# Cantilever Pipe Assembly - Statics

• NewEngineer
In summary, the engineer is installing a horizontal cantilever pipe which will be connected to a vertical pipe by a T-connection. At the end of the cantilever the pipe bends up at 90 degrees for 12". At the top of the vertical pipe (at the end of the cantilever) will be a device (weight approx. 10 Lb = 4.53592 kg). The cantilever assembly pipe is most likely carbon steel, thickness 0.2159" (based on a 3" nominal diameter steel pipe schedule 40). The engineer is considering installing a vertical support under point B for the extended pipe, but is unsure if the pipe will hold fine.
NewEngineer
To simplify my situation, I am installing a horizontal cantilever pipe (30” length, 3” nominal diameter) which will be connected to a vertical pipe (3” nom diameter, acting as the wall) by a T-connection. See the diagram below. At the end of the cantilever the pipe bends up at 90 degrees for 12”. At the top of the vertical pipe (at the end of the cantilever) will be a device (weight approx. 10 Lb = 4.53592 kg). The cantilever assembly pipe is most likely carbon steel, thickness 0.2159” (based on a 3” nominal diameter steel pipe schedule 40).

What I want to know is given these conditions, do I need to install a vertical support (under point B) for the extended pipe or would the pipe hold fine here? I’ve calculated the moment at point A as -95.922 lb*ft. If you look at the FBD you can see how I modeled the problem. I summed the forces of the Mass (M) and the vertical piece of pipe (MBC).

@Mech_Engineer To calculate the stress, could I model it as a cantilever beam with end-loading? is there a different equation that I would have to use to include the pipe's weight and the fact that it's a cylindrical tube?

Stress = (F*L)(h/2)/I

Not sure where I'm going wrong I calculated the bending stress (Stress = My/I) and I got 57808.827 lb*ft2.

Note: I changed the weight on the end of the beam, so the moment I calculated is 58.1625 lb*ft

I think you just have to be careful about your units, the units of the result should be force/area (psi or equivalent). When I assume 1/4" wall thickness for the pipe, the result would be about 11 ksi (see calculation here).

Another important thing to keep in mind will be max deflection and first vibration mode. Even if the stress seems acceptable, this kind of application usually has limitation on acceptable deflection and vibration as well.

Thanks for the tips. My answer above actually was a typo my answer is 401.52 psi. (remember I changed the weight at the end so my moment is only 58.162)

Why does your equation include the pipe's length (30 inch)?

NewEngineer said:
Thanks for the tips. My answer above actually was a typo my answer is 401.52 psi. (remember I changed the weight at the end so my moment is only 58.162)
I hadn't seen that you changed your moment load, I updated the calculation here (it turns out there was an order of operations error in the second moment of area as well): calculation link. Is your pipe wall thickness about 0.34"?

NewEngineer said:
Why does your equation include the pipe's length (30 inch)?
Good catch, that was supposed to be 3 inches (the diameter of the pipe). The pipe diameter divided by two (a.k.a. the radius) gives you the neutral axis distance for the stress calculation.

I need to be more rigorous and always be on the look out for a missed factor of 2 and factor of 10!

According to engineeringtoolbox.com, a 40 schedule steel pipe with nominal pipe size of 3" has a wall thickness of 0.2159 inch and a weight of 7.58 lb/ft. I should have mentioned this in the original post, sorry bout that.

Anyway, even with my bending stress calculated at below 0.6*yield Stress I think I am still planning to install a support for the structure. I haven't calculated the deflection, but given that the assembly will be outside and have vapor flowing through the pipes I think it may be the safer option.

Mech_Engineer

## 1. What is a cantilever pipe assembly?

A cantilever pipe assembly is a type of structure where a horizontal pipe is supported at one end and hangs freely at the other end. It is used to transfer loads or fluids over a span without any intermediate support.

## 2. How does a cantilever pipe assembly work?

The cantilever pipe assembly works by using the principles of statics, specifically the law of equilibrium. The weight of the pipe and any applied loads are balanced by the reactions at the fixed end, allowing the pipe to remain in a stable position.

## 3. What are the main components of a cantilever pipe assembly?

The main components of a cantilever pipe assembly include the pipe itself, the fixed support or anchor point, and any applied loads such as fluid pressure or weight of the pipe. Additional components may include braces or supports to increase stability.

## 4. What are the key considerations in designing a cantilever pipe assembly?

When designing a cantilever pipe assembly, key considerations include the magnitude and direction of the applied loads, the material and strength of the pipe, and the support or anchor point. It is also important to consider potential external factors such as wind or seismic forces.

## 5. What are some real-world applications of cantilever pipe assemblies?

Cantilever pipe assemblies are commonly used in various industries such as oil and gas, water treatment, and construction. They can be found in structures such as bridges, pipelines, and offshore platforms, where they are used to transfer fluid or structural loads over a span without the need for intermediate supports.

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