Real life engineering problem I or guidance

[nickatkins]

Hi everyone,

I work as a mechanical engineer in Ws Atkins in the analysis and asessment of offshore structures. We are producing a MatchCad spreadsheet at the moment to do what we call a stiffened joint check.

I am posting here to try and get some advice on how to approach and/or solve my problem. I have a solid background in maths and have made some headway.

I will try to give some background to the problem in case anyone is interested :)

background:
A joint is simply the point where two structural members meet, for example a pipe joining onto another pipe.
If you can imagine inside the pipes we sometimes have what are called ring stiffeners, these are internal rings with a web and flange that stiffen the joint to reesist bending moments and shear forces.
Now imagine a smaller pipe joining a larger pipe, the main pipe is called the chord and the smaller joining pipe the brace. The chord is the one that contains stiffeners and can contain several of them. A stiffener only has an effect if it lies within the footprint of the joining brace as it resists incoming forces from the brace by using up its shear capacity. The flange like shape also helps to resist minor axis bending and compression/squashing of the pipe as it increases what's called the 2nd moment of area. In a cross section these internal stiffeners look like a T shape on the inside wall of a pipe. Internal stiffeners are used in a variety of structures not just joints and are similar to adding a web plate to a beam.

Now the problem:


I need to calculate the effective width of the stifferners within the footprint:
see attached image.

Imagaine two circular pipes one of diameter D and one d where D>d.

The smaller pipe intersects the larger one much like in the problem of two intersecting cylinders. In this case however the pipes can intersect at angle theta wherby θ ranges from 0-90 degrees.
Now if you imagine the area of contact of the two pipes eg. If you take a single pipe and take an angled cut you end up with an oval shape yes? we can solve the width of this oval at any point by using the equation of an elipse.
In my case however you do not get an oval shape because the surface is curved in 3 dimensions its like an oval projected onto a cylinder. The shape you actually get is more like an egg shape see my attached picture.

I need to solve the equation of this shape to give x for a given y and also for any given angle. I.e work out the projected width (as if you measured the 2d image) of the shape at any y position and also accounting for the fact that the egg shape is going to vary with the angle theta.

I know its a long shot posting here so I'm looking for advice as to where I should be looking or possible methods I can try to use.

I have found some useful information Ovals and Egg Curves it appears as though i need to add a factor into my elipse equation and this factor will vary with theta.

another approach i thought of was trying to work out the arc lengths at different points along the main pipe but I am not sure how to approach this.

If anyone has any feedback or knows of anyone that can help I would really appreciate your efforts!

Kind Regards

Nick

 

[Studiot]

Hello nick,

You may like to tax the corporate library for these books to help you

Geometry of Spatial Forms
(Analysis, synthesis, concept formulation and space vision for CAD)

Gasson

Computational Geometry for Design and Manufacture

Faux and Pratt

The Mathematical Description of Shape and Form

Lord and Wilson



I once worked for Atkins in another life are they still alive and kicking?

 

[nickatkins]

Hi Studiot,

Thanks for your reply I'll see if i can get a hold of those books they sound quite usefull.

Atkins is indeed still going strong, which department where you in?

 

[Studiot]

I would add to this list a book on old fashioned engineering drawing such as

Geometry of Construction

Nichols and Keep

They have several chapters on interpenetration and intersection of complicated shapes.

, which department where you in?

Bridges

 

[blue_raver22]

Hi Nick,

Thank you for providing background information on your engineering problem. It sounds like you are working on a challenging and important task in the analysis and assessment of offshore structures. I can offer some guidance and suggestions on how to approach and potentially solve your problem.

Firstly, it is great that you have a solid background in mathematics as it will be essential in finding a solution. Based on your description, it seems like you are trying to calculate the effective width of the internal stiffeners within the footprint of the joining brace. This is a complex problem as it involves curved surfaces and angles, but there are a few approaches you can try.

One approach is to use numerical methods, such as finite element analysis, to model and analyze the joint. This would involve breaking down the curved surfaces into smaller elements and using equations and algorithms to calculate the effective width at different points along the joint. This can be a time-consuming process, but it can provide accurate results.

Another approach is to use analytical methods, such as equations and formulas, to approximate the effective width. This may involve simplifying the curved surfaces into simpler shapes, such as circles or ellipses, and using known equations for those shapes to calculate the effective width. This approach may be faster, but it may not provide as accurate results as the numerical method.

I see that you have already found some information on ovals and egg curves, which could be helpful in your calculations. It is also a good idea to consult with other engineers or experts in the field, as they may have encountered similar problems and can offer valuable insights and advice.

In terms of your specific problem of calculating the projected width at any y position and angle theta, it may be helpful to break down the problem into smaller steps and tackle them one at a time. For example, you could first solve for the width at a specific y position and then incorporate the variable of angle theta into your calculations.

I hope these suggestions can help guide you in finding a solution to your engineering problem. Don't be afraid to reach out to colleagues or experts for assistance, and continue to explore different methods and approaches. Good luck!

Best regards,