Optimization of the design of a polymer flat plate solar ...
Design of Flat Plate
description
Transcript of Design of Flat Plate
-
. .
-
(a) (b) (c) band beam
(d) (e)
1.
-
1. (SLS)2. (ULS)3.
-
2.
2.1 PTI (Post-tensioning Institute)
1 L/h h/L 48 45 ( L/6)
50
4 55
L = 9 L/45 = 900/45 =20 cm
-
2. 2
1 1.5 2 3 4
siliceous 89 108 127 159 178 carbonate 83 105 117 146 168 lightweight 67 83 95 117 133 3
1 1.5 2 3 4
siliceous 19 32 38 54 - carbonate 19 27 35 48 -
lightweight 19 25 32 41 - siliceous 19 19 19 25 32 carbonate 19 19 19 25 32
lightweight 19 19 19 19 25
-
3. (Load balancing theory)
Pb
Pb
y
L
=PPv
2LPy8w =
-
LL05.0L =
y
2LPy8w =
9w9w(a)
(b)
-
0.08
0.068
0.03
Interior span
y = 0.08+0.068+0.03 = 0.178 m
-
0.1L=0.8 m
0.068
0.080
0.030.03
0.049
y = 0.08 + 0.5x(0.068+0.3) = 0.08 + 0.049 = 0.129 m
-
LL05.0L =
y
2LPy8w =
9w9w(a)
(b)
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tendonsDeformed bars Tendon layout
8 tendons
-
l1
l2
-
4.
1 (design strip)
-
2 2.1
lc
l1
c1h h2l
IE4Kc
cc =
2/clIE4K
11
cs =
-
2.2 ( ecK )
tcec K1
K1
K1 +=
cK tK
3222
cst )l/c1(l
CE9K =
( )3
/63.01 13
1 chchC = h c1 torsional member
c2c1
h
Torsional member(including beam if present)
l2
-
3 1. prestress loss secondary moment 2. ( ) 3.
equivalent column
slab dead load
equivalent column
1. 2.
psLDSLS MMMM ++=
psLDULS MM7.1M4.1M ++=
-
5.
ACI cf6.1 0 cf53.0 0 cf45.0 5.2
Bonded Prestressing system Unbonded prestressing system
5.1
0 0.004A 0 0.00075hl
0 0* 0 )f5.0/(N yc
-
1.
1.5h 4 30 cm l/6
2. l/3
20 cm 6060 cm = 8.0 m = hl00075.0 = 8002000075.0 = 12 cm2
11 DB 12 ( sA = 12.4 cm2)
11 DB12 each way
330 cm
c2 + 3h =120 cm
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5.3
free edge regions not prestressed in direction parallel to concentrated tendons
interior panel edge panel
corner panel
ps
s 5.00015.0bdA ==
b ,d p
-
6
nu MM 6.1 psf
(1)
( )
+
=pc
pup
1
ppups d
dff
1ff
puf = 1 = 0.85 280fc ksc
= 65.000005.0)280f(85.0 c 280fc > ksc p = 0.4 stress-relieved 85.0f/f pupy
= 0.28 low-relaxation 90.0f/f pupy
-
p = = pps bd/A d =
pd = = cy f/f = cy f/f = = bd/As = = bd/As
1. ( sef ) puf5.0 2. 0= pd15.0d >
-
(2) (2.1) 35
p
cseps 100
f700ff
++=
pyps ff 4000fse + (2.2) 35
p
cseps 300
f700ff ++=
pyps ff 2000fse + sef
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6.2 stress block stress block
bf85.0fAfA
ac
yspsps
+=
)2/ad(fA)2/ad(fAM ysppspsn +=
-
6.3 2
(1) ACI crn M2.1M
(2) ACI (2.1)
1p 36.0 cpspp f/f = (2.2)
1p
p 36.0dd)( +
cy f/f = cy f/f =
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7 Wide beam shear failure
d/2
Punching shear failure
h/2
Shear and moment transfer
Corner shear failure
-
7.1
dbf53.0V wcc = wb
d 0.8h h/2
-
7.2 d/2 4 ACI
p0pccpc Vdb)f3.0f(V ++=
p = 0.93 )5.1b/d(27.0 0s + s = 40
= 30 = 20
0b = pcf =
8.8 ksc 35 ksc cf = 350 ksc
pV =
-
pV
+= )dc()L(Ph2V 12
2p
pV
(a) Tendon pro file through column region
point of inflection of tendon profile
h2
d/2Vp
1 l
c1 +d
21
21 )l2(
Ph8)l2(
Ph8r,forceradial 22 ==
P P
(b) Free- body diagram of tendonc1
-
4h pcf 8.8 ksc
( ) dbf/4227.0V 0ccc += dbf)2b/d(27.0 0c0s + dbf06.1 0c
c
-
7.3
c1Vu
Mu1
fMu1
C2+3h
c2
Vu (1-gf) Mu1
span
= uM (unbalanced moment) uf M h3c 2 + ufuv M)1(M =
2
22u2v
1
11u1vuu J
eMJ
eMAVv
++=
dbVv
0
cu
uf M h3c2 +
-
d/2D
Vu
vMu1
1
2
B
C
Acritical section
AVu
A = area of critical
= bod
u1
11u1vu VJ
eMAV =+
+e1
1
11u1v
JeM
-
)2(2)}(){(2 2121 dccdddcdcA ++=+++=
2)dc(e 11
+=
2)dc)(dc(d
6d)dc(
6d)dc(J
212
31
31
1++++++=
dcdc
321
11
2
1v
+++
=
e
1
c
1
+
d
c
1
c2+d
c2
Mu1
-
)d2cc2(dA 21 ++=
2)dc(
e 22+=
21
11
212
31
31
1 ]e2)2/dc([d)2/dc(2]e[d)dc(
6]d)2/dc(d)2/dc[(J ++++++++=
dc2/dc
321
11
2
11v
+++
=
)d2cc2(
)2dc(
e21
21
1 +++
=
211
32
32
2 ]e[d)2/dc(212d)dc(d)dc(J +++++=
2/dcdc
321
11
1
22v
+++
=e
c
1
+
d
/
2
1
e2
c2+d
c2 Mu1Mu2
-
)dcc(dA 21 ++=
)]dcc(2[)2/dc(e
21
21
1 +++=
2/dc2/dc
321
11
2
1v
+++
=
211
212
31
31
1 ]e2)2/dc(
[d)2/dc(]e[d)2/dc(12
]d)2/dc(d)2/dc[(J ++++++++=
c
1
e
1
c
1
+
d
/
2
c2
c2+d/2
Mu1
-
(column capital drop panel) shear head
scn VVV +=
= dbfsdfA
dbf cyv
c 00 6.106.1 + vA
columnShear cracks
ldS < 0.75h
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Plan
Elevation
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8. ACI 1. 2. (sustained load)
x
yx
y
ly
l x
yx +=
-
ll ll
w
EIwl 4
3841=
EIwl 4
38465.2=
EIwl
38460.2 4=
EIwl
38480.3 4=
-
9.
1 2 3 4 5 6
1
B
C
D5 @ 8 = 40.0
3
@
8
=
2
4
.
0
-
60 65 cm : = 240 . .. () = 120 . .. ( ) 2 = 3.6 m =cf 345 ksc yf = 4000 ksc 15 mm Grade 1860 (low-relaxation) bonded 2 . 75% = 20% l/360 l
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1.
cm8.1745
80045lh ===
22 cm 2 4 2
2. 2
1 1.5 2 3 4
siliceous 89 108 127 159 178 carbonate 83 105 117 146 168 lightweight 67 83 95 117 133
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2. 6060 (1) B2 = 528240022.0 = . .. ( ) 315,12407.11205284.1w u =++= . .. 160,84315,188Vu == . uV 20% 992,100160,842.1Vu == . d = 0.8h = 6.17228.0 = cm 4.310)6.1760(4b0 =+= cm 13fpc = ksc pV
674,1156.174.310)133.034593.0(Vc =+= .
674,115V814,11885.0992,100V
cu === . okay
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(2) B1 uV 50% 120,63315,1485.1Vu == . 2.215)2/6.1760(26.1760b0 =+++= cm 197,806.172.215)133.034593.0(Vc =+= . 197,80V259,74
85.0120,63V
cu =
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3. 80-100%
= 90% 2.4755289.0w b == . ..
8.612.1211eEW == cm
8.428.6eNS == cm N-S E-W
81211ee NSEW === cm
20 mm
(a) At columns
12 mm
N-S tendons
E-W tendons
20 mm
110 mm
20 mm (b) Near midspan
4 4.1
-
4.2 0.1L ( 0.05-0.125L)
80L = cm 1.0=
For exterior span1.0=5.0=
m08.0e1 =m068.0e2 =
m)068.008.0(5.01.0h2 +=
m03.0=
For interior span1.0=5.0=
m08.0e1 =m068.0e2 =
m)068.008.0(5.01.0h2 +=
m03.0=
Sym.
0.5L=4.0 m 0.5L=4.0 m
0.1L=0.8 m
0.0680.080
E-W
064.0)80/605.0(03.0068.0e 2 ==
h2 )ee(h 212 +=
222 )
2/(
Lhhee c=
-
0.5L=4.0 m 0.5L=4.0 m
0.1L=0.8 m
0.048
0.080
For exterior span
1.0=5.0=
m08.0e1 =m048.0e2 =
m)048.008.0(5.01.0h2 +=
m026.0=
For interior span
1.0=5.0=
m08.0e1 =m048.0e2 =
m)048.008.0(5.01.0h2 +=
m026.0=
N-S
044.0)80/605.0(026.0048.0e 2 ==
Sym.
h2
-
E-W 178.003.0068.008.0y =++ m
357,21178.08
82.475P2
i == kg/m
129.0)03.0068.0(5.008.0y =++ 470,29
129.0882.475P
2
e == kg/m
N-S 154.0026.0048.008.0y =++ m
686,24154.08
82.475P2
i == kg/m
117.0)026.0048.0(5.008.0y =++ 492,32
117.0882.475P
2
e == kg/m
y8wLP
LPy8w
2
2 ==
-
5. 5.1
15 = 1.4 cm2 040,26600,184.1Fpu == . Jacking force 040,2675.0Fpj = = 19,530 . 624,15195308.0Fpe == .
5.2 E-W 70-75%
2 N-S
2
-
5
(kg)
(kg) P/A (ksc)
E-W 856,1708357,21
== 12 8 4 187,488 10.7
E-W 760,235
8470,29=
= 16 12 (8+4) 4 (4+0) 249,984 14.2
N-S 488,1978686,24
== 13 7 6 203,112 11.5
N-S 936,2598492,32
== 17 9 (7+2) 8 (6+2) 265,608 15.1
pcf = 11.1 ksc = 14.7 ksc
-
1. 6.1
631213121 1008.16060bhI === cm4 h = 22 cm, l = 3.6 m
c6
ccc E671,13222360
1008.1E4h2lIE4K =
== ( ) 766,163
36022)60/2263.01(
3yxy/x63.01C
33=== cm4
c33222
ct E656,4)800/601(800
766,163E92)l/c1(l
CE9K =
==
tcec K
1K1
K1 += ccec E656,4
1E671,132
1K
1 +=
cec E979,3K =
-
6.2 867,70922800bhI 31213121 === cm4
cc
11
cs E688,3)2/60800(
867,709E42/cl
IE4K ===
6.3 Distribution factor (DF) Carry over factor distribution factor
+= )KK(KDF
ecs
s
carry over factor 0.5
-
7. . = 240 < 75% . = 486 . (0.75(528+120)) B (E-W) 2 (N-S)
1 2 3 4 5 6
A
B
C
D5 @ 8 = 40.0
3
@
8
=
2
4
.
0
-
1. E-W
0.48 0.32 0.32
Given Ks = 3688 EcGiven Kec = 3979 Ec
1
48.039793688
3688KecKs
KsDF12 =+=+=32.0
39793688x23688
KecKs2KsDF 21 =+=+=
1 2
Fixed
-
WD = 528+120 = 648 kg/m2 WL = 240 kg/m
2
WD = 648x 8 = 5,148 kg/m WL = 240x 8 = 1920 kg/m WDU = 1.4x5,148 = 7,258 kg/m WLU = 1.7x5,148 = 3,264 kg/m
FEM D = WD x L2/12 k.m FEM D = WD x L
2/12 k.m
= 5184 x 82/12 =27,648 kg.m = 1,920 x 82/12 =10,240 kg.mWSLS = 5,184+1,920 = 7,104 kg/m WULS = 7,258+3,264 =10,522 kg/m
FEM - : + :
-
FEM due to restraining post-tension
129.0049.008.0f =+=086.0129.0f 3
232 ==
499,21086.0984,249FEML ==
0.5L=4.0 m 0.5L=4.0 m
0.1L=0.8 m
0.068
0.080
Exterior span (E-W)
0.03
0.03
0.11
0.049
0.086
0.086
0.012
New
000,3012.0984,249FEMR ==
CGC
-
0.5L=4.0 m 0.5L=4.0 m
0.1L=0.8 m
0.048
0.080
Exterior span (N-S)
0.026
0.026
0.11
0.037
117.0037.008.0f =+=078.0117.0f 3
232 ==
0.078
0.078
0.004
717,20078.0608,265FEML ==
New
062,1004.0608,265FEMR ==
CGC
-
0.08
0.068
0.03
178.003.0068.008.0f =++=119.0178.0f 3
232 ==
937,3021.0488,187FEML == 937,3021.0488,187FEMR ==
Interior span (E-W)
0.119
new
0.021
-
0.08
0.048
0.03
158.003.0048.008.0f =++=105.0158.0f 3
232 ==
484,5027.0112,203FEML == 484,5027.0112,203FEMR ==
Interior span (N-S)
0.105
new
0.027
-
Due to P/T
0.48 0.32 0.3221,499 3,000 3,937 3,937- 10,320- 5,160-
284- 569- 569- 284- 136 68 11- 22- 22- 11-
5 3 1- 1-
11,026 2,680- 3,346 4,232-
E-W
1. EW
-
Due to DL
0.48 0.32 0.3227,648- 27,648 27,648- 27,648 13,271 6,636
1,062- 2,123- 2,123- 1,062- 510 255
41- 82- 82- 41- 20 10
3- 3-
14,950- 32,340 29,856- 26,546
E-W
-
Due to L
0.48 0.32 0.3210,240- 10,240 10,240- 10,240
4,915 2,458 393- 786- - - 189 94
15- 30- 30- 15- 7 4
1- 1-
5,537- 11,978 10,271- 10,225
Sum SLS 9,461- 41,638 36,782- 32,538 Sum ULS 19,318- 62,958 55,914- 50,314
E-W
-
2. N-S
0.48 0.39 0.19
Given Ks = 3688 EcGiven Kec = 3979 Ec
To take into account symmetry48.039793688
3688KecKs
KsDF12 =+=+=
19.0397936883688x5.0
3688x5.0DF CB =++=
39.0397936883688x5.0
3688DF CD =++=
-
WD = 528+120 = 648 kg/m2 WL = 240 kg/m
2
WD = 648x 8 = 5,148 kg/m WL = 240x 8 = 1920 kg/m WDU = 1.4x5,148 = 7,258 kg/m WLU = 1.7x5,148 = 3,264 kg/m FEM D = WD x L
2/12 k.m FEM D = WD x L2/12 k.m
= 5184 x 82/12 =27,648 kg.m = 1,920 x 82/12 =10,240 kg.mWSLS = 5,184+1,920 = 7,104 kg/m WSLS = 7,258+3,264 =10,522 kg/m
-
Due to P/T
0.48 0.39 0.1920,717 1,062- 5,484 9,944- 4,972-
107 215 105 52 51- 26- 5 10 5 2 2- 1-
0.5 0.2
10,831 5,836- 5,594 55
N-S
-
Due to DL
0.48 0.39 0.1927,648- 27,648 27,648- 27,648 13,271 6,636
1,294- 2,588- 1,261- 630- 621 311
61- 121- 59- 30- 29 15
6- 3-
15,081- 31,894 28,971- 26,988
N-S
-
Due to L
0.48 0.39 0.1910,240- 10,240 10,240- 10,240
4,915 2,458 479- 958- 467- 233- 230 115
22- 45- 22- 11- 11 5
2- 1-
5,586- 11,813 10,730- 9,996
Sum SLS 9,836- 37,871 34,107- 37,038 Sum ULS 19,778- 58,897 53,206- 54,831
N-S
-
8.
psLDSLS MMMM ++= psLDULS MM7.1M4.1M ++=
6 E-W 1-2 () 2-3 () P/T 11,025 -2,681 3,345 -4,233 DL -14,952 32,340 -29,857 26,543 LL -5,537 11,979 -11,057 9,832 SLS -9,464 41,638 -37,569 32,142 ULS -19,321 62,959 -57,252 49,642
-
1. SLS E-W
2. ULS E-W
7,104 kg/m1 2
V1=24,394 kg
M2=41,638 kg.mM2= 9,464 kg.m
V2= 32,438 kg
SLS E-W EXTERIOR
7,104 kg/m1 2
V1=24,394 kg
M2=41,638 kg.mM2= 9,464 kg.m
V2= 32,438 kg
SLS E-W EXTERIOR
10,522 kg/m1 3
V1=36,633 kg
M2=62,959 kg.mM2=-19,321 kg.m
V2=47,543 kg
ULS E-W EXTERIOR
10,522 kg/m1 3
V1=36,633 kg
M2=62,959 kg.mM2=-19,321 kg.m
V2=47,543 kg
ULS E-W EXTERIOR
-
3. SLS E-W
4. ULS E-W
7,104 kg/m2 3
V1=29,098 kg
M2=-32,142 kg.mM2=-37,596 kg.m
V2=27,734 kg
SLS E-W INTERIOR
7,104 kg/m2 3
V1=29,098 kg
M2=-32,142 kg.mM2=-37,596 kg.m
V2=27,734 kg
SLS E-W INTERIOR
10,522 kg/m1 3
V1=43,039 kg
M2=49,642 kg.mM2=52,252 kg.m
V2= 41,137 kg
ULS E-W INTERIOR
10,522 kg/m1 3
V1=43,039 kg
M2=49,642 kg.mM2=52,252 kg.m
V2= 41,137 kg
ULS E-W INTERIOR
-
7 N-S D-C () C-B () P/T 10,832 -5,836 5,594 SYM DL -15,085 31,895 -28,971 SYM LL -5,587 11,813 -10,730 SYM SLS -9,840 37,872 -34,107 SYM ULS -19,785 58,899 -53,206 SYM
-
5. SLS N-S
6. ULS N-S
7,104 kg/mD C
VD=24,912 kg
M2= 37,872 kg.mMD= 9,840 kg.m
V2= 31,920 kg
SLS N-S EXTERIOR
7,104 kg/mD C
VD=24,912 kg
M2= 37,872 kg.mMD= 9,840 kg.m
V2= 31,920 kg
SLS N-S EXTERIOR
10,522 kg/m1 3
V1=37,199 kg
M2=58,899 kg.mM2=19,785 kg.m
V2=46,977 kg
ULS N-S EXTERIOR
10,522 kg/m1 3
V1=37,199 kg
M2=58,899 kg.mM2=19,785 kg.m
V2=46,977 kg
ULS N-S EXTERIOR
-
7. SLS N-S
8. ULS N-S
7,104 kg/mC B
V1=28,416 kg
M2=-34,107 kg.mMc=-34,107 kg.m
V2=28,416 kg
SLS N-S INTERIOR
7,104 kg/mC B
V1=28,416 kg
M2=-34,107 kg.mMc=-34,107 kg.m
V2=28,416 kg
SLS N-S INTERIOR
10,522 kg/m1 3
V1=42,088 kg
M2=53,206 kg.mM2=53,206 kg.m
V2= 42,088 kg
ULS N-S INTERIOR
10,522 kg/m1 3
V1=42,088 kg
M2=53,206 kg.mM2=53,206 kg.m
V2= 42,088 kg
ULS N-S INTERIOR
-
8 E-W 1-2 () 2-3 () SLS -2,465 31,281 -32,226 -29,186 21,997 -26,459 ULS -8,805 44,449 -49,170 -44,814 30,770 -37,774 9 N-S D-C () C-B() SLS -2,686 33,840 -28,616 -25,902 22,725 -25,902 ULS -9,099 45,971 -45,279 -41,053 30,970 -41,053
-
9.
2
2cen )L/c5.0(hee = E-W 064.0)80/605.0(03.0068.0e 2 == m N-S 044.0)80/605.0(026.0048.0e 2 == m 533,6411/22800c/bhc/IS 31213121 ==== cm3
9.293506.1f6.1 c == ksc 9.935053.0f53.0 c == ksc 5.15735045.0f45.0 c == ksc
-
9.1 10 E-W 1-2 () 2-3 () SLS (kg-m) -2,465 31,281 -32,226 -29,186 21,997 -26,459
eP (kg) 249,984 249,984 249,984 - 187,488 187,488 A/Pe (ksc) -14.2 -14.2 -14.2 - -10.7 -10.7
e (cm) 0 8.0 6.4 - 8.0 6.4 0 31.0 -24.8 - 23.2 -18.6
S/ePe (ksc) 0 -31.0 24.8 - -23.2 18.6 3.8 -48.5 49.9 - -34.1 41.0 M/S (ksc) -3.8 48.5 -49.9 - 34.1 -41.0 -10.4 -31.7 10.9 - -21.6 11.7 (ksc) -18.0 3.3 -39.3 - 0.2 -33.1
status - Sym.
0.5L=4.0 m 0.5L=4.0 m
0.1L=0.8 m
0.0680.080
E-W- +
-
9.2 11 N-S D-C () C-B() SLS -2,686 33,840 -28,616 -25,902 22,725 -25,902
eP (kg) 265,608 265,608 265,608 - 203,112 203,112 A/Pe (ksc) -15.1 -15.1 -15.1 - -11.5 -11.5
e (cm) 0 8.0 4.4 - 8.0 4.4 0 32.9 -18.1 - 25.2 -12.6
S/ePe (ksc) 0 -32.9 18.1 - -25.2 12.6 4.2 -52.4 44.3 - -35.2 40.1 M/S (ksc) -4.2 52.4 -44.3 - 35.2 -40.1 -10.9 -34.6 11.1 - -21.5 16.0 (ksc) -19.3 4.4 -41.3 - -1.5 -39.0
status - - +
0.5L=4.0 m 0.5L=4.0 m
0.1L=0.8 m
0.048
0.080
N-SSym.
h2
-
10.
10.1
9.935053.0f53.0 c == ksc
= 0.002A
4.422100002.0A mins ==+ cm2/m DB12 @ 0.25 #, 5.4A prov,s = cm2/m
-
10.2 0.00075 hl 1.5h 4 30 cm l/6
2.138002200075.0A mins == cm2/ 12 DB12 @ 0.10 # 126225.1260 =+ say 120 cm 10.3
DB12 @ 0.25 #
-
11.
( )
+
=pc
pup
1
ppups d
dff
1ff
-
11.1 12 E-W 1-2 () 2-3 () ULS -8,805 44,449 -49,170 - 30,770 -37,774 16 16 16 - 12 12
psA 22.4 22.4 22.4 - 16.8 16.8 sA 13.6 0 13.6 - 0 13.6
pd 11.0 19.0 17.4 - 19.0 17.4 d 18.2 18.2 18.2 - 18.2 18.2
)10( 3p 2.55 1.47 1.61 - 1.11 1.21 )10( 3 0.93 0 0.93 - 0 0.93
0.011 0 0.011 - 0 0.011 psf (ksc) 17,610 18,091 17,968 - 18,216 18,106
a (cm) 1.89 1.70 1.92 - 1.29 1.51 nM (kg-m) 44,145 66,196 67,992 - 50,554 54,109
ULS -8,805 44,449 -49,170 - 30,770 -37,774 status
-
11.2 13 N-S D-C () C-B() ULS -9,099 45,971 -45,279 - 30,970 -41,053 17 17 17 - 13 13
psA 23.8 23.8 23.8 - 18.2 18.2 sA 13.6 0 13.6 - 0 13.6
pd 11.0 19.0 15.4 - 19.0 15.4 D 19.4 19.4 19.4 - 19.4 19.4
)10( 3p 2.70 1.57 1.93 - 1.20 1.48 )10( 3 0.88 0 0.88 - 0 0.88
0.01 0 0.01 - 0 0.01 psf 17,551 18,057 17,850 - 18,184 18,006
a (cm) 1.98 1.81 2.01 - 1.39 1.61 nM (kg-m) 46,645 69,988 64,045 - 54,522 52,150
ULS -9,099 45,971 -45,279 - 30,970 -41,053 status
-
12 12.1
B2
56.74)60.400.4()10.457.4(A =++= m2 d = 0.8h = 17.6 cm
315,12407.1)120528(4.1W7.1W4.1W LuDuu =++=+= . .. ( )( ) 255,97176.060.056.74315,1V 2u =+= .
1
4.57 4.10
4.46
4.00
2 3
A
B
C
3.43
3/8WL 5/8WL 5/8WL 3/8WL
-
pV
+= )dc()L(Ph2V 12
2p
243,48.0
)176.06.0(026.0624,15228.0
)176.06.0(03.0624,1522V 22p =+++=
(unbalanced moment)
356,4814,44170,49M EW,u == .. 226,4053,41279,45M NS,u == ..
( ) 463,56.17260606.172dbA 0 =++== cm2 8.38
26.1760ee 21 =+== cm
-
( )2
)6.1760)(6.1760(6.176
6.176.176066.17)6.1760(JJ
23
3
21++++++==
= 61055.5 cm4 40.0
111
6.17606.1760
322v1v
=+== ++
2
22u2v
1
11u1vuu J
eMJ
eMAV
v++=
66u 1055.58.38100226,44.0
1055.58.38100356,44.0
463,5255,97v
++= =20.2 ksc
-
dbV
f3.0fv0
ppccpc ++=
310)6.1760(4b0 =+= cm 1.11fpc = ksc
p 0.93 02.1)5.1310/6.1740(27.0)5.1b/d(27.0 0s =+=+ 93.0p =
5.21)6.17310(
243,41.113.035093.0vc =++= ksc
5.218.2385.0
2.20vu >== ksc
-
6565 cm ( ) 815,56.17265656.172dbA 0 =++== cm2
3.412
6.1765ee 21 =+== cm
( )2
)6.1765)(6.1765(6.176
6.176.176566.17)6.1765(JJ
23
3
21++++++==
= 61069.6 cm4 40.0
111
6.17656.1765
322v1v
=+== ++
89.181069.6
3.41100226,44.01069.6
3.41100356,44.0815,5255,97v 66u =
++=
2.2285.089.18vu == 21.5
-
14 E-W N-S )M( u 4,356 4,226 uuf M6.0M = 2,614 2,536 h3c + (cm) 126 126 2 2
psA (cm2) 2.8 2.8 sA (cm2) 13.6 13.6
psf (ksc) 17,968 17,850 dp (cm) 17.4 15.4 d (cm) 18.2 19.4
a (cm) = bf85.0
fAfA
c
yspsps
+ 2.79 2.78
))2/ad(fA)2/ad(fA(M ysppspsn += 15,473 15,118 )M( u 4,356 4,226 status
-
12.2 B1 = 6.3146.8)3.043.3( =+ m2
315,1W7.1W4.1W LuDuu =+= . .. ( )( ) 852,40)176.06.0(2/176.060.06.31315,1Vu =++= .
pV E-W = 19,321 . .
2.230)6.1765()2/6.1765(2b0 =+++= cm 052,4)6.17265652(6.17A =++= cm2
7.236.17265652
)2/6.1765(e2
1 =+++= cm
-
14.57 4.10
4.46
4.00
2 3
A
B
C
3.43
-
( ) 22331 7.2322/6.17656.172/6.176527.236.17)6.1765(
66.17)2/6.1765(6.17)2/6.1765(J
++++++++=
61052.2 = cm4 387.0
111
6.17652/6.1765
321v
=+= ++
uM = 784,12100/6.17633,36321,19 = . .
73.823.717.6
-
uV uM 7.14
1052.27.23)100(784,12387.0
052,4852,40v 6u =
+= ksc
( ) 3.30350)42(27.0f/4227.0v ccc =+=+= ksc 7.21350)22.230/6.1730(27.0f)2b/d(27.0 c0s =+=+ ksc 8.1935006.1f06.1 c == ksc 8.19vc = ksc 8.19v3.1785.0/7.14/v cu =
-
15 E-W )M( u 4,356 uuf M6.0M = 2,614 h3c + (cm) 126 2
psA (cm2) 2.8 sA (cm2) 13.6
psf (ksc) 17,968 dp (cm) 17.4 d (cm) 18.2
a (cm) = bf85.0
fAfA
c
yspsps
+ 2.79
))2/ad(fA)2/ad(fA(M ysppspsn += 15,473 )M( u 4,356 status
-
13. 13.1
EIwl
38480.3
EIwl
38480.3 44
i +=
78.070986735015120384
8008001024080.3244
=
=
cm (7.8 mm) < 800/360 = 2.22 cm (22 mm)
-
13.2 90%
10% 30% = 1252403.05281.0 =+ kg/m2 creep factor )( = 2 56.0
709867350151203848008001012565.222
44
l =
=
cm (5.6 mm)
1.116.58.77.07.0 liT =+=+= mm < 22 mm
-
2 2.1
lc
=Il1
cccIE
=I
IEcs
c1
222
1cs
)l/c1(IE
lnc1/2
c1/2
h1h2lIE4K cc =
2/clIE4K
11
cs =
-
lc
=Il1
cccIE
=I
1csIE
c1
222
2cs
)l/c1(IE
lnc1/2
c1/2
2csIE
h1