# Solving Beam Bending Problem: 600N Load, 3.5mm Radius, 193GPa Young's Mod

• TowlieUK
In summary, the conversation discusses the design of a pedal box for a vehicle and the calculation of stresses in a pin that is used for its adjustment. Various equations and resources are mentioned, and clarification is sought on certain dimensions and calculations. The discussion ultimately leads to the calculation of the maximum bending stress in the pin.
TowlieUK

## Homework Statement

Hi there all,

I am designing a pedal box for a vehicle, and its adjustment is does by removing some pit-pins and sliding the pedal box along a rail and reinserting the pins. I need to calculate the stresses in the pin given a 600N total load applied by the feet of the driver. The pin is of radius 3.5mm, and has a Youngs Modulus of 193GPa.

That diagram basically shows what is happening after i have simplified the problem. The beam is not supported at the ends. The black part is the pin, or beam, and where the loads and reactions are are where the pin is in contact with the chassis/pedal box.

## Homework Equations

I am trying to work through this website:

http://www.engineersedge.com/beam_bending/beam_bending7.htm

but can not get any decent answers. I am not too sure what dimensions u, x and c are to be honest.

I make the Moment of Inertia to be 1.18 x 10^-10 .

## The Attempt at a Solution

Working through a mechanics book i get the ractant forces to be 300N, and a shear force diagram that goes 300N-0N--300N along the length of the beam, which i can't help but think is wrong. I was expecting a more complex outcome to be honest.

Any help wold be much appreciated as this is making me feel very stupid!

TowlieUK, welcome to PF!
TowlieUK said:
I am not too sure what dimensions u, x and c are to be honest.
c is the overhang distance 0.001 m; u is the distance between the support and the point of interest where you wish to calculate the stress, measured from the support toward the near free end.
I make the Moment of Inertia to be 1.18 x 10^-10
yes
Working through a mechanics book i get the ractant forces to be 300N, and a shear force diagram that goes 300N-0N--300N along the length of the beam, which i can't help but think is wrong. I was expecting a more complex outcome to be honest.
you were expecting too much, your shear force diagram is correct. What is the maximum bending stress in the pin?

Dear student,

It looks like you are on the right track with using the mechanics book and the website you mentioned to solve this beam bending problem. However, it is important to make sure that all of your inputs and assumptions are correct in order to get accurate results.

First, the dimensions u, x, and c in the website's equations refer to the x-coordinate of the point of interest, the distance from the neutral axis, and the distance from the end of the beam, respectively. Make sure you are using the correct values for these parameters in your calculations.

Second, it is important to consider the boundary conditions of the beam. In this case, the beam is not supported at the ends, so there will be a non-zero moment at both ends. This will affect the shear force and bending moment diagrams and should be taken into account in your calculations.

Lastly, it is always a good idea to double check your calculations and assumptions to make sure they are reasonable. If your shear force diagram is showing a constant 300N, it is possible that there is an error in your calculations or assumptions.

I would also recommend consulting with a professor or colleague who is knowledgeable in mechanics or structural engineering to get a second opinion on your approach and calculations. They may be able to offer additional insights or point out any errors.

Overall, solving beam bending problems can be challenging, but with careful attention to detail and double checking your work, you should be able to arrive at a reasonable solution. Best of luck with your pedal box design!

## 1. How do I calculate the bending stress on a beam?

The bending stress on 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-section.

## 2. What is the maximum stress that the beam can withstand?

The maximum stress that a beam can withstand is dependent on the material properties, specifically the yield strength. For a beam with a rectangular cross-section, the maximum bending stress can be calculated using the formula σmax = My/I, where σmax is the maximum stress, M is the bending moment, y is the distance from the neutral axis to the point of interest, and I is the moment of inertia.

## 3. How do I determine the deflection of the beam?

The deflection of the beam can be calculated using the formula δ = (PL^3)/(3EI), where δ is the deflection, P is the applied load, L is the length of the beam, E is the modulus of elasticity, and I is the moment of inertia. It is important to note that this formula assumes linear elastic behavior and small deflections.

## 4. How do I choose the appropriate beam material for my design?

The appropriate beam material for a design depends on several factors such as the desired strength and stiffness, the expected load and loading conditions, and the cost. It is important to consider the material's yield strength, modulus of elasticity, and density when selecting a material for a specific application.

## 5. What is the significance of Young's modulus in beam bending problems?

Young's modulus, also known as the modulus of elasticity, is a measure of a material's stiffness. It relates the stress and strain in a material and is an important factor in determining the bending behavior of a beam. A higher modulus of elasticity indicates a stiffer material, which can result in less deflection and higher bending stress in a beam.

Replies
2
Views
3K
Replies
1
Views
2K
Replies
5
Views
4K
Replies
16
Views
3K
Replies
1
Views
12K
Replies
2
Views
3K
Replies
2
Views
10K
Replies
1
Views
3K
Replies
4
Views
3K
Replies
11
Views
3K