Linearly varying force and bending moment problem.

[ajayguhan]

I have attached both the question and my attempt at solution.

My problem is reducing the equation further to get the value of a/L

 

[SteamKing]

Have mercy on us. Rotate your phone when you take images of your work. It's very difficult to rotate the thumbnails and get a legible image. Good luck with your problem.

 

[ajayguhan]

You can rotate it easily nah ...? What's the problem in rotating the image. If my work is not legible then just say, I'll repost it better than now.

 

[SteamKing]

Sorry, I tried downloading and viewing the thumbnails attached to the OP. Things just got worse after that. I'd like to help, but not at the cost of a sore neck.

 

[rezeew]

I would like to provide a response to your question about reducing the equation further to get the value of a/L in the problem of linearly varying force and bending moment.

Firstly, it is important to understand the context of the problem and the variables involved. In this case, we have a beam subjected to a linearly varying force and bending moment along its length. The beam has a length of L and is supported at both ends. The force acting on the beam varies from 0 at one end to F at the other end, and the bending moment varies from 0 at one end to M at the other end.

To reduce the equation further and obtain the value of a/L, we need to use the equations of equilibrium and the relationship between force, bending moment, and stress in a beam. By applying the equations of equilibrium, we can determine the reactions at the supports, which will help us in solving for a/L.

Next, we can use the relationship between force, bending moment, and stress in a beam, which is given by the equation σ = My/I, where σ is the stress, M is the bending moment, y is the distance from the neutral axis, and I is the moment of inertia. By substituting the values of force and bending moment at any point along the beam, we can determine the corresponding stress value.

Once we have the stress value, we can use the stress formula for a rectangular cross-section beam, which is given by σ = (6M/aL)(h/2), where h is the height of the beam. By equating this formula with the stress value obtained from the previous equation, we can solve for a/L.

In summary, to reduce the equation further and obtain the value of a/L in the problem of linearly varying force and bending moment, we need to use the equations of equilibrium, the relationship between force, bending moment, and stress in a beam, and the stress formula for a rectangular cross-section beam. I hope this explanation helps you in solving the problem.