Beam Deflection in a Tapered Pipe

In summary, The person is seeking help for comparing the deflection of two different types of pipes - regular non-tapering and tapered. They have set the variables to be equal for comparison but are facing some discrepancies. Someone suggests that the issue may lie in the double integral setup and recommends a change in the definition of the bending moment. The person makes the suggested changes and the results agree using both methods. However, they are still unsure about their integrals and seek further help.
  • #1
jrmainia
4
0
I need help comparing the deflection of pipe with two different cases. Case 1 is a regular non-tapering pipe. The case 2 is a tapered pipe that should deflect less than the straight pipe. I am working in MathCad and can change the value of my variables, so I have set the two cases to be equal to one another (by saying that the variable D.w is equal to D) for the sake of comparison. The answers should be equal to one another so I know that there is a problem but I am not sure where. I think that it is within setting up the double integral since I checked the case 1 pipe deflection against a different pipe deflection calculator. Any help would certainly be appreciated.

View attachment Mathcad - Tapered Pipe Bending.pdf
 
Engineering news on Phys.org
  • #2
The problem is that 100 ft. of 6" pipe which is cantilevered is well outside of the elastic range for which the beam equations are valid. Your stress calculation of 113 ksi. should have tipped you off. Grade A pipe has a tensile yield of 30 ksi and Grade B pipe goes to 35 ksi. You are trying to analyze a piece of spaghetti.
 
  • #4
I think the problem is with your definition of the bending moment in the tapered beam calculation.

For a cantilever beam, the bending moment is a maximum at the fixed end (x = 0 in your coordinate system) and zero at the free end (x = L). By defining the bending moment as W*x in your MathCad integral, the BM is zero at the fixed end and W*L at the free end. If you change the BM to W*(L-x), this should solve your problem.
 
  • #5
That makes sense.

I changed my coordinate system picture in Case 2 so that the distance measured for the moment is zero at the free end.

I added equation y3. It is only to show that using a constant value for I, the deflection found through double integration is still incorrect, so this makes me think that the issue lies in the way I have the integrals set up.

D.w still is equal to D so all the deflection should still be equal to each other.

View attachment Mathcad - Tapered Pipe Bending.pdf

View attachment Tapered Pipe Bending.xmcd
 
  • #6
In your latest MathCad calculation, you have introduced a new variable x1, which you set equal to zero.
Not surprisingly, your integral also evaluates to zero.

Instead of using x1, I think if you had defined the moment as W*(L-x) instead of W*x in your integral, the calculation would have worked out.

Let MathCad work through the algebra instead of introducing additional unnecessary variables.
 
  • #7
In an effort to simplify the calc and let mathcad do the work, I defined (x=0) @ the free end and (L=x) at the fixed end and set up functions in terms of x. I also included graphs for the diameter, moment, moment of inertia, deflection angle, and deflection all in terms of x.

I think that the functions for diameter, moment and moment of inertia are correct. The deflection graph seems opposite what I expect in that @ x=L the angle should be 0deg. Could that be due to the definite integration range? Should this change to something else?

The deflection graph crosses 0 so I know that can't be right.

I still think that I have an error in how I define the integrals.

View attachment Alt Tapered Pipe Bending.xmcd
View attachment Mathcad - Alt Tapered Pipe Bending.pdf

Thanks for the help!
 
Last edited:
  • #8
I don't understand why you don't realize that your definition of the bending moment as a function of x is in error, and this is why your MathCad calculation of deflection fails to agree with your initial calculation.

Look, the bending moment M(x) must equal -1000 lbs times 120 in = -120000 in-lbs. at x = 0
and M(x) = 0 at x = 120 in. If M(x) = W*(L-x) is used in the MathCad calculation, then the results will agree using both methods.
 
  • #9
jrmainia: Your attached pdf file in post 3 is fine, as-is, except just change M*x in your two double-integral equations therein to W*(L - x).
 

1. What is beam deflection in a tapered pipe?

Beam deflection in a tapered pipe refers to the amount of bending or deformation that occurs in a tapered pipe when a load or force is applied to it. This phenomenon is caused by the distribution of the load and the varying thickness of the pipe along its length.

2. How is beam deflection in a tapered pipe calculated?

Beam deflection in a tapered pipe can be calculated using mathematical equations such as the Euler-Bernoulli beam theory or the Timoshenko beam theory. These equations take into account factors such as the material properties, dimensions, and loading conditions of the pipe to determine the amount of deflection.

3. What factors affect the amount of beam deflection in a tapered pipe?

The amount of beam deflection in a tapered pipe is affected by several factors, including the material properties of the pipe, the dimensions and taper ratio of the pipe, the magnitude and distribution of the load, and the support conditions of the pipe.

4. How does beam deflection in a tapered pipe impact the structural integrity?

Excessive beam deflection in a tapered pipe can cause stress and strain on the material, which can lead to structural failure over time. It is important to consider the potential deflection when designing a tapered pipe to ensure its structural integrity and longevity.

5. Can beam deflection in a tapered pipe be minimized or controlled?

Yes, beam deflection in a tapered pipe can be minimized or controlled through proper design and material selection. Adding support structures or using materials with higher stiffness can help reduce deflection and improve the overall structural performance of the pipe.

Similar threads

Simply supported beam with a spring support in the middle - deflection
    • Mechanical Engineering
Replies
6
Views
810
Bernoulli vs. Reynold Transport Theorem Problem for Raincap
    • Mechanical Engineering
Replies
11
Views
1K
Cantilever beam deflection with point mass and point load at the end
    • Mechanical Engineering
Replies
3
Views
2K
Underground pump vault airflow considerations
    • Mechanical Engineering
Replies
15
Views
818
Leaf Spring Deflection: Calculating Force & Displacement
    • Mechanical Engineering
Replies
4
Views
2K
What is the best beam design for my aluminum tandem axle trailer?
    • Mechanical Engineering
Replies
33
Views
3K
Force of pressurized water exiting a hose or pipe?
    • Mechanical Engineering
Replies
20
Views
7K
Bernoulli equation and parallel pipe branch
    • Mechanical Engineering
Replies
31
Views
2K
Pipe Design to pump sea water from the ocean to a boiler via intermediate tanks
    • Mechanical Engineering
Replies
4
Views
1K
Cantilever Beam Small Deflection Approximation
    • Mechanical Engineering
Replies
8
Views
3K

Hot Threads

Recent Insights

Back
Top