Find Axial Force P: Stress Concentration Homework

In summary, the question asks to find the approximate axial force P in kip based on the stress distribution shown in the diagram. The attempt at a solution involves using the average stress formula, but the resulting answer is incorrect. After further discussion, it is suggested that an empirical equation may be used instead to get the correct answer.
  • #1
gv3
27
0

Homework Statement


The stress distribution along the section of a bar is shown below. From this distribution, find the approximate axial force P in kip.
Engineering 2.jpg

Homework Equations


δavg=P/A
A= (.6+.6)(.5)
δavg=30ksi[/B]

The Attempt at a Solution


P=(30ksi)(.6in2)=18kip

It says this answer is wrong but i don't see where i am going wrong here? .8in is the diameter of the whole so it is not considered when finding the area.[/B]
 
Physics news on Phys.org
  • #2
gv3 said:

Homework Statement


The stress distribution along the section of a bar is shown below. From this distribution, find the approximate axial force P in kip.
View attachment 203331

Homework Equations


δavg=P/A
A= (.6+.6)(.5)
δavg=30ksi[/B]

The Attempt at a Solution


P=(30ksi)(.6in2)=18kip

It says this answer is wrong but i don't see where i am going wrong here? .8in is the diameter of the whole so it is not considered when finding the area.[/B]
What answer is considered the correct answer?
 
  • #3
Chestermiller said:
What answer is considered the correct answer?
Not sure. I've still been unable to get the answer. I don't see any other way to approach this. My professor approached it the same way when he did a similar problem.
 
  • #4
This might be a silly . The average stress is actually a bit less than 30 ksi so your answer for force P is a little high . As near as can be judged from such a small diagram the average stress is actually about 28.7 ksi giving a value of force P of about 17.2 kip .

So maybe 17 kip is the 'correct' answer ?
 
  • Like
Likes Chestermiller
  • #5
Nidum said:
This might be a silly . The average stress is actually a bit less than 30 ksi so your answer for force P is a little high . As near as can be judged from such a small diagram the average stress is actually about 28.7 ksi giving a value of force P of about 17.2 kip .

So maybe 17 kip is the 'correct' answer ?
The next question asked for the max stress/average stress and used 30ksi as he average stress which gave me the right answer. I am hesitant to try because i only have 2 attempts left.
 
  • #6
Have you been given an empirical equation such as the one in Table 6-1-2 here? In this case, by plugging in the numbers, the stress concentration factor would be 2.23, and the nominal stress would therefore be 16.12. But this is just an empirical fit, of course.
 

1. What is axial force P in the context of stress concentration?

Axial force P is a type of mechanical force that acts parallel to the longitudinal axis of a structure. In the context of stress concentration, it refers to the force applied to a specific point on a structure, causing stress to accumulate and concentrate at that point.

2. How is the axial force P calculated?

The axial force P can be calculated using the formula P = F/A, where F is the applied force and A is the cross-sectional area of the structure. It is important to note that this calculation assumes a uniform distribution of stress over the entire cross-section of the structure.

3. What is stress concentration and how does it relate to axial force P?

Stress concentration occurs when the stress in a structure is not evenly distributed, resulting in a localized region of increased stress. This is often caused by the presence of sharp corners, holes, or changes in cross-sectional area. Axial force P can contribute to stress concentration by applying a force to a specific point on the structure, causing stress to accumulate and concentrate at that point.

4. How can stress concentration due to axial force P be reduced?

There are several ways to reduce stress concentration caused by axial force P. One method is to use fillets or rounded corners instead of sharp corners in the design of the structure. Another approach is to use materials with higher strength and ductility, which can help distribute the stress more evenly. Additionally, increasing the cross-sectional area of the structure can also help reduce stress concentration.

5. What are some common applications of stress concentration analysis for axial force P?

Stress concentration analysis for axial force P is commonly used in the design and analysis of mechanical and structural components, such as beams, columns, and shafts. It is also important in industries such as aerospace, automotive, and civil engineering, where structural integrity and safety are crucial.

Similar threads

  • Engineering and Comp Sci Homework Help
Replies
5
Views
2K
  • Engineering and Comp Sci Homework Help
Replies
2
Views
935
  • Engineering and Comp Sci Homework Help
Replies
1
Views
1K
  • Engineering and Comp Sci Homework Help
Replies
1
Views
1K
  • Engineering and Comp Sci Homework Help
Replies
1
Views
1K
  • Engineering and Comp Sci Homework Help
Replies
18
Views
2K
  • Engineering and Comp Sci Homework Help
Replies
7
Views
2K
  • Engineering and Comp Sci Homework Help
Replies
6
Views
2K
  • Engineering and Comp Sci Homework Help
Replies
3
Views
4K
  • Engineering and Comp Sci Homework Help
Replies
8
Views
7K
Back
Top