Civil Engineering Reference
In-Depth Information
longitudinal axis remain plane, will have a linear distribution. Furthermore, it is
assumedthatPoisson'seffectandsheardeformationscanbeneglectedduetopractical
beam member geometry (Wang et al., 2000). Therefore, for an elastic design where
stress is proportional to strain (Hooke's Law), the distribution of stress is shown in
Figure 7.1.
It should be noted that no instability or stress concentration effects are
considered.
Equilibrium of moments (ignoring signs because tension and compression are
easily located by inspection) results in
y
c
σ
c
d
A( y)
y
2
d
A
=
σ
c
c
=
σ
c
M
=
0
=
c
I
x
.
(7.1)
Therefore, the maximum bending stress is
Mc
I
x
=
M
S
x
σ
max
=
,
(7.2)
where
I
x
c
.
S
x
=
The AREMA (2008) allowable stress design uses a factor of safety against the
tensile yield stress of 1.82. The required section modulus of the beam or girder is then
M
0.55
F
y
S
x
≥
,
(7.3)
where
M
is the externally applied bending moment;
y
is the distance from the neutral
axis to the area under consideration;
c
is the distance from the neutral axis to the
M
d
A
y
y
c
σ
c
c
σ
c
FIGURE 7.1
Bending of a beam.
