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

[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!

 

[PhanthomJay]

TowlieUK, welcome to PF!

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?

 

[Mene]

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!