since you are apparently allowed to use tables, look it up in a table that gives the rotation angle at the midpoint of the end plate, using the moment at the end of the cantilever as the applied couple at that point. Otherwise , use the calculus of beam theory.hatchelhoff said:
Chestermiller said:
I can't seem to find any such table. Can you point me int the right direction.PhanthomJay said:
So you have MB. From the solution to the second problem, you can get the initial slope. You multiply that by the length of the beam to get the additional dip at the far end.hatchelhoff said:
I don't want to have to go through this entire problem and do the detailed calculations. My goal was just to point out the general concept of how to approach this problem. I assume you understood the concept. The rest was up to you. If you have questions about the general concept, I will be glad to address them.hatchelhoff said:
A cantilever beam is a type of structural element that is supported at only one end, with the other end projecting outward. It is commonly used in architecture and engineering to create overhangs or to support structures such as bridges and balconies.
Cantilever beams deflect when an external load or force is applied to the unsupported end, causing it to bend or sag. This is due to the distribution of stress and strain along the length of the beam, with the highest amount of deflection occurring at the free end.
The deflection of a cantilever beam is affected by several factors, including the length of the beam, the type and magnitude of the applied load, the material properties of the beam, and the support conditions at the fixed end.
The deflection of a cantilever beam is typically calculated using beam deflection equations, such as the Euler-Bernoulli beam theory or the Timoshenko beam theory. These equations take into account the various factors that affect deflection and provide a solution for the amount of deflection at a given point along the beam.
Cantilever beams have a wide range of practical applications in various fields, such as civil engineering, architecture, and product design. Some examples include bridges, balconies, diving boards, roof overhangs, and shelves.
