and depending upon your failure criteria, then it's just another one of those many calc'n checks to add to the never ending list!

 

[HTURKAK]

It is also possible that this cannot be calculated without knowing the fabrication methods.

Apparently this is 'HOT BEND ' . The strain even for mild ductile steel is less than 0.2. In this case , A simple calculation predicts that , the strain would be in the range of 0.4 . ( Almost double the max strain ). and tension cracks will develop for this dia and bending radius.

I would assume hot worked circular eye and follow the formulas at any strength of material handbook or ROARK's formulas.

PS. The strain could be 0.4 at fracture for stainless steel . I think the material is not SS.

 

[twils9]

Thank you for the ideas. I will have to look more into Roark's formulas for this.
Based on my initial analysis the tension and shear are adequate using structural steel design clauses/formulas. The force on the rod is pulling in pure tension (shear at the center of the circular eye) so there shouldn't be any external bending forces.

Just out of curiosity, using Roark's formulas 7th edition (Table 9.1, Case 6 - Solid circular or elliptical section), and the dimensions given, under a bending moment you'll see a stress intensity at the inner radius of 1.458 x a unit stress calculated by an ordinary flexure formula. As long as your rod can take this stress level (in addition to your shear and tension loading), and depending upon your failure criteria, then it's just another one of those many calc'n checks to add to the never ending list!

Would this be an amplification of external bending being applied to the circular eye? Or would you think that this would have an effect on the tensile and shear resistances?

Apparently this is 'HOT BEND ' . The strain even for mild ductile steel is less than 0.2. In this case , A simple calculation predicts that , the strain would be in the range of 0.4 . ( Almost double the max strain ). and tension cracks will develop for this dia and bending radius.

I would assume hot worked circular eye and follow the formulas at any strength of material handbook or ROARK's formulas.

PS. The strain could be 0.4 at fracture for stainless steel . I think the material is not SS.

It is galvanized 44W steel. Would you expect tension crack of this magnitude to be visible by eye? Or would they remain microscopic? In practice the rods do not show any visible cracks.

 

[Stress_Eng]

Although this diagram is for a lug with a rectangular cross section, it may help to understand the loading.

When theta is at 90 degrees, the section will see tension, bending and shear. The thing is, the stress distribution through a curved section is nonlinear, peaking at the inner radius. The diagram below is a typical stress distribution through the lug wall, due to bending and tension, the peak at the inner radius. The stress distribution is at a theta angle of appox. 90 degrees. The blue line is the average stress level based on the applied tension load from the pin. As you can see, the kt is quite high! At the end of the day, depending on your failure criteria, you're going to have high stress levels. What is your allowable stress? Under ultimate static loading, are you permitting permanent plastic deformation? What about fatigue, low or high fatigue cycles? Having this sort of stress distribution, the onset of plasticity will be earlier. There's a lot to consider.

 

[mfgenggear]

Op
Does budget allow for a heet treatable steel.
Bend and weld on the annealed condition.
Then heat treat to the required tensile u & y .

 

[EdStainless]

Being galvanized adds some complications.
I would hope that these were welded, then galvanized, and baked.

 

[HTURKAK]

It is galvanized 44W steel. Would you expect tension crack of this magnitude to be visible by eye? Or would they remain microscopic? In practice the rods do not show any visible cracks.

Yes .. visible. Moreover, compression cripplings will develop along the inner perimeter. You can try and see with making a test . It should not be a big issue to bend 1-1/4" steel rod 180 degr with bending radius 7/8" .