AE4630 - Aerospace Structural Design:
Lecture 2
Introduction, Structural Idealization, and Scaling
Axial members carry extensional and compressive loads
Also called columns
Bending members carry bending moments
- A subset of bending members are called beams
Torsion members carry twisting moments (torques)
- A subset can be called shafts (but not all torsion members should
be called shafts)
- i.e., Crankshafts
- Other structural members carry torsion
- fuselages
- wings
Shear panel
- A thin sheet of material used to carry in-plane shear load
- Skin (shear member, i.e wing panel)
Beam on an elastic foundation
Membrane
Plates and shells
Curved beams
Combinations
Optimal aerostructures typically combine several structural features:
Load Paths
Wing skins \(\Longrightarrow\) stringers \(\Longrightarrow\) ribs \(\Longrightarrow\) spars \(\Longrightarrow\) fuselage
787 Fuselage (Composite Construction)
Galileo’s scaling problem
Galileo was among the earliest to document the sizing problem
"Who does not know that a horse falling from a height of three or four cubits will break his bones, while a dog falling from the same height or a cat from a height of eight or ten cubits will suffer no injury? … and just as smaller animals are proportionately stronger and more robust than the larger, so also smaller plants are able to stand up better than the larger.
I am certain you both know that an oak two hundred cubits high would not be able to sustain its own branches if they were distributed as in a tree of ordinary size; and that nature cannot produce a horse as large as twenty ordinary horses or a giant ten times taller than an ordinary man unless by miracle or by greatly altering the proportions of his limbs and especially his bones, which would have to be considerably enlarged over the ordinary"
As J.B.S. Haldane put it in his classic essay “On Being the Right Size”:
“You can drop a mouse down a thousand-yard mine shaft; and, on arriving on the bottom, it gets a slight shock and walks away… A rat is killed, a man broken, a horse splashes.”
Cube \(B = 10 \times\) Cube \(A\)
- Bone strength is proportional to cross sectional area of the bone (\(L^2\))
- Weight is function of volume (\(L^3\))
- Relative strength decreases inversely with length scale (\(L^{-1}\))
Human bone strength
- Rats, Humans, and Cows have similar bone strengths
- With scaling, eventually, an animal’s bones will break under its own
weight.
- Gait and activity level matter.
- Larger animals tend to move much slower
