# What is Proof Load of Bolts?

I seem to be getting conflicting information. Shigley's Mechanical Engineering Design textbook states that, "proof load is the maximum load (force) that a bolt can withstand without acquiring a permanent set". Other sources online say that proof load is approximately 90% of yield strength. Based on Shigley's definition, a bolt begins to yield before reaching the yield point?

First of all, I'd like to point out that you are mixing (not without reason) the concept of proof load which is intended for bolts and the concept of proof stress and yield stress that is intended for materials.

## Yield stress vs proof stress (and others)

Typically, the stress needed to produce 0.2% of plastic deformation is considered proof stress (sometimes Proof stress is also called offset yield stress). It's important to determine the value or level of stress that can be applied before a material "yields" or changes its composition, size, or shape, when a material does not have a distinct yield point (see below comparison of mild steel with aluminium). In my opinion the reason that the 0.2% strain was used for proof stress, is that it offers a more straight forward comparison with the yield stress of hot worked and annealed steel. You can see more on that in the question.

So by definition, when a material reaches proof stress then plastic deformation has started (although very small levels of plastic deformation). So the terms of proof stress and yield stress are used respectively for materials that do not or do exhibit yield points respectively.

Despite being different, in most applications yield stress and proof stress are used interchangeably without any significant consequences.

If you wanted to be absolutely pedantic, you'd need to look at the following diagram, where proportionality and elastic limit are also defined. • Proportionality limit, is the region in the mild steel stress strain curve that $$\sigma = E \epsilon$$

• Elastic limit: between the proportionality limit and the elastic limit, the stress is not strictly proportional to E (i.e. $$\sigma \ne E\epsilon$$), AND the material does not exhibit plastic deformation.

• yield point is a very clear feature on the stress/strain curve of mild steel, and it coincides with 0.2% permanent deformation.

As you can see there is some breathing room (arguably very very small) between elastic limit and the definition of yield point (which usually sets the upper yield stress). However, again the differences between proportionality/elastic/lower yield/upper yield stress are so small, that they basically collectively merge in the consciousness of engineers as yield stress.

From that merging, all these conflicting accounts for proof stress and yield stress emerge.

Now, coming onto Proof load for bolts. Bolts are a structural element. As such they can be made from different materials and/or different treatments. So you could have bolts from a how worked steel with a clear yield point, but you could also have a bolt from titanium (or a cold worked steel) which does not have a yield point, so proof stress is more appropriate.

The most general approach is to use the proof stress and thus proof load.

Regarding Shigley's statement that "proof load is the maximum load (force) that a bolt can withstand without acquiring a permanent set", my interpretation is that its extending the simplified version of the concept of proof stress (and yield stress) to bolts. To clarify it further, by simplified version, I mean that proof (and yield) stress are the stress at which there is no (in the sense that 0.2% is very very small) plastic deformation on material.

To put this into perspective, an 80mm bolt, assuming its stresses along its entire length would need to deform about 0.160mm.

Proof load is the maximum load the bolt can carry without exceeding deformation criteria. Below are quotes from two sources:

1. Proof load is an amount of force that a fastener must be able to withstand without permanently deforming.

2. Proof load is defined as the maximum tensile force that can be applied to a bolt that will not result in plastic deformation. A material must remain in its elastic region when loaded up to its proof load typically between 85-95% of the yield strength. Acceptable clamp load is typically 75% of proof load.