# Difference Between FEA Result and Hand Calculation in Beam Bending?

• Kajan thana
In summary, there was an error in the analytical calculation of the maximum deflection along the Z-axis of a beam with a length of 306mm. The incorrect value was -2.39mm, but after finding and correcting the error, the correct value is now 0.8mm. The Ansys analysis also showed an average deflection of 0.3mm.

#### Kajan thana

TL;DR Summary
Hi Guys,
I am doing some lab work on bending cantilever beam and its deflections in both directions y and z directions. For the deflection on the Z-axis, the ANSYS value is positive and the analytical value is negative. I don't know whether I am doing the calculation wrong or is there a specific reason why the direction differs? I have also made sure that the orientation of the axis is the same for both works.
This is the analytical working out. I substituted the value of 306mm ( the maximum length of the beam) to find the maximum deflection along the Z-axis. Which came out to be -2.39mm. But according to Ansys the average deflection is 0.3mm and the maximum deflection is 0.8mm.

This is the Ansys Values.

There are at least two problems with your question.
1) You have not told us how the axes are oriented (there is no universal orientation),
Please fix these for us, and then maybe there will be help.

Kajan thana
I managed to find the error. Thank you.

Kajan thana said:
I managed to find the error. Thank you.

berkeman said:
I ignored a negative sign in my analytical calculation, this is why I had two values in the opposite direction.

berkeman

## What is FEA and hand calculation in the context of beam bending?

FEA, or Finite Element Analysis, is a computerized method for solving engineering problems by dividing a complex structure into smaller, simpler parts called finite elements. Hand calculation, on the other hand, involves using mathematical equations and principles to analyze the behavior of a structure.

## What are the main differences between FEA results and hand calculations in beam bending?

The main difference is that FEA takes into account more complex factors such as material properties, geometric variations, and boundary conditions, while hand calculations typically make simplifying assumptions. FEA also allows for a more detailed and accurate analysis of stress and deformation compared to hand calculations.

## Which method is more accurate for analyzing beam bending?

FEA is generally considered to be more accurate due to its ability to model complex structures and account for various factors. However, hand calculations can still provide a good estimate of the behavior of a beam if the assumptions made are appropriate and the calculations are done correctly.

## What are the advantages and disadvantages of using FEA for beam bending analysis?

The main advantage of FEA is its ability to provide a detailed and accurate analysis of complex structures. It also allows for easy visualization of stress and deformation patterns. However, FEA requires specialized software and expertise, which can be costly. Hand calculations, on the other hand, are more accessible and can provide a quick estimate of the behavior of a beam, but they may not be as accurate as FEA.

## When should FEA be used instead of hand calculations for beam bending analysis?

FEA should be used when a more detailed and accurate analysis is needed, especially for complex structures or when the behavior of the beam is affected by various factors. FEA is also useful for optimizing designs and evaluating the effects of different loading conditions. Hand calculations can be used for simpler structures or as a quick estimate, but may not be sufficient for more complex situations.