Untitled

188 M. Majowiecki
µ =Vector of mean values of ∆ε =0(i.e., all possible actions on the cables are
considered by the load combination itself).
σ =Vector of standard deviations of ∆ε ∆ε = 0. Theσ values were varied from
0.5 × 10 −3 to 0.1 × 10 −3 so that the sensibility of the system can be studied.
These values were selected to cover the range offailure probabilities of
practical significance.
f∆ f∆ f∆ f∆ε f ∆ (∆ε ∆ ) = Probability density function =Normal distribution with parameters µ
and σ.
3.3 Failure Condition
For load case “i” the bending moments, Mx M ,My M and Mxy M in the 130 points of the
plate can be computed as follow:
Mx M = MGx M i +
My M = MGy M i +
Mxy M = MGxy M i +
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j=1
34
j=1
34
j=1
Axi,j
Ayi,j
Axyi,j
· ∆εj
· ∆εj
(8)
· ∆εj
Considering the bending moments in each direction, the failure functions at each
point of the plate (1 ≤ r ≤ 130), Gr (ɛ), are the following hyperplanes,
MUpx M − (MGx M i +
MUpy M − (MGy M i +
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j=1
34
j=1
MUnx M − Abs(MGx M i +
MUny M − Abs(MGy M i +
MUxy M − Abs(MGxy M i +
Axi,j · ∆εj) < 0
Ayi,j · ∆εj) < 0
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j=1
34
j=1
34
j=1
Axi,j · ∆εj) < 0
Ayi,j · ∆εj) < 0
(9)
(10)
Axyi,j · ∆εj) < 0 (11)
where Gr ≤ 0 is failure and MUxy M is computed from the Johanssen Theory as the
smallest of the following expressions
MUxy M =(MUpx M + MUpy M )/2 MUxy M = (MUnx M + MUny M )/2 (12)