Civil Engineering Reference
In-Depth Information
9. Calculating strain ε
si
and corresponding stress
f
si
in each bar in the given
section by using the steel material model of elastic-perfectly plastic.
(
)
(
)
GP
EA
TM
HY Y
−−
β
TM
BX X
−−
β
x
c
si
y
c
si
ε= +
EI
+
EI
si
y
x
2
2
(
)
(
)
TM
BX X
−−
β
TM
HY Y
−−
β
x
c
si
y
c
si
−
EI
−
EI
(7.118)
xy
xy
2
2
10. Calculating the new section properties: axial rigidity
EA
;
flexural rigidities
about the inelastic centroid
EI
x
,
EI
y
,
EI
xy
; moment of axial rigidity about
inelastic centroid
EAM
x
,
EAM
y
; internal axial force
F
z
; and internal bending
moments about the inelastic centroid
M
0
x
,
M
0
y
:
∑∑
EA
=
Ewt
+
(
E
−
EA
)
(7.119)
c
i
ii
s
i
c
i
s
i
i
i
∑
∑
EAM
=
EwtH YY
(
− −+ −
)
(
EEAH YY
)
(
−
−
)
(7.12 0)
x
c
i
ii
c
i
s
i
c
i
s
i
c
s
i
i
i
∑
∑
EAM
=
EwtB XX
(
− −+ −
)
(
EEAB XX
)
(
−
−
)
(7.121)
y
c
i
ii
c
i
s
i
c
i
s
i
c
s
i
i
i
∑∑
F
=
f wt
+
(
f
−
f
)
A
z
c
i
ii
s
i
c
i
s
i
(7.122)
i
i
∑
∑
2
2
EI
=
EwtH YY
(
− −+ −
)
(
EEAH YY
)
(
−
−
)
(7.123)
x
c
i
ii
c
i
s
i
c
i
s
i
c
s
i
i
i
∑
∑
2
2
EI
=
EwtB XX
(
− −+ −
)
(
EEAB XX
)
(
−
−
)
(7.12 4)
y
c
i
ii
c
i
s
i
c
i
s
i
c
s
i
i
i
∑
∑
(
)
EI
=
EwtH YYBX X
(
−
−
)
−
−
xy
c
i
ii
c
i
c
i
i
(
)
(7.125)
+
(
EEAH YY BX X
−
)
(
−− −−
)
s
i
c
i
s
i
c
s
i
c
s
i
i
∑
∑
(
)
M
=
f wt HY Y
(
− −+ −
)
(
f
fAHY Y
)
−
−
(7.126)
0
x
c
i
ii
c
i
s
i
c
i
s
i
c
s
i
i
i
∑
∑
(
)
M
=
f wt BX X
(
− −+ −
)
(
f
fABX X
)
−
−
(7.127)
0
y
c
i
ii
c
i
s
i
c
i
s
i
c
s
i
i
i
Search WWH ::
Custom Search