J.P. Den Hartog Strength of Materials
J.P. Den Hartog Strength of Materials
(OP)
Hi all ! Been reading this incredible little book on Strength of materials by an amazing engineer J. P. Den Hartog. He has a method of calculating beam deflection by what he calls the Myosotis method. Its absolutely an amazingly simple and quick method which Ive never come across before in any textbook including Timoshenko's work. Anyone ever heard of this method or indeed use it in their work ? I'd be very interested to hear from anyone who knows more about the method and where it derives from.
Thanks all especially eng.Tips its great !!
Thanks all especially eng.Tips its great !!






RE: J.P. Den Hartog Strength of Materials
RE: J.P. Den Hartog Strength of Materials
RE: J.P. Den Hartog Strength of Materials
RE: J.P. Den Hartog Strength of Materials
Can you describe the myosotis method further? Is it based on standard beam theory?
RE: J.P. Den Hartog Strength of Materials
RE: J.P. Den Hartog Strength of Materials
RE: J.P. Den Hartog Strength of Materials
The method uses standard linear and angular deflections of 3 simple cantilevers.
1. moment at end
2. Load at end
3. Uniformly distributed load
These equations are obtained by the usual standard methods e.g. integration method. With these results any deflection for any loading conditions can be obtained and the deflection equation may be written down immediately on paper.
The most complicated beam deflection can be solved just from these formulas and the principle of superposition. Again I stress that the expression for deflection can be written down in one simple step.
The book is very cheap and still in print from Dover publishing and just this method is worth probably 10 times the cost of the book.
I actually used it in one of my designs early this year (simple beam deflection) and had to explain it to the engineer who checked the comps who was equally impressed.
Its really very impressive and Den Hartog himself says in the introduction to the book that after the alphabet and the table of multiplication, nothing has proved quite so useful as this method. Apparently it derives from his lecturer a Professor C. B. Biezeno of which I could not find any references at all of him.
Slickdeals hows the advanced strength of materials book ? Is there anything useful for structural engineers or is it more for mechanical engineers? Let me know because I may purchase it.
RE: J.P. Den Hartog Strength of Materials
RE: J.P. Den Hartog Strength of Materials
RE: J.P. Den Hartog Strength of Materials
Just by quoting the method (just the name myositis starts intrigue!) in your structural computations will raise quite a few eyebrows even amongst the most experienced of engineers!
Cheers !
RE: J.P. Den Hartog Strength of Materials
RE: J.P. Den Hartog Strength of Materials
Cheers !
RE: J.P. Den Hartog Strength of Materials
I believe the AISC manual uses the double integration method for the moment and deflection equations. If you have a simple beam with uniform loading AND a point load at midspan, you can use superposition to get moment using (Wl^2)/8 + Pl/4 and to get deflection using the sum of the two deflection equations.
I am not understanding how the myosotis method differ?
RE: J.P. Den Hartog Strength of Materials
question, how does he determine the internal moment (to be applied to the end ot the cantilever)? simple solutions like from Roark ?
observation, it looks like this method isn't as universal as the OP would have us believe, how do you treat intermediate point loads ? (convert them to UDLs?) how about varying distributed loads ?
observation, i think this method is born in a time when computing power was limited. for example, I have a spreadsheet for solving doubly redundant beams (no, I'm not bragging, just an example of the complexity we can solve today without being too smart). i think this method might be useful in meetings (to impress people) by quickly coming up with an answer.
RE: J.P. Den Hartog Strength of Materials
It uses the results of the cantilever solutions I described above and breaks a simply supported beam into 2 cantilever beams and then writes down an identity equations from the compatabilty of the 2 cantilevers and then the desired deflection is obtained. In one of the examples it uses compatibilty to check an answer using myositis. Your quite correct in what your saying the principal of superposition is valid and can be used as long as the beam is in the elastic range.
My apology I didn't have the book in front of me when I was describing the method.
RE: J.P. Den Hartog Strength of Materials
and how do you back out the cantilever end moment ?
personally, i'd file this method with my slide ruler (but then i never had one) ... come to think of it using a slide ruler in a meeting might be just as impressive (either in a good "isn't he smart to be able to use a slide rule" or bad "what a dinosoar!" way !!)
RE: J.P. Den Hartog Strength of Materials
Armed with this information he solves any simply suppoeted beam deflection. in 2 to 3 lines.
rb1957 have you seen the examples in the book? If you have your missing the point. If you haven't then I invite you to do so.
Intermediate point loads are not a problem, varying UDL's it cant handle. I dont get a hell of alot of these anyway. If I do then its the computer. Im just comparing this method to moment area, virtual work and the other conventional methods in Mechanics of Solids and I personally think its a very clever method.
Cheers!
RE: J.P. Den Hartog Strength of Materials
But if you think this is equivalent to a slide rule then so to is double integration , moment area and the virtual work method of solving beam deflections. I guarantee you that students at University today would still be using them today.
I simply am saying its a clever method of solving beam deflections. Nothing to do with meetings.
RE: J.P. Den Hartog Strength of Materials
"back in the day" of slide rulers these sorts of methods were needed to solve structures, short of pages of error-prone calculations. today a spreadsheet solves these and much more complicated things as well.
i guess you're usually interested in displacemnts, too. i rarely need these, and analyzing a SS beam (internal moments) isn't a problem. typically i only get into displacemnts and virtual work for solving redundant beams ('cause i know i can, and don't want to use FE on something as simple as this).
RE: J.P. Den Hartog Strength of Materials
I learned several methods of calculating slopes and deflections in two undergrad analysis classes. Conjugate beam method, double integration, I used stiffness matrices for something but I'll be damned if I can remember anymore, virtual work, there may be a couple more that I am forgetting, and Castigliano's method (my personal favorite).
If I had to solve a rather difficult deflection problem or indeterminate problem by hand, I would definitely use Castigliano's method.
RE: J.P. Den Hartog Strength of Materials
Structural engineers have to design for strength and serviceability i.e. they have to assess deflection. In a simply supported beam I wouldn't be using a computer or a spreadsheet. I would simply do a hand calculation using a table or design aid I would have around. Some can be pretty time consuming and no spreadsheet is around to solve them, so why not use this method ? No need to use a slide rule.
One further point to write a spreadsheet for beam deflection you would need to use one of these methods anyway.
My point was mainly directed to structural engineers who have a knowledge of Mechanics of Solids and the traditional textbook methods of solving for deflections as I stated above (Another method in the list may be Castiglianos strain energy method).
This is simply another method.
At the end of the day you use whichever method you feel comfortable with.
Thats all from me !
RE: J.P. Den Hartog Strength of Materials
RE: J.P. Den Hartog Strength of Materials
RE: J.P. Den Hartog Strength of Materials
RE: J.P. Den Hartog Strength of Materials
For your example as I said I would look up solutions in standard solutions (2 of for different load cases) and then use superposition as you and I have already suggested.
I repeat myself here. Mysotis is just another method (different albeit!) from the classical methods such as those already mentioned. The standard solutions used these methods to work out deflections so indirectly your using these methods in calculations if your using design aids.
I repeat myself again
At the end of the day use whichever method you feel comfortable with. StructuralEIT if it takes you 40 seconds to calculate a deflection then continue this method and dont bother buying the book.
Cheers !
RE: J.P. Den Hartog Strength of Materials
If you like Castigliano's method for difficult problems then Myosotis is definitely worth looking at in my opinion.
My personal favourite for the difficult problems was and still is virtual work method and it can be used for varying UDL as well (with a table of integrals!)
If your getting the book you'll be glad you did for the money it cost. Even Castigliano's method is very well covered as is many other topics.
Anyway thats enough from me now !
Cheers Mate !
RE: J.P. Den Hartog Strength of Materials
http://en.wikipedia.org/wiki/J._P._Den_Hartog
RE: J.P. Den Hartog Strength of Materials
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