Civil Engineering Reference
In-Depth Information
3
2
c
−
147.42
c
−
8,091.82
c
+
765,106.36
=
0
80
c
=
57.67 mm,
ε =
0.41
=
0.0085
> ε
fd
fcd
1
×
155,000
×
1.2
0.00419
240
c
ε=
−
×
57.67
=
0.00133
<
0.003
No crushing
57.67
0.00419
240
(
)
ε=
203
−
57.67
=
0.00334
<
0.005
Steel in the transition zone
s
−
57.67
f
E
532
204,000
<ε
Tension steel has yielded
y
s
ε= =
=
0.00261
y
s
0.25
0.00334
−
0.00261
φ=
0.65
+
=
0.726
0.005
−
0.00261
0.00419
240
(
)
ε=
57.67
−= <ε
Compression steel has
not
yielded
37
0.000475
s
y
−
57.67
(
)
(
)
(
)
MAfd c
=φ
−β +φΨ
A fd
−β+φβ−
cAf
cd
u
s y
f
ffef
ss
1
312
1
ε
1
3
0.00133
12
cf
−
−
ε
×
0.00325
β=
c
=
=
0.346
−
ε
ε
0.00133
30.00325
cf
c
1
−
3
×
(
)
M
u
=
0.726
× ×× −
339
532
203
0.346
×
57.67
+
0.726
× ××
0.85
120
1.2
(
)
×
155,000
×
0.00419
×
240
−
0.346
×
57.67
+ ××
0.726
226
204,000
(
)
×
0.000475
×
0.346
×
57.67
−
37
=
36,394,940.42 N-mm
=
36.4kN-m
P
=
97.5kN
=
P
n
failure_exp
P
=×=
M
1.1
53.625 kN-m
n
2
M
M
u
φ
=
=
0.679
<
0.726
Slightly conservative
implied
n
On the other hand, Beam F10 is identical to Beam F7 except for having a
shorter FRP plate,
Ll
af
(
== <
550 mm
638 mm forBeam F7)
. In this case,
b
l
=
550 mm
>
l
=
129.45 mm
b
b
,max
Ac
cordingly, the rest of the calculations are the same as that of Beam B7 (i.e.,
36.4kN-m
M
u
=
). But,
P
=
82 kN
=
P
n
failure_exp
P
=×=
M
1.1
45.1kN-m
n
2
M
M
u
Slightly nonconservative
φ
=
=
0.807
>
0.726 N.G.
implied
n
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