Maximum working shear stress and working force?

• BlueCB
In summary: But you have the decimal point in the wrong place. You've calculated 78.5 kN as the max force. But it's 78.5 kN per bolt, and there are multiple bolts.In summary, the maximum working shear stress per bolt is 250 MPa, with a cross sectional area of 0.0314 m^2 and a maximum working force of 78.5 kN.
BlueCB

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?

How many square centimeters are in 1 square meter?

10,000...

BlueCB said:
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:
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?

SteamKing said:
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.

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?

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

SteamKing said:
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)?

BlueCB said:
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?

haruspex said:
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:
BlueCB said:
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.

1 person

1. What is the definition of maximum working shear stress?

The maximum working shear stress, also known as the yield shear stress, is the maximum amount of stress that a material can withstand before it starts to deform plastically.

2. How is maximum working shear stress calculated?

Maximum working shear stress is calculated by dividing the maximum shear force applied to a material by its cross-sectional area.

3. What factors affect the maximum working shear stress of a material?

The maximum working shear stress of a material is affected by its composition, microstructure, and any external factors such as temperature and loading rates.

4. Can the maximum working shear stress of a material change over time?

Yes, the maximum working shear stress of a material can change over time due to factors such as fatigue, corrosion, and environmental exposure.

5. How is maximum working force related to maximum working shear stress?

Maximum working force is directly related to maximum working shear stress. As the applied force increases, so does the maximum working shear stress until it reaches the material's yield shear stress.

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