Machine elements stress concentration

In summary, the problem involves a flat part with constant thickness b that is loaded in tension. The height changes from 50 to 87 mm with a radius of 4.0 mm. The task is to find how much lower a load can be transmitted through the bar if the height increases from 50 to 100 mm and the radius increases from 4.0 to 10 mm. The equations used are σ = P/A = P/bh and Kc = σmax/σave, and the initial values for r/h, H/h, and Kc are calculated. However, the material and actual stress are unknown, and the thickness of the part is not given. The problem only asks for the load the modified piece
  • #1
Triathlete
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Homework Statement



A flat part with constant thickness b is loaded in tension as shown. The height changes from 50 to 87 mm with a radius r = 4.0 mm. Find how much lower a load can be transmitted through the bar if the height increases from 50 to 100 mm and the radius increases from 4.0 to 10 mm.

media%2F9c6%2F9c638aea-a63a-46d9-8257-a6802214c9e8%2Fphp907Bhf.png


Homework Equations



σ = P/A = P/bh

Kc = σmax/σave

The Attempt at a Solution



For the fist case, r/h = 4/50 = 0.08, H/h = 87/50 = 1.74, Kc = 2.5

But I'm stuck because I don't know the material or the stress so I don't know how to determine the load. Do I even need the Kc value?
 
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  • #2
Triathlete said:

Homework Statement



A flat part with constant thickness b is loaded in tension as shown. The height changes from 50 to 87 mm with a radius r = 4.0 mm. Find how much lower a load can be transmitted through the bar if the height increases from 50 to 100 mm and the radius increases from 4.0 to 10 mm.

media%2F9c6%2F9c638aea-a63a-46d9-8257-a6802214c9e8%2Fphp907Bhf.png


Homework Equations



σ = P/A = P/bh

Kc = σmax/σave

The Attempt at a Solution



For the fist case, r/h = 4/50 = 0.08, H/h = 87/50 = 1.74, Kc = 2.5

But I'm stuck because I don't know the material or the stress so I don't know how to determine the load. Do I even need the Kc value?
The problem isn't asking you to calculate the actual stress or the actual load. You are not even given the thickness of the part.

You should assume that both pieces are made from the same material, which will have the same strength. All you are asked to find is the load the modified piece can carry in relation to the original piece as shown.
 

1. What is stress concentration in machine elements?

Stress concentration refers to the localized increase in stress at a specific point or area in a machine element, usually caused by a sudden change in shape or cross-section. This can lead to premature failure or damage to the component.

2. What are some common causes of stress concentration in machine elements?

Some common causes of stress concentration include sharp corners, changes in cross-sectional area, holes or notches, and abrupt changes in material properties. These can all lead to an increase in stress at the affected area, making it more susceptible to failure.

3. How does stress concentration affect the performance of a machine element?

Stress concentration can significantly reduce the strength and durability of a machine element. It can lead to cracks, fractures, and ultimately, failure of the component. It can also cause a decrease in the overall load-bearing capacity of the machine.

4. What are some ways to reduce stress concentration in machine elements?

One way to reduce stress concentration is to design machine elements with smooth, gradual transitions between sections. This can help distribute stress more evenly throughout the component. Another method is to use fillets or rounded corners instead of sharp edges, which can help reduce stress concentrations.

5. Can stress concentration be completely eliminated in machine elements?

While it is not possible to completely eliminate stress concentration, it can be minimized through careful design and material selection. It is important to consider potential stress concentration points during the design phase and make appropriate modifications to reduce their effects on the component.

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