a statistical method for predicting the axial load capacity of
TRANSCRIPT
International Journal of Civil & Environmental Engineering IJCEE-IJENS Vol: 11 No: 02 20
111702-3737 IJCEE-IJENS © April 2011 IJENS I J E N S
Abstract— Concrete filled steel tubular (CFST) structures
have been used widely in high-rise buildings and bridges due to the
efficiency of structurally favorable interaction between the steel
tube and the concrete core. In this research, a simplified statistical
method based on the results of 663 tests is developed to predict the
ultimate strength of circular CFST columns under concentric
loading conditions. This method considers the confinement effect
on the concrete and the influence of relative slenderness. The
standard deviation of the predictions by the current method is very
close to those predicted by the Eurocode 4 and the Chinese CECS
methods. Therefore this simplified method is a good alternative to
other prediction methods. However, the Chinese CECS method
tends to overestimate the ultimate load capacity when the
compressive strength of concrete is high.
Index Term— Concrete Filled Steel Tubular Column;
Confinement Effect; Slenderness Influence; Statistical Method;
Ultimate Load Capacity
X.M. Yu is with the School of Civil and Environmental Engineering, Harbin
Institute of Technology (Shenzhen), University Town in Xili, Shenzhen
518055, China (Corresponding Author, phone: 0086 159 8958 9733; fax: 0086
755 2603 3509; e-mail: [email protected])
B.C. Chen is with the College of Civil Engineering, Fuzhou University,
Fuzhou 350108, China (e-mail: [email protected]).
Nomenclature
Aa Area of the steel section
Ac Area of the concrete section
D Outer diameter of CFST column
Ea Young’s modulus of steel
Ecm Secant modulus of concrete
fa Yield strength of steel
fc Characteristic cylinder compressive strength
of concrete
l Length of CFST column
el Effective length of CFST column
N0 Design strength of short CFST column,
)1(0 cc AfN
Ncr Euler buckling strength of CFST column,
22 /)( lEIN ecr
Npl,R Plastic sectional resistance of CFST column,
ccaaRpl AfAfN ,
Nu Ultimate load capacity of CFST column
t Thickness of steel tube wall
22.021.015.0
e Eccentric loading reduction factor
l Slenderness effect reduction factor
Confinement factor, ccaa AfAf /
Column buckling reduction factor
Relative slenderness, crRpl NN /,
Factor used in the current statistical method,
see Eq.(12)
1 and 2 Factors considering confinement effect in
circular CFST columns
A Statistical Method for Predicting the Axial
Load Capacity of Concrete Filled Steel Tubular
Columns X.M. Yu, and B.C. Chen
International Journal of Civil & Environmental Engineering IJCEE-IJENS Vol: 11 No: 02 21
111702-3737 IJCEE-IJENS © April 2011 IJENS I J E N S
I. INTRODUCTION
THE concrete filled steel tubular (CFST, and hereafter)
columns have been used widely in high-rise buildings and
bridges in recent years, such as the 56-storey (150m high) Two
Union Square in Seattle, Washington, the 43-storey (166m
high) Casselden Place in Melbourne, Australia and the
79-storey (355.8m high) SEG Plaza in Shenzhen, China. A
research by Chen et al. [1] shows that more than 200 CFST
arch-bridges had been built in China since 1990. More and more
CFST high-rise buildings will be built and become city
landmarks.
The commonly used cross section of CFST can be circular or
rectangular (mainly square). The concrete strength is improved
in tri-axial stressing state due to lateral confinement provided
the steel tube. Also the existence of concrete core prevents or
delays the steel tube from local buckling (i.e., deformation
towards core direction). The steel is located farthest to the
centroid of the CFST column so that maximum moment of
inertia can be achieved. Further more, the steel tube acts as a
permanent framework for concreting during the construction.
Consequently, the building can be ascended more quickly
compared to reinforced concrete structure since the steelwork
can precede the concrete by several stories [2]. Compared with
reinforced concrete (RC, and hereafter) bridges and steel
arch-bridges, CFST arch-bridge presents a more artistic
appearance and improved seismic resistance due to less
self-weight. Advance in erection and closure technologies in
bridge construction further accelerates the implementation of
CFST members.
The performance of CFST columns is affected by the
slenderness ratio. Many authors agree that L/D=15 generally
marks a rough boundary between short and long column
behavior [2]. According to JSCE [3], if L/D exceeds 35, the
influence of lateral displacement should be considered for the
composite column. The confinement effect is significant in short
columns but negligible in short ones due to overall buckling.
The influence of diameter to thickness ratio (D/t) was also
heavily studied [4]-[6]. In short, both geometrical parameters
and material characteristics should be considered when
calculating the axial strength of CFST columns.
A lot of design methods have been proposed based on
different consideration of the slenderness influence and the
confinement effect on the ultimate load capacity (UL, and
hereafter) of CFST columns. A comparison by Giakoumelis et
al. [7] showed that the EC4 [8] provided a better prediction than
the ACI [9] and the AS [10] codes. Comparative studies carried
out by Muhammad et al. [11] and Ma et al. [12] showed that the
LRFD [13] and ACI were too conservative and the Chinese
CECS Code [14] gave good predictions in terms of both mean
value and standard deviation; the EC4 gave the “best” [12]
prediction. The discrepancy largely comes from the limit
number of test data available.
With more and more experiments be done, it is now possible
to find out statistically the relationship between the UL and the
columns configurations. Therefore the aim of this research is to
develop a simplified prediction method based on a large number
of test data available.
II. DEVELOPMENT OF A SIMPLIFIED STATISTICAL
METHOD FOR PREDICTING THE AXIAL LOAD
CAPACITY OF CIRCULAR CFST COLUMNS
A. The Definition of the UL
Researchers have different interpretation of the UL of a
CFST column. Cai [15] used the maximum load capacity
attained as the UL. Han [16] and Li et al.[17] defined the UL as
the load when a certain axial strain limit is reached. Miao [18]
defined the UL as the load when a cut through crack is formed,
which is difficult to measure. In this research, the UL is defined
as the maximum load attained.
B. The Selection of Parameters
As reviewed above, there are lots of UL predictions methods
available. These methods consider the geometrical and material
configuration of the CFST columns in different ways. Only the
EC4 method and the Chinese CECS method are briefly
discussed here.
CECS code specification
In the CECS code, the basic requirements for the CFST
structural members are: a) mmD 100 ; b) mmt 14 ; c)
3/3.0 ccaa AfAf ; d) D/t should be in the range
of af/23585~15 , which depends on the type of steel
used; e) Dl / should not exceed a permissible limit, which is
20 for CFST columns.
The UL of CFST columns is calculated by
0NN elu (1)
where 0N is the UL of short CFST columns,
aaccaacc
cc
AfAfAfAf
AfN
)1(0 (2)
The e and l are reduction factors consider the eccentric
loading effect and slenderness influence, respectively. For
concentric loading, 1e , and
4/for 1
4/for 4/115.01
Dl
DlDl
el
eel
(4)
where el is the effective length of the column, which is
determined by the supporting conditions.
EC 4 specification
In the EC4, the UL of concentrically loaded circular CFST
columns is calculated by
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111702-3737 IJCEE-IJENS © April 2011 IJENS I J E N S
cc
c
a
aau fAf
f
D
tfAN 12 1 (5)
where 1 and 2 are factors considering confinement effect,
determined by the relative slenderness, .
2325.0
175.189.4
2
2
1 (6)
5.0/, crRpl NN ; (7)
where RplN , is the plastic strength of the composite column
calculated by
ccaaRpl AfAfN , (8)
and the Ncr is defined as the Euler buckling strength of the
composite column.
2
2 )(
l
EIN e
cr
(9)
where cmcaae EAEAEI 6.0 with Ecm be the secant
modulus of concrete.
The buckling strength reduction factor is used to reduce
the plastic compressive resistance of the cross section of slender
columns.
1
1
22
(10)
where
22.021.015.0 (11)
The parameters used in this research
It can be seen from above that both the EC4 and the CECS
consider the confinement effect and the strength reduction by
slenderness. The CECS considers the confinement effect
equally on the steel tube and the concrete core
by aacc AfAf , which can be reflected by the steel and
concrete capacity ratio, . However, in the EC4, the
confinement effect caused axial strength reduction on the steel
tube by 2 and strength gain on the concrete core by
ca ffDt //1 . The 1 and 2 are determined by the
relative slenderness, , instead of . The confinement effect
does reduce with length of column due to lateral buckling, but it
is unclear why is not included in the EC4 method. The
buckling resistance is taken into account in the CECS by
arbitrarily restricting the ratio of l/D; while in the EC4, the
buckling reduction factor is derived analytically from the stress
at an admissible deflection at mid-height [19], which seems
more reasonable.
Despite of the different concepts behind the CECS and the
EC4 methods, both methods cab be used to obtain reasonable
prediction of the UL of CFST columns. Therefore, in this study,
the used in the CECS and the used in the EC4 are chosen
as governing parameters to predict the UL of CFST columns. It
is assumed that the confinement strengthening effect and
slenderness influence can be attributed to a single factor, ,
acting on the concrete core alone. The is assumed to be a
second order function of and , which is derived
statistically from a large number of test results.
C. Development Of the Simplified Statistical Method for The
UL Prediction
In order to develop a simplified method for predicting the UL
of the circular CFST columns subject to concentric loading, a
total of 663 test data (listed in Table I) extracted from [20] are
adopted. The selected data are those axially loaded circular
specimens categorized with “no moment” unless otherwise
specified. The following two steps are applied to obtain a
simplified expression.
Step 1. Calculating the relative slenderness, . If 1 ,
then the buckling load is taken as the ultimate load capacity of
the column, that is, cru NN ; otherwise, go on to Step 2.
Step 2. Assuming the confinement and the slenderness effects
can be attributed to a single coefficient, , acting on the
concrete only, that is,
ccaau fAfAN (12)
The parameter can be interpreted as a factor transforming
equivalently the confinement and slenderness effects into
concrete. To make the expression simple, only the second order
expression of is assumed as given in Eq. (13). The term
3a in the equation considers the coupled effect of the two
parameters.
5543
2
2
2
1 aaaaaa (13)
From the specimen specifications and test results of the 663
tests, a series of ' can be calculated. Then, with the
' obtained, the coefficients 51 ~ aa in Eq. (13) can be
evaluated using the second order curve fitting function,
polyfit(), in the MATLAB. Finally the can be approximately
calculated by
5081.18880.25872.0
5211.00665.20260.0 22
(14)
The UL predictions of all the 663 tests by this model as well
as the EC4 and the CECS methods are listed in Table I. The
predictions by all the methods agree well with the test data. The
International Journal of Civil & Environmental Engineering IJCEE-IJENS Vol: 11 No: 02 23
111702-3737 IJCEE-IJENS © April 2011 IJENS I J E N S
standard error deviations by using the current method, the EC4
method and the CECS method are 0.1386, 0.1306 and 0.1846,
respectively. The predictions by the current method and the EC4
method are close to each other. The error predicted by the CECS
seems a bit greater, however, this is because of the CECS
method is only applicable to those with MPafc 80,30
[21]. The CECS tends to overestimate the UL for high strength
concrete columns. The comparison shows that the current
method is a good alternative to the other methods.
Apart from the 663 tests, to evaluate the accuracy of the
prediction using the current method, the UL of three CFST
columns tested by Huang et al. [22] (see Table II) are also
calculated using the current method. The comparison listed in
Table II shows the current method gives very good prediction of
the UL of the CFST columns tested.
III. CONCLUSION
In this research a simplified statistical method is developed to
predict the ultimate load capacity of circular CFST columns
subject to concentric loading. The statistically based method
assumes a single correction factor acting on the concrete core
alone to account for the coupled effect of confinement effect
and slenderness influence on the ultimate load capacity of
circular CFST columns. This is done by second order curve
fitting of two parameters, the steel/concrete capacity ratio, ,
used in the CECS and the relative slenderness, , used in the
EC4, based on 663 test results. It is shown that the predictions
by this method agree well with the test results and those
predicted by the EC4 and the CECS methods. Therefore, the
current method provides an alternative way to evaluate the
ultimate strength of circular CFST columns in structural design.
REFERENCES
[1] B.C. Chen and T.L. Wang, "Overview of Concrete Filled Steel Tube Arch
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[6] V.C. Manojkumar, C.N. Mattur and S.M. Kulkarni, “Axial strength of
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[8] Eurocode 4: Design of composite steel and concrete structures, Part 1.1:
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[10] Australia Standards AS4100 Steel structures. Sydney: Standards
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[11] N.B. Muhammad, J. Fan and J. Nie, “Strength of concrete filled steel
tubular columns”, Tshinghua Science and Technology, vol. 11, no. 6, pp.
657-666, 2006.
[12] X.B. Ma, S. Zhang and C.D. Goode, “Comparison of design methods for
circular concrete filled steel tube beam columns in different codes”, in
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[14] CECS 28:90, “Specification for design and construction of
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[15] S. H. Cai, Modern Steel Tube Confined Concrete Structures, China
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[16] L.H. Han, Modern Concrete Filled Steel Tubular Structures, Beijing
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[17] J.D. Li and W.X. Duan, “Experimental Research on Strength of CFST
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[18] R.Y. Miao, “The deformation mechanism and the ultimate load of
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[20] C.D. Goode, ASCCS Database of Concrete-Filled Steel Tube Columns:
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International Journal of Civil & Environmental Engineering IJCEE-IJENS Vol: 11 No: 02 24
111702-3737 IJCEE-IJENS © April 2011 IJENS I J E N S
TABLE I
UL PREDICTION BY THE EC4 AND THE CURRENT STATISTICAL METHODS
(Nt=test data; Nc=UL calculated using current method; Nec4=UL calculated using the EC4 method; Nce=UL calculated using the CECS method)
=============================================================================================================================
No. L(mm) D(mm) t(mm) fa(MPa) fc(MPA) Ea(GPa) Ec(GPa) Nt(KN) Nc(KN) Nc/Nt-1 Nec4 Nec4/Nt-1 Nce Nce/Nt-1
----------------------------------------------------------------------------------------------------------------------------
1 305.00 168.80 2.64 302.40 18.20 200 29 1326 1138 -0.142 1076 -0.188 1197 -0.097
2 305.00 168.80 2.64 302.40 34.70 200 34 1219 1576 0.293 1407 0.154 1696 0.391
3 305.00 169.30 2.62 338.10 37.10 200 35 1308 1713 0.310 1535 0.174 1850 0.415
4 305.00 169.30 2.62 338.10 34.10 200 34 1330 1635 0.229 1474 0.109 1762 0.325
5 305.00 168.30 3.60 288.40 27.00 200 32 1557 1537 -0.013 1429 -0.082 1630 0.047
6 305.00 168.30 3.60 288.40 33.30 200 34 1432 1700 0.187 1551 0.083 1819 0.270
7 305.00 168.30 3.60 288.40 33.30 200 34 1463 1700 0.162 1551 0.060 1819 0.243
8 305.00 168.80 5.00 200.20 33.40 200 34 1966 1661 -0.155 1501 -0.237 1759 -0.105
9 305.00 168.80 5.00 200.20 33.40 200 34 1970 1661 -0.157 1501 -0.238 1759 -0.107
10 305.00 168.80 5.00 200.20 27.90 200 32 1984 1520 -0.234 1396 -0.296 1600 -0.193
11 305.00 168.80 5.00 200.20 27.90 200 32 1984 1520 -0.234 1396 -0.296 1600 -0.193
12 229.00 114.30 3.50 350.00 33.40 200 34 969 1025 0.058 971 0.002 1087 0.122
13 229.00 114.30 4.50 339.00 33.40 200 34 1069 1157 0.083 1107 0.036 1208 0.130
14 360.00 178.00 9.00 283.00 22.20 200 31 2120 2564 0.210 2541 0.199 2574 0.214
15 360.00 178.00 9.00 283.00 22.20 200 31 2060 2564 0.245 2541 0.234 2574 0.250
16 360.00 178.00 9.00 283.00 45.40 200 36 2720 3199 0.176 2976 0.094 3374 0.241
17 360.00 178.00 9.00 283.00 45.40 200 36 2730 3199 0.172 2976 0.090 3374 0.236
18 360.00 179.00 5.50 249.00 22.10 200 31 1410 1765 0.252 1691 0.200 1840 0.305
19 360.00 179.00 5.50 249.00 23.90 200 31 1560 1818 0.165 1729 0.108 1904 0.221
20 360.00 179.00 5.50 249.00 43.70 200 36 2080 2373 0.141 2144 0.031 2564 0.233
21 360.00 179.00 5.50 249.00 43.70 200 36 2070 2373 0.146 2144 0.036 2564 0.239
22 360.00 174.00 3.00 266.00 23.90 200 31 1220 1335 0.094 1225 0.004 1434 0.176
23 360.00 174.00 3.00 266.00 23.90 200 31 1220 1335 0.094 1225 0.004 1434 0.176
24 360.00 174.00 3.00 266.00 45.70 200 36 1640 1918 0.169 1687 0.029 2100 0.280
25 360.00 174.00 3.00 266.00 45.70 200 36 1710 1918 0.122 1687 -0.013 2100 0.228
26 477.00 159.00 5.07 381.50 41.50 200 36 2230 2211 -0.008 2049 -0.081 2478 0.111
27 1890.00 630.00 7.00 291.40 36.00 200 34 16650 18317 0.100 16563 -0.005 21255 0.277
28 1890.00 630.00 7.61 349.50 35.00 200 34 18000 19682 0.093 17955 -0.002 22929 0.274
29 1890.00 630.00 8.44 350.00 34.50 200 34 18600 20331 0.093 18588 -0.001 23607 0.269
30 1890.00 630.00 10.21 323.30 38.40 200 35 20500 22492 0.097 20535 0.002 26108 0.274
31 1890.00 630.00 11.60 347.20 46.00 200 37 24400 26745 0.096 24475 0.003 31314 0.283
32 2160.00 720.00 8.30 312.00 15.00 200 28 15000 15751 0.050 14739 -0.017 17419 0.161
33 2460.00 820.00 8.93 331.00 45.00 200 36 33600 36738 0.093 33488 -0.003 43337 0.290
34 3060.00 1020.00 9.64 336.00 16.90 200 29 30000 31399 0.047 29003 -0.033 35246 0.175
35 3060.00 1020.00 13.25 368.70 28.90 200 33 46000 49077 0.067 45116 -0.019 56432 0.227
36 264.00 131.80 2.38 235.00 17.40 200 29 535 636 0.188 596 0.115 672 0.255
37 264.00 134.30 3.12 235.00 26.60 200 32 681 907 0.331 834 0.224 966 0.419
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38 264.00 130.60 4.30 235.00 26.60 200 32 725 1012 0.396 952 0.314 1064 0.468
39 264.00 132.50 5.25 235.00 26.60 200 32 872 1150 0.318 1094 0.255 1195 0.371
40 264.00 134.10 6.20 235.00 26.60 200 32 1006 1284 0.276 1231 0.224 1320 0.312
41 200.00 101.80 2.94 320.00 18.00 200 29 628 604 -0.038 600 -0.045 617 -0.018
42 200.00 101.80 2.94 320.00 37.40 200 35 660 787 0.192 731 0.108 843 0.277
43 200.00 101.80 5.70 305.00 18.00 200 29 954 900 -0.056 923 -0.032 886 -0.071
44 200.00 101.80 5.70 305.00 37.40 200 35 971 1089 0.122 1039 0.070 1119 0.153
45 200.00 100.00 0.52 244.00 18.00 200 29 239 241 0.007 205 -0.144 252 0.055
46 200.00 100.00 0.52 244.00 37.40 200 35 396 419 0.057 351 -0.114 434 0.096
47 270.00 86.49 2.73 226.70 30.20 200 33 412 430 0.044 396 -0.038 478 0.160
48 270.00 89.27 4.00 226.70 30.20 200 33 491 551 0.123 513 0.044 594 0.210
49 270.00 86.54 2.79 226.70 48.00 200 37 489 537 0.099 487 -0.005 616 0.260
50 270.00 89.19 4.05 226.70 48.00 200 37 605 661 0.093 600 -0.007 740 0.223
51 660.80 165.20 4.17 358.70 40.90 200 35 1594 1934 0.213 1787 0.121 2319 0.455
52 266.00 76.00 2.20 390.00 57.00 200 39 470 537 0.143 495 0.053 642 0.365
53 266.00 76.00 2.20 390.00 57.00 200 39 480 537 0.119 495 0.031 642 0.337
54 266.00 76.00 2.20 390.00 57.00 200 39 420 537 0.279 495 0.178 642 0.528
55 266.00 76.00 2.20 390.00 57.00 200 39 465 537 0.155 495 0.064 642 0.380
56 356.00 101.70 2.40 380.00 57.00 200 39 770 865 0.123 800 0.039 1050 0.364
57 356.00 101.70 2.40 380.00 57.00 200 39 775 865 0.116 800 0.033 1050 0.355
58 356.00 101.70 2.40 380.00 57.00 200 39 740 865 0.169 800 0.082 1050 0.419
59 356.00 101.70 2.40 380.00 57.00 200 39 690 865 0.253 800 0.160 1050 0.522
60 356.00 101.70 2.40 380.00 57.00 200 39 775 865 0.116 800 0.033 1050 0.355
61 580.50 165.00 2.82 363.30 48.30 200 37 1662 1798 0.082 1669 0.005 2193 0.320
62 663.50 190.00 1.94 256.40 41.00 200 35 1678 1647 -0.018 1523 -0.093 1981 0.180
63 664.50 190.00 1.52 306.10 48.30 200 37 1695 1797 0.061 1697 0.001 2205 0.301
64 664.50 190.00 1.13 185.70 41.00 200 35 1377 1401 0.018 1306 -0.051 1635 0.187
65 659.00 190.00 0.86 210.70 41.00 200 35 1350 1373 0.017 1289 -0.045 1599 0.185
66 580.50 165.00 2.82 363.30 80.20 200 42 2295 2376 0.035 2269 -0.011 3034 0.322
67 663.50 190.00 1.94 256.40 74.70 200 42 2592 2472 -0.046 2409 -0.071 3097 0.195
68 663.50 190.00 1.52 306.10 80.20 200 42 2602 2553 -0.019 2539 -0.024 3254 0.251
69 662.50 190.00 1.13 185.70 80.20 200 42 2295 2339 0.019 2366 0.031 2869 0.250
70 663.50 190.00 0.86 210.70 74.70 200 42 2451 2175 -0.113 2204 -0.101 2659 0.085
71 577.50 165.00 2.82 363.30 108.00 200 46 2673 2845 0.064 2788 0.043 3735 0.397
72 660.00 190.00 1.94 256.40 108.00 200 46 3360 3213 -0.044 3275 -0.025 4159 0.238
73 661.50 190.00 1.52 306.10 108.00 200 46 3260 3157 -0.032 3268 0.002 4142 0.271
74 660.00 190.00 1.13 185.70 108.00 200 46 3058 2940 -0.039 3107 0.016 3722 0.217
75 662.00 190.00 0.86 210.70 108.00 200 46 3070 2888 -0.059 3097 0.009 3682 0.199
76 339.00 111.30 2.00 354.60 60.80 200 39 855 966 0.130 888 0.038 1159 0.355
77 338.00 113.60 3.20 354.60 60.80 200 39 1145 1203 0.050 1100 -0.039 1406 0.228
78 338.00 114.80 3.90 357.70 60.80 200 39 1116 1342 0.203 1227 0.100 1547 0.387
79 356.00 115.90 4.90 309.50 60.80 200 39 1174 1398 0.191 1273 0.084 1599 0.362
80 396.00 130.60 2.30 324.30 60.80 200 39 1250 1285 0.028 1178 -0.058 1535 0.228
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81 397.00 133.10 4.50 324.30 60.80 200 39 1535 1714 0.117 1563 0.018 1982 0.292
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International Journal of Civil & Environmental Engineering IJCEE-IJENS Vol: 11 No: 02 27
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124 840.00 204.00 2.00 235.20 40.28 200 35 1691 1737 0.027 1658 -0.019 2092 0.237
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167 300.00 100.00 3.00 426.30 35.17 200 34 777 853 0.097 797 0.026 942 0.212
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253 714.00 238.00 4.54 507.00 77.00 200 42 5578 5854 0.049 5437 -0.025 7167 0.285
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288 418.00 140.00 3.60 325.30 49.10 200 37 1582 1526 -0.035 1396 -0.117 1765 0.116
289 420.00 139.70 3.61 325.30 49.10 200 37 1540 1521 -0.012 1392 -0.096 1761 0.143
290 396.00 133.40 5.17 351.00 56.50 200 39 1810 1852 0.023 1696 -0.063 2103 0.162
291 396.00 133.20 5.03 351.00 56.50 200 39 1770 1822 0.030 1669 -0.057 2074 0.172
292 397.00 133.20 5.07 351.00 56.50 200 39 1835 1829 -0.003 1675 -0.087 2081 0.134
293 420.00 138.90 3.28 331.70 61.70 200 39 1688 1637 -0.030 1497 -0.113 1938 0.148
294 418.00 138.70 3.28 331.70 61.70 200 39 1680 1634 -0.027 1494 -0.111 1934 0.151
295 418.00 139.00 3.29 331.70 61.70 200 39 1629 1642 0.008 1501 -0.079 1943 0.193
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296 477.00 159.30 5.36 356.30 61.70 200 39 2480 2578 0.039 2357 -0.050 2986 0.204
297 476.00 160.20 5.01 356.30 61.70 200 39 2440 2526 0.035 2309 -0.054 2937 0.204
298 478.00 159.30 5.07 356.30 61.70 200 39 2460 2513 0.021 2298 -0.066 2923 0.188
299 396.00 133.30 5.10 351.00 61.70 200 39 1930 1904 -0.014 1739 -0.099 2182 0.130
300 396.00 133.40 5.20 351.00 61.70 200 39 1955 1924 -0.016 1757 -0.101 2201 0.126
301 397.00 133.10 5.04 351.00 61.70 200 39 1955 1888 -0.034 1725 -0.118 2166 0.108
302 397.00 133.30 5.43 392.00 61.70 200 39 1820 2082 0.144 1907 0.048 2369 0.301
303 397.00 133.10 5.44 392.00 61.70 200 39 1915 2079 0.086 1904 -0.006 2365 0.235
304 397.00 133.10 5.43 392.00 61.70 200 39 1930 2077 0.076 1902 -0.015 2363 0.224
305 447.00 149.00 2.96 308.00 25.40 200 32 941 1109 0.179 1031 0.096 1239 0.317
306 447.00 149.00 2.96 308.00 40.50 200 35 1064 1377 0.294 1257 0.182 1591 0.495
307 447.00 149.00 2.96 308.00 40.50 200 35 1080 1377 0.275 1257 0.164 1591 0.473
308 447.00 149.00 2.96 308.00 77.00 200 42 1781 1972 0.107 1813 0.018 2375 0.333
309 903.00 301.00 2.96 279.00 25.40 200 32 2382 3213 0.349 2898 0.217 3667 0.540
310 900.00 300.00 2.96 279.00 41.10 200 36 3277 4319 0.318 3905 0.192 5027 0.534
311 900.00 300.00 2.96 279.00 41.10 200 36 3152 4319 0.370 3905 0.239 5027 0.595
312 903.00 301.00 2.96 279.00 80.30 200 42 5540 6916 0.248 6531 0.179 8321 0.502
313 1350.00 450.00 2.96 279.00 25.40 200 32 4415 6358 0.440 5672 0.285 7226 0.637
314 1350.00 450.00 2.96 279.00 41.10 200 36 6870 8872 0.291 8030 0.169 10238 0.490
315 1350.00 450.00 2.96 279.00 41.10 200 36 6985 8872 0.270 8030 0.150 10238 0.466
316 1350.00 450.00 2.96 279.00 85.10 200 43 11665 15216 0.304 14709 0.261 18241 0.564
317 366.00 122.00 4.54 576.00 25.40 200 32 1509 1645 0.090 1586 0.051 1714 0.136
318 366.00 122.00 4.54 576.00 40.50 200 35 1657 1839 0.110 1721 0.038 1995 0.204
319 366.00 122.00 4.54 576.00 40.50 200 35 1663 1839 0.106 1721 0.035 1995 0.200
320 366.00 122.00 4.54 576.00 77.00 200 42 2100 2235 0.064 2049 -0.024 2597 0.237
321 717.00 239.00 4.54 507.00 25.40 200 32 3035 3698 0.218 3495 0.151 4085 0.346
322 714.00 238.00 4.54 507.00 40.50 200 35 3583 4356 0.216 4042 0.128 5030 0.404
323 714.00 238.00 4.54 507.00 40.50 200 35 3647 4356 0.194 4042 0.108 5030 0.379
324 714.00 238.00 4.54 507.00 77.00 200 42 5578 5854 0.049 5437 -0.025 7167 0.285
325 1083.00 361.00 4.54 525.00 25.40 200 32 5633 6778 0.203 6341 0.126 7704 0.368
326 1083.00 361.00 4.54 525.00 41.10 200 36 7260 8388 0.155 7756 0.068 9929 0.368
327 1080.00 360.00 4.54 525.00 41.10 200 36 7045 8352 0.186 7723 0.096 9885 0.403
328 1080.00 360.00 4.54 525.00 85.10 200 43 11505 12419 0.079 11746 0.021 15565 0.353
329 324.00 108.00 6.47 853.00 25.40 200 32 2275 2366 0.040 2412 0.060 2503 0.100
330 327.00 109.00 6.47 853.00 40.50 200 35 2446 2672 0.092 2536 0.037 2792 0.142
331 324.00 108.00 6.47 853.00 40.50 200 35 2402 2639 0.099 2507 0.044 2758 0.148
332 324.00 108.00 6.47 853.00 77.00 200 42 2713 3022 0.114 2734 0.008 3286 0.211
333 666.00 222.00 6.47 843.00 25.40 200 32 4964 6053 0.219 5822 0.173 6356 0.280
334 666.00 222.00 6.47 843.00 40.50 200 35 5638 6726 0.193 6280 0.114 7345 0.303
335 666.00 222.00 6.47 843.00 40.50 200 35 5714 6726 0.177 6280 0.099 7345 0.286
336 666.00 222.00 6.47 843.00 77.00 200 42 7304 8049 0.102 7399 0.013 9456 0.295
337 1011.00 337.00 6.47 823.00 25.40 200 32 8475 10187 0.202 9687 0.143 11022 0.301
338 1011.00 337.00 6.47 823.00 41.10 200 36 9668 11636 0.204 10848 0.122 13242 0.370
International Journal of Civil & Environmental Engineering IJCEE-IJENS Vol: 11 No: 02 32
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339 1011.00 337.00 6.47 823.00 41.10 200 36 9835 11636 0.183 10848 0.103 13242 0.346
340 1011.00 337.00 6.47 823.00 85.10 200 43 13776 15180 0.102 14152 0.027 18768 0.362
341 399.00 133.05 5.00 351.00 70.80 200 41 1890 1992 0.054 1816 -0.039 2318 0.226
342 417.00 138.50 3.24 331.70 70.80 200 41 1851 1748 -0.056 1601 -0.135 2090 0.129
343 399.00 133.34 5.01 351.00 70.80 200 41 2004 2001 -0.001 1824 -0.090 2328 0.162
344 399.00 133.10 5.05 351.00 70.80 200 41 2514 2002 -0.204 1825 -0.274 2328 -0.074
345 417.00 139.30 3.36 331.70 70.80 200 41 1920 1789 -0.068 1637 -0.147 2134 0.112
346 417.00 138.25 3.34 331.70 70.80 200 41 2330 1761 -0.244 1612 -0.308 2103 -0.097
347 400.00 133.25 4.91 351.00 75.30 200 42 2347 2036 -0.133 1856 -0.209 2386 0.017
348 400.00 133.21 5.05 351.00 75.30 200 42 2366 2059 -0.130 1876 -0.207 2409 0.018
349 400.00 133.42 5.41 351.00 75.30 200 42 2324 2128 -0.084 1937 -0.167 2475 0.065
350 400.00 133.22 6.07 392.00 75.30 200 42 2234 2369 0.060 2157 -0.034 2724 0.219
351 400.00 133.29 6.17 392.00 75.30 200 42 2267 2390 0.054 2176 -0.040 2744 0.210
352 400.00 133.29 6.11 392.00 75.30 200 42 2275 2378 0.045 2166 -0.048 2733 0.201
353 418.00 139.40 3.27 331.70 75.30 200 42 2120 1836 -0.134 1683 -0.206 2203 0.039
354 416.00 138.70 3.23 331.70 75.30 200 42 2147 1813 -0.156 1662 -0.226 2176 0.013
355 416.00 138.70 3.27 331.70 75.30 200 42 2185 1820 -0.167 1669 -0.236 2184 -0.001
356 477.00 158.60 5.17 356.30 75.30 200 42 3198 2758 -0.137 2519 -0.212 3261 0.020
357 477.00 158.90 5.12 356.30 75.30 200 42 3095 2757 -0.109 2518 -0.186 3260 0.053
358 477.00 159.10 5.11 356.30 75.30 200 42 3031 2761 -0.089 2522 -0.168 3265 0.077
359 1420.00 95.00 12.50 279.00 20.60 209 30 947 938 -0.009 884 -0.066 775 -0.182
360 1420.00 95.00 12.75 277.00 20.60 209 30 938 940 0.003 891 -0.050 779 -0.170
361 1420.00 95.00 12.40 277.00 20.60 209 30 907 933 0.028 874 -0.036 766 -0.155
362 860.00 95.00 12.60 279.00 20.60 209 30 1018 1066 0.047 959 -0.058 931 -0.085
363 860.00 95.00 12.70 277.00 20.60 209 30 1008 1064 0.055 959 -0.049 930 -0.077
364 860.00 95.00 12.70 277.00 20.60 209 30 1034 1064 0.029 959 -0.073 930 -0.101
365 1980.00 95.00 12.80 283.00 20.60 209 30 886 840 -0.052 802 -0.095 677 -0.236
366 1980.00 95.00 12.50 280.00 20.60 209 30 907 832 -0.082 784 -0.136 662 -0.270
367 1980.00 95.00 12.60 294.00 20.60 209 30 917 851 -0.072 813 -0.113 693 -0.244
368 860.00 95.00 3.66 332.00 25.30 209 32 656 578 -0.119 491 -0.252 543 -0.173
369 860.00 95.00 3.68 392.00 25.30 209 32 686 651 -0.051 545 -0.206 606 -0.116
370 860.00 95.00 3.40 340.00 25.30 209 32 656 558 -0.150 475 -0.275 529 -0.193
371 1420.00 95.00 3.86 332.00 25.30 209 32 567 523 -0.078 461 -0.187 467 -0.177
372 1420.00 95.00 3.91 392.00 25.30 209 32 606 594 -0.020 516 -0.149 524 -0.135
373 1420.00 95.00 3.58 340.00 25.30 209 32 576 503 -0.127 446 -0.225 455 -0.211
374 1980.00 95.00 3.76 332.00 25.30 209 32 536 472 -0.120 394 -0.264 392 -0.268
375 1980.00 95.00 3.78 392.00 25.30 209 32 567 533 -0.059 427 -0.247 438 -0.227
376 1980.00 95.00 3.51 340.00 25.30 209 32 488 457 -0.064 382 -0.217 383 -0.214
377 2220.00 216.00 4.06 289.00 23.20 209 31 1023 1593 0.557 1494 0.461 1674 0.637
378 2220.00 216.00 4.11 304.00 23.20 209 31 1834 1653 -0.099 1537 -0.162 1727 -0.058
379 2220.00 216.00 4.04 293.00 30.20 209 33 2289 1727 -0.245 1704 -0.255 1930 -0.157
380 2220.00 216.00 4.11 291.00 30.20 209 33 2239 1739 -0.223 1711 -0.236 1937 -0.135
381 2220.00 216.00 6.05 395.00 23.20 209 31 2462 2546 0.034 2176 -0.116 2438 -0.010
International Journal of Civil & Environmental Engineering IJCEE-IJENS Vol: 11 No: 02 33
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382 2220.00 216.00 5.97 399.00 23.20 209 31 2421 2539 0.049 2171 -0.103 2435 0.006
383 2220.00 216.00 6.50 300.00 30.20 209 33 2804 2365 -0.157 2134 -0.239 2406 -0.142
384 2220.00 216.00 6.30 411.00 30.20 209 33 2932 2831 -0.034 2483 -0.153 2832 -0.034
385 1980.00 95.00 3.86 337.00 24.40 209 31 498 482 -0.031 401 -0.195 397 -0.203
386 1980.00 95.00 3.40 343.00 24.40 209 31 473 446 -0.057 373 -0.212 374 -0.210
387 1980.00 95.00 3.58 360.00 24.40 209 31 473 479 0.013 394 -0.167 397 -0.161
388 1980.00 95.00 3.73 332.00 24.40 209 31 413 466 0.128 389 -0.057 385 -0.067
389 1050.00 121.00 3.66 300.00 21.40 209 30 695 722 0.039 627 -0.098 690 -0.008
390 1050.00 121.00 3.73 333.00 21.40 209 30 746 784 0.051 673 -0.098 743 -0.004
391 1050.00 121.00 3.76 313.00 24.60 209 31 837 780 -0.068 680 -0.188 759 -0.093
392 1050.00 121.00 3.99 332.00 24.60 209 31 867 845 -0.025 728 -0.161 811 -0.064
393 1050.00 121.00 5.61 349.00 21.40 209 30 998 1085 0.087 905 -0.093 970 -0.028
394 1050.00 121.00 5.41 348.00 21.40 209 30 1018 1055 0.036 881 -0.134 947 -0.070
395 1050.00 121.00 5.46 336.00 24.60 209 31 1099 1063 -0.033 892 -0.188 972 -0.115
396 1050.00 121.00 5.56 327.00 24.60 209 31 1079 1056 -0.021 888 -0.177 965 -0.106
397 2310.00 121.00 3.71 300.00 21.40 209 30 641 584 -0.090 523 -0.184 512 -0.202
398 2310.00 121.00 3.76 333.00 21.40 209 30 629 634 0.009 556 -0.116 549 -0.127
399 2310.00 121.00 3.71 313.00 24.60 209 31 695 618 -0.111 556 -0.200 555 -0.201
400 2310.00 121.00 3.86 332.00 24.60 209 31 755 663 -0.122 585 -0.225 587 -0.223
401 2310.00 121.00 5.69 349.00 21.40 209 30 786 890 0.132 749 -0.046 720 -0.084
402 2310.00 121.00 5.49 348.00 21.40 209 30 816 865 0.061 730 -0.105 704 -0.138
403 2310.00 121.00 5.64 336.00 24.60 209 31 874 881 0.008 748 -0.144 729 -0.165
404 2310.00 121.00 5.44 327.00 24.60 209 31 865 842 -0.027 720 -0.168 702 -0.189
405 1524.00 101.70 3.07 614.00 34.70 212 34 818 783 -0.043 675 -0.174 751 -0.082
406 1524.00 101.70 3.10 614.00 31.60 212 33 801 776 -0.032 665 -0.170 731 -0.088
407 1050.00 120.70 4.09 459.00 34.90 194 34 1156 1134 -0.019 973 -0.159 1143 -0.011
408 1050.00 120.80 4.09 459.00 30.00 194 33 1092 1103 0.010 932 -0.146 1081 -0.010
409 1050.00 120.80 4.09 459.00 26.30 194 32 950 1077 0.134 901 -0.051 1032 0.086
410 1676.00 152.60 3.15 421.00 21.20 207 30 939 1024 0.090 905 -0.037 1009 0.074
411 1676.00 152.70 3.15 421.00 21.20 207 30 881 1025 0.163 905 0.028 1010 0.147
412 1524.00 76.50 1.70 369.00 25.30 200 32 245 221 -0.097 194 -0.208 205 -0.164
413 610.00 76.40 1.73 369.00 41.50 200 36 411 329 -0.200 312 -0.240 373 -0.093
414 609.00 76.50 1.73 369.00 26.30 200 32 330 290 -0.122 259 -0.215 300 -0.092
415 914.00 114.30 3.18 420.00 29.40 203 33 712 829 0.164 722 0.013 839 0.178
416 914.00 114.30 3.18 420.00 29.40 203 33 756 829 0.096 722 -0.046 839 0.109
417 914.00 127.00 2.41 294.00 35.60 203 34 627 725 0.157 700 0.117 822 0.311
418 914.00 127.00 2.41 294.00 35.60 203 34 623 725 0.165 700 0.124 822 0.319
419 914.00 127.00 2.41 294.00 35.60 203 34 658 725 0.103 700 0.064 822 0.249
420 914.00 152.40 1.55 336.00 21.40 203 30 682 701 0.028 665 -0.025 775 0.136
421 914.00 152.40 1.55 336.00 26.30 203 32 721 768 0.065 742 0.029 874 0.212
422 914.00 152.40 1.55 336.00 26.30 203 32 733 768 0.048 742 0.012 874 0.193
423 1880.00 355.60 11.18 361.00 38.60 203 35 11460 9399 -0.180 8535 -0.255 10054 -0.123
424 1880.00 355.60 11.18 361.00 33.30 203 34 10710 8991 -0.161 8138 -0.240 9415 -0.121
International Journal of Civil & Environmental Engineering IJCEE-IJENS Vol: 11 No: 02 34
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425 1880.00 355.60 4.72 281.00 21.30 203 30 3517 4137 0.176 3878 0.103 4501 0.280
426 2083.00 355.60 7.98 361.00 23.80 203 31 7433 6464 -0.130 5859 -0.212 6664 -0.103
427 711.00 127.30 1.63 376.00 67.20 203 40 1285 992 -0.228 1046 -0.186 1280 -0.004
428 711.00 127.30 1.63 334.00 67.20 203 40 1285 960 -0.253 1020 -0.206 1235 -0.039
429 711.00 127.10 2.95 376.00 67.20 203 40 1305 1260 -0.035 1228 -0.059 1527 0.170
430 711.00 127.10 2.95 334.00 67.20 203 40 1305 1201 -0.080 1180 -0.095 1457 0.117
431 406.00 140.10 9.68 270.00 32.60 203 34 2949 2009 -0.319 1885 -0.361 2075 -0.296
432 406.00 140.10 9.68 273.00 32.60 203 34 2949 2024 -0.314 1901 -0.355 2091 -0.291
433 406.00 140.40 4.93 293.00 33.20 203 34 1824 1446 -0.207 1347 -0.261 1581 -0.133
434 406.00 140.40 4.93 302.00 33.20 203 34 1824 1472 -0.193 1373 -0.247 1608 -0.119
435 813.00 168.20 4.52 302.00 31.90 203 33 2006 1661 -0.172 1532 -0.236 1793 -0.106
436 813.00 168.40 4.52 302.00 43.80 203 36 2233 1878 -0.159 1744 -0.219 2112 -0.054
437 813.00 168.20 4.52 302.00 43.80 203 36 2113 1874 -0.113 1741 -0.176 2107 -0.003
438 813.00 168.30 4.47 302.00 23.40 203 31 1744 1489 -0.146 1373 -0.213 1549 -0.112
439 850.00 114.00 1.79 266.00 37.00 200 32 515 491 -0.047 507 -0.015 602 0.169
440 850.00 114.00 3.35 291.00 37.00 200 32 785 724 -0.078 668 -0.149 794 0.011
441 850.00 114.00 4.44 332.00 37.00 200 35 902 945 0.047 829 -0.080 968 0.073
442 850.00 114.00 6.00 486.00 37.00 200 35 1334 1519 0.139 1262 -0.054 1445 0.083
443 1250.00 114.00 5.91 486.00 25.00 200 35 1177 1281 0.089 1084 -0.079 1133 -0.037
444 1750.00 114.00 1.93 266.00 33.00 200 35 461 373 -0.191 412 -0.106 449 -0.026
445 1750.00 114.00 3.32 291.00 30.00 200 32 628 539 -0.142 520 -0.172 557 -0.113
446 1750.00 114.00 5.94 486.00 37.00 200 32 1138 1243 0.092 1057 -0.072 1119 -0.017
447 2250.00 114.00 1.78 266.00 28.00 200 32 373 340 -0.090 320 -0.141 352 -0.058
448 2320.00 114.00 3.31 291.00 24.00 200 32 535 488 -0.087 423 -0.209 440 -0.178
449 2250.00 114.00 6.14 486.00 28.00 200 35 1000 1134 0.134 877 -0.123 934 -0.066
450 2220.00 215.90 4.09 292.00 22.90 184 24 1650 1595 -0.033 1491 -0.096 1676 0.016
451 2220.00 215.90 4.09 292.00 30.00 186 24 2264 1722 -0.239 1698 -0.250 1928 -0.148
452 2220.00 215.90 6.00 392.00 22.90 200 24 2442 2498 0.023 2137 -0.125 2401 -0.017
453 2220.00 215.90 6.00 350.00 30.00 215 24 2869 2448 -0.147 2199 -0.233 2511 -0.125
454 1050.00 120.90 3.76 312.00 21.10 215 22 721 748 0.038 645 -0.106 712 -0.013
455 2310.00 120.90 3.76 312.00 21.10 184 21 636 601 -0.055 531 -0.165 524 -0.176
456 1050.00 120.90 5.53 343.00 21.10 186 20 1010 1052 0.042 877 -0.131 945 -0.065
457 1050.00 120.90 5.53 343.00 24.20 215 24 1090 1079 -0.010 902 -0.173 986 -0.095
458 1370.00 95.00 3.65 350.00 25.00 184 22 667 522 -0.217 460 -0.310 473 -0.291
459 1420.00 95.00 3.65 350.00 25.00 186 23 583 517 -0.113 456 -0.218 466 -0.200
460 1980.00 95.00 3.65 350.00 25.00 215 22 529 477 -0.098 391 -0.261 397 -0.249
461 2440.00 165.00 4.30 317.70 43.30 184 21 1149 1254 0.092 1309 0.139 1417 0.234
462 2420.00 160.00 4.50 317.70 43.30 186 21 1561 1231 -0.212 1261 -0.192 1361 -0.128
463 1150.00 190.70 6.00 505.00 55.90 200 20 3064 3552 0.159 3196 0.043 3953 0.290
464 2300.00 190.70 6.00 505.00 55.90 215 21 2610 2854 0.093 2760 0.057 3184 0.220
465 2450.00 190.70 6.00 505.00 55.90 200 31 2060 2807 0.363 2703 0.312 3111 0.510
466 1150.00 190.70 6.00 505.00 48.40 200 33 3150 3417 0.085 3037 -0.036 3705 0.176
467 3450.00 190.70 6.00 505.00 48.40 200 31 2130 2613 0.227 2106 -0.011 2518 0.182
International Journal of Civil & Environmental Engineering IJCEE-IJENS Vol: 11 No: 02 35
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468 1600.00 267.40 7.00 461.00 55.90 200 33 5180 5961 0.151 5531 0.068 6858 0.324
469 3200.00 267.40 7.00 461.00 55.90 200 30 4540 4696 0.034 4796 0.056 5527 0.217
470 4800.00 267.40 7.00 461.00 55.90 200 30 3630 4580 0.262 3851 0.061 4668 0.286
471 1600.00 267.40 7.00 461.00 48.40 200 30 5190 5695 0.097 5206 0.003 6382 0.230
472 4800.00 267.40 7.00 461.00 48.40 200 31 3900 4309 0.105 3679 -0.057 4344 0.114
473 1100.00 166.00 5.00 274.40 29.62 200 32 1985 1486 -0.251 1347 -0.321 1534 -0.227
474 710.00 166.00 5.00 277.34 39.06 200 32 1656 1815 0.096 1671 0.009 2039 0.231
475 710.00 166.00 5.00 277.34 42.24 200 32 1906 1873 -0.017 1727 -0.094 2123 0.114
476 870.00 166.00 5.00 313.60 42.24 200 36 1828 1906 0.043 1754 -0.040 2092 0.145
477 870.00 166.00 5.00 284.20 42.24 200 36 1862 1812 -0.027 1674 -0.101 1994 0.071
478 1700.00 166.00 5.00 294.00 42.24 200 36 1544 1496 -0.031 1442 -0.066 1657 0.073
479 1700.00 166.00 5.00 313.60 42.24 200 38 1460 1552 0.063 1483 0.016 1710 0.171
480 2700.00 166.00 5.00 289.10 28.09 200 38 1117 1156 0.035 1101 -0.014 1131 0.012
481 2700.00 166.00 5.00 289.10 28.09 200 38 1271 1156 -0.091 1101 -0.133 1131 -0.110
482 3700.00 166.00 5.00 287.14 28.09 200 37 984 1098 0.116 933 -0.052 959 -0.026
483 3700.00 166.00 5.00 287.14 28.09 200 37 958 1098 0.146 933 -0.026 959 0.000
484 648.00 108.00 4.00 338.88 28.99 200 38 825 830 0.005 737 -0.107 827 0.002
485 648.00 108.00 4.00 338.88 28.99 200 38 828 830 0.002 737 -0.110 827 -0.001
486 864.00 108.00 4.00 338.88 28.99 200 38 766 778 0.016 672 -0.123 760 -0.008
487 864.00 108.00 4.00 338.88 28.99 200 37 802 778 -0.029 672 -0.162 760 -0.051
488 864.00 108.00 4.00 338.88 28.99 200 37 869 778 -0.105 672 -0.227 760 -0.125
489 1080.00 108.00 4.00 338.88 28.99 200 33 837 734 -0.124 630 -0.247 709 -0.152
490 1080.00 108.00 4.00 338.88 28.99 200 35 783 734 -0.063 630 -0.195 709 -0.094
491 1620.00 108.00 4.00 338.88 28.99 200 36 708 651 -0.080 589 -0.168 611 -0.137
492 1620.00 108.00 4.00 338.88 28.99 200 36 647 651 0.006 589 -0.090 611 -0.055
493 1620.00 108.00 4.00 338.88 28.99 200 36 644 651 0.011 589 -0.086 611 -0.051
494 2160.00 108.00 4.00 338.88 28.99 200 36 672 609 -0.093 518 -0.230 533 -0.207
495 2160.00 108.00 4.00 338.88 28.99 200 36 698 609 -0.127 518 -0.258 533 -0.236
496 2160.00 108.00 4.00 338.88 28.99 200 32 676 609 -0.099 518 -0.235 533 -0.211
497 524.00 104.00 2.00 344.00 32.65 200 32 540 567 0.049 527 -0.024 631 0.168
498 530.00 105.00 2.50 344.00 35.65 200 32 613 669 0.091 618 0.008 737 0.202
499 536.00 106.00 3.00 344.00 33.47 200 32 674 736 0.091 673 -0.002 787 0.168
500 542.00 107.00 3.50 379.80 31.87 200 33 835 857 0.026 775 -0.072 891 0.067
501 542.00 107.00 4.00 379.80 31.87 200 33 889 934 0.050 840 -0.055 955 0.074
502 548.00 108.00 4.50 344.00 33.50 200 33 917 968 0.055 871 -0.050 987 0.077
503 548.00 108.00 5.00 379.80 33.50 200 33 1084 1107 0.021 989 -0.088 1110 0.024
504 960.00 160.00 2.50 433.20 32.22 200 33 1426 1279 -0.103 1194 -0.163 1435 0.006
505 840.00 140.00 2.50 433.20 38.88 200 33 1124 1127 0.003 1057 -0.060 1284 0.143
506 840.00 140.00 3.00 426.30 33.06 200 33 1208 1177 -0.026 1071 -0.113 1275 0.055
507 600.00 100.00 2.50 433.20 45.77 200 33 750 735 -0.020 676 -0.099 824 0.098
508 600.00 100.00 3.00 426.30 29.13 200 33 723 720 -0.004 636 -0.120 730 0.010
509 980.00 200.00 2.00 237.20 24.24 200 33 1411 1180 -0.164 1118 -0.207 1328 -0.059
510 1040.00 210.00 2.50 237.20 27.07 200 33 1607 1468 -0.086 1394 -0.133 1657 0.031
International Journal of Civil & Environmental Engineering IJCEE-IJENS Vol: 11 No: 02 36
111702-3737 IJCEE-IJENS © April 2011 IJENS I J E N S
511 1040.00 210.00 3.00 233.20 27.07 200 33 1705 1567 -0.081 1477 -0.134 1752 0.027
512 860.00 180.00 3.00 233.20 24.24 200 33 1352 1177 -0.130 1095 -0.190 1292 -0.044
513 1480.00 250.00 7.00 243.00 46.57 200 33 4116 3703 -0.100 3509 -0.147 4169 0.013
514 1440.00 240.00 10.00 269.00 49.80 200 33 5135 4475 -0.128 4083 -0.205 4817 -0.062
515 1040.00 166.00 5.00 288.10 54.33 200 33 1862 1909 0.025 1812 -0.027 2179 0.170
516 1040.00 166.00 5.00 288.10 43.89 200 33 1764 1764 0.000 1639 -0.071 1942 0.101
517 1040.00 166.00 5.00 288.10 26.73 200 33 1372 1503 0.096 1357 -0.011 1529 0.114
518 1040.00 166.00 5.00 288.10 29.72 200 33 1495 1551 0.038 1405 -0.060 1603 0.073
519 1040.00 166.00 5.00 288.10 23.00 200 33 1392 1441 0.035 1296 -0.069 1433 0.030
520 1040.00 166.00 5.00 288.10 44.11 200 33 1695 1767 0.043 1642 -0.031 1947 0.149
521 1040.00 166.00 5.00 288.10 55.65 200 33 1852 1927 0.040 1834 -0.010 2209 0.193
522 1040.00 166.00 5.00 288.10 37.75 200 33 1627 1675 0.029 1537 -0.055 1798 0.105
523 840.00 140.00 5.30 378.30 21.86 200 34 1326 1431 0.079 1262 -0.048 1364 0.029
524 840.00 140.00 5.00 378.30 30.58 200 34 1379 1483 0.075 1310 -0.050 1489 0.080
525 840.00 140.00 5.00 378.30 34.92 200 34 1501 1533 0.021 1358 -0.095 1570 0.046
526 840.00 140.00 5.30 378.30 51.50 200 33 1664 1767 0.062 1590 -0.044 1911 0.149
527 840.00 140.00 5.00 378.30 42.25 200 33 1539 1612 0.048 1441 -0.064 1702 0.106
528 460.00 92.00 3.00 260.70 20.71 200 34 501 442 -0.119 407 -0.189 443 -0.115
529 920.00 92.00 3.00 260.70 20.71 200 34 431 382 -0.114 330 -0.233 360 -0.165
530 1380.00 92.00 3.00 260.70 20.71 200 33 409 339 -0.171 307 -0.248 310 -0.242
531 648.00 108.00 4.50 259.70 20.22 200 35 665 687 0.033 618 -0.070 652 -0.020
532 972.00 108.00 4.50 259.70 20.22 200 34 666 636 -0.045 542 -0.187 578 -0.132
533 1296.00 108.00 4.50 259.70 20.22 200 36 563 592 0.051 498 -0.115 525 -0.067
534 1620.00 108.00 4.50 259.70 20.22 200 33 524 556 0.061 487 -0.071 482 -0.081
535 1994.00 108.00 4.50 259.70 20.22 200 31 495 524 0.058 461 -0.070 438 -0.115
536 540.00 108.00 4.00 327.10 39.23 200 32 836 915 0.094 831 -0.006 972 0.162
537 756.00 108.00 4.00 337.60 35.33 200 32 785 841 0.071 741 -0.055 855 0.090
538 972.00 108.00 4.00 337.60 33.54 200 31 736 777 0.055 677 -0.080 776 0.055
539 1188.00 108.00 4.00 327.10 34.03 200 37 686 719 0.048 642 -0.064 718 0.047
540 1404.00 108.00 4.00 332.00 33.15 200 37 686 686 -0.000 629 -0.083 675 -0.017
541 1620.00 108.00 4.00 347.70 33.15 200 38 672 678 0.009 622 -0.074 655 -0.026
542 648.00 108.00 4.20 259.70 20.54 200 36 722 659 -0.087 594 -0.178 631 -0.126
543 972.00 108.00 4.20 259.70 22.84 200 32 640 622 -0.029 536 -0.163 583 -0.089
544 1040.00 210.00 2.50 237.20 27.07 200 33 1607 1468 -0.086 1394 -0.133 1657 0.031
545 1670.00 210.00 2.50 237.20 26.56 200 31 1323 1236 -0.066 1257 -0.050 1423 0.075
546 1322.00 165.20 4.17 358.70 40.90 200 36 1445 1606 0.111 1502 0.039 1786 0.236
547 1982.00 165.20 4.17 358.70 40.90 200 38 1305 1391 0.066 1401 0.074 1565 0.199
548 2974.00 165.20 4.17 358.70 40.90 200 35 1180 1277 0.082 1200 0.017 1321 0.120
549 1830.00 168.80 2.64 200.20 18.20 200 31 823 654 -0.206 638 -0.225 687 -0.165
550 1830.00 168.80 2.64 200.20 34.70 200 33 916 829 -0.095 939 0.025 1015 0.109
551 1830.00 169.30 2.62 338.10 37.10 200 34 756 1062 0.405 1153 0.524 1295 0.713
552 1830.00 169.30 2.62 338.10 34.10 200 38 689 1034 0.500 1096 0.590 1233 0.790
553 2135.00 168.30 3.60 288.40 27.00 200 36 947 988 0.043 989 0.044 1078 0.138
International Journal of Civil & Environmental Engineering IJCEE-IJENS Vol: 11 No: 02 37
111702-3737 IJCEE-IJENS © April 2011 IJENS I J E N S
554 2135.00 168.30 3.60 288.40 33.30 200 30 1050 1044 -0.006 1095 0.043 1202 0.145
555 2135.00 168.80 5.00 302.40 33.40 200 30 1130 1370 0.213 1319 0.167 1427 0.263
556 2135.00 168.80 5.00 302.40 27.80 200 30 1165 1318 0.131 1225 0.052 1312 0.126
557 1727.00 88.90 5.84 406.00 41.50 200 30 615 758 0.234 611 -0.007 636 0.034
558 1422.00 88.90 5.84 406.00 41.50 200 30 712 796 0.118 682 -0.042 698 -0.020
559 1118.00 88.90 5.84 406.00 41.50 200 30 715 852 0.192 734 0.026 769 0.075
560 813.00 88.90 5.84 406.00 41.50 200 30 919 928 0.011 766 -0.166 857 -0.067
561 508.00 88.90 5.84 406.00 41.50 200 30 992 1023 0.031 885 -0.108 985 -0.007
562 508.00 88.90 5.84 406.00 41.50 200 35 890 1023 0.150 885 -0.005 985 0.107
563 1422.00 82.55 1.40 490.00 41.50 200 34 295 310 0.053 289 -0.018 333 0.131
564 1118.00 82.55 1.40 490.00 41.50 200 34 356 315 -0.114 327 -0.080 369 0.037
565 813.00 82.55 1.40 490.00 41.50 200 34 400 350 -0.126 353 -0.117 413 0.032
566 508.00 82.55 1.40 490.00 41.50 200 34 489 414 -0.154 389 -0.205 476 -0.028
567 580.50 165.00 2.82 363.30 48.30 200 34 1662 1799 0.082 1669 0.005 2193 0.320
568 663.50 190.00 1.94 256.40 41.00 200 30 1678 1650 -0.017 1523 -0.092 1981 0.180
569 664.50 190.00 1.52 306.10 48.30 200 31 1695 1801 0.063 1697 0.002 2205 0.301
570 664.50 190.00 1.13 185.70 41.00 200 32 1377 1393 0.012 1305 -0.052 1635 0.187
571 659.00 190.00 0.86 210.70 41.00 200 32 1350 1367 0.012 1288 -0.046 1599 0.185
572 580.50 165.00 2.82 363.30 80.20 200 35 2295 2377 0.036 2269 -0.011 3034 0.322
573 663.50 190.00 1.94 256.40 74.70 200 35 2592 2477 -0.044 2410 -0.070 3097 0.195
574 663.50 190.00 1.52 306.10 80.20 200 35 2602 2559 -0.016 2541 -0.023 3254 0.251
575 662.50 190.00 1.13 185.70 80.20 200 35 2295 2324 0.013 2363 0.030 2869 0.250
576 663.50 190.00 0.86 210.70 74.70 200 35 2451 2162 -0.118 2202 -0.101 2659 0.085
577 577.50 165.00 2.82 363.30 108.00 208 29 2673 2846 0.065 2789 0.043 3735 0.397
578 660.00 190.00 1.94 256.40 108.00 208 34 3360 3220 -0.042 3277 -0.025 4159 0.238
579 661.50 190.00 1.52 306.10 108.00 199 35 3260 3165 -0.029 3270 0.003 4142 0.271
580 660.00 190.00 1.13 185.70 108.00 199 34 3058 2920 -0.045 3104 0.015 3722 0.217
581 662.00 190.00 0.86 210.70 108.00 168 32 3070 2871 -0.065 3094 0.008 3682 0.199
582 2475.00 165.00 4.70 355.00 33.40 168 34 1058 1351 0.277 1295 0.224 1364 0.289
583 2476.00 165.00 4.70 355.00 33.40 208 34 1037 1351 0.303 1295 0.249 1364 0.315
584 2477.00 165.00 4.70 355.00 10.00 208 32 800 1104 0.380 938 0.172 884 0.105
585 2478.00 165.00 4.70 355.00 10.00 217 35 834 1104 0.323 938 0.124 884 0.060
586 2200.00 110.00 1.90 350.00 33.40 217 35 437 418 -0.044 391 -0.106 421 -0.036
587 2200.00 110.00 1.90 350.00 33.40 217 35 368 418 0.135 391 0.062 421 0.144
588 2200.00 110.00 1.90 350.00 33.40 217 35 355 418 0.176 391 0.101 421 0.186
589 2200.00 110.00 1.90 350.00 33.40 217 35 374 418 0.116 391 0.045 421 0.126
590 2200.00 110.00 1.90 350.00 10.00 217 35 269 304 0.130 265 -0.016 246 -0.085
591 2200.00 110.00 1.90 350.00 10.00 217 35 252 304 0.206 265 0.051 246 -0.024
592 2200.00 110.00 1.90 350.00 10.00 217 35 211 304 0.441 265 0.255 246 0.166
593 2200.00 110.00 1.90 350.00 10.00 217 35 219 304 0.388 265 0.209 246 0.123
594 2000.00 200.00 3.00 303.50 46.80 217 35 1830 1570 -0.142 1804 -0.014 2032 0.110
595 2001.00 200.00 3.00 303.50 46.80 217 35 1806 1569 -0.131 1804 -0.001 2031 0.125
596 2002.00 200.00 3.00 303.50 46.80 201 37 1882 1569 -0.166 1804 -0.041 2031 0.079
International Journal of Civil & Environmental Engineering IJCEE-IJENS Vol: 11 No: 02 38
111702-3737 IJCEE-IJENS © April 2011 IJENS I J E N S
597 2003.00 200.00 3.00 303.50 46.80 205 35 2060 1568 -0.239 1804 -0.124 2031 -0.014
598 2004.00 200.00 3.00 303.50 46.80 207 37 2115 1568 -0.259 1804 -0.147 2030 -0.040
599 540.00 108.00 4.00 332.02 40.40 178 35 836 932 0.114 846 0.012 993 0.188
600 445.00 108.00 4.50 409.64 28.60 177 35 970 1081 0.114 996 0.027 1135 0.170
601 485.00 108.00 4.50 409.64 28.60 201 42 1205 1068 -0.114 975 -0.191 1087 -0.098
602 840.00 140.00 5.00 378.28 45.10 205 42 1667 1642 -0.015 1473 -0.117 1752 0.051
603 970.00 108.00 4.50 259.70 32.20 207 42 741 704 -0.050 619 -0.165 694 -0.063
604 2400.00 220.00 10.00 224.22 36.60 178 42 1729 2742 0.586 2479 0.434 2743 0.586
605 2400.00 240.00 12.00 191.79 54.50 177 42 3900 3617 -0.073 3476 -0.109 3920 0.005
606 912.00 152.00 7.00 283.22 42.90 201 46 1693 1867 0.102 1671 -0.013 1930 0.140
607 840.00 140.00 5.50 333.20 42.90 205 46 1380 1589 0.152 1424 0.032 1669 0.209
608 1700.00 164.00 6.00 356.82 31.50 207 46 1634 1746 0.069 1514 -0.073 1712 0.048
609 860.00 95.00 3.50 348.88 26.20 178 46 665 581 -0.127 493 -0.259 554 -0.168
610 1420.00 95.00 3.50 348.88 26.20 177 46 582 504 -0.135 449 -0.229 462 -0.206
611 1050.00 121.00 4.00 311.15 22.20 227 34 703 790 0.124 679 -0.034 750 0.068
612 1050.00 121.00 4.00 317.03 26.50 227 34 852 831 -0.024 722 -0.152 814 -0.044
613 1050.00 121.00 6.00 349.37 22.20 227 26 1007 1142 0.134 949 -0.058 1022 0.014
614 1050.00 121.00 6.00 325.85 26.50 227 26 1089 1122 0.031 940 -0.137 1030 -0.054
615 2220.00 216.00 6.00 391.02 24.10 220 34 2440 2519 0.032 2169 -0.111 2447 0.003
616 2220.00 216.00 6.00 379.26 31.40 220 34 2866 2604 -0.091 2337 -0.184 2682 -0.064
617 2220.00 216.00 4.00 289.39 24.10 220 34 1869 1588 -0.150 1506 -0.194 1697 -0.092
618 2220.00 216.00 4.00 287.14 31.40 220 34 2262 1711 -0.244 1715 -0.242 1946 -0.140
619 1679.00 153.00 3.20 413.56 21.80 220 26 902 1029 0.141 916 0.015 1023 0.134
620 1530.00 101.00 3.40 602.70 32.20 220 26 803 809 0.008 684 -0.148 756 -0.058
621 1048.00 121.00 4.80 449.82 33.90 220 26 1147 1256 0.095 1058 -0.077 1224 0.067
622 1048.00 121.00 4.80 449.82 29.10 220 26 1078 1222 0.134 1018 -0.055 1161 0.077
623 1048.00 121.00 4.80 449.82 25.60 207 37 941 1195 0.270 990 0.052 1113 0.183
624 4200.00 318.50 6.90 301.84 47.00 207 37 5495 4306 -0.216 4827 -0.122 5280 -0.039
625 5000.00 500.00 11.00 253.20 47.00 207 37 12838 10988 -0.144 11838 -0.078 13440 0.047
626 5000.00 500.00 11.00 235.20 43.70 207 37 11838 10363 -0.125 11068 -0.065 12492 0.055
627 1670.00 210.00 2.50 235.20 27.70 207 37 1323 1255 -0.051 1287 -0.027 1457 0.101
628 756.00 108.00 4.00 337.61 36.30 200 35 785 846 0.078 748 -0.047 865 0.102
629 972.00 108.00 4.00 337.61 34.50 200 33 737 782 0.060 683 -0.073 786 0.066
630 1404.00 108.00 4.00 332.02 34.10 200 33 686 689 0.005 635 -0.074 683 -0.005
631 1620.00 108.00 4.00 351.23 34.10 200 36 637 686 0.078 631 -0.009 666 0.046
632 840.00 140.00 5.00 378.28 23.10 200 33 1284 1390 0.083 1227 -0.044 1343 0.046
633 840.00 140.00 5.00 378.28 31.60 200 35 1392 1495 0.074 1321 -0.051 1508 0.084
634 840.00 140.00 5.00 378.28 45.10 200 38 1686 1642 -0.026 1473 -0.126 1752 0.040
635 840.00 140.00 5.00 178.28 51.00 200 36 1705 1175 -0.311 1115 -0.346 1306 -0.234
636 600.00 100.00 2.50 244.02 43.40 200 36 686 544 -0.206 519 -0.244 615 -0.104
637 900.00 100.00 2.00 236.18 43.40 200 33 587 414 -0.295 438 -0.253 500 -0.148
638 600.00 100.00 2.00 236.18 36.70 200 32 559 451 -0.193 432 -0.226 509 -0.090
639 600.00 100.00 2.00 236.18 36.70 200 32 513 451 -0.120 432 -0.156 509 -0.008
International Journal of Civil & Environmental Engineering IJCEE-IJENS Vol: 11 No: 02 39
111702-3737 IJCEE-IJENS © April 2011 IJENS I J E N S
640 1080.00 100.00 4.50 259.70 28.10 200 31 744 586 -0.212 504 -0.323 550 -0.260
641 1080.00 106.00 3.50 259.70 28.10 200 32 560 543 -0.029 486 -0.131 543 -0.030
642 1080.00 104.00 2.50 259.70 28.10 200 31 433 424 -0.021 401 -0.075 450 0.039
643 1188.00 108.00 4.00 327.12 35.00 200 32 686 723 0.054 649 -0.054 727 0.060
644 690.00 169.00 7.50 360.00 70.80 200 31 3080 3320 0.078 3032 -0.016 3897 0.265
645 690.00 169.00 7.50 360.00 70.80 200 33 4190 3320 -0.208 3032 -0.276 3897 -0.070
646 1768.00 169.00 7.50 360.00 70.80 200 31 2870 2512 -0.125 2468 -0.140 2852 -0.006
647 1555.00 76.00 2.00 275.00 41.60 200 33 355 238 -0.330 221 -0.377 237 -0.333
648 1556.00 76.00 2.00 275.00 41.60 200 31 330 238 -0.279 221 -0.330 237 -0.282
649 1000.00 219.00 6.00 325.00 58.00 200 33 2989 3776 0.263 3537 0.183 4431 0.482
650 1000.00 219.00 4.00 325.00 47.60 200 34 1931 2889 0.496 2743 0.421 3425 0.774
651 1000.00 219.00 4.00 325.00 52.30 200 33 1980 3025 0.528 2892 0.461 3628 0.832
652 990.00 219.00 7.00 273.00 38.20 200 32 3278 3166 -0.034 2913 -0.111 3483 0.063
653 990.00 219.00 7.00 273.00 38.20 200 37 3278 3166 -0.034 2913 -0.111 3483 0.063
654 990.00 219.00 7.00 273.00 38.20 200 37 3278 3166 -0.034 2913 -0.111 3483 0.063
655 1200.00 219.00 7.00 273.00 38.20 200 36 3200 3038 -0.051 2790 -0.128 3267 0.021
656 1200.00 219.00 7.00 273.00 38.20 200 32 3200 3038 -0.051 2790 -0.128 3267 0.021
657 1200.00 219.00 7.00 273.00 38.20 200 34 3200 3038 -0.051 2790 -0.128 3267 0.021
658 1420.00 219.00 7.00 273.00 38.20 200 34 3070 2912 -0.052 2670 -0.130 3110 0.013
659 1420.00 219.00 7.00 273.00 38.20 200 34 3070 2912 -0.052 2670 -0.130 3110 0.013
660 1420.00 219.00 7.00 273.00 38.20 200 34 3070 2912 -0.052 2670 -0.130 3110 0.013
661 1640.00 219.00 7.00 273.00 38.20 200 31 2956 2795 -0.055 2569 -0.131 2983 0.009
662 1640.00 219.00 7.00 273.00 38.20 200 33 2956 2795 -0.055 2569 -0.131 2983 0.009
663 1640.00 219.00 7.00 273.00 38.20 200 36 2956 2795 -0.055 2569 -0.131 2983 0.009
-----------------------------------------------------------------------------------------------------------------------------
Standard deviation: 0.1386 0.1306 0.1846
Average error: 0.0176 -0.0607 0.1018
Maximum error: 0.5858 0.5905 0.8325
Minimum error: -0.4145 -0.4544 -0.3684
=============================================================================================================================
TABLE II
VALIDATION OF THE CURRENT STATISTICAL METHOD
UL prediction of experiments [21] by the current methods and the EC4 and the CECS methods
(Nt=test data; Nc=UL calculated using current method; Nec4=UL calculated using the EC4 method; Nce=UL calculated using the CECS method)
=============================================================================================================================
L(mm) D(mm) t(mm) fa(MPa) fc(MPA) Ea(GPa) Ec(GPa) Nt(KN) Nc(KN) Nc/Nt-1 Nec4 Nec4/Nt-1 Nce Nce/Nt-1
-----------------------------------------------------------------------------------------------------------------------------
324.00 108.00 4.00 336.00 44.00 200 36 1175 1051 -0.106 969 -0.175 1174 -0.001
1296.00 108.00 4.00 336.00 44.00 200 36 774 750 -0.032 715 -0.076 792 0.023
1944.00 108.00 4.00 336.00 44.00 200 36 735 678 -0.077 620 -0.156 669 -0.090
============================================================================================================================