Civil Engineering Reference
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and cross sectional stress resultants
()
()
()
(
)
⎡
⎤
⎡
Qx
Qxt
,
,
,
⎤
y
y
⎢
⎥
⎢
⎥
(
)
Q
x
Qxt
+
⎢
⎥
⎢
⎥
(1.7)
z
z
⎢
⎥
⎢
⎥
(
)
M
x
Mx t
⎢
x
⎥
⎣
x
⎣
⎦
⎦
are also referred to the shear centre, while bending moment and axial stress resultants
()
()
()
(
)
⎡
M
x
⎤
⎡
Mx t
,
,
⎤
y
y
⎢
⎥
⎢
⎥
(
)
M
x
Mx t
+
(1.8)
⎢
⎥
⎢
⎥
z
z
⎢
⎥ ⎢
⎥
(
)
N x
Nx t
,
⎢
⎥
⎣
⎦
⎣
⎦
are referred to the centroid of the cross section (where, as shown above, the centriod is
defined as the origo of main neutral structural axis).
Fig. 1.4
Structural axes and displacement components
Thus, it is assumed that structural response in general can be predicted as the sum of a
mean value and a fluctuating part, as illustrated in Fig. 1.4. It is assumed that within the
time window considered the mean values are constant as well as the statistical properties
of the fluctuating parts.
