Civil Engineering Reference
In-Depth Information
Table 4.4 (first row) shows these parameters for ordinary steel RC beams
subject to the limit state of flexure.
For a structural element, safety is measured in terms of the reliability
index,
β
,
which is a function of the statistical parameters of the resistance of
an element and the loads applied to it:
β
=
f
[(
ϕ
,
λ
R
,
δ
R
), (
γ
,
λ
Q
,
δ
Q
)
1
, (
γ
,
λ
Q
,
δ
Q
)
2
, …, (
γ
,
λ
Q
,
δ
Q
)
n
]
(4.55)
where the index
R
denotes the resistance,
Q
the load, and 1 to
n
the differ-
ent types of loading that are applied to the element (dead, live, seismic, etc.)
in the load combination for which the reliability index is calculated.
γ
1
to
γ
1
are, then, the load factors that constitute the combination. Traditionally, the
reduction factors are calibrated by targeting a preset level of reliability for all
the design combinations:
β
=
β
T
(4.56)
Table 4.4 also shows this target reliability for ordinary RC beams subject to
flexure.
The essence of the concept of comparative reliability is to calibrate the
unknown strength-reduction factor of a newly introduced element (element 2
in this case) by equalizing its reliability index to that of the element 1, whose
reduction factor and reliability level are agreed upon. In other words, it solves
this set of equations by eliminating the load parameters:
=β
f
(
,
,
)
,
(
,
,
) (
,
,
,
)
,
,
(
,
,
)
β=
φλδγλδ
γλ δ
γ λδ
…
1
1
11
QQ
QQ
QQ
n
T
1
2
(4.57)
=β
f
(
,
,
)
,
(
,
,
) (
,
,
,
)
,
,
(
,
,
)
β=
φλδγλδ
γλ δ
γ λδ
…
2
2
22
QQ
QQ
QQ
n
T
1
2
NN
φ=φ
11
22
Jawaheri Zadeh and Nanni [14] found a solution for this set as
φ
φ
λ
λ
1
2
2
1
ln
δ−δ
δ+δ
β
(4.58)
2
1
=
T
1
2
2
δ+δ
1
2
where the unknown
ϕ
2
has to be calculated from other known parameters.
Table 4.4 (second and third rows) summarizes the statistical data (bias
factor and coefficient of variation) obtained from tests discussed in detail
in Gulbrandsen [12], its assumptions (minimum target reliabilities), and
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