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# Inconsistencies between FEA and Manual Calculations

## Inconsistencies between FEA and Manual Calculations

(OP)
I am attempting to replace a 38kg solid pin with a hollow 16kg pin - ambitious, I know, but that’s what we’re here for. The pin is in double shear and has an estimated load of 140T, or 1,373.4kN.

FEA
“FEA Boundary Conditions.JPG” shows the layout of my FEA Analysis in SolidWorks Simulation. I’ve applied two separate loads of 70T of the flat sections of the housing (purple arrows). The central member can be thought of as a central strut and is fixed on the flat underside area (green arrows). A global no-penetration contact set has been applied with a friction coefficient of 0.15. The friction coefficient is the only feature holding the pin in place. The maximum stress shows 756.1 MPa on the ID in the 4.5mm gap.

Manual Calculation
“Hollow Pin with UDL on ends_SkyCiv Beam.pdf” shows my attempt at a manual representation, where I’ve treated the pin as a beam. I’ve used the shear force and bending moments to calculate the average shear stress and bending stress respectively. I am aware the FEA and this manual representation is different in the sense that the mid-way point of the beam can bend freely whereas in the FEA and in real life, the pin will flex only to the extent of the clearance in the housing (0.33mm) before fouling. The shear stress is 124.4 MPa (P/A), and the bending 229.9MPa (See “Bending calc.pdf”.

I can see there are some differences between the two methods, and that the FE method fundamentally uses the spring equation which is different to my manual calcs but I wouldn’t have expected such large differences.

Can anyone explain why the FEA results are so high, or my manual calculation is so low? I don’t know which results to work with, which probably means neither.
I’ve attached the SolidWorks files for reference. Let me know if you require more information and ill have a response within 24 hours.

http://files.engineering.com/getfile.aspx?folder=5...

### RE: Inconsistencies between FEA and Manual Calculations

Wow 140 tons, some things to think about

Apples to Apples: Your outputs from FEA are in VON mises stress which combines shear and normal stresses to a single envelope. You haven't put shear and bending together to compare with Von Mises Stress

Also I dont agree with your simple cantilever bending. The pin is controlled by shear failure. It is far too short for basic beam theory to work. Your outside blocks that are loaded are pretty rigid and will prevent rotation along the length of the pin. Using a cantilever type analysis isn't really the right approach here.

You also need to remember your FEA results are coming from a stress concentration. If you increase your mesh quality (convergence) you may see the stress in FEA reduce.

### RE: Inconsistencies between FEA and Manual Calculations

(OP)
Hi JGard1985

Thanks for the helpful response. Although the issue still remains, I've taken your suggestions on board. The max stress reduced slightly after refining the mesh and achieved convergence to approx. +-5%.

Although i agree the pin is short to consider it in a bending type model, moving from a solid pin to hollow would allow the pin to bend more easily. This is the primary reason i decided to consider the bending stresses. It also happens to be a conservative approach, since the calculated bending stress turns out to be almost double that of the average shear. The transverse shear would be somewhere between 4/3 (Solid circular CS) to 2 times (Thin Hollow Circular CS) the average stress. I would expect to see the bending stresses at a maximum at the top & bottom surface of the central section of the pin.

Anymore contributions would be greatly appreciated.

### RE: Inconsistencies between FEA and Manual Calculations

Unless the hollow version is very thin (which I doubt) the stiffness will be very similar to the solid version. I can't see the bending portion being significantly different between the two.

= = = = = = = = = = = = = = = = = = = =
P.E. Metallurgy, Plymouth Tube

### RE: Inconsistencies between FEA and Manual Calculations

Also going to a hollow pin will increase shear forces and deformation faster than it will increase bending forces.

### RE: Inconsistencies between FEA and Manual Calculations

(OP)
Hi Nereth1,

You're right. Shear stress will increase faster with a decreasing cross sectional area. Thanks for that.

For the record, my calculated Von Mises stress is 369 MPa. This has been taken by assuming a point where both bending and transverse shear stress are at a maximum. The mentioned point is where the four high stress points are on the FEA. Strictly speaking the bending will not be at a maximum because that would occur on the OD, whereas this point in the calculation & FEA is on the ID. Relating this to the bending equation sigma = My / I, the y value will be max at ro, instead its ri. To save me time and to be conservative I've just assumed them both to be max at one point.

### RE: Inconsistencies between FEA and Manual Calculations

(OP)
Also, I hear what you're all saying about the pin being too short to consider bending, however that brings me further away from my goal of matching the FEA to the manual calcs. I would be properly convinced if i could see a reliable reference that says bending theory can only be applied to L/d ratios or d/L ratios of *this value*. I haven't been able to find anything like that, only just a rule of thumb type approach where one looks at the pin in general and makes a judgement solely on how "stumpy" or long it looks overall in relation to the cross section.

### RE: Inconsistencies between FEA and Manual Calculations

JGard1985 is absolutely correct, shear governs, period.

Beam calcs only apply for L/D>5,

The 3D analytical solutions for short pins were performed in the 1880's, are still valid, but the 1D beam model you invoke are not.

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