J.P. Den Hartog Strength of Materials

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 !!

 

[civeng80]

Anyone familiar at all with the book?

 

[haynewp]

I have it, but I prefer Gere & Timoshenko.

 

[civeng80]

Timoshenko is good but tends to be a little dry at times!

 

[graybeach]

civeng80,
Can you describe the myosotis method further? Is it based on standard beam theory?

 

[Lion06]

Yes, please describe the method. I may purchase the book because of it.

 

[slickdeals]

The book is dirt cheap on Amazon. I purchased that and advanced SOM for $26. Can't go wrong.

 

[civeng80]

graybeach and StructuralEIT

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.

 

[slickdeals]

I have just ordered it, will let you know

 

[slickdeals]

http://translate.google.com/transla...irefox-a&rls=org.mozilla:en-US:official&hs=sq

 

[civeng80]

Thanks slickdeals very interesting historical information. I think you too will be impressed with the myositis method of beam deflection.

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 !

 

[prost]

Amazon is dirt cheap, $10.17 plus shipping, for this Den Hartog book. (when did Amazon boost their minimum order for free shipping from $25 to $45?)

 

[civeng80]

curious to know if "Advanced Strength of Materials" is useful for structural engineers ? I think it would be mostly for mechanical engineers and material testing. Anyone who has it I would like your comments !

Cheers !

 

[Lion06]

Am I missing something? Aren't the principals of superposition valid for any set of deflection equations (provided you are using them properly - e.g. using simple beam equations for a simple beam).
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?

 

[rb1957]

no i don't think you're missing anything ... all this method is is superposition. i think the insight was assume you have a doubly cantilevered beam; this beam can be cut anywhere along it's length producing statically determinate cantilevers.

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.

 

[civeng80]

Sorry I may have been misleading.
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.

 

[rb1957]

sorry, but IMHO what a horribly complicated way to solve a simply supported beam !

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 !!)

 

[civeng80]

He doesn't determine the internal moment at all and certainly doesn't use Roark. He just writes an identity relating angles and deflections of the 2 cantilevers which is easily seen from the 2 broken cantilevers and the result of those cantilevers I refered to above.
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!

 

[civeng80]

With respect rb1957

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.

 

[rb1957]

i haven't seen the book. maybe something is being lost in translation, but i don't see the value in today's world of very cheap calculating ability.

"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).