1
COMPRESSION TESTS ON LARGE SOLID STEEL ROUND BARS
Khaled Sennah
A
and John Wahba
B
A Department of Civil Engineering, Ryerson University, Toronto, Ontario, Canada
B Radian Communications Services Corp, Oakville, Ontario, Canada
ABSRTACT: Canadian Standard of 1994, CAN/CSAS16.194, and AISCLRFD Specification of 1993
provide the factored compressive resistance of steel members other than solid rounds. However, the
Canadian Standard for Antennas, Towers, and AntennaSupporting Structures of 2001, CAN/CSAS3701,
presented expressions for compressive strength of solid rounds, based on results of testing a limited number
of solid rounds back to 1965. This paper summarizes the results of testing tofailure six round bars, three
of stressrelieved steel and the other three of nonstressrelieved steel. The experimental ultimate load
carrying capacity is compared to the superseded expressions found in the CAN/CSAS3794 as well as
the new expressions found in the CAN/CSAS3701. This is in addition to the expression found in the
AISCLRFD specification of 1993. Reported testing in this paper is part of an experimental program on
performancebased compressive strength of solid steel rounds of different material properties and
geometry.
1. INTRODUCTION
In the information industry, satellites, antenna towers and cables are used to transmit the signal from
communication tools. Some of these communication tools are mobile phones and pagers. Antenna towers
are the best choice because they are relatively economical and effective for remote transmission, especially
in North America where land area is large and distances among the cities and towns are great. These kinds
of steel towers have their own characteristic. They are very tall and very slender (Fig. 1). They can be
classified into three types, namely: (a) monopoles with heights up to 70 m; (b) selfsupporting towers with
heights up to 120 m; and (c) guyed towers with heights up to 620 m. The most popular crosssection of the
tower is the triangular shape (Fig. 2). Legs, diagonals and horizontals are made of solid round steel bars with
varying diameters and with all the joints welded or bolted. Design loads during fabrication, erection and
service can be classified as two categories, vertical loads and transverse loads. Leg members (chords) bear
vertical loads and bending moments caused by transverse loads. But most of the shear force is borne by
crossbrace diagonals, one in compression and the other in tension. In designing these members, not only
the strength and stiffness but also the stability problems should be considered. The advancement of
knowledge and technology has always resulted in an improvement in the specifications and the underlying
philosophy through which various structures are designed. Since antenna towers are made of steel, the
progress in the specifications concerning the design of steel structures generally, and the antenna towers
specially, should be studied.
4
e
Conférence spécialisée en génie des structures
de la Société canadienne de génie civil
4
th
Structural Speciality Conference
of the Canadian Society for Civil Engineering
Montréal, Québec, Canada
58 juin 2002 / June 58, 2002
2
Fig. 1. View of an antenna tower Fig. 2. View of solid round as leg members
This paper presents a brief summary of the available literature on the compressive strength of solid round
bars. Also, results from testing six large solid rounds are presented, with a discussion regarding the
correlation with the available specifications for the design of solid rounds.
2. PREVIOUS WORK
Steel columns are conventionally classified as short, intermediate, or long members, and each category has
an associated characteristic type of behavior. A short column is one, which can resist a load equal to the yield
load. A long column fails by elastic buckling on which the maximum load depends only on the bending
stiffness and length of the member. Columns in the intermediate range are most common in steel structures.
Failure is characterized by inelastic buckling and is greatly influenced by the magnitude and pattern of
residual stresses that are present and the magnitude, shape of the initial imperfections or outofstraightness
and the end restraint. These effects lessen for both shorter and longer columns. To take into account these
effects, a computerized maximum strength analysis was performed (Bjorhovde 1972) first on basic data
available from carefully constructed column tests performed at Lehigh University on Wshaped and hollow
column sections. Next, a set of 112 column curves was generated for members from which measured
residualstress distributions were available, assuming an initial crookedness of 1/1000 of the column length
and zero end restraint. Bjorhovde (1972) grouped the whole spectrum of column behavior to three column
curves known as SSRC Column Strength Curves 1, 2 and 3 (Galambos 1988).
Galambos (1965) summarized the results of a research program sponsored by the United States Steel
Corporation on the compressive resistance of solid rounds on USS "T1" constructional alloy steel and on
AISI C1020 structural carbon steel. In this study, twentyseven bars with diameter 70 mm and four bars
of diameter 190.5 mm were tested to failure as axially loaded columns. The effects of residual stresses
and initial crookedness on column strength were also considered. The initial outofstraightness (also
refereed as initial crookedness or initial curvature) also affects the primary column strength. The analysis of
the strength of inelastic, initially curved columns have either made use of assumed values and shapes of the
initial outofstraightness, or can use actually measured data. The former is the most common, mostly
3
because the measurements that are available for columns are rare. This applies in particular to the
magnitude of the maximum outofstraightness, normally assumed to occur at the midheight of the member.
The latter is usually thought to be that of a half–sine wave (Bjorhovde 1972).
Residual stresses in structural steel shapes and plates result primarily from uneven cooling after rolling of
hotrolled steel columns and influence the buckling load. The quick cooling parts of sections when solidified
resist further shortening, while those parts that are still hot tend to shorten further as they cool. The net result
is that the area that cooled more quickly has residual compressive stresses, while the slower cooling areas
have residual tensile stresses. In the elastic region, residual stresses and initial crookedness have a
significant influence on the strength of solid round bars. The influence of the initial crookedness is
predominant if only small residual stresses are present. For materials, which are quenched without stress
relieving, the effect of residual stresses and initial crookedness is significant (Galambos 1965). Few authors
(among them: Hetenyi, 1957; Watanabe et al., 1955; Bühler, 1954) measured experimentally the residual
stresses in cylindrical steel bars by the boringout technique. According to the study by Nitta and Thürlimann
(1962b) on the effect of thermal residual stresses and initial deflections on solid round steel bars, members
containing high residual stress caused by water quenching, for example, carry approximately a 10 to 20%
lower load than aircooled or stressrelieved steel columns, provided that the generalized slenderness ratio
and initial deflections are the same. Few authors utilized analytical and numerical simulation techniques, such
as the finiteelement method, to predict residual stresses produced by the manufacturing process (Jahanian,
1995; Toparli and Aksoy, 1991; Kamamato, 1985; Weiner and Huddleston, 1959). Most recently, Ding (2000)
used the classical boringout method to determine the residual stresses on fourteen samples of hotrolled
solid round steel bars. The diameter of the specimens ranged from 38.1 to 152.4 mm, with yield strength of
456 MPa. It should be noted that the residual stresses are an unavoidable consequence of the manufacturing
process. So, the measurement of them is needed in order to assess the performance of columns under
combined effect.
The strength of coldstraightened columns is, in general, greater that that of the corresponding asrolled
members because of the improved straightness and redistribution of residual stress. According to the study
by Nitta and Thürlimann (1962a) on the effect of coldstraightening on the ultimate strength of circular
columns, the tangent modulus concept can not be used for predication of coldstraightening columns as there
exists no bifurcation point in the loaddeflection curve of coldstraightened column which contains ant
symmetric residual stress. The strength depends upon the magnitude of the coldstraightening residual
stresses and the outofstraightness remaining after coldstraightening operation. The load carrying capacity
of such column can be determined by ultimate load analysis. Fujita and Driscoll (1962) tested nine axially
loaded bars and two eccentrically loaded bars (eight USS "T1" constructional alloy steel bars and one
structural carbon steel bar). The bars were of 23/4 in. diameter, with slenderness ratio ranging from 30 to 73.
The bars were cold straightened and subsequently stressrelieved, followed by aircooling. Comparison with
the theory based on the "tangent modulus" concept for axially loaded columns, and with an inelasticstrength
theory for the eccentrically loaded columns shows that the ultimate strength of solid round columns may be
predicated adequately by the tangent modulus concept.
Most recently, Mull (1999) experimentally determined the compressive resistance of forty steel solid round
specimens for five different diameters of specimens ranging from 31.75 to 57.15 mm. The effective
slenderness ratios of the specimens varied from 59 to 117. The specimens were tested as pinnedend
columns loaded concentrically. From the measured strain data, it was determined that only sixteen of the
forty specimens had load eccentricities less than or equal to 1/500
th
of the effective length of the
specimen. For these sixteen specimens, the ratio of the resistance computed from the Canadian
Standard CAN/CSAS16.194 to the experimental failure loads ranged from 0.98 to 0.79, and, for
resistances computed from AISCLRFD Specification, the ratios ranged from 1.10 to 0.89. So, more tests
need to be carried out of wide range of solid rounds, especially of large diameters, to reach
recommendations that may provide considerable savings in the design and evaluation of solid round bars.
Previous studies on the effective length factors of solid round bars used as bracing diagonals (Jaboo,
1998; Sun, 1999, Chen, 2000; Lim, 2000) and as chord members (Qureshi, 1999).
4
3. NORTH AMERICAN CODES OF PRACTICE
The expressions of Clause 13.3.1 in the Canadian Standard, CAN/CSAS16.194 for the compressive
resistance of steel columns are based on Column Curve 2 of the Structural Stability Research Council
(Galambos 1988) for Wshapes and is used as the basis for the description of compressive resistance of W
shapes and for coldformed nonstress relieved, Class H, hollow structural sections (Clause 13.3.1), based
on Bjorhovde and Birkemoe (1979). The experimental investigation on the compressive resistance of solid
rounds carried out so far was back to 1965 on structural carbon and construction alloy steel (Galambos
and Ueda, 1962; Galambos, 1965). Since there is no other literature on the compressive resistance of
solid rounds, the Canadian Standard for Antennas, Towers, and AntennaSupporting Structures, CAN/CSA
S3794, assumed the applicability of Clause 13.3.1 of the CAN/CSAS16.194 to hot rolled solid round bars
51 mm in diameter and less and to hotrolled solid round bars greater than 51 mm in diameter that are stress
relieved to manufacturer’s recommendations after initial coldstraightening at the mill. This Clause is listed as
follows:
[1]
15.00 ≤≤ λ
yr
FAC..φ=
[2]
0.115.0 ≤λp
]222.0202.0035.1[..
2
λλφ −−=
yr
FAC
[3]
0.20.1 ≤λp
]087.0636.0111.0[..
21 −−
++−= λλφ
yr
FAC
[4]
6.30.2 ≤λp
]877.0009.0[..
2−
+= λφ
yr
FAC
[5]
0.56.3 ≤λp
][..
2−
= λφ
yr
FAC
where:
E
F
r
KL
y
2
π
λ=
; F
y
= yield stress; φ = resistance factor; A= crosssectional area.
Also, CAN/CSAS3794 presented other set of expressions of the compressive resistance of solid round bars
greater than 51 mm in diameter and not stressrelieved after cold straightening, based on Column Curve 3 of
the Structural Stability Research Council (Galambos 1988).
[6]
8.00 ≤λp
]622.0093.1[..λφ −=
yr
FAC
[7]
3.28.0 ≤λp
]102.0707.0128.0[..
21 −−
−+−= λλφ
yr
FAC
[8]
0.53.2 ≤λp
]792.0008.0[..
2−
+= λφ
yr
FAC
Most recently, CAN/CSAS3701 for Antenna towers and Antenna Supporting Structures was released to the
public, with some modifications to the expressions found in the superseded version of 1994 for compressive
strength of solid rounds. These modifications were based on results of testing a limited number of solid
rounds back to 1965. The factored axial compressive resistance, C
r
, of a member is determined by the
following formula:
[9]
n
n
y
r
AF
C
1
2
]1[ λ
φ
+
=
where:
φ= 1.34 for hot rolled round bars 51 mm in diameter and less; hot rolled solid round bars greater than
51 mm in diameter and stress relieved to manufacturer's recommendations after initial cold
straightening at the mill.
= 0.93 for hotrolled solid round bars greater than 51 mm in diameter and not stress relieved after
cold straightening.
5
According to the AISCLRFD, “Load and Resistance Factor Design Specifications for Structural Steel
Buildings”, [American Institute of Steel Construction Inc. 1993], the compressive resistance is given by:
[10]
crr
FAC..φ=
Where,
ycr
FF ]658.0[
2
λ
=
for
5.1≤λ
, and
ycr
FF ]
877.0
[
2
λ
=
for
5.1fλ
To design economically any steel round bars, the practicing engineer must have a clear understanding of its
behavior under different manufacturing conditions as well as at service. So, the objective of this study is (i) to
experimentally determine the compressive strength of selected solid round steel bars; (ii) to compare the
experimental failure load with compressive resistance calculated from the available Standards in North
America.
4. EXPERIMENTAL INVESTIGATION
The experimental investigation includes testing tofailure six steel solid round specimens. Three of these
specimens are of stressrelieved steel, while the other three specimens are of nonstressrelieved steel.
The diameter of the specimens is 109.5 mm, with a length of 762 mm. Monotonic testingtofailure is
conducted on the available MTS compressiontesting machine at Ryerson University. A spherical bearing
block at the upper end of the machine provided a uniform distribution of applied stress in the test specimen
and ensured the pinended restraint of the specimens. While flatended conditions were considered at the
lower end of the specimens. Each bar supplied was saw cut to the required lengths for compressive strength
tests and the ends of each specimen were machined parallel to each other and perpendicular to the
longitudinal axis of the bars. Figure 3 shows view of the test setup for specimen No. 4. Strain gauges were
utilized in specimen No. 4 at the middle of the specimen to examine the strain distribution around the
perimeter with increase in load applications. Coupon tests on two ASTM standard 12.8mm diameter, 50.8
mm gagelength, tensiontest specimens were machined from a sample of the steel obtained from the
center point, and edge point locations of the specimen, respectively. These coupons were axially loaded
in tension to determine the mechanical properties of the bar material. After testing tofailure all the
specimens, the experimental ultimate load carrying capacity is then compared to the superseded
expressions found in the CAN/CSAS3794, the new expressions found in the CAN/CSAS3701 and the
expression found in the AISCLRFD of 1993.
Fig.3. View of the test setup Fig. 4. View of Specimen S4 after failure
6
5. RESULTS
From the tensile stressstrain curves from coupon testing, the average yield strength of the coupons was 398
MPa, with and average modulus of elasticity of 181,000 MPa. It should be noted that the steel provided was
GRADE 50 steel, with nominal yield strength of 345 MPa (50 ksi. For the sake of comparison with the
equations provided by the codes, the actual (tested) steel grade is used. When testing the column
specimens, compressive load was applied in increments. Each test was run in about 45 to 60 minutes. Figure
4 shows view of the specimen No. 4 after failure. It was observed that the failure pattern was a typical
bucking in a hingedfixed member. At each time increment, test control software recorded the applied load as
well as the axial displacement between the two ends of the specimens, or the movement of the actuator.
Figure 5 shows the applied axial loadaxial displacement curve for specimen No. 4. It was observed that the
material of the specimens behaved elastically till a load level very close to the failure load. For any load
behind this elastic load limit, specimen started to yield and excessive axial deformation was observed till the
specimen buckled laterally at Failure.
Table 1. Experimental and theoretical ultimate compressive load of column specimens
Theoretical failure load (kN)
CSAS3794 CSAS3701
Specimen number
Experimental
Failure load
(kN)
AISC
LRFD
Nonstress
relieved
Stress
relieved
Nonstress
relieved
Stress
relieved
S1nonstressrelieved 3986 3615 3411  3374 
S2nonstressrelieved 4200 3615 3411  3374 
S3nonstressrelieved 4071 3615 3411  3374 
S4stressrelieved 4494 3615  3585  3646
S5stressrelieved 4467 3615  3585  3646
S6stressrelieved 4490 3615  3585  3646
Fig. 5. Loadaxial displacement curve of specimen S4
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
0 2 4 6 8 10 12 14 16 18
Axial displacement, mm
Axial load, k
N
7
Table 2. Ratios of experimental / theoretical ultimate compressive load of column specimens
Experimental / theoretical failure load ratio
Specimen number
CSAS3794 CSAS3701
AISC
LRFD
Nonstress
relieved
Stress
relieved
Nonstress
relieved
Stress
relieved
S1nonstressrelieved 1.10 1.17  1.18 
S2nonstressrelieved 1.16 1.23  1.24 
S3nonstressrelieved 1.13 1.19  1.20 
S4stressrelieved 1.24  1.25  1.23
S5stressrelieved 1.24  1.25  1.23
S6stressrelieved 1.24  1.25  1.23
It was also observed that the average ultimate load of the three specimens with nonstressrelieved steel was
4085 kN, while it was 4484 kN for specimens with stressrelieved steel. An average decrease of the
compressive strength of 10 % was observed in the nonstressrelieved steel specimens due to the presence
of residual stresses. Table 1 shows the results of the experimental ultimate load of the column specimens.
Also, it shows the theoretical ultimate compressive load as determined from the Current American Standard
for steel buildings, AISCLRFD, the superseded expressions found in the CAN/CSAS3794 and the
current Canadian Standard CSAS3701. While Table 2 shows the theoretical failure loads normalized to the
corresponding experimental failure loads. It can be observed that the equations provided by the current
Canadian Standard overestimates the compressive resistance of solid round of nonstressrelieved steel by
an average of 20% when compared to the current experimental results, while it overestimates the
compressive resistance of the solid rounds of stressrelieved steel by 23%. It is also observed the AISC
LRFD Standard overestimates the compressive resistance of the nonstressrelieved solid rounds by 13%,
while it overestimates the compressive resistance of stressrelieved steel by 24%. This means that the
stressrelieved steel gives more benefits to the compressive strength due to the absence of the residual
stresses. It should be noted that the new expression for the compressive strength of solid rounds (Eq. 9)
found in the CSAS3701 provide almost similar results obtained from expressions found in the superseded
Canadian Standard, CAN/CSAS3794.
6. CONCLUSIONS
Based on the results from testing six large solid round bars to collapse, the following conclusions are drawn:
1 the experimental ultimate load of solid rounds of nonstressrelieved steel is about 10 % less than that for
solid rounds of stressrelieved steel. This may be attributed to the effect of the residual stresses.
2 Canadian Standard for Antenna Towers and Antenna Supporting Structures specifies the compressive
resistance of solid round bars, which is conservative by about 20% in case of nonstressrelived steel and
23% in case of stressrelieved steel. Also, the AISCLRFD Standard is conservative by about 13% in case of
nonstress –relieved solid rounds and by 24% in case of stressrelieved solid rounds.
3 more experimental testing is required to provide experimental results for the compressive resistance of
solid rounds of broad range of slenderness ratios and steel grades. This will provide confidence in modifying
the existing code equations for stressrelieved and nonstressrelieved steel.
7. ACKNOWLEDGMENTS
The support of Radian Communications Services Corp (formerly LeBlanc Communications Ltd.) of
Oakville, Ontario, Canada, is appreciated.
8. REFERENCES
American Institute of Steel Construction, Inc. (1993) Load and Resistance Factor Design Specification for
Structural Steel Buildings, Chicago, Illinois, USA.
8
Bjorhovde, R. (1972) Deterministic and Probabilistic Approaches to the Strength of Steel Columns, Ph.D.
Dissertation, Lehigh University, Bethlehem, Pa.
Bjorhovde, R. and Birkemoe, P. C. (1979) Limit States Design of HSS Columns, Canadian Journal of Civil
Engineering, 6(2).
Bühler, H. (1954) Complete Determination of the State of Residual Stress in Solid and Hollow Metal
Cylinders, Residual Stresses, Residual Stresses in Metals and Metal Construction, Edited by W. R.
Osgood, Reinhold Publishing Corporation, New York, N. Y., PP. 305329.
Canadian Standards Association. (1994) Antennas, Towers, and AntennaSupporting Structures, CAN/CSA
S3794, Rexdale, Ontario, Canada.
Canadian Standards Association. (1994) Limit States Design of Steel Structures, CAN/CSAS16.194,
Rexdale, Ontario, Canada.
Canadian Standards Association. (2001) Antennas, Towers, and AntennaSupporting Structures, CAN/CSA
S3701, Rexdale, Ontario, Canada.
Chen, Z. (2000) Theoretical Effective Length Factors for CrossBraced Solid Round Diagonals, M.Sc. Thesis,
Civil and Environmental Engineering, University of Windsor, Windsor, Ontario, Canada.
Ding, Y. (2000) Residual Stresses in HotRolled Solid Rounds Steel Bars and Their Effect on Compressive
Resistance of Members, M.Sc. thesis, Department of Civil and Environmental Engineering, University of
Windsor, Windsor, Ontario, Canada.
Fujita, Y. and Driscoll, G. (1962) Strength of Round Columns, ASCE Journal of the Structural Division, ST
(2): 4359.
Galambos, T. V. (1988) Guide to Stability Design Criteria for Metal Structures, 4
th
Edition.
Structural Stability Research Council, John Wiley & Sons Inc., New York, N.Y.
Galambos, T. V. (1965) Strength of Round Steel Columns, ASCE Journal of the Structural Division, 91(ST1):
121140.
Galambos, T. V., and Ueda, Yukio. (1962) Column tests on 7 ½ in. Round Solid Bars, ASCE
Journal of the Structural Division, 88(ST4): 117.
Hetenyi, M. (1957) Handbook of Experimental Stress Analysis, Third Edition, John Wiley & Sons Inc., New
York, N.Y.
Jaboo, K. S. (1998) Effective Length Factors for Solid Round Diagonal Bracing Members in Latticed Towers,
M.Sc. Thesis, Civil and Environmental Engineering, University of Windsor, Windsor, Ontario, Canada.
Jahanian, S. (1995) Residual and Thermoelastoplastic Stress Distributions in a Heat Treated Solid Cylinder,
Materials at High Temperatures, 13(2): 103110.
Kamamato, S., Nihimori T., and Kinoshita, S. (1985) Analysis of Residual Stress and Distortion Resulting
from Quenching in Large LowAlloy Steel Shafts, Journal of Material Science and Technology, 1:798804.
Lim, H. L. (2000) Effective Length Factors for Solid Round Members in KBraced and ZBraced Antenna
Towers, M.Sc. Thesis, Civil and Environmental Engineering, University of Windsor, Windsor, Ontario,
Canada.
Mull, N. C. (1999) Compressive Resistance of Solid Rounds,” M.Sc. Thesis, Civil & Environmental
Engineering, University of Windsor, Windsor, Ontario, Canada.
Nitta, A. and Thürlimann, B. (1962a) Ultimate Strength of High Yield Strength Constructional Alloy Circular
Columns – Effect of ColdStraightening, Publication, IABSE, 22: 265288.
Nitta, A. and Thürlimann, B. (1962b) Ultimate Strength of High Yield Strength Constructional Alloy Circular
Columns – Effect of Thermal Residual Stresses, Publication, IABSE, 22: 231264.
Qureshi, A. K. (1999) Effective Length Factors for Solid Round Chord Members of Guyed Towers, M.Sc.
Thesis, Civil and Environmental Engineering, University of Windsor, Windsor, Ontario, Canada.
Sun, Y. (1999) Effective Length Factors for Solid round Diagonal Members in Guyed Communication Towers,
M.Sc. Thesis, Civil and Environmental Engineering, University of Windsor, Windsor, Ontario, Canada.
Toparli, M. and Aksoy, T. (1991) Calculation of Residual Stresses in Cylindrical Steel Bars Quenched in
Water from 600
o
C, Proceedings of AMSE Conference, New Delhi, India, 4: 93 104.
Watanabe, M., Sato, K., and Goda, S. (1955) Thermal and Residual Stresses of Circular Cylinders Suddenly
Cooled From the Uniformly Heated Conditions, Journal of the Society of Naval Architects of Japan, 88:
155164.
Weiner, J. H. and Huddleston, J. V. (1959) Transient and Residual Stresses in HeatTreated Cylinders,
Journal of Applied Mechanics, 26E(1): 3139.
Enter the password to open this PDF file:
File name:

File size:

Title:

Author:

Subject:

Keywords:

Creation Date:

Modification Date:

Creator:

PDF Producer:

PDF Version:

Page Count:

Preparing document for printing…
0%
Σχόλια 0
Συνδεθείτε για να κοινοποιήσετε σχόλιο