Civil Engineering Reference
In-Depth Information
3.6 Strength, stiffness and rigidity
The strength of a material is the maximum shear stress which it can sustain and its
stiffness is the ratio of change of stress to the resulting strain. These were discussed in
Secs. 3.3 and 3.5.
A material may be relatively strong or relatively weak: it may be relatively stiff
or relatively soft. Concrete (in compression) and rubber have similar strengths but
concrete is much stiffer than rubber. Aluminium and glass have similar stiffnesses but
glass is much stronger than aluminium. There is no requirement for any relationship
between strength and stiffness.
The ratio of stiffness to strength is called rigidity
R
and this is commonly defined as
E
q
f
R
=
(3.18)
where
E
is Young's modulus given by Eq. (3.16) and
q
f
is strength expressed as
the diameter of the Mohr circle at failure. Table 3.1 gives typical values for stiffness,
strength and rigidity for some commonmaterials, including soft and stiff clays, showing
that values of rigidity vary over several orders of magnitude.
Figure 3.7(a) shows the stress strain response of a material which is linear with
Young's modulus
E
and which first fails at a stress
q
f
when the strain is
ε
f
. Figure 3.7(b)
is the corresponding relationship between stiffness and strain. Hence,
from the
geometry of Fig. 3.7(a), the rigidity
R
is
E
q
f
=
1
ε
f
R
=
(3.19)
From Fig. 3.7(a)
q
f
=
E
ε
f
(3.20)
Table 3.1
Typical values for stiffness, strength and rigidity
of some common materials
Material
Young's modulus
E
MPa
Strength
q
f
MPa
Rigidity
R
Concrete
28,000
40
700
Glass
70,000
1000
70
Mild steel
210,000
430
500
Copper
120,000
200
600
Aluminium
70,000
100
700
Rubber
10
20
0.5
Timber
10,000
20
500
Soft clay
100
0.05
2000
Stiff clay
300
0.3
1000
