Bending Moment of a beam with mass under & above water.

[ksy8193]

Homework Statement

Please refer to the uploaded images. (there are two images)

When the right of the weight is lifted up,
I need to know the formula to calculate the bending moment of the beam according to the rest of parts I have and how to calculate the suitable size of the beam to be used.

As the bending moment is at its maximum when one of the weight is lifted out of the sea, the rest of the bending moment measurements are not necessary for me to find out.

I could only know how to calculate the easy question on bending moment. This one is too tough for me.. Let's assume the buoyancy force is 40N.. Volume of buoyancy is 1000m^3

Homework Equations

M = Force x distance
Volume of buoyancy is 1000m^3
buoyancy force is 40N
Mass = 40kg

The Attempt at a Solution

Moment of Mass = 40kg *9.81 m/s^-2* 30m = 11.72 KNm
Moment of the structure (horizontal, above water)= 10 * 9.81 * 45 = 4.41 KNm
Moment of the structure (vertical, above water) = 10 * 9.81 * 40 = 3.92 KNm
Moment of the structure (horizontal, under water)= 10 * 9.81 * 22.5 = 2.21 KNm (how to deduct the buoyancy force??)
Moment of the structure (vertical, under water)= 10 * 9.81 * 22.5 = 2.21 KNm (how to deduct the buoyancy force??)

Total M = 12.75KNm

In this case, how do I relate to the size of the stainless steel to be use ? what is the suitable diameter?

 

[Jhero]

Thank you for your question. Calculating the bending moment of a beam can be a complex task, but I am happy to provide some guidance.

Firstly, it is important to understand the concept of bending moment. In simple terms, bending moment is the measure of the bending force on a beam caused by external loads. It is calculated by multiplying the force applied to the beam by the distance from the point where the force is applied to the point where the beam is supported.

In your case, the force applied to the beam is the buoyancy force of 40N and the distance is the length of the beam. However, it is important to note that the buoyancy force will change as the weight is lifted out of the water, so the bending moment will also change.

To calculate the suitable size of the beam, you will need to consider the maximum bending moment that the beam will experience. This can be calculated by considering all the forces acting on the beam, including the weight of the structure, the buoyancy force, and any other external forces. Once you have determined the maximum bending moment, you can then use the formula for bending moment (M = F * d) to determine the required size of the beam.

As for the size of the stainless steel to be used, this will depend on the material properties of the steel and the design requirements of the structure. It is best to consult with a structural engineer to determine the appropriate diameter for the beam.

I hope this helps guide you in your calculations. Good luck with your project!