Civil Engineering Reference
In-Depth Information
where
E
ci
= secant modulus of elasticity of the concrete filament =
ε
f
ci
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
GM
=− −
M
PY
(
Y
)
(7.128)
0
x
0
x
Gc
GM
=− −
M
PX
(
X
)
(7.129)
0
y
0
y
Gc
12. Checking the convergence of the inelastic centroid
)
(7.130)
TOL
=
EAM
/(
EA
×
Y
x
x
c
TOL
=
EAM
/(
EA
×
X
)
(7.131)
y
y
c
13. Comparing the internal force to applied force and the internal moments to
applied moments, and making sure the inelastic centroid converges:
−
5
GP
−≤×
F
z
110
(7.132)
−
5
−
5
GM
−
GM
≤ ×
110 nd
GM
−
GM
≤×
110
(7.133)
x
0
x
y
0
y
−
5
−
5
TOL
≤×
110 nd
TOL
≤×
110
(7.134)
x
y
If Equations (7.132), (7.133), and (7.134) are not satisfied, the location of the inelas-
tic centroid is updated by
EAM
x
/
EA
and
EAM
y
/
EA
, and steps 5 to 12 are repeated
until Equations (7.132), (7.133), and (7.134) are satisfied.
YY
EAM
EA
x
=+
(7.135)
c
c
new
old
XX
EAM
EA
y
=+
(7.136)
c
c
new
old
Once equilibrium is reached,
the
algorithm checks for ultimate strain in concrete
ε
ec
and steel ε
es
not to exceed ε
ccu
and 0.05, respectively, and then it increases the
loading by Δ
GP
and runs the analysis f
or t
he new load level using the latest sec-
tion properties. Otherwise, if ε
ec
equals ε
ccu
or ε
es
equals 0.05, the target force and
resultant moment are reached as a point on the interaction diagram for the amount
of eccentricity, and angle α used.
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