# How to analyze a bent beam: Stress concentration?

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.

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.

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?

• 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 Commented Jun 24, 2019 at 16:12
• 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. Commented Jun 24, 2019 at 22:30

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.

• 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. Commented Jun 20, 2019 at 18:23
• @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. Commented Jun 20, 2019 at 18:51
• Geometric change tends to cause stress concentrated at the changes because the properties will vary and chances of secondary stress arise.
– r13
Commented Sep 2, 2021 at 11:22

Given:

• the size of the mesh
• the difference of element sizes (large elements contacting small - apparently there is some contact definition between the two)
• the perceived ratio of stresses (there is no actual legend for the scale)
• no detailed of the analysis performed (type, element formulation loading, etc)

I would say it would be very dubious any attempt at interpreting the data.

Given the above, my suggestion is that if the actual ratio of the orange areas compared to the green ones, is within 20% to 50% I would attribute the errors on simulation artifacts. The relative error will be artificially larger if there are loads, or constraints near the stress concentration areas.

• Yes, I suspect the enormous triangular web element is loading the tiny little flange elements in an unrealistic fashion. At the very least there needs to be a transition in element density, Commented Dec 26, 2022 at 19:53