# Bending stress of beam in contact with a flat surface?

• cabellos6
In summary, to determine the thickness of the metal endplates for a spinal disc design, one suggestion is to use finite element analysis (FEA) to simulate different loading conditions and calculate the stresses on the endplates. This will help determine the appropriate thickness of the material needed to withstand bending and compressive forces and check for any potential failure points in the design.

#### cabellos6

I am designing a spinal disc with 2 metal endplates. These endplates are rectangular in shape and are fixed to form a flat contact surface with the vertebrae bone surface.

My question is based on the bending stress of these metal endplates. I need to work out the possible thickness of these endplates. I understand how a beam can be modeled with simple supports, cantilever etc but in this case the endplate is flat pressed against a flat surface so contact is over the whole surface area and it is to support a compressive force in the centre of the endplate length L.

Please could anyone offer me suggestions as to how i could calculate this?

One way to calculate the thickness of the endplates would be to use a finite element analysis (FEA) software. FEA is a computer simulation technique which can be used to understand the behavior of a design under different types of loading conditions, including bending and compressive forces. By applying various loads to the model, the stresses on the end plates can be determined, and the thickness of the material can then be adjusted accordingly to ensure that it meets the required strength criteria. Additionally, FEA can also be used to check for any potential failure points in the design, such as defects in the material or weak areas in the joint between the endplates.

As a scientist, the first step I would take in addressing this question is to gather all the necessary information and data. This would include the dimensions and material properties of the endplates, as well as the expected compressive force and contact surface area.

Next, I would use mathematical equations and principles from mechanics and materials science to analyze the bending stress of the endplates. This could involve calculating the bending moment and stress distribution along the length of the endplate using the applied force, contact area, and material properties.

It is also important to consider the boundary conditions of the endplates, as the fixed contact with the vertebrae bone surface may affect the bending stress. Finite element analysis (FEA) could also be used to simulate and analyze the behavior of the endplates under different loading conditions.

Additionally, I would also consider any potential failure modes, such as buckling or yielding, and ensure that the endplates are designed to withstand these stresses and forces.

In conclusion, the calculation of bending stress in this scenario would require a thorough understanding of mechanics and materials science principles, as well as accurate data and proper analysis techniques. It is important to carefully consider all factors and potential failure modes in order to design endplates that can effectively support the compressive force and maintain their structural integrity.

## 1. What is bending stress in a beam?

Bending stress in a beam is the stress caused by a force applied perpendicular to the beam's longitudinal axis, causing the beam to bend or flex.

## 2. How do you calculate bending stress in a beam?

Bending stress in a beam can be calculated using the formula σ = (Mc)/I, where σ is the bending stress, M is the bending moment, c is the distance from the neutral axis to the outermost fiber, and I is the moment of inertia of the cross-sectional area of the beam.

## 3. What is the neutral axis of a beam?

The neutral axis of a beam is an imaginary line that divides the cross-sectional area of the beam into two equal parts. This is the axis where the bending stress is zero.

## 4. How does a flat surface affect the bending stress of a beam?

A flat surface in contact with a beam can cause an additional type of stress known as contact stress. This stress is caused by the pressure between the beam and the surface, and it can increase the overall bending stress in the beam.

## 5. How can bending stress of a beam in contact with a flat surface be minimized?

To minimize bending stress in a beam in contact with a flat surface, the beam should be designed with a strong material and appropriate cross-sectional shape. The surface should also be smooth to reduce any potential friction and resulting contact stress. Additionally, adding supports or reinforcement to the beam can help distribute the load and reduce the overall bending stress.