# Maximum working shear stress and working force?

## Homework Statement

The maximum shear force of a set of bolts is 1000 kN.
The ultimate shear stress is 750 MPa and the safety factor is 3.
The diameter of each bolt is 20 mm.

a) What is the maximum working shear stress in each bolt?

b) The cross sectional area of each bolt?

c) The maximum working force of each bolt?

## The Attempt at a Solution

Radius = half of diameter = 10 mm = 1 cm = 0.01 m
Cross sectional area = pi*r^2 = 3.14*1^2 = 3.14 cm^2 = 0.0314 m^2

a) 1000 kN / 0.0314 = 31847133.76 Pa?

b) 3.14*1^2 = 3.14 cm^2 = 0.0314 m^2?

c) Force = Stress*Area = 31847133.76*0.0314 = 1000000 N = 1000 kN?

Is the above correct or do completely different formulas apply when it comes to shear stress and working force?

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SteamKing
Staff Emeritus
Homework Helper
How many square centimeters are in 1 square meter?

10,000...

haruspex
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Gold Member
2020 Award
10,000...
So correct this:
3.14 cm^2 = 0.0314 m^2

So 3.14 cm^2 = 0.000314 m^2?

So this would change the other answers:

a) Working shear stress = Force / Area = 1,000,000 N*0.000314 m^2 = 3184713376 Pa?

b) Area = pi*r^2 = pi*1 cm^2 = 3.14 cm^2 = 0.000314 m^2?

c) Working force = Stress*Area = 3184713376 Pa*0.000314 m^2 = 1,000,000 N?

Last edited:
SteamKing
Staff Emeritus
Homework Helper
Reread the problem statement carefully. Why haven't you used this information:
"The ultimate shear stress is 750 MPa and the safety factor is 3."

Do you understand what this means?

Reread the problem statement carefully. Why haven't you used this information:
"The ultimate shear stress is 750 MPa and the safety factor is 3."

Do you understand what this means?
If I'm honest, not really ; ultimate shear stress, safety factor, maximum working force? The terminology and what their relative units used are, is really confusing me.

Although would I be right in saying that 750 MPa = 750,000,000 N/m^2?

Some clarification would be very much appreciated.

SteamKing
Staff Emeritus
Homework Helper
Ultimate stress is the maximum stress which can be sustained before failure. A safety factor is applied to the ultimate stress to produce the maximum allowable safe working stress, item a) above. The safety factor accounts for dynamic loading, stress concentrations, and any other unknown factors in calculating stress. Knowing the maximum safe working stress and the size of the bolts, you should be able to calculate c) above.

In order to work the problem, you must understand the units as well. The pascal is the SI unit of pressure or stress and 1 Pa = 1 N/m^2.

Is there a formula for shear stress that involves the ultimate shear stress and safety factor?

SteamKing
Staff Emeritus
Homework Helper
Take this is steps.
1. Knowing the ult. shear stress and the safety factor, what is the max. allowable working stress?

Take this is steps.
1. Knowing the ult. shear stress and the safety factor, what is the max. allowable working stress?
750 MPa = 750,000,000 Pa / 3 = 250,000,000 Pa = 250 MPa (max working stress)?
or
750,000,000 Pa*3 = 2,250,000,000 Pa = 2.25 GPa (max working stress)?

haruspex
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2020 Award
750 MPa = 750,000,000 Pa / 3 = 250,000,000 Pa = 250 MPa (max working stress)?
or
750,000,000 Pa*3 = 2,250,000,000 Pa = 2.25 GPa (max working stress)?
It's a safety factor. To be safe, do you think the working stress to which it should be subjected would be more or less than its calculated ultimate stress?

It's a safety factor. To be safe, do you think the working stress to which it should be subjected would be more or less than its calculated ultimate stress?
Less, would make more sense (if its to be safe).

So in that case, does 250 MPa sound about right for the max working shear stress?

And then: max working shear stress*cross sectional area = max working force
= 250,000,000 Pa*0.000314 m^2 = 78500 N = 78.5 kN?

Last edited:
haruspex
Homework Helper
Gold Member
2020 Award
Less, would make more sense (if its to be safe).

So in that case, does 250 MPa sound about right for the max working shear stress?

And then: max working shear stress*cross sectional area = max working force
= 250,000,000 Pa*0.000314 m^2 = 78500 N = 78.5 kN?
Looks right.

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