" /> Force and Torque Balance - Essay Writing Pros

Force and Torque Balance

Force and torque balance on a section of the plate in a force balance on a section of the plate, as shown in Figure 3–15. Since P = 0 and since we have established V = 0, Equation (3–59) requires that M = constant. The constant must be Ma, the applied torque, as shown by a moment balance on an arbitrary section of the plate. To determine the deflection of the plate, we could integrate Equation (3–74) with q = P = 0. However, since we already know M ≡Ma, it is simpler to integrate Equation (3–73), the twice integrated form of the fourth-order differential equation. The boundary conditions are w = 0 at x = 0 and dw/dx = 0 at x = 0. These boundary conditions at the left end of the plate clarify what is meant by an embedded plate; the embedded end of the plate cannot be displaced, and its slope must be zero. The integral of Equation (3–73) subject to these boundary conditions is w = −Max 2 2D . (3.75)

The bent plate has the shape of a parabola. w is negative according to the convention we established if M is positive; that is, the plate is deflected upward.

Don't use plagiarized sources. Get Your Custom Essay on
Force and Torque Balance
Just from $13/Page
Order Essay

What is the displacement of a plate pinned at both ends (w = 0 at x = 0, L) with equal and opposite bending moments applied at the ends? The problem is illustrated. As a second example we consider the bending of a plate embedded at its left end and subjected to a concentrated force Va at its right end, as illustrated in Figure 3–17. In this situation, q = 0, except at the point x = L, and Equation (3–57) gives V = Bending of a plate pinned at both ends.

An embedded plate subjected to a concentrated load.

Va, as shown by the vertical force balance on the plate sketched in Figure 3–18. With P also equal to zero, Equation (3–59) for the bending moment simplifies to dM dx = Va. (3.76) This equation can be integrated to yield M = Vax+ constant, (3.77) and the constant can be evaluated by noting that there is no applied torque at the end x = L; that is, M = 0 at x = L. Thus we obtain M = Va(x− L). (3.78)

The bending moment changes linearly from −VaL at the embedded end to zero at the free end. A simple torque balance on the section of the plate shown in Figure 3–18 leads to Equation (3–78), since M must balance the torque of the applied force Va acting with moment arm L− x.

Essay Writing Pros
Calculate your paper price
Pages (550 words)
Approximate price: -

Why Work with Us

Top Quality and Well-Researched Papers

Our writers have been trained on how to handle papers placed by our clients. The writer must read and understand before embarking on writing the papers. In case of any issue that needs clarification, writers are encouraged to ask the client or support.

Professional and Experienced Academic Writers

Our team comprises of the best writers and editors. We do thorough vetting during recruitment to make sure that our writers have the knowledge and experience we aspire in the team.

Free Unlimited Revisions

Our aim is to give the client the best outcome. If for some reason you are not satisfied with the wok done, you can ask the paper to be revised or rewritten. This will be done to your satisfaction with no extra charges.

Prompt Delivery and 100% Money-Back-Guarantee

We have writers who work round the clock. This helps in making sure that all our clients’ papers are delivered on time. If we have issues with the deadline, we will ask for extension. If its not possible, the money is fully refunded.

Original & Confidential

Our clients’ confidentiality is highly respected. We can never disclose our clients’ details to third parties. In the same regard, we strive to give our clients 100% original papers. We do not tolerate plagiarism from our writers.

24/7 Customer Support

Clients can reach us any time of the day, and any day of the week. There is a live chat, email or phone numbers to help in ease of communication.

Try it now!

Calculate the price of your order

Total price:

How it works?

Follow these simple steps to get your paper done

Place your order

Fill in the order form and provide all details of your assignment.

Proceed with the payment

Choose the payment system that suits you most.

Receive the final file

Once your paper is ready, we will email it to you.

Our Services

You should never be worried about your papers even in the middle of the night. Our team will work round the clock to deliver.


Essay Writing Service

We have an able team that can deliver your work in the shortest time possible. The academic level or the type of work should never be a hindrance. Our highly competent support team is always around (24/7) to give you any assistance you may need.


Admission Essays & Business Writing Help

Do you need to be admitted in your dream institution but find it challenging to write an admission essay? Our team is in a position to write the best letter that will guarantee you an admission. We do as well write the best business proposals and reports.


Editing Support

Writing can be fun and enjoyable when everything has been done right. Writing is not just enough without proper editing and proofreading. We have a team of editors that ensure everything falls in place, whether its issues to do with grammar or referencing styles.


Revision Support

Once the paper has been done and submitted, that is not the end of it. You can always ask for amendment or improvement if you feel something has not been done right. Our team of writers and editors will gladly assist you to your satisfaction. Revision is free of charge.