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Calculate the stress applied to a bronze flange from a expanding pipe

Calculate the stress applied to a bronze flange from a expanding pipe

Calculate the stress applied to a bronze flange from a expanding pipe

(OP)
I have 4 foot carbon steel pipe in the vertical direction. The top of the pipe is in a T joint that is welded down. The bottom of the pipe is connected to a 90 degree elbow to a 6 inch pipe in the horizontal pipe. The horizontal pipe is connected to a cast bronze flange, and is then connected to a 6 inch pipe to a boiler. The schematic can be seen by this picture

I am suppose to calculate the the stresses applied on this flange, and the calculations that I did are shown on the attachment. I was told that I did the calculations wrong because I chose the wrong deflections. Is there another way that I am supposed to calculate the stress applied on that flange?

RE: Calculate the stress applied to a bronze flange from a expanding pipe

If only it were so simple.

You have calculated the thermal stress, as if each piece was separate from the other and each was fully restrained in the axial direction. You have not considered that pipe which is free to expand would have no stress, or that pipe which is partially restrained would not have that full level of stress. In fact, the vertical pipe is partially restrained by the horizontal pipe and the horizontal stress is partially restrained by the vertical pipe. Neither is fully restrained in the axial direction, since each partial restraint allows some movement of the other. The horizontal deflection of the vertical pipe, caused by the partial expansion of the horizontal pipe, creates a bending moment at the elbow, just as the vertical deflection of the horizontal pipe, caused by growth of the vertical pipe, in the same manner creates a moment at the same elbow, which both then are added together. In the end, you must find that the axial stresses will be less than the fully restrained stresses that you have calculated, some of the axial load in each pipe being converted into bending stress. Once you know the bending moment at the elbow, you can calculate the moments at opposite ends of the pipe. With that information, you can at last calculate what the stress must be at the flange joint.

The best way to do this by hand, or spreadsheet, is to use a method known as "moment distribution".

"People will work for you with blood and sweat and tears if they work for what they believe in......" - Simon Sinek

RE: Calculate the stress applied to a bronze flange from a expanding pipe

(OP)
Wow! That is going way over my head. Now what if I simplified the problem but taking out the 6 inch pipe and 90 degree elbow?

RE: Calculate the stress applied to a bronze flange from a expanding pipe

The conservative way to do it is to calculate the moment at the elbow using the deflection , Δ, of each member caused by the other. Moment = 6EIΔ/L Add the two together for moment at the elbow. Take one half of each of those components and put them at opposite ends of their respective members. Take free body diagrams of each member, assuming the flange is connected. Figure the bending moment, axial and shear stresses at the flange point.

Do you have a copy of B31.1? That approximate, but conservative, method is explained in the part describing the calculation of anchor and virtual anchor forces.

"People will work for you with blood and sweat and tears if they work for what they believe in......" - Simon Sinek

RE: Calculate the stress applied to a bronze flange from a expanding pipe

(OP)
Okay, that makes sense. No I dont have that. Where can I find a copy of B31.1?

RE: Calculate the stress applied to a bronze flange from a expanding pipe

Local library?

"People will work for you with blood and sweat and tears if they work for what they believe in......" - Simon Sinek

RE: Calculate the stress applied to a bronze flange from a expanding pipe

(OP)
BigInch,

What if I used the cantilever method approach?

Vertical piping = 48 inches
horizontal piping = 6 inches
temperature difference = 180 - 70 = 110 F
alpha = 6.5E6 in/in F for carbon steel

delta_y = .0343 inches
delta_x = .00429 inches

Fx = 12*E*I*delta/L^3 = 12*29.5E6*(pi*(2.875^4 - 2.5^4)/64)*.00429/6^3 = 10097 lbs (from my understanding this force is applied in the vertical direction?)
Mx = 6*E*I*delta/L^2 = 6*29.5E6*(pi*(2.875^4 - 2.5^4)/64)*.00429/6^2 = 30293 lbs*in

Fy = 12*E*I*delta/L^3 = 12*29.5E6*(pi*(2.875^4 - 2.5^4)/64)*.0343/48^3 = 157lbs
Mx = 6*E*I*delta/L^2 = 6*29.5E6*(pi*(2.875^4 - 2.5^4)/64)*.0343/48^2 = 3784 lbs*inches

Can I do this? Now from here how do I get my stresses?

RE: Calculate the stress applied to a bronze flange from a expanding pipe

The canteliver method should be conservative.
If the left end of the 6"+6" beam is fixed and the flange can rotate, then you should use 12", not 6".
If you are ignoring the left 6" and considering the flange as a fixed end, then your 6" length is correct.

The moments and forces on each end of the 48" length are equal value, but opposite in direction. Same for the 6" or 12", whatever you decide. If you decide that the flange is fixed, then you have the moment and lateral shear, Fx, but add the vertical load to the shear too.

"People will work for you with blood and sweat and tears if they work for what they believe in......" - Simon Sinek

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