Civil Engineering Reference
In-Depth Information
10. Calculating the new section properties: axial rigidity EA,
flexural rigidity
about the inelastic centroid
EI
, moment of axial rigidity about inelastic cen-
troid
EAM
, internal axial force
F
z
, and internal bending moments about the
inelastic centroid
M
0
,
∑∑
EA
=
Ewt
+
(
E
−
EA
)
(7.74)
ci
ii
si
ci
si
i
i
∑
∑
EAM
=
EwtH YY
(
− −+ −
)
(
EEAH YY
)
(
−
−
)
(7.75)
ci
ii
c
i
si
ci
si
c
si
i
i
∑∑
F
=
f wt
+
(
f
−
f
)
A
z
ci
i i
si
ci
si
(7.76)
i
i
∑
∑
(7.77)
EI
=
EwtH YY
(
− −+ −
)
2
(
EEAH YY
)
(
−
−
)
2
ci
ii
c
i
si
ci
si
c
si
i
i
∑
∑
Mf wt HY Y
=
(
− −+ −
)
(
f
fAHY Y
)
(
−
−
)
o
ci
i i
c
i
si
ci
si
c
si
(7.78)
i
i
where
f
ci
E
ci
= secant modulus of elasticity of the concrete layer =
ε
f
si
ci
E
si
= secant modulus of elasticity of the steel bar =
ε
si
11. Transferring back the internal moment about the geometric centroid
(7.79)
GM
=− −
M
PY
Gc
(
)
0
12. Checking the convergence of the inelastic centroid
EAM
EA
TOL
=
×
Y
c
(7.8 0)
13. Comparing the internal force to applied force, internal moments to applied
moments, and ensuring that the moments are calculated about the geomet-
ric centroid
−
5
GP
−≤×
F
z
110
(7.81)
−
5
GM
−
GM
≤ ×
110
(7.82)
0
≤×
−
5
Tol
110
(7.83)
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