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I am analyzing a beam, that has a bend in it. Intuitively and inspecting FEA results using a linear solver, there is a stress concentration at the bend of this I-beam.

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When I was learning about stress concentrations in Shigley's, they talked about notches and holes, but not bends. Is there a factor one should apply for an x degree bend?

Any thoughts?

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  • $\begingroup$ Keep in mind the color scale. For insufficiently loaded elements the range of stress can be small, and yet the viewer is going to represent the max in a bright red, leading you to think that there's a stress concentration. While this might not be the case here, it's always a good idea to check out the values more than the colors $\endgroup$ – PavoDive Jun 24 at 16:12
  • $\begingroup$ It's a good point. The red threshold is set to 18ksi, which is the maximum allowable stress for A36 mild steel with a safety factor of 3 under non-cyclical loading. $\endgroup$ – user33108 Jun 24 at 22:30
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If the bend has passed the elastic limit ( assuming material is steel) it have caused strain hardening in that spot.

Hardening or stiffness both attracts stress and keeps residual stress.

We take advantage of this hardening when we want to break metal wires by bending and unbending them repeatedly until stress concentrated at the bend will break it.

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  • $\begingroup$ I suppose I should clarify. The part was not a straight I-beam that was later bent. Instead it was made with this bend by welding a curved web onto two flanges constructed of formed pieces of sheet metal. While there was some plastic deformation in the forming, the I-beam has mostly not gone through any yielding. My question is more related to, what stress concentrations arise from this modified geometry. Most analysis of beams pertains only to straight beams. $\endgroup$ – user33108 Jun 20 at 18:23
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    $\begingroup$ @user33108, stress concentration can be caused by many things along the process of making your beam: small missalignment of the web and flanges, welding,, forcing the parts together. There are many arcs and hangars built with non-straight beams. Geometry of the beam shouldn't per se cause stress concentration. Except at known cases such as sudden stepwise changes in web or flange dimensions or as you say notches and cuts. $\endgroup$ – kamran Jun 20 at 18:51

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