# Modeling bolt holes as stress concentrators in I beam bending

• foundry
In summary, proper modeling of a beam with a bolt hole on the top flange involves considering the symmetry of the beam and calculating the centroid for bending moment of inertia equations. The stress at the bolt hole can be calculated using the maximum moment from a free body diagram and the stress concentration factor. Depending on the location and geometry of the hole, it may have a significant effect on the beam's ability to withstand load, and proper bolt preloading may not always solve the issue. In some cases, FEA may be necessary to accurately predict the stress at the bolt hole.
foundry
curious as to the proper way to model this.

beam is symmetric so centroid is in the middle (used to calculate distance from centroid d in bending moment of inertia equation)

bending moment of inertia is

I =$\sum$(I + Ad2)
I=$\frac{1}{12}$bh
b=base
h=height
d=distance of the area's center to total centroid
A=area of section

using max moment from a FBD the stress is calculated

σ = $\frac{Md}{I}$

say a bolt hole is placed on the top flange, to me it makes sense to model it this way...

take just the top flange use stress calculated from above equation to find the compressive load P via this equation and the cross sectional area of the flange A

σ = $\frac{P}{A}$

now modeling the hole as a stress concentrator

σaverage = $\frac{P}{(w-2r)t}$

w = width of flange
r = radius of hole
t = thickness of flange

calculate $\frac{r}{w}$ in order to find a value for K (tabled value)

σmax = K σaverage

like I said this makes sense to be but when I run through a sample calculation a beam originally having a factor of safety of 2 ends up not being able to withstand the load just by introducing a bolt hole. thanks for your time.

I take it with the proper bolt preloading, these holes aren't an issue? Is that a correct assumption?

Their effect on the beam will depend largely on the geometry and their location on the flange. It could be as long as the holes are far from an edge that you can just consider them to be located in a plate in tension, in which case there are well-documented stress concentration factors to calculate their stress rise. It will also depend on your loading conditions, but I wouldn't assume proper preload on a bolt in the hole will solve your problem.

Otherwise your best bet is FEA, but it brings its own set of limitations and challeges. Interestingly, many stress concentration factors (e.g. Peterson's Stress Concentration Factors) are calculated using parametric FEA models and curve fits to their outputs.

## 1. What is a stress concentrator?

A stress concentrator is a region in a material where stress is significantly higher than the surrounding area. This can occur due to geometric irregularities or changes in material properties.

## 2. Why are bolt holes considered stress concentrators in I beam bending?

Bolt holes in I beams are considered stress concentrators because they create a sudden change in the geometry of the beam, causing stress to concentrate around the edges of the hole.

## 3. How do bolt holes affect the overall stress and strength of an I beam?

Bolt holes can significantly reduce the strength of an I beam by creating stress concentrations that can lead to cracks and failure. The overall stress of the beam is also increased due to the presence of the holes.

## 4. Can modeling bolt holes as stress concentrators help in predicting failure of I beams?

Yes, modeling bolt holes as stress concentrators can provide valuable insights into the behavior of I beams under bending stress. It can help identify potential failure points and inform design decisions to improve the strength and durability of the beam.

## 5. How can the effects of bolt holes as stress concentrators be mitigated in I beam design?

There are several ways to mitigate the effects of bolt holes as stress concentrators in I beam design. Some options include using thicker or stronger materials, increasing the distance between bolt holes, or adding reinforcements such as fillets or gussets around the holes. Finite element analysis can also be used to optimize the design and minimize stress concentrations.

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