# Shear stress in bolts help

• Matthew Heywood
In summary, the conversation is about solving a problem involving bolts and torque. The person has solved everything up to part d) and is struggling with the remaining steps. They initially calculated the separation of the bolts, but were unsure of how to proceed. They then attempted to calculate the force on each bolt and used this to find the diameter of the bolt. However, their approach was incorrect due to neglecting friction on the solid shaft. Eventually, with the help of the expert, they were able to correctly calculate the force on each bolt and determine the correct diameter of 11.3mm.

## Homework Statement

jan 2012 q3.jpg
I've solved everything up to part d). I generally struggle with questions on bolts and I'm really not sure how to tackle this problem.

## Homework Equations

τ = Tr/J, τ = 200MPa, T=1kNm

## The Attempt at a Solution

I worked out the separation of the bolts (I think).
Circumference around the inside: 2π(25mm) = 0.157m ∴ Separation: 0.157/2 = 0.0785m

Not sure where to go next, if I'm honest. I tried this:

T = 1kNm ⇒ F = 1kNm/0.0785m = 12.7kN
so σ = F/2A as double shear so A = F/2σ = 12.7kN/2(200MPa) = 3.19x10-5m2

so πr2 = 3.19-5 ⇒ r = 3.18mm ⇒ d = 6.37mm

so I went wrong somewhere as the answer is 11.28mm

any help appreciated. Thanks

#### Attachments

• jan 2012 q3.jpg
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Last edited:
Matthew Heywood said:

## Homework Statement

jan 2012 q3.jpg
I've solved everything up to part d). I generally struggle with questions on bolts and I'm really not sure how to tackle this problem.

## Homework Equations

τ = Tr/J, τ = 200MPa, T=1kNm

## The Attempt at a Solution

I worked out the separation of the bolts (I think).
Circumference around the inside: 2π(25mm) = 0.157m ∴ Separation: 0.157/2 = 0.0785m

It's not clear how the circumference of the solid shaft is useful here. You were instructed by the problem statement that friction between the shaft surface and the coupling was to be neglected. Therefore, all of the torque transmitted to the solid shaft must be resisted by the two bolts. What force on the bolts would produce an equal torque?

Not sure where to go next, if I'm honest. I tried this:

T = 1kNm ⇒ F = 1kNm/0.0785m = 12.7kN
so σ = F/2A as double shear so A = F/2σ = 12.7kN/2(200MPa) = 3.19x10-5m2

so πr2 = 3.19-5 ⇒ r = 3.18mm ⇒ d = 6.37mm

so I went wrong somewhere as the answer is 11.28mm

any help appreciated. Thanks
This approach is not correct for the reason given above.

Ah okay. So the for the force on each bolt:
T = Fm ⇒ F = 1kNm/50mm = 20kN
So 10kN on each bolt?

Matthew Heywood said:
Ah okay. So the for the force on each bolt:
T = Fm ⇒ F = 1kNm/50mm = 20kN
So 10kN on each bolt?
You might want to check that figure of 10 kN/bolt.

Oh okay. So would it be 20kN?

Matthew Heywood said:
Oh okay. So would it be 20kN?
Yes.

And then use σ = F/A?

so A = 20kN/200Mpa = 1x10-4
then r = √(1x10-4/π) = 5.64mm
so d = 11.3mm
Thanks :D

## What is shear stress in bolts?

Shear stress in bolts is the force that acts parallel to the cross-sectional area of a bolt, causing it to deform or fail.

## Why is shear stress important in bolts?

Shear stress is important because it determines the strength and stability of a bolted joint. If the shear stress exceeds the strength of the bolt, the joint can fail.

## How is shear stress calculated in bolts?

Shear stress in bolts can be calculated by dividing the applied force by the cross-sectional area of the bolt.

## What factors affect shear stress in bolts?

The factors that affect shear stress in bolts include the material and size of the bolt, the applied load, and the type of joint and connection it is used in.

## How can shear stress in bolts be minimized?

To minimize shear stress in bolts, engineers can use larger bolts, increase the number of bolts in a joint, or use materials with higher strength. Proper installation and tightening techniques can also reduce shear stress.

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