Beam Theory Explained - How Spars Work

HomeBuiltAirplanes.com

Help Support HomeBuiltAirplanes.com:

Status
Not open for further replies.

wsimpso1

Super Moderator
Staff member
Log Member
Joined
Oct 18, 2003
Messages
6,721
Location
Saline Michigan
Billski,

I thought it was complicated, but your intro made it simple enough to follow (I hope that was the intent!). Then toward the end, you made a statement that made me wonder.... And I recall those engineering classes, I fell asleep in two before I gave up on engineering (bad teachers). I actually completed Diff E-Q (only non-engineer in the class), Mathematical Models, Calculus 1 through 3; I was computer science track, so I was math/physics heavy. However, this was all twenty five plus years ago, and I do not use any of it professionally/personally.

Tim
Tim,

I was attempting to make the big picture followable. Glad to hear it mostly worked... Thanks!

The biggest problem with things like this is that any errors get cascaded. The untrained types could at least then have some idea what the big picture looked like, and the trained types could then start executing the pieces and do the whole thing. Once you start down that path, spar design is all very doable and can fit on a couple good sized spreadsheet pages using the scheme I covered.

Now, what made you wonder?

Bill
 

gtae07

Well-Known Member
Joined
Dec 13, 2012
Messages
1,960
Location
Savannah, Georgia
Beam analysis and design is a substantial part of an undergraduate mechanical and/or aeronautical engineering class on structures. This particular course is preceded by one semester each of linear algebra, differential equations, statics, dynamics, and at least two semesters of integral calculus,
This, unfortunately, is where my undergrad structures classes stopped. We never got past prismatic constant-section beams and columns.


shear flow, fastener system design, rib design, skin and bay sizing, and others. Then you have buckling and crippling checks, inspection port placement and sizing, mountings, and so on.i
None of this was covered in any of my undergrad classes. I got a little introduction to it in the Flabel distance course my employer subsidized a while ago but I have never used it in practice.


At least in my alma mater's AE program there is a very pronounced dislike of "nuts and bolts" engineering; everything is highly theoretical and taught with the idea that you'll be applying the knowledge for grad school and fundamental research. Most of the structures education was geared towards preparing you for doing finite element stuff.


For some reason, structural analysis is just one of those things that is very, very hard for me to grasp. I don't know why. Qualitatively I get it, but trying to translate a full wing design into something analyzable through traditional methods, how to break down that complex structure into representative parts, etc. just doesn't compute. I've found my niche on the systems side of things--how does this work, what makes it tick, what happens if something stops working, etc.--and I'm pretty good at the troubleshooting side of things. Heavy numerical analysis, though...
 

BJC

Well-Known Member
HBA Supporter
Joined
Oct 7, 2013
Messages
11,079
Location
97FL, Florida, USA
None of this was covered in any of my undergrad classes.
We covered shear flow and column buckling pretty thoroughly back in the class of ‘70.

At least in my alma mater's AE program there is a very pronounced dislike of "nuts and bolts" engineering; everything is highly theoretical and taught with the idea that you'll be applying the knowledge for grad school and fundamental research. Most of the structures education was geared towards preparing you for doing finite element stuff.
We covered lots of virtural work and complementary energy methods; none with text books, which apparently didn’t exist back in the dark ages. We had to pick up tensor calculus on our own.

I liked Jim Craig as a person. He got interested in the GT Flying Club, and I got to know him there, but he was a new PhD with no real teaching experience when I was in his classes. New teacher, no text available, self taught math - not fun. There are better ways. I hope things improved by the time you were there.

For some reason, structural analysis is just one of those things that is very, very hard for me to grasp. I don't know why. Qualitatively I get it, but trying to translate a full wing design into something analyzable through traditional methods, how to break down that complex structure into representative parts, etc. just doesn't compute. I've found my niche on the systems side of things--how does this work, what makes it tick, what happens if something stops working, etc.--and I'm pretty good at the troubleshooting side of things. Heavy numerical analysis, though...
We had two quarters of Design Lab, taught by Professor Harper as a culmination of his Performance, Stability and Control courses. He also was responsible for the 9’ wind tunnel, which was being used extensively on the C-5 program (headed up by an EAAer who scratch built an EAA Biplane). He was the only professor with any common sense that I had.

Note that there is a real lack of training in how to actually perform design work in mechanical and electrical engineering too. The Chemical Engineers and the Civil Engineers with emphasis on dirt and water seem to come out of school with the ability to design. The Architecture guys seem to know how to design too.

The general attitude at GT seemed to be that a graduate would have a good understanding of the physics and the theories, and could figure out the rest while on the job. That worked for some, but not for others.


BJC aka GTAE70
 

wsimpso1

Super Moderator
Staff member
Log Member
Joined
Oct 18, 2003
Messages
6,721
Location
Saline Michigan
Aero engineering departments always seem to give short shrift to structural mechanics. Funny thing is, we Mechanical Engineers think we are more broadly educated, but that AE's are doing mechanical engineering with a highly reduced material set, you know, mostly air and aluminum. Grin.

All of what I have talked about was either in Mechanics of Materials by Timoshenko and Gere or in Mechanical Engineering Design by Shigley. Shear and bending curves, stresses, Mohr's Circle, von Mises stresses, shear flow, energy methods, fastener design, etc. These books were current in the 1970's.

Billski
 

BJC

Well-Known Member
HBA Supporter
Joined
Oct 7, 2013
Messages
11,079
Location
97FL, Florida, USA
Aero engineering departments always seem to give short shrift to structural mechanics. Funny thing is, we Mechanical Engineers think we are more broadly educated, but that AE's are doing mechanical engineering with a highly reduced material set, you know, mostly air and aluminum. Grin.

All of what I have talked about was either in Mechanics of Materials by Timoshenko and Gere or in Mechanical Engineering Design by Shigley. Shear and bending curves, stresses, Mohr's Circle, von Mises stresses, shear flow, energy methods, fastener design, etc. These books were current in the 1970's.

Billski
I seem to recall a class in Shaky Mech (a required course taught in the Engineering Mechanics school rather than the AE school) with a text by Timoshenko, but I don’t have the book. I sold as many books as I could. I liked eating better than book collecting.

The “no textbooks” comment referred to study of virtural work and complementary energy methods.


BJC

PS Some people are surprised to learn that the math for designing resonance into an electrical circuit, designing it out of mechanical systems / designing to avoid flutter, and designing to achieve stability in a system by the addition of automatic controls are essentially the same.
 

gtae07

Well-Known Member
Joined
Dec 13, 2012
Messages
1,960
Location
Savannah, Georgia
We covered shear flow and column buckling pretty thoroughly back in the class of ‘70.
Column buckling we did, but nothing really with shear flow and definitely no thin-wall structures stuff or crippling of sections.

We covered lots of virtural work and complementary energy methods; none with text books, which apparently didn’t exist back in the dark ages. We had to pick up tensor calculus on our own.
I think we did virtual work at least (with redundant trusses) but I have no idea what a tensor is or how you do calculus on it :ponder: Maybe it's a terminology thing...

I liked Jim Craig as a person. He got interested in the GT Flying Club, and I got to know him there, but he was a new PhD with no real teaching experience when I was in his classes. New teacher, no text available, self taught math - not fun. There are better ways. I hope things improved by the time you were there.
I don't know what happened in the meantime...

We had two quarters of Design Lab, taught by Professor Harper as a culmination of his Performance, Stability and Control courses. He also was responsible for the 9’ wind tunnel, which was being used extensively on the C-5 program (headed up by an EAAer who scratch built an EAA Biplane). He was the only professor with any common sense that I had.
I had a couple of good ones... Juan Cruz from NASA (he was a visiting prof) did a lot of work on Mars entry/descent/landing systems and worked on a human-powered airplane at one point. He taught my performance class.
We also had a guy who retired from Scientific Atlanta and had worked on the original satellite dish pointing algorithms there. He taught my dynamics class one summer.
Jerry Seitzman taught our propulsion class; I don't know if he had industry experience but he at least put concrete examples of things out there for us, and took us to Delta's engine shop one day.
These three guys had a real knack for explaining things that a lot of other professors did not. Contrast with a calc TA who issued a veiled threat ("I grade your exams, you know!") when I asked him to explain a concept in a way other than repeating the proof. :tired:

Note that there is a real lack of training in how to actually perform design work in mechanical and electrical engineering too. The Chemical Engineers and the Civil Engineers with emphasis on dirt and water seem to come out of school with the ability to design. The Architecture guys seem to know how to design too.

The general attitude at GT seemed to be that a graduate would have a good understanding of the physics and the theories, and could figure out the rest while on the job. That worked for some, but not for others.
Lots of emphasis on doing math, very very little on design or any practical considerations. I had classmates that could do stability plots (cue "Poles on the left side of the plane!" joke) in their sleep but had no idea what any of it meant.

You got really good at numerical optimization, but even the capstone design classes were heavily oriented towards steering you to one particular design, and you were basically graded on how well you did the math. I picked the space mission design track, and even there the biggest emphasis was not on the design of our spacecraft or our chosen equipment fit, but whether we happened to pick the data formats and antennas that JPL would want us to use.

By contrast, I hear about Autoreply's experience at Delft, and my neighbor's time at Embry-Riddle doing an Engineering Technology major... and it really makes me grateful for the experiences I had at home, building and flying real airplanes. Because in comparison to those programs, Tech's aero program is doing a disservice to all its graduates who go on to work in industry.


PS Some people are surprised to learn that the math for designing resonance into an electrical circuit, designing it out of mechanical systems / designing to avoid flutter, and designing to achieve stability in a system by the addition of automatic controls are essentially the same.
I wasn't surprised by it, just completely puzzled by all of it. It all made no sense to me, so it worked ;)

The aero department taught that class when I was there, under the title "system dynamics", and I failed it the first time around. Almost all of the AE profs were terrible. Judging by discussions with my ME friends they had a much easier go of it.
 

BJC

Well-Known Member
HBA Supporter
Joined
Oct 7, 2013
Messages
11,079
Location
97FL, Florida, USA
My worst experience at GT was when I had a Professor from China for a series of aero classes. I could not understand a word that he said, and he could not understand me when I asked questions. The frat boys had copies of his previous exams, but I did not.


BJC
 

gtae07

Well-Known Member
Joined
Dec 13, 2012
Messages
1,960
Location
Savannah, Georgia
My worst experience at GT was when I had a Professor from China for a series of aero classes. I could not understand a word that he said, and he could not understand me when I asked questions. The frat boys had copies of his previous exams, but I did not.
Yeah, my low-speed aero prof had a very thick accent, and he could not hear well. Even asked us to blink the lights in the room if we had a question.

Calc 3 prof would write one line at a time on the board, turn and ask "Is this clear?" in a thick Turkish accent, then "OK" and erase it in about as long as it took to read that.
 

BJC

Well-Known Member
HBA Supporter
Joined
Oct 7, 2013
Messages
11,079
Location
97FL, Florida, USA
Remind me at Oshkosh or Lakeland and I’ll tell you about a 600 level math course prof who went crazy. Literally.


BJC
 

BJC

Well-Known Member
HBA Supporter
Joined
Oct 7, 2013
Messages
11,079
Location
97FL, Florida, USA
It’s a long story. He would walk into the classroom, never look at the students, pick up a chalk and eraser, and start writing on the board, talking to himself, and erasing as he went. After a few classes, a masters in math student tried to ask a question. He tried to ignore the student, but the student was persistent. The professor shouted, “That is the dumbest f***ing question that I have ever heard” and went back to writing. The student, politely, persisted. The prof threw the chalk at the student, missed, threw the eraser, missed grabbed two more erassors, threw them, missed and ran out the door. He did not show for the next scheduled class. It went downhill from there. At the end of the quarter, GT suspended his teaching and enrolled him in a psychiatric treatment program. I heard that he never taught again, but I graduated at the end of that quarter and lost interest in him, so I don’t know for sure.

Darn, I was hoping to get a beer out of gtae07 to tell the story. But there is more to it, so perhaps there still is a chance.


BJC

PS. I know crazy; my home town had the world’s largest mental hospital in the world, with approximately 13,000 inmates at its peak. http://www.atlantamagazine.com/great-reads/asylum-inside-central-state-hospital-worlds-largest-mental-institution/
 

plncraze

Well-Known Member
HBA Supporter
Joined
May 11, 2006
Messages
1,781
I've had a few teachers who were losing it. That's why I asked. Good story!
 

Pops

Well-Known Member
Log Member
Joined
Jan 1, 2013
Messages
8,037
Location
USA.
I've had a few teachers who were losing it. That's why I asked. Good story!
I had an English teacher that lost it and ended up in a mental hospital for a while. English was my worse subject, so maybe I was at fault. She would throw her arms up and run out of the class crying several times. Before I could start school in the first grade, my playmate 2 doors away and myself had our own language and no one outside of our family could understand us and they had a lot of trouble. So we had a lot of speech therapy before starting school and any language has been a struggle for me and him all of our lives. Growing up with my NA Grandfather from 6 to 15 years old , that also had problems with English didn't help.
 

tspear

Well-Known Member
Joined
Feb 12, 2014
Messages
795
Location
Oneida
Tim,


Now, what made you wonder?

Bill
Post #8, where you stated the following:
For loads that are only in the y direction, you do EXACTLY the same thing but the computations are run the other way across the cross section - the I computed and y dimensions are most likely different;

If loads occur in z and y direction simultaneously, one way is to run the loads and EI's in each direction, compute the tau and sigmas at critical places around the cross section from each, add them up at each location, then at each place compute von Mises stresses. Watch your notation so that you keep what is going on in each plane straight;

Or if you have simultaneous loads in both y and z directions and then you can compute the simultaneous direction of each of the combined loads, compute the I's for the combined sections in the direction of each of the combined loads, and superimpose them all;
More a case, of me over simplifying what you stated. The way I originally read it, I assumed simple addition of the stresses.

Tim
 

TFF

Well-Known Member
Joined
Apr 28, 2010
Messages
12,832
Location
Memphis, TN
Well, speaking the wrong language when starting school is not the student's fault. You were previously taught what you were doing was OK. I worked with this one guy who did not send his kids to school; they faked the home school papers. the 5 year old could not talk, just grunt. The sister about 7 talked like a baby. One of those things where you dont want to interfere but I should have. He would have gotten out of it, anyway.

I gave up on engineering because I wanted to know why stuff worked not just learn what I was told too. I dont learn without a reason, so I was just treading water. GT is the family school, but I did not take the shot.
 

Pops

Well-Known Member
Log Member
Joined
Jan 1, 2013
Messages
8,037
Location
USA.
Well, speaking the wrong language when starting school is not the student's fault. You were previously taught what you were doing was OK. I worked with this one guy who did not send his kids to school; they faked the home school papers. the 5 year old could not talk, just grunt. The sister about 7 talked like a baby. One of those things where you dont want to interfere but I should have. He would have gotten out of it, anyway.

I gave up on engineering because I wanted to know why stuff worked not just learn what I was told too. I dont learn without a reason, so I was just treading water. GT is the family school, but I did not take the shot.
I guess our language was a mixture of some of our words mixed with Cherokee and English words. I could read English before starting school, just refused to speak just English. I was a avid reader before attending school and my mother bought me mostly books instead of toys.
 

DaveD

Well-Known Member
Joined
May 28, 2010
Messages
320
Location
Perth, Western Australia
If V is "horizontal shear" ( Maximum at neutral axis)
What is "vertical shear"? ( mentioned in Peery, chapter 6.2)
I don’t think this really got answered so I’ll chip in.

Firstly, just to clarify, there is shear load, shear stress and shear strain:

Shear load – The load (force) acting perpendicular to the axis of the beam. This is the lift when considering the vertical forces acting on a wing spar.
Shear Stress – The internal shear forces acting within the material of the beam
Shear strain – The deformation of the beam material in response to the shear load

(If you want a more in depth explanation of loading, stress and strain read this: https://ultralightdesign.wordpress.com/2017/11/15/biscuits-jelly-nylon-steel/)

Now we’ve cleared that up, the ‘horizontal’ and ‘vertical’ shear BBerson is asking about is the shear stress. Looking at the attached diagram (below) which shows a beam with a load applied perpendicularly (and, just to be clear, completely ignores bending).

Shear.png

If we take an imaginary slice through the beam as shown in (A)you can see there must be a vertical shear acting on the sliced surfaces (shown in red) to balance the load applied to the end of the beam.

Next we’ll look at (B). imagine we have chopped a small square out of the beam web. It must have the vertical shear acting on it we identified in (A), but if that was the only forces acting it would spin clockwise, because the forces aren’t completely balanced (the up and down forces are equal but they are separated horizontally so there’s no net vertical force but there is a torque). So (B) can’t be accurate – we know statically loaded beams don’t spin!

The final part (C) has the complimentary horizontal shear shown. You can’t have the vertical shear force without the horizontal shear to counteract the torque and keep the element in equilibrium. The two must go together, you simply can’t have one without the other.

It can be more intuitive to think in terms of tension and compression. The right hand side of (C) shows what happens if you look at the stress in a different way. A shear stress is simply what you get from pure tension and pure compression if you rotate your “frame of reference” 45°. Imagine drawing a square on the beam web and then applying the load, the square will distort into a rhombus shape…

Adding in the effect of bending makes things more complex as the beam web is not really in “pure shear” but as Billski said there is an excellent explanation in Gere & Timoshenko’s “Mechanics of Materials” Book.

I hope this helps

DD.
 

BBerson

Well-Known Member
HBA Supporter
Joined
Dec 16, 2007
Messages
13,102
Location
Port Townsend WA
Thanks David.
The books I have largely ignore vertical shear. (J.E. Gordon, Strojnic and others)
I am thinking that the web thickness is sized for horizontal shear, so perhaps it will be adequate for vertical shear, and so vertical shear can be ignored. At least in metal.
The web usually has vertical angles and ribs. These are in compression, I assume, and may or may not be related to vertical shear?

I will look for the book. (but don't want to complicate beam design more than needed)
 
Last edited:

ragflyer

Well-Known Member
Joined
Apr 17, 2007
Messages
233
Thanks David.
The books I have largely ignore vertical shear. (J.E. Gordon, Strojnic and others)
I am thinking that the web thickness is sized for horizontal shear, so perhaps it will be adequate for vertical shear, and so vertical shear can be ignored. At least in metal.
BB , vertical sheer and horizontal shear are equal ( for equilibrium) and as such not separated. In other words if you size web for one you are good for other.
 
2
Status
Not open for further replies.
Top