Civil Engineering Reference
In-Depth Information
1 . 0
N
/
N
y
= 0.3
L
/
i
y
= 0
0 . 8
Analytical
solutions
L
/
i
y
= 60
0 . 6
0 . 4
Linear interactions equations
(equations 7.62 and 7.63)
0 . 2
Modified interactions equations
(equation 7.64 ( = 1.7),
equations 7.66 and 7.67)
0
0
0
0.2
0.4
0.6
0.8
1.0
M
y
/
M
b,r,y,Rd
or
M
y
/ M
pl,r,y
Figure 7.18
Interaction curves for biaxial bending.
Atthesametime,thelinearmemberinteractionequation(equation7.62)should
be replaced by
α
L
α
L
M
y
M
b
,
r
,
y
,
Rd
M
z
M
c
,
r
,
z
,
Rd
+
≤
1,
(7.66)
where
M
b
,
r
,
y
,
Rd
, the maximum value of
M
y
when
N
acts but
M
z
=
0, is obtained
from equation 7.57,
M
c
,
r
,
z
,
Rd
is similarly obtained from an equation similar to
equation 7.21, and the index
α
L
is given by
α
L
=
1.40
+
N
N
y
.
(7.67)
The approximations of equations 7.64-7.67 have been shown to be of reasonable
accuracy when compared with test results [27]. This conclusion is reinforced
by the comparison of some analytical solutions with the approximations of
equations 7.64-7.67 (but with
α
0
=
1.70 instead of 1.725 approximately for
N
/
N
y
=
0.3) shown in Figure 7.18. Unfortunately, these approximations are of
limitedapplication,althoughitseemstobepossiblethattheirusemaybeextended.
7.4.2 Design rules
7.4.2.1 Cross-section resistance
Thegeneralbiaxialbendingcross-sectionresistancelimitationofEC3isgivenby
N
c
,
Rd
+
M
y
,
Ed
N
Ed
M
c
,
y
,
Rd
+
M
z
,
Ed
M
c
,
z
,
Rd
≤
1
(7.68)
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