by J E Gordon
Wall thickness t
Mean radius r ⅔πrt3
Any continuous thin-walled tube of thickness
t, perimeter U and
enclosed area A
Again, considerably more detailed information is to be found in Roark.
Appendix 4 The efficiency of columns and panels under compression loads
For a column
Assuming that the column is of such proportions that it is liable to fail by elastic buckling (Chapter 13), then the critical or Euler load P is given by
where E = Young’s modulus
I = second moment of area of cross-section
L = length.
Now suppose the column to have a cross-section which can be expanded or contracted while remaining geometrically similar so that its size is characterized by a dimension t, say.
Then I = Ak2 = constant. t4
where A = area of cross-section
k = radius of gyration (Appendix 2).
If there are n columns, the total load sustained
so
so
But the weight of n columns = constant.nt2Lρ = W, say where ρ is the density of the material.
So
So efficiency of structure
The parameter is known as a ‘structure loading coefficient’ and depends solely upon the dimensions and loading of the structure. The parameter is called a ‘material efficiency criterion’ and depends solely upon the physical characteristics of the material.
For flat panels
The above arguments apply to a column whose thickness can be varied in two dimensions. The thickness of a flat panel can only be varied in one dimension.
Suppose second mpment of area per unit width of panel = I = Const.t3
for n panels
so
Const.
Weight of n panels per unit width = W,
So efficiency
Again is a ‘structure loading coefficient’
and is a ‘material efficiency criterion’.
Suggestions for further study
At the end of the day, the best way to learn about structures is through observation and practical experience: that is, by looking at structures with a seeing eye and by making them and breaking them. Of course the opportunities for the amateur to build real aeroplanes or bridges are likely to be rather limited; but do not be ashamed to play with Meccano, or even with old-fashioned building blocks. These things, incidentally, are much more instructive than the modern plastic toys which clip together in various ingenious ways. When you have built your bridge, load the thing up in a realistic way and see how it fails. You will probably be both surprised and disconcerted. When you have done this the rather dry books on structures will seem a good deal more relevant.
Although there is not much scope for the amateur bridge-builder, it has often seemed to me that the field is wide open in biomechanics. This is a new subject about which very little is known, either by the engineers or by the biologists. It is very possible that there is an opportunity here for the enterprising amateur to make a name for himself.
Though there are rather few good books, as yet, on biomechanics there are any number on materials and elasticity, A small and admittedly arbitrary selection is given below.
Books about materials
The Mechanical Properties of Matter, by Sir Alan Cottrell. John Wiley (current edition).
Metals in the Service of Man, by W. Alexander and A. Street, Penguin Books (current edition).
Engineering Metals and their Alloys, by C. H. Samans. Macmillan, New York, 1953.
Materials in Industry, by W. J. Patton. Prentice-Hall, 1968.
The Structure and Properties of Materials, Vol. 3 ‘Mechanical Behavior’, by H. W. Hayden, W. G. Moffatt, and J. Wulff. John Wiley, 1965.
Fibre-Reinforced Materials Technology, by N. J. Parratt. Van Nostrand, 1972.
Materials Science, by J. C. Anderson and K. D. Leaver. Nelson, 1969.
Elasticity and the theory of structures
Elements of the Mechanics of Materials (2nd edition), by G. A. Olsen, Prentice-Hall, 1966.
The Strength of Materials, by Peter Black. Pergamon Press, 1966.
History of the Strength of Materials, by S. P. Timoshenko. McGraw-Hill, 1953.
Philosophy of Structures, by E. Torroja (translated from the Spanish). University of California Press, 1962.
Structure, by H. Werner Rosenthal. Macmillan, 1972.
The Safety of Structures, by Sir Alfred Pugsley. Edward Arnold, 1966.
The Analysis of Engineering Structures, by A. J. S. Pippard and Sir John Baker. Edward Arnold (current edition).
Structural Concrete, by R. P. Johnson. McGraw-Hill, 1967.
Beams and Framed Structures, by Jacques Heyman. Pergamon Press, 1964.
Principles of Soil Mechanics, by R. F. Scott. Addison-Wesley, 1965.
The Steel Skeleton (2 vols.) by Sir John Baker, M. R. Home, and J. Heyman. Cambridge University Press, 1960–65.
Biomechanics
On Growth and Form, by Sir D’Arcy Thompson (abridged edition). Cambridge University Press, 1961.
Biomechanics, by R. McNeil Alexander. Chapman and Hall, 1975.
Mechanical Design of Organisms, by S. A. Wainwright, W. D. Biggs, J. D. Currey and J. M. Gosline. Edward Arnold, 1976.
Archery
Longbow, by Robert Hardy. Patrick Stephens, 1976.
Building materials
Brickwork, by S. Smith. Macmillan, 1972.
A History of Building Materials, by Norman Davey. Phoenix House, 1961.
Materials of Construction, by R. C. Smith. McGraw-Hill, 1966.
Stone for Building, by H. O’Neill. Heinemann, 1965.
Commercial Timbers (3rd edition), by F. H. Titmuss. Technical Press, 1965.
Architecture
There are many hundreds of books on architecture. I have picked out two, almost at random:
An Outline of European Architecture, by Nikolaus Pevsner. Penguin Books (current edition).
The Appearance of Bridges (Ministry of Transport). H.M.S.O., 1964.
Index
Aberdeen, Lord
Aeroelasticity
Aesthetics
Agincourt, battle of
Aircraft:
biplanes
Comet
Concorden
Fokker
gliders
Master
monoplanes
Mosquito R
‘Reindeer’
strength of
wooden
Aneurisms
Antigone
Arches:
brick and stone
bridges
collapse of
corbelled
hinge-points in
names of parts
thrust lines in
Architecture:
Byzantine
Corinthian
Doric
Gothic
modern
Mycenaean
Norman
Romanesque
trabeate
Arteries
Austen, Jane
Babel, Tower of
Ballistae
Bats
Beams
cantilever
hogging and sagging
pre-stressed
rolled steel joists’
simply supported
stresses in
wooden
Benezet, Saint
Bias cut dresses
Biggs, Prof. W. D.
Blown-up structures
Blyth, Dr Henry
Boilers
bursting of
Bonds, interatomic, distortion of
Bones
calcium in
properties of
work of fracture
Bows:
broken
composite
cross-
long-
Odysseus’s
palintonos
Parthian
>
rate of shooting
strain energy in
Tartar
Brazier bucklingr
Bridges:
arch, with suspended roadway
Avignon
Bridges
bowstring girder
Britannia
cast
iron
Clare
Clifton
Hell Gate
Humber
London
Maidenhead
masonry arch
Menai suspension
Saltash
San Luis Rey
Severn
suspension
Sydney Harbour
Tacoma Narrows
thrust lines in
trestle
Brunei, Isambard Kingdomn
Brunel, Sir Marcn
Buttresses
Cable-cars
Cars
Carthage, siege of
Catapults
ballista efficiency of
palintonon
trebuchet
Cats’ tails
Cauchy, Baron Augustin
Cayley, Sir George
Chaplin, Dr Richard
Coal, effect of pressure on
consumption of
Coles, Captain Cowper
Collagen
Compression failures:
by crushing
by buckling
Conn, Prof. J. F. C.
Coulomb, Charles Augustin de
Cox, H. L.
Dams
Davy, Sir Humphry
de Havilland Aircraft Co.
Dionysius
Discs, slipped
Dixon, Prof. Macneile
Dracone barges
Ecole Polytechnique
Egg membrane, fracture of
Elastin
Empire State building
Energy:
conservation of
definition of
potential
strain
units of
Euler, Leonhard
Euler’s formula
Eurymachus
Everest, Mount
Fatigue of metals
Finlay, James
Flexural centre in beams
Foetuses
Fracture, work of:
of bones
definition of
table of
variation with tensile strength
Fracture mechanicsn
Franklin, Benjamin
Friars, bridge building
Galileo
and square cube law
Germain, Sophien
Griffith critical crack length
Griffith principle
Guns, bursting of
Hagia Sophia
Hall, Sir Arnold
Heyman, Prof. Jacques
Hieroglyphics, Egyptian
Hooke, Robert passim
Hooke’s law passim
Hupozomata
Ictinus
Ignorance, factor of
Inglis, Prof. C. E.
Insulae, Roman
Joints:
butt welded
in columns
glued
lapped
in masonry
to plastic
in rigging
riveted
in roof-trusses
scarfed
in tendons in tension members
welded
Kenedi, Prof. R. M.
King’s College Chapel
Kipling, Rudyard
Lanchester, F. W.
Larynx, in men and women
Libel, law of
Mariotte, Edme
Masts
Material efficiency criteria
Mathematics
May, George
Meredith, George
Mersenne, Marin
Michell, A. G. M.
Middle third rule
Monocoques
Muscle:
collagen in
as an energy converter
energy dispersed in
in legs and arms
mechanism of contraction
strength of
Navier, Claude Louis Marie Henri
Newton, Sir Isaac
New York Trade Center
Odysseus
Paine, Thomas
Palintonon
Parthenon
Paul, Prof. J. P.
Penelope
Pipes
Poisson, S. D.
Poisson’s ratio
Polygon, funicular
Pretlove, Dr Tony
Pterodactyls
Pugsley, Sir Alfred
Pyramid, Great
Resilience Rheims Cathedral
Rigging:
of ships
of young ladies
Riveted joints
RNA-DNA mechanism
Rockets
Roofs:
air supported
archaic Greek
over one’s head
vaulted
Roof trusses
hammer beam
Rubber:
strain energy storage
stress-strain curve of
useless in biology
work of fracture of
Sacrifices, human
Safety, factors of
Sails
Salisbury, Lord
Salisbury Cathedral
Sandwich construction
Shear:
in dressmaking
failure in solids
modulus, G, definition of
nature of
relation with E and q
in rockets
in sails
in skin
strain, g, definition of
stress, N, definition of
in worms
Ships:
America, yacht
beauty of
Birkenhead, troopship
Captain, H.M.S.
Chinese
Cobra, H.M.S.
Egyptian
Great Eastern, S.S.
Greek
Leviathan, S. S.
Majestic, R.M.S.
Maltese
river steamers
sailing
steam
stresses in
structure of
Venetian
Victory, H. M.S.
Viking
Wolf, H.M.S.
wooden
Shute, Nevil
Siloam, Tower of
Skiamorphs
Ski-ing
Soane, Sir John
Solomon, King
Space-frames
Stephenson, Robert
Strain:
shear, definition of
tensile and compressive:
definition of; expression of
Strain energy:
as a cause of fracture
definition of
storage capacity, table of
units of
Strength:
of a material, definition of
of solids, tables of
of a structure, definition of
Stress:
factor
shear, definition of
tensile and compressive, definition
of
units of
Stress concentrations passim
how to live with
Stress trajectories
Stringed musical instruments
Structure loading coefficients
Suez Canal
Surface tension
Surgery, orthopaedic
Telford, Thomas
Temple of the Olympian Zeus
Tendon:
Achilles or calcaneal
in bows
in catapults in kangaroos
in legs and arms
strain energy in
strength of
Test pieces, tensile
Thompson, Sir D’Arcy
Thrust lines passim
in backbones
in bridges
Torsion:
in aircraft
in bridges
in cars
in chickens
in legs
Trees:
deflections of
growth of
height of
names of
scarcity of
strength of
Trusses:
Bollman
bowstring
Fink
hogging
hupozomata
Pratt or Howe
in shipbuilding
Warren
See also Roof-trusses
Tyres
Vincent, Dr Julian
Vionnet, Mlle
Vitruvius
Vocal cords
Voussoirs
Wagner tension field
Wainwright, Prof. Steve
Wallace, Sir Barnes
Watson, G. L.
Welding
Wheels
Wilkinson, John
Windows
Wine jars
Yachts: see Ships
Yew timber
Young, Thomas
Young’s modulus:
definition of
table of
units of
Young’s own definition of