Civil Engineering Reference
In-Depth Information
This value is in fact the angle that the beammakes with the horizontal. The deflection,
s
, due to shear at the free end is therefore
s
=
0
.
001
×
500
=
0
.
5mm
In practice, the solution of this particular problemwould be a great deal more complex
than this since the shear stress distribution is not uniform. Deflections due to shear
are investigated in Chapter 13.
7.8 P
OISSON
E
FFECT
It is common experience that a material such as rubber suffers a reduction in cross-
sectional area when stretched under a tensile load. This effect, known as the
Poisson
effect
, also occurs in structural materials subjected to tensile and compressive loads,
although in the latter case the cross-sectional area increases. In the region where the
stress-strain curve of a material is linear, the ratio of lateral strain to longitudinal
strain is a constant which is known as
Poisson's ratio
and is given the symbol
ν
. The
effect is illustrated in Fig. 7.9.
Consider now the action of different direct stress systems acting on an elemental cube
of material (Fig. 7.10). The stresses are all tensile stresses and are given suffixes which
designate their directions in relation to the system of axes specified in Section 3.2.
In Fig. 7.10(a) the direct strain,
ε
x
, in the
x
direction is obtained directly from either
Lateral strain
F
IGURE
7.9
The Poisson
effect
Tension
Compression
Longitudinal strain
s
y
s
y
s
z
s
x
s
x
s
x
s
z
s
x
s
x
s
x
y
F
IGURE
7.10
The Poisson
effect in a cube of
material
s
y
s
y
z
x
(a)
(b)
(c)
