# Stress in a hole due to pin force

1. Feb 18, 2010

### guideonl

Hi everyone,

What is the area should be taken to determine the compression stress of pin-hole in tention force (i.e plate with known thickness having a hole for lifting shakle pin) where the hole diameter is greater than the pin diameter (> x3) (theoretically, it is not an area just line of contact between the hole and the pin, which is the thickness of the plate).
Thank you, Guideon

2. Feb 18, 2010

### Unit91Actual

3. Feb 19, 2010

### guideonl

Thank you,
Hereby a sketch attached to clarify the question, I hope it would explain it better.

Guideon

#### Attached Files:

• ###### pin acting in a hole 001.jpg
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4. Feb 19, 2010

### Unit91Actual

Oh wow, that's great, thanks for the clarification. When I get home from work today I'll hook you up. Do you have numbers? I could also run a FE solution for you.

5. Feb 19, 2010

### stewartcs

Your attachment calcs look like you're trying to solve for bearing stress. However, since the pin is much smaller than the socket, the max compressive stress is actually given by:

$$\sigma c_{max} = 0.798 \cdot \sqrt{\frac{p}{K_D \cdot C_E}}$$

Where,

p = load per unit length
E1 = modulus of elasticity of bottom socket
E2 = modulus of elasticity of pin
v1 = poisson's ratio of bottom socket
v2 = poisson's ratio of pin

$$K_D = \frac{D_2 \cdot D_1}{D_1 - D_2}$$

$$C_E = \frac{1- \nu_1^2}{E_1} + \frac{1- \nu_2^2}{E_2}$$

CS

#### Attached Files:

• ###### CompressiveStressCyl.JPG
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6. Feb 19, 2010

### Unit91Actual

I agree with Stewart, though I would also add that the stress in your plate increases due to the hole.

For an elliptical center hole,

$$\sigma_{A} = \sigma_{c}\left(1+\frac{2a}{b}\right)$$

Since your hole is circular, a = b = r, thus

$$\sigma_{A} = 3\sigma_{c}$$

where

$$\sigma_{c}$$ is compressive stress
$$\sigma_{A}$$ is the actual stress, taking into account the geometry of the hole
$$2a$$ is the major axis
$$2b$$ is the minor axis
$$r$$ is the radius of your circular hole

Source: Anderson, T.L., Fracture Mechanics Fundamentals and Applications, 3rd Ed., CRC / Taylor and Francis, 2005, p27.

7. Feb 19, 2010

### Brian_C

The stress concentration formula you're talking about was derived for uniaxial tension. I don't think those boundary conditions apply in this case. Also, since this is a contact stress problem, the stresses will be altered because traction forces are applied to the hole.

8. Feb 20, 2010

### guideonl

Thank you all, you are great
stewartcs,
a) Is the stress equation you sent depends on the units you use in the equation (SI/american)?
b) The 0.798 factor is dimentionless?
Unit91Actual
a) Is the compressive stress you used in the equation for an elliptical center hole is the result of the max compressive stress equation in stewartcs reply? If not, how can I calculate this sress? that was my original question.
b) According to your important note, actually, the major stress is not where the pin force acts, but at 90 degrees right/left from the hole center (3 times the compressive stress)?

Thank you all again, Guideon

9. Feb 22, 2010

### stewartcs

As with all engineering formulas, the equation should be dimensionally consistent.

The 0.798 is a dimensionless factor.

CS