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where A is the cross-sectional area and L is the length of the member,
V is the volume of the member, and ρ is the unit weight of the
material. The stress in any tension member is given by:
Stress Force Area or
F A
=
=
σ
For a given material stress level, σ y , the required cross-sectional area
becomes:
A
F
required
y
= σ
From the mass expression:
M
A L
L F
mass
r
y
=
= ( )
ρ
ρ
σ
If we put all the material-related parameters into one place, the
mass becomes:
M
FL
or M
A L FL
mass
y
mass
r
y
= (
)
=
= (
)
ρ σ
ρ
ρ σ
Note that if we minimize the factor (ρ/σ y ) or maximize its inverse
(σ y /ρ), we will get a minimum weight tension member. The latter
factor (σ y /ρ) is typically called a material index or performance index,
in this case for tension:
Material index for tension member m t
y
= = (
)
σ ρ
To find what material should be used to minimize the weight of
the tension member, all we have to do is find a material with a
maximum value of (σ y /ρ). As described in the text, this measure
can be used in conjunction with material property charts to select
an appropriate material.
Material indices for other design situations can be similarly determined (see Further Reading). Relevant indices are listed in the
tables.
appendix: Material indices