Transcript Selection of Material and Shape

Selection of Material and
Shape
Case Studies
7/20/2015
Floor Joists: Wood or Steel?
Aim: Light, stiff and strong
joist for supporting floors in
buildings
Traditionally, wood with
rectangular section of
aspect ratio 2:1 is used;
steel I-beam with 15Be25
could be used instead
Which one is better?
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Floor Joists: Wood or Steel?
M1 
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 E 
e
B
12

Floor Joists: Wood or Steel?
M3

 

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f 13
B

 2f 3
Floor Joists: Wood or Steel?
Density (Mg/m3)
Modulus (GPa)
Strength (MPa)
Shape factor Be
Shape factor Bf
M1
M3
Wood (Pine)
Steel (Mild)
0.7
15
80
2.1
7.9
210
310
15-25
2.8
20-35
8.0
34
7-9
16-19
While M1 are more or less the same, M3 of
pine wood is much better than that of steel
The cellular structure is the nature’s answer
to bending! But steel can be standardized.
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Forks for a Racing Bicycle
Aim: light strong frame
Loading on frame is not
obvious, but that on the
fork is predominantly
bending.
M3

 

f 13
B
 2f 3

First maximize f2/3/,
regardless of shape
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Forks for a Racing Bicycle
Six materials are
singled out and
shown in the next
page
All except wood
can be made into
tubes
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Forks for a Racing Bicycle
Material
M3
Comment
(MPa)2/3/(Mg/m3)
Aluminium alloy (7075),
Bf =20
55
A popular choice for racing
bicycles; less expensive than CFRP
Titanium alloy, Bf = 15
54
Expensive, not offering any
advantage over aluminium
Magnesium alloy,
Bf = 12
45
Can be die-cast to shape, but with
relatively poor .
Steel (Reynolds 531),
Bf = 30
39
Standard for cheaper light bicycles
CFRP (with some glass
or Kevlar), Bf = 15
70
Outstanding, but expensive
Wood, Bf = 1
45
Material properties outstanding, but
not easily shaped
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Efficient Spring
1 F2
Consider a leaf spring, the stored energy U 
2 SB
2
C EI C
A
The bending stiffness S B  1 3  1 E Be 3
l
4
l
The force F is limited by yielding
Ff 
C2
4
12


l
f
B

3 12
A
f
Substituting F and SB into the equation for U
2
U max C22   Bf  f 

V
8C1   Be E 
2
 Bf  f
M5  e
B E
For torsion bars or helical springs
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2


f
M6 
 E
f
T
e
T
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