# Average Shear Stress on a Plate

• Colt 45 J
In summary, the problem involves determining the average normal stress in the bolt shank, the average shear stress along the cylindrical area of the plate, and the average shear stress in the bolt head. The distribution of forces was found to be 4kN, resulting in an average shear stress of 18.52MPa. However, after correcting a typo, the correct answer is 4.72MPa, calculated using a force of 8000N.
Colt 45 J
1. Problem Statement
The long bolt passes through the 30-mm-thick plate. If the force in the bolt shank is 8kN, determine the average normal stress in the shank, the average shear stress along the cylindrical area of the plate defined by the section lines a-a, and the average shear stress in the bolt head along the cylindrical area defined by the section lines b-b.

http://img340.imageshack.us/img340/698/solidsproblem1102.jpg

Note: I have solved the shear on the bolt head, as well as the average normal stress in the shank, it's the average shear along the plate that I am having issues with.

τ = V / A
o= N / A

## The Attempt at a Solution

Distribution of forces so the equivalent is 4kN

τ = 4000/(pi*(.009^2-.0035^2))
τ = 18.52MPa

The answer key (which has yet to be wrong in my experience for this textbook) says that the average shear should be 4.72MPa

Edit:
Figured out my error

τ= 8000/(pi*(.018*.03))
τ=4.716MPa

Last edited by a moderator:
I'm pleased you are happy with your answer, but I didn't understand why it is 4 kN, and not 8kN. If you have a moment to explain I would be grateful.

Ah originally it was because with a rectangular element it's usually double shear instead of single, in the case of the answer thank you, as I had put a typo and meant to put 8000N in instead of the 4000, the answer was calculated using the 8000 however and is correct.

## 1. What is average shear stress on a plate?

Average shear stress on a plate is a measure of the internal forces acting on a plate due to shear or sliding forces.

## 2. How is average shear stress on a plate calculated?

Average shear stress on a plate is calculated by dividing the total shear force acting on the plate by the total area of the plate.

## 3. What is the importance of understanding average shear stress on a plate?

Understanding average shear stress on a plate is important in the design and analysis of structures, as it helps determine the maximum load a plate can withstand before failure due to shear forces.

## 4. What factors affect the average shear stress on a plate?

The average shear stress on a plate is affected by the magnitude of the shear force, the geometry and dimensions of the plate, and the material properties of the plate.

## 5. How can average shear stress on a plate be minimized?

Average shear stress on a plate can be minimized by increasing the thickness of the plate, reducing the magnitude of the shear force, or selecting a material with higher shear strength.

• Engineering and Comp Sci Homework Help
Replies
2
Views
5K
• Engineering and Comp Sci Homework Help
Replies
1
Views
2K
• Engineering and Comp Sci Homework Help
Replies
18
Views
2K
• Engineering and Comp Sci Homework Help
Replies
4
Views
4K
• Engineering and Comp Sci Homework Help
Replies
6
Views
3K
• Mechanical Engineering
Replies
1
Views
1K
• Engineering and Comp Sci Homework Help
Replies
4
Views
11K
• Introductory Physics Homework Help
Replies
6
Views
1K
• Mechanical Engineering
Replies
1
Views
1K
• Mechanical Engineering
Replies
1
Views
1K