Author: Richard

Cozzone Beam Section Shape Factor k

Cozzone k shape factorNote added 1 March 2017: The Cozzone shape factor for common cross sections is now in the Section Properties of Common Cross Sections spreadsheet. There are expressions for many more cross sections. This subject is covered in depth in the new edition of our free textbook. This post can be considered obsolete.

In writing the plastic bending section for our (soon to be released) free textbook I started to look into the origin of the shape factor for the cross section of a beam for plastic bending. It is explained in Bruhn and in other references but in the past I have always just used the existing section shape factors without making the to find out what they really were.

It is no secret (it is defined in most of the references) that the shape factor ‘k’ is equal to the plastic section modulus divided by the elastic section modulus – so it is an expression of the plastic bending capacity over the elastic bending capacity.

The elastic bending modulus is easily found – there are many references and methods available to calculate the elastic modulus (2nd moment of area divided by the distance to the outer fiber or I/c). The plastic bending modulus is less simple and less easily available.

In the figure to the left, I have collected the traditional, and some additional expressions, for the cozzone shape factor.

We have also produced a spreadsheet that will calculate the cozzone shape factor for a symmetrical section of compound rectangular shapes. Make sure to read the note at the top of the spreadsheet and always sanity check the result.

If anyone out there knows a better general method for the calculation of section plastic modulus I would love to hear from you.

Happy Stressing!

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Neuber Method for Reducing Elastic Stress Values

This is a method that can be used to reduce the apparent high stresses caused by geometric stress concentrations in fine mesh FE models with linear material properties……which is quite a mouthful.

In my few years in the analysis trade I have noticed that structures, despite the advances in analysis tools, have not been getting much lighter. In part this is due to inexperience with interpreting static analysis models. It is easy now to create a quick fine mesh model and check your stresses for the critical case, size the part and move on to the next bracket or fitting. However, these quick linear static analyses include geometric Kt effects and report high elastic stress values. Using these stress results to size the component or select a material is incorrect. It will be conservative and the part will be heavy.

If you were to size the same component with a hand analysis you would calculate the properties at a section, apply the loads and moments by hand, maybe calculate the principal stresses and use that resulting value to size to. Nowhere in the hand analysis would you take account of Kt effects and you would also consider using plastic bending effects (Cozzone) where appropriate to reduce peak linear bending stress values.  A linear static FE model include KT effects and does not account for material plasticity.

Common features will have a Kt of 3 or greater –  if your field stress is at an ultimate value of 50ksi (which can be matched using a hand analysis) you will be fine for most aluminum alloys, a fine mesh model with a hole will report at least 150ksi, only because of the geometry of the hole and the stress concentration created by that geometry.

There are two problems with this

  1. In the real world, if you are using a common aluminum alloy, the stress will be reduced by plastic redistribution which is fine for an ultimate level check
  2. You should not consider Kt effect for static analysis regardless

NeuberSo – how do you mitigate the Kt effects from linear static fine mesh model results?

The triangular area of the strain energy under the elastic material line can be equated to the point where the line of constant strain energy related to the linear stress and strain crosses the elasto-plastic material curve.

This approach is slightly conservative as you could equate this to the total area under the elasto-plastic material curve which would further lower the corrected stress.

The Neuber method equates the areas of the two triangles to reduce the high elastic stress.

Note that this method does not remove the Kt effect per se, but it does remove the artificially high stress that the linear elastic model results report, and gives you the equivalent plastic stress at the peak linear stress location.

We have updated and improved our free spreadsheet to give the reduced Neuber stress here

This improved version of the spreadsheet automatically solves for the Neuber stress at the intercept between the line of constant strain energy and the elasto-plastic material curve.

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Engineering in Excel?

For years we have been using Microsoft Excel to write technical reports. Microsoft Excel is a compromise choice – it does nothing very well, but it allows you to do many useful things, the negative aspects can be managed and it is nearly universally used across the world, at least on desktop and laptop PC’s.

Recently we have been writing reports for two clients who are using Microsoft Word and this has thrown into sharp relief the reasons why we use Excel and not Word.

I started using Excel for reporting while working at the Morson Projects Stress office in the UK in the early/mid 1990’s. Over the following years of experience working at various locations on contracting jobs and working with some great engineers I picked up better habits for using Excel – how to create and govern report templates, creating analysis methods in final report formats, ways to make Excel bend without breaking it.

Then you have to switch back to using Word …….. I have spent a lot of the last few weeks pulling out my graying hair to get Word to just behave itself. Random changes of text formatting,  random page template changes, random crashes, random section numbering changes, random font changes, random randomness…..

In engineering terms Excel is determinate, Word is indeterminate. Word seems to inhabit some quantum state of probability and, indeed, merely observing a Word document does seem to affect the outcome. Honestly – anything seems to affect the outcome – the weather, the USD-CAD exchange rate, the color of my pants, whether I sit with my legs crossed or I sit man-spreading at my desk……

I don’t blame Word – it is not optimized for technical report writing. Word, however, is especially poor at adapting to doing anything other than prose and pictures.

I also believe that engineers like Excel because it does a of of things moderately well. Opening up Excel in the morning to start work feels like like the first time I saw a leatherman multi-tool for the first time or a particularly well appointed swiss army knife – a faint thrill created by all of the possibilities and potential that the tool represents.

Excel is ‘good enough’ in almost every aspect, and ‘good-enough’ is perfection for an engineer.

To quote the full verse; the second half, which is the critical part, is almost always forgotten:

Jack of all trades and master of none

Oft times better than a master of one

To me Excel is a natural fit for engineers, as a simple analysis tool, a makeshift database and, when used properly, the best tool for writing reports.  To force engineers to use Word (designed for use by secretaries and….err….poets?), is like forcing a tree surgeon to use an egg whisk when a chainsaw is what they really need to do the job.

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FAA part 23 revamp – good or bad?

AIRCRAFT QUESTIONThis month the FAA released their draft of the new part 23 regulations.  The reformulation of the regulations was prompted by the increasing cost of part 23 aircraft certification programs. It is true that the certification cost of part 23 programs has been increasing, it is also true that the cost of these certification programs has been increasing disproportionately to the increase in the complexity of the safety standards.

It is my experience that the interpretation of the existing regulations by the FAA has been getting progressively more conservative and cautious
regardless of the change to the wording of the regulations. Changing the wording of the regulations is going to do little to encourage as less conservative interpretation and is likely to increase the anxiety level of FAA staff and, understandably, their caution in making a finding of compliance.

What do you think is the solution? Do I have it wrong? Are the FAA doing the right thing?

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New Engineering Font

viking-2Our sister company, XL-Viking, has released something they have been working on for a little while. A custom engineering font that works with the XL-Viking add-in – but is fully enabled and useful in its own right:

http://www.xl-viking.com/free-engineering-analysis-font/

This font is compatible with our free engineering analysis spreadsheets: HERE

Enjoy!

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Moving you, your family and your business to Cayman – Part 3

If you have been following our previous posts on this subject you will now have your business set-up and be on the way to obtaining your residency status established – or at least be thinking about it.

Schools – as a non Caymanian you are not allowed to use the state school system and you have to put your children in private school. If you move here with your children you must have places at a private school arranged in advance. There are a range of private schools on the island that cater to the US and the UK school systems and the US system private school offers a limited IB (International Bacceloriat) program. On the whole our experience with our choice of school has been positive and out kids were in shock with the increase in academic standard compared to the Canadian school system.

Pets – in order to bring your pet here you require advance planning and some patience. The process is outlined here. In general the process will take around 3-6 months. Also be warned that most carriers will not take animals in the hold during the summer months so if you have a large dog you may have to wait until the winter months to bring it to the island. This was the most complex aspect of our move to Cayman. Some pets have to be registered with the department of agriculture – most breeds of dogs have to be registered. You can take your dog onto the patio of most restaurants (unless they are ‘fine dining’) and dogs are generally accepted as a part of life on the island. You can take then on all the beaches and as long as they are well behaved and you are considerate and pick up after your pet, they are accepted and welcome.

Bank accounts – opening bank accounts here was a surprise. Not a pleasant surprise. Because of the scrutiny on Cayman Island banks some banks have become very cautious about taking on new customers, After we waited 3 weeks to go through the screening process for our business accounts our account manger calmly told us that we were the first people to get a business bank account approved during her 3 months at the bank. She did not tell us this before we applied. Butterfield Bank and RBC are stricter than the rest of the banks on the island and you can choose to go with one of the banks with lower requirements. We have found that it is very important to choose a bank with adequate parking at the branch in Georgetown – RBC is particularly strong in this aspect. In general the cost of banking is high and the fees are more numerous and more expensive than we are used to in Canada or the US. At first the bank staff were standoff-ish and not very helpful but once they realize you are there to run a legitimate business in the local community the customer service is excellent.

Cayman offers many great things, climate, quality of life, safety, security and an economy refreshingly free from well-intentioned but ultimately burdensome government intervention. I cannot recommend it without reservation but I can recommend it overall. Every morning we wake up, look out at the blue sky and the blue ocean and thank our lucky stars that we are able to spend some time in a location that is great for business, has a culture that is welcoming and safe and is blessed with a fabulous environment that is so much fun to explore.

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Forest Products Laboratory Reports – Sandwich Panel analysis

FPL ReportsIt is a little known fact that most (all?) of the analysis for sandwich panels – Mil-Hdbk-23, NASA Papers and many different OEM stress manuals are based on the work done 50 years ago by the Forest Products Laboratory.

This excellent work was collected in a series of reports and put on a US government server and largely forgotten about. I came across them researching the text book, delving into the references cited in other classic sandwich panel references.

These references are priceless in that they represent the earliest public domain derivation of the classical analysis methods in wide use today. They are also very well laid out and easy to follow – unlike many other references. I have taken the mathematical curve derivations for the general cases in these references and constructed the curved from scratch and they work beautifully.

I will upload those spreadsheets as soon as they are ready. This great series of references can be found HERE.

 

 

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Composite Analysis Spreadsheets

AA-SM-101-108We have been checking and up loading our latest set of free composite analysis spreadsheets to our website. These include basic laminate material properties derivation (ABD Matrix), laminate envelope strain analysis and lamina stress analysis methods.

The set of laminate analysis sheets uploaded so far can be found HERE

We have also updated our un-cored laminate panel buckling set of spreadsheets, I am much happier with these than the previous methods we had used. The subset of laminate buckling analysis sheets can be found HERE 

In total we have uploaded over 100 free analysis spreadsheets to the new website and are working on getting another 100 more ready to upload over the next few weeks. You can browse all of our free spreadsheets HERE

We love that we are able to make all of the library materials available for free. If you want to help us continue to expand our work please make a donation using the button at the top of this page.

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AGARD Papers

AGARDIn the last few years I have been coming into contact with more and more AGARD reference papers. These papers are the NATO or European version of NACA or NASA papers and while each paper is less focused and they tend to cover wider subjects they are still a great resource. All of the AGARD papers we are posting are tagged with AGARD and can be found here.

We have posted 50 papers initially and are going to follow up with hundreds more. Let us know what you think.

 

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Weld Strengths for Steel and Aluminum

One of the problems that I have found over the years is that the quality of data for the strength of welded steel and aluminum is generally low. There is a table in Bruhn that gives conservative allowables for some steels but there is not much else that gives data you can use in a certification analysis. As background work for the textbook chapter on welded joints I have started to collect some NACA and NASA reports that go into more detail and includes some data on aluminum welds as well. These few documents can be found here.

There is also some data in section 8 of the Mil-Hdnk-5 or MMPDS. This data only includes spot welding data for aluminum alloys and the combination of spot welding and aircraft structure is generally seen as a bad thing and to be avoided……

If you have any data from a credible source for weld strengths that can be referenced drop me a line and let me know.

Happy Stressing.

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