# Why exactly does a washer help distribute the stress around a bolt?

Usually the reason for having a washer under a bolt head is stated to be that it helps to evenly distribute the stress to the clamped material surface. But why is this?

I would understand if the washer was significantly larger than the bolt head. Then there would understandably be more surface area. But for a bolt like in the picture, the washer is only slightly larger than the bolt head, so why would it make much difference?

EDIT: Thank you everyone for good discussion and answers! Didn't expect this to spark such a discussion.

• What do you consider "significantly larger"? A circle circumscribed around a hexagon (a washer the exact same size as the bolt head) has 21% more surface area than the hexagon, and it only goes up from there. A washer with a radius just 28% larger than the bolt head has fully twice as much surface area. Jun 16 '21 at 14:52
• @NuclearHoagie You have a point, but don't forget to subtract the bolt's own cross-sectional area from the bolt head's area, and the washer's hole from the washer's.
– Kaz
Jun 17 '21 at 14:58
• @Kaz Very good point. For a washer that fits the bolt reasonably well, the surface area increase will be even larger than the figures I quoted. Jun 17 '21 at 15:17
• A 12" pizza is twice as much food as an 8" pizza. Why (do I have this question)? Because increasing the area of a circle or comparing two different ones is non-intuitive. Jun 18 '21 at 0:14
• Not an answer, just a comment: Wonderfully enlightening conversation/discussion. I'm a non-technical layman but mechanically-inclined and I found these comments fascinating!!! (HOwever, I knew intuitively about the stress reduction, as so wonderfully illustrated by Mauve Ranger's comment.) Jun 18 '21 at 19:35

I will expand on DKNguyen answer, because to my knowledge also the two reasons are:

• reduce contact/bearing stresses (having a significant effect on thin finishes live galvanisation)
• change the joint tightening characteristics (see joint diagram).

## reduce contact stresses on surfaces.

The basic idea is that since contact stress is defined as:

$$\sigma = \frac{F}{A}$$

Obviously the larger the area the less the stress. Also, like Nuclear Hoagie pointed out the area changes with a square law of the diameter.

UPDATE 2 - Calculation for M6 bolt (thanks to BenC)

*The question gathered enough interest for me to carry out a simple calculation on the M6 and M6 washer.

An M6 Bolt has the following characteristics:

figure 1: source (itafasteners.com)

• s=10 mm (See image above)
• diameter d = 6 mm
• M6 Hole Clearance $$d_{M6,clear} = 6.6 mm$$ (this is the typical diameter of a hole that will fit an M6).

The entire area of the bolt head (calculated as a hexagon area) is $$86.6 mm^2$$, but because of the clearance the effectively available area is about 52.4 $$mm^2$$.

On the other had the M6 washer has:

• $$d_{in}$$ = 6.4 mm (inner diameter)
• $$d_{out}$$ = 12 mm (outer diameter)

Therefore its effective contact area (on the side of the material) would be calculated as $$A_{washer} = \frac\pi 4 (d_{out}^2- d_{M6,clear}^2)= \frac\pi 4 (12^2- 6.6^2)= 78.8 mm^2$$

So effectively the area with the washer is about 1.5 times greater than the area without the washer. Therefore, the contact stresses between the clamped material and the washer will be 1.5 times less that the clamped material and only the bolt.

Although with steel itself there is usually not much worry, the main problem with increased stresses on coatings of the material.

An interesting example I came across once: the forces on lap joint with a fastener were so great that the bearing stress of the zinc in the coating was exceeded. The result was that the coating would basically be removed. In the particular application the long term was that the anti-corrosion protection was removed.

Using wide washers solved the problem.

An additional benefit (related to the reduction of stresses) is that the washer is a replaceable item. So while tightening might damage the surface of the bolt and the clamp, the use of a washer might damage the contact surface between the bolt and the washer, but at the end of the day they can both be replaced.

## Changing the tightening characteristics.

(this part is a bit more involved and I would suggest anyone interested to read more in a textbook like Shigley if they are interested).

The washer indeed changes the characteristics of a joint. The reason is that the affected area between the nut and the bolt head is not a cylinder but has a frustum/barrel like shape.

Figure 1: Realistic parabolic stress distribution in a preloaded bolted connection (left) and simplified linear stress distribution following VDI 2230 (source:sciencedirect )

When a washer is used the affected diameter will also change correspondingly (i.e. with the washer the diameter increases and so does the overall volume). So the forces are spread over more of the clamped material. The end effect is that the clamped materials appear to be stiffer (in a similar sense that cutting through butter with knife with the edge or the broad side).

The end result, can be better seen in the joint diagram. (A joint diagram is a means of displaying the load deflection characteristics of the bolt and the material that it clamps. Joint diagrams can be used to assist in visualising how a bolted joint sustains an external force and why the bolt does not sustain the whole of this force.)

Figure 2: Joint diagram comparison without and with washer

With the washer the maximum available preload of the joint increases (for the same number of thread turns).

Why does changing the tightening characteristics reduce stress: (it might not be so obvious) When you use a washer, in the above example essentially what happens is that more of the clamped material engages in the transfer of forces. As a result, the clamped material becomes stiffer than the bolt (hence the change in slope in the diagram above). For a given level of preload force, because more clamped material is engaged (larger crosssection) there are less stresses within the material (the bolt stresses remain the same).

• Does the fact that the washer doesn't have corner have an effect? Jun 18 '21 at 16:13
• If you are wondering about stress concentrations on the edges of the bolt, then IMHO there is not much point to consider (while they are present their effect ought to be limited). The reason is that the angle at each corner of the hexagon is 120 degrees, and there is always the other edge (along the contact surface between the bolt and the clamped material) that is at a 90 degrees angle (that edge is common to both the hexagon and the washer). Jun 18 '21 at 17:46
• Wouldn't you have to use the same 6.6 mm hole clearance as the effective inner diameter of the washer instead of the washers actual 6.4 mm inner diameter when calculating the effective contact area? Thus reducing the contact area somewhat. Jun 18 '21 at 19:56
• @glenyates that's what I did. Is my calculation wrong? Jun 18 '21 at 22:00
• I think the area of the hexagon should be doubled... Area = 6 * area of equilateral triangle = 6 * (1/2 * base * height) = 6 * (1/2 * (10/2) * ((10/2) * (2/sqrt(3)))) = 50 * sqrt(3) = 86.6. Jun 19 '21 at 11:52

It is for spreading out the stress.

But it is also for giving the bolt a bearing surface to turn on. The washer always goes on the side (nut or bolt) that is being turned. It prevents it from marring up the work surface and also changes the tightening characteristics. I don't know the specifics of that though but that's what I was told by a toolmaker. Always use a washer he says (except counter sunk holes...scratches head)

Which objective has higher priority, I do not know but I rarely, if ever, have seen a washer on both sides of the workpiece which might indicate that the bearing surface has greater priority than spreading out the stress. After all, washers are still used on huge blocks of steel which should be able to handle the concentrated stress just fine.

• Re, "except counter sunk holes." The screw head that fits in a countersunk hole doesn't have any corners (e.g., like the corners on a hex head) that stick out, or could mark the surface in any place that will be exposed to view when the screw is turned. Also, the washer that you put under a hex head protects the surface from contact with the tool that you use to drive it. But, the tool that you use to drive a countersunk screw should not ever come close to touching the surface. Jun 17 '21 at 15:33
• @SolomonSlow Ahh, I see. Jun 17 '21 at 22:23
• @SolomonSlow then you get into things like cap-heads (and button-heads), which in many ways are similar to CSK (no corners, tool goes into fastener). When not going into a counterbore it's common to use a washer there too. With an aluminium or other soft workpiece it reduces marring from friction (very obvious on anodised surfaces) and even a little indentation. Jun 18 '21 at 11:28

Except for special applications, most washers are made of dead soft steel, which deforms under the compressive load imposed by a tightened bolt head. As the washer smooshes, it minimizes stress concentrations caused by bumps under the bolt head and surface flaws in the part the bolt is running through.

• The washers used on cylinder head bolts are not soft and do not deform either. Jun 16 '21 at 19:28
• @SolarMike, will edit. -NN Jun 17 '21 at 0:20
• Is smoosh a technical term? Jun 17 '21 at 1:42
• @DKNguyen, yes it is a highly technical term used only by real hip dudes in the materials science field. Jun 17 '21 at 3:47
• @neils and that's a perfectly cromulent comment which leaves the discussion fully copascetic. Jun 17 '21 at 12:48

To visualize part of Nmech's answer: in the image, the washer actually greatly increases the contact area of the bolt head.

The bolt head looks pretty big:

But most of that is the shaft, which obviously does not spread out load on the material. So the actual contact area looks like this:

Comparatively, the bolt head on the washer looks like this:

That's a big difference in area.

• Nicely illustrated. Even larger than the area of the shaft is the area of the hole the shaft is in. In addition you want to put the stress further away from the hole there the material is more capable to bear the stress. Jun 18 '21 at 9:48

Another important part of the answer is the symmetry of the stress pattern. The stress caused by a bolt head varies greatly between the points of the bolt head and the straight sides. As a result local stresses, which are what you really care about because those are what the materials have to withstand, can be much higher than the average stress. A washer's circular symmetry smooths those out.

https://www.researchgate.net/figure/Contours-of-warping-displacement-a-shear-stress-b-and-components-of-shear-stress_fig5_267129617

• You would think they would stamp a circular base to round out the hex at the same time they make the rest of the bolt...or nut, I suppose. Jun 20 '21 at 6:33
• @DKNguyen This appears to be called a "Hex flange bolt" Jun 26 '21 at 23:18