INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH VOLUME 10, ISSUE 01, JANUARY 2021
ISSN 2277-8616
Effect Of Batten Plates On Elastic Moment
Capacity Of Standard Ipe Profiles
Omar Metwally, Ihab M. El-Aghoury, Sherif M. Ibrahim
Abstract : Lateral torsional buckling (LTB) failure mode controls the flexural capacity of I-beams. The main parameter that affects the (LTB) capacity of
the steel I-beam is the unsupported length of the compression flange. Several configurations to increase flexural capacity include using lateral bracing,
vertical stiffeners or batten plates. In this research double-sided batten plates configuration is studied on standard IPE profiles. For this aim finite
element model is prepared using ANSYS v19.2. The developed finite element model is validated using experimental results previously conducted by
other researchers. A parametric study is conducted using finite element model to evaluate the increase in elastic moment capacity of the IPE profiles that
are strengthened with double-sided batten plates. The parameters studied in the research include the span of the steel beam, the location of batten
plates relative to beam span and the batten plates dimensions. A Proposed design equations are presented to predict the elastic moment capacity of
steel I-beams with various batten plates configurations.
Index Terms : Lateral torsional buckling, Batten plates, simply supported beams, Finite element analysis, standard profiles, elastic moment capacity.
————————————————————
1 INTRODUCTION
Lateral-torsional buckling (LTB) controls the flexural
capacity of steel beams. When applying vertical loads to a
steel I-beam that results in compression and tension in the
flanges of the section. The compression flange tries to
deflect laterally away from its original position, whereas the
tension flange tries to keep the member straight In addition
to the lateral movement of the section the forces within the
flanges cause the section to twist about its longitudinal axis.
Numerous experimental and numerical investigations [1 to
9] on steel I-beams strengthened with stiffeners and batten
plates have been carried out to improve their behavior to
lateral-torsional buckling. Lateral bracing is used also to
reduce the compression flange unsupported length by
preventing the lateral displacement at braced points. The
previous studies showed that the batten plates have a
significant effect on the elastic moment capacity of laterally
unsupported simply supported I-beams. This effect is
noticed for double-sided batten plates configurations.
This research aims to investigate the behavior of simply
supported laterally unsupported steel standard (IPE)
profiles strengthened by double-sided batten plates and
propose a simplified design equation to predict the increase
in elastic moment capacity.
2 LITERATURE REVIEW
Szewczak et al [1] numerically evaluated the behavior of
steel beams stiffened with longitudinal, box-type,
transversal, and cross stiffeners. They suggested that
transversal stiffeners are the least effective and the boxtype stiffener was the most efficient. However, longitudinal
stiffeners (i.e. batten plates) are moderately effective in
increasing flexural strength.
————————————————
 Assistant lecturer, Department of structural engineering, Ain
Shams University, Egypt.
E-mail: omar.metwaly@eng.asu.edu.eg
 Associate Professor, Department of structural engineering, Ain
Shams University, Egypt.
E-mail: ihab.elaghoury@eng.asu.edu.eg
 Professor, Department of structural engineering, Ain Shams
University, Egypt.
E-mail: sherif.ibraim@eng.asu.edu.eg
Takabatake [2]&[3] mathematically and experimentally
studied the lateral buckling of the I-shaped steel beams with
longitudinal and transverse stiffeners. His mathematical
results for the beam with batten plates located near the
support showed increasing by 260% over the unstiffened
beam. Experimental results showed that the batten plates
have a better enhancement on the flexural strength more
than the stiffeners. Moreover, their location near the support
give better enhancement in flexural strength. However, there
was an disagreement between his experimental and
mathematical workPlum and Svensson [4] analytically
studied the resistance of lateral-torsional buckling of Ishaped steel beams with box-type stiffeners welded to web
and flanges of sections to prevent warping at the beam end.
Hassanien [5] numerically investigated a cantilever beam
stiffened by vertical stiffeners against (LTB) and suggested
that the lateral displacement would be decreased by
connecting the compression flange to the tension one using
these vertical stiffeners. Yang and Lui [6] numerically
investigated the use of inclined stiffeners with an angle θ on
the flexural capacity of steel I-beams. Their study showed
that the inclined stiffeners have significant enhancement on
the flexural strength of steel I-beam and its location near the
beam supports give the best enhancement in flexural
strength. Sorensen and Rasmussen [7] experimentally and
numerically investigated a simply supported beam stiffened
with vertical stiffeners and batten plates. The loading
condition was point load at mid-span, the span of the beam
was 5 m and the beam section was IPE 80. Their study
showed that the stiffeners or batten plate does not affect
increasing the warping resistance or load-carrying capacity.
when it’s located at mid-span of steel beamHassan et al. [8]
numerically investigated the effect of using vertical web
stiffeners, single and double-sided batten plates, full-depth
and partial depth T-stiffeners on the flexural strength of
laterally unsupported beams. A set of steel beams simply
supported and subjected to uniform moment with various
spans were studied, the cross-sections used were standard
hot rolled sections (HEB 260 and IPE500). The study
showed that the vertical web stiffeners and partial depth Tstiffeners do not affect the flexural strength on the other side.
The double and single-sided batten plates have a significant
effect on the flexural strength, the best location for batten
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plate is near the beam supports and have no effect at the
mid-span. The increase in the number of batten plates or
the batten plate dimension leads to an increase in the
flexural strength of the beam Prado et al. [9] experimentally
examined the behavior of I-shaped steel beams with batten
plates under the action of lateral-torsional buckling. Simply
supported laterally unsupported beam loaded by applying
upward point loads located at one-third of the specimen
length from each end. The cross-section used is a standard
hot rolled section (IPE 140) with and without batten plates
with a laterally unbraced length ranging from 0.69 to 6.0 m.
The results of this study showed that the use of batten
plates on I-shaped steel beams has a significant increase
on the moment capacity in the elastic buckling zone and
has a slight increase in the inelastic buckling zone. The
study showed that the use of batten plates provided
acceptable lateral stability on I-shaped steel beams
subjected to bending stresses. Moreover, they concluded
that using batten plates on I-shaped steel beams decreases
the failure twist angle both in the elastic and inelastic
buckling zonesThe previous literature indicates that batten
plates are very efficient in increasing the elastic LTB
capacity of steel I-beams in cases when it is challenging to
other configurationsFrom the review of the literature, the
authors were motivated to propose simplified design
equations for beams strengthened with batten plates to
predict the increase in elastic moment capacity of steel Ibeams with various batten plates configurations.
3 NUMERICAL MODELING
3.1
Finite Element Model
A numerical finite element analysis is used to study the
effect of using double-sided batten plates on the flexural
strength of simply supported laterally unsupported steel Ibeams. The program used in modeling is ANSYS
WORKBENCH v19.2 [10]. All beam components which are
flanges, web and batten plates are modeled using solid
element (SOLID 185) which is defined by eight nodes each
having three degrees of freedom. The contact between
beam and batten plates is modeled using (CONTACT 174)
bonded type. The beam supports are defined to simulate
true hinged support condition which is prevented from
torsion and free to warp using remote points with
deformable behavior and remote displacements prevented
from lateral movement and vertical movement (Ux and Uy)
and rotation (Rz). Only one of the ends of the beam was
prevented from longitudinal movement (Uz) to achieve
beam stability conditions. The loading condition is a uniform
moment modeled as a concentrated moment at the remote
points. The finite element model with the aforementioned
criteria is shown in Fig.1.
ISSN 2277-8616
Fig. 1. FEM support and loading conditions
For all the specimens, material properties are considered.
The material considered is steel grade S235 with a modulus
of elasticity (E=210 GPa), yield stress (Fy=235 MPa) and
Poisson’s ratio (υ=0.3).
3.2
Model Verification
Bo Yang [11] experimentally and numerically investigated the
behavior of simply supported laterally unsupported beam
under a concentrated load. The material properties from a
tensile test are (Yield stress Fy= 410 MPa, Ultimate strength
Fu=570 MPa, Poisson ratio υ=0.3 and Young’s modulus
E=211 GPa). In the finite element modeling, the stress-strain
curve is approximated using a bilinear shape with tangent
modulus Et = 0.1E. The initial geometrical imperfections are
considered as span/1000. Table (1) shows the comparison
between the current finite element model and Bo Yang [11]
results. For specimens DTS2 and DTS3, the verification
results show good agreement for both experimental and
numerical work. However, for specimen DTS1,
the
experimental results were far from the finite element results
of Yang's work and the current proposed finite element
model. That’s maybe because of incorrect measurements
during the experiment or an incorrect setup of the specimen
and experiment procedures.
TABLE 1
VERIFICATION RESULTS WITH Bo YANG’s [11] WORK
Specimen
ID
DTS-1
DTS-2
DTS-3
Bo Yang
results [13]
𝑀
52.6
179
268
𝑀
47.3
166.5
277.2
Current
finite
element
model
𝑀
44.5
180
270
𝑀
𝑀
0.846
1.006
1.007
𝑀
𝑀
0.94
1.081
0.974
Units for moments are kN.m
Hassan et al. [8] studied [HEB 260 and IPE500] to determine
the effect of double and single-sided batten plates on the
LTB capacity. The material considered is S235 with a
modulus of elasticity (E=210 GPa, yield stress Fy=235 MPa
and Poisson’s ratio υ=0.3). The initial imperfections were
considered as span/1000 for finite element modeling. As
indicated in Tables (2 and 3) the results for HEB 260 and
IPE500 specimens using double-sided batten plates show
good agreement with Hassan et al. work. In these tables; L is
the span of the steel beam, Np is the batten plates number
and W b is the batten plate width.
TABLE 2
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VERIFICATION RESULTS WITH Hassan et al. [8] IPE 500
SPECIMENS
𝐿
𝑟
𝑁
𝑊
𝐿
Hassan et al.
results
Current finite
element
model
Plain
Stiff.
Plain
Stiff.
Mcr
Mcr
𝑀
𝑀
122.
8
234.
5
372
115.5
184
133.
8
255
311.5
374
303
4
0.02
110
189
8
113
12
0.03
3
0.03
3
177.
6
302.
5
𝑀
𝑀
Plain
DETAILED VERIFICATION RESULTS WITH Prado et al. [9]
STIFFENED SPECIMENS
𝑀
𝑀
Stiff.
Laterally
unbraced
length (m)
Prado et al.
𝑀
6
4.8
3.6
1.05
13.6
14.9
19.8
Current
finite
element
model
𝑀
13.8
16.56
21
𝑀
𝑀
1.015
1.11
1.06
Units for moments are kN.m
1.08
9
1.08
7
1.00
5
1.03
4
1.02
9
ISSN 2277-8616
Units for moments are kN.m
TABLE 3
VERIFICATION RESULTS WITH Hassan et al. [8] HEB260
SPECIMENS
𝐿
𝑟
𝑁
𝑊
𝐿
213
4
0.02
160
8
133
12
0.03
3
0.03
3
Hassan et al.
results
Current finite
element
model
Plain
Stiff.
Plain
Stiff.
Mcr
Mcr
𝑀
𝑀
196.
2
230.
2
247.
8
216.
9
264.
9
276.
3
207
231
240
270
255
285
𝑀
𝑀
Plain
𝑀
𝑀
Stiff
1.05
5
1.04
3
1.02
9
1.06
5
1.01
9
1.03
1
Units for moments are kN.m
Prado et al. [9] investigated the behavior of I-shaped steel
beams with batten plates under the action of lateraltorsional buckling. The material properties from a tensile
test are (Yield stress Fy= 391 MPa, Young’s modulus
E=217 GPa and Poisson ratio υ=0.3). The initial
imperfections for the finite element modeling were
considered as span/1000. Thirty-three IPE-140 steel beams
were tested by bending. Three specimens for each sample
to take the average. A comparison between Prado et al.’s
[9] results and the current finite element model is shown in
Tables (4 and 5). The verification results for these
specimens show a good agreement for both numerical and
experimental work. Fig.2. shown that there is agreement
also at the deformation shape of experimental work and the
finite element model.
TABLE 4
VERIFICATION RESULTS WITH Nestor Prado et al. [9]
PLAIN SPECIMENS
Laterally
unbraced
length (m)
6
4.8
3.6
Prado et al.
𝑀
7.5
9.6
14.7
𝑀
7
8.9
12.3
Current
finite
element
model
𝑀
6.96
8.84
12.01
Units for moments are kN.m
𝑀
𝑀
0.928
0.921
0.82
𝑀
𝑀
0.994
0.993
0.976
Fig. 2. Failure mode of the stiffened specimen. a) Prado
et al experimental b) Current F.E. model
4 PARAMETRIC STUDY AND DISCUSSION
Various standard IPE profiles with different spans are studied
to determine the effect of using double-sided batten plates
on the LTB capacity. The used steel IPE cross-section is
classified as a compact sections regarding local buckling
conditions. The studied spans are 6, 8, 10, 12 and 14
meters. 𝑀
is the elastic critical moment from the finite
element model. 𝑀
is the elastic critical moment from the
proposed equation and 𝑀
is the elastic critical moment of
unstiffened steel beam which can be determined by most
design specifications such as the AISC [12] or the SSRC
Guide [13]. Different parameters for the batten plate are
considered. Fig.3. shows the layout for the steel beam
strengthened with double-sided batten plates. The batten
plate’s centerline location ( 𝑍 ) varie from 0.1L to 0.45L
with an increment of 0.05L. The batten plate width ( 𝑊 ) is
taken with several values of L/50, L/40, L/30, L/20 or L/10.
The batten plate thickness ( 𝑇 ) is considered to be equal
to 4, 6, 8, 10 and 12 mm
TABLE 5
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𝑀
𝜋 𝐸 𝐼 𝐺 𝐽
𝜋 𝐸 𝐼 𝐸 𝐶
=√
+
(𝐿 )
(𝐿 )
ISSN 2277-8616
(1)
The weighted average values for the warping constant and
the torsional constant can be represented as :
Fig.3. steel beam strengthened with double-sided batten
plates.
Elastic moment capacity of beam stiffened by
double-sided batten plates
By changing the cross-section profiles, it seems that all
the cross-sections have the same behavior while using 4
batten plates per span. Fig.4. shows the relation between
(𝑀 / 𝑀 ) at the vertical axis and length of beam for
different standard profiles at the horizontal axis. While
𝑀
is the elastic critical moment from the finite element
model for the stiffened beam with 4 batten plates at 0.1 L
from both sides. Batten plates width is L/30 and thickness
is equal to beam web thickness.
4.1
Fig. 4. different profiles of standard cross sections
strengthened with double-sided batten plates.
The previous studies indicated that the double-sided batten
plates have a significant effect on the elastic moment
capacity of simply supported laterally unsupported I-beams.
This effect is noticed for double-sided batten plates
configurations. The main parameters affecting elastic
flexural strength are the warping constant, moment of
inertia about the weak axis of the beam and torsional
constant. The main concept of the proposed equation is to
get the weighted average values for the warping constant
and the torsional constant from the properties of IPE section
and a box section consisting of IPE and batten plates. Thus,
a modified torsional constant ( J* ) and a modified warping
constant (𝐶 ) are proposed to the elastic critical moment
equation for the case of a beam simply supported subjected
to a uniform moment can be written as follows:
𝐽 =
𝐽 𝐿 +𝐽 𝐿 𝐹
𝐿
𝐶
=
𝐶
𝐿 +𝐶
𝐿
(2)
𝐿
(3)
From the finite element model the elastic critical moment
(𝑀 ) of the stiffened beam is obtained for different cases
studied in the parametric study. Then modification factor (F)
is calculated using equations ( 1,2 and 3 ).
Best fitting techniques are used to define Polynomial
equations for this factor.
𝐹 = 0 1106(
) − 0 1347
+ 0 0413
(4)
Where:
𝐿 : is the total length of the steel beam
𝐿 : is equal to (𝐿 − 𝐿 )
𝐿 : is the total length of batten plates used at one side of the
beam equal to (2𝑊 ).
𝐽 : is the torsional constant of IPE beam
𝐽 : is the torsional constant of the box section consisting of
IPE with double-sided batten plates which according to
AISC [2] equals to
2𝑡 𝑡 𝑏 ℎ
b
𝐽 =
;
> 10
𝑏 𝑡 +ℎ 𝑡
𝑡
𝑡 : is the thickness of flange of IPE beam
𝑡 : is the thickness of batten plate
b : is the width of box section and equal to IPE flange width
h : is the depth of box section and equals to IPE depth
𝐶 : is the warping constant of IPE beam
𝐶 : is the warping constant of the box section consisting of
IPE with double-sided batten plates which is
approximately equal to zero for box sections according
to AISC [2]
𝐹: is a factor that represents the effect of batten plate on
increasing the elastic moment capacity of the beam and
depends on the batten plate centerline location (
)
𝑍 : is the batten plate centerline location to the beam end
Fig.5. shows the equation annotations
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ISSN 2277-8616
standard deviation of 2.5 %.
TABLE 6
COMPARISON BETWEEN THE PROPOSED
EQUATION'S RESULTS AND THE FEM RESULTS FOR
DIFFERENT STANDARD IPE PROFILES
IPE 100
profile
Fig. 6. the relation between the batten plate centerline
location ( ) and the F factor
4.2
Accuracy of the proposed equation
Table (6) shows the ratio between the finite element
results and the proposed equation's results for different
standard IPE profiles strengthened with double-sided
batten plates under a uniform bending moment with
simply supported end conditions, where 𝑀
is the final
elastic moment capacity obtained from the proposed
design equation (2), and 𝑀
is the final flexural strength
obtained from finite element analysis. The used span is 10
m, the batten plate width is L/30, the number of batten
plates is four batten plates per span and the batten plate
thickness is equal to the web thickness of the beam. The
results of the finite element results show an excellent
agreement with the proposed design procedure, with an
average ratio for (𝑀 / 𝑀 ) equals to 0.997 and a
IPE 300
IPE 400
IPE 600
IPE 500
Fig.6. shows the relation between the batten plate
centerline location (
) and the (F factor) which
represents the effect of the batten plate on increasing the
elastic moment capacity of the beam. The batten plate
width is L/30 and the thickness is equal to beam web
thickness. The beam span is 12m. It shows that for the
different standard profiles, the best location for the batten
plate is at 0.1L and gets reduced while moving away from
the beam ends towards the mid-span of the beam. The
effect of the batten plate at the mid-span position on the
enhancement of the elastic moment capacity of the beam
is insignificant as agreed with most of the literature such
as Yang and Lui [11], Sorensen and Rasmussen [11] and
Hassan et al [12].
IPE 200
Fig. 5. Beam strengthened with double-sided batten plates
equation annotations
𝑍
L
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
𝑀
(kN.m)
2.00
1.97
1.94
1.90
1.86
1.84
1.81
1.80
16.27
15.81
15.18
14.59
14.09
13.70
13.44
13.27
59.80
58.53
55.95
53.23
51.13
49.36
48.12
47.33
146.90
143.42
138.52
132.75
127.69
123.79
120.89
118.98
244.49
240.91
233.18
225.06
217.00
210.11
204.82
201.71
416.78
414.46
400.86
387.41
374.73
364.12
356.11
350.97
𝐹
0.0289
0.0236
0.0188
0.0145
0.0108
0.0077
0.0051
0.0031
0.0289
0.0236
0.0188
0.0145
0.0108
0.0077
0.0051
0.0031
0.0289
0.0236
0.0188
0.0145
0.0108
0.0077
0.0051
0.0031
0.0289
0.0236
0.0188
0.0145
0.0108
0.0077
0.0051
0.0031
0.0289
0.0236
0.0188
0.0145
0.0108
0.0077
0.0051
0.0031
0.0289
0.0236
0.0188
0.0145
0.0108
0.0077
0.0051
0.0031
𝐽 x104
(mm4)
1.48
1.41
1.35
1.30
1.25
1.22
1.18
1.16
9.90
9.27
8.71
8.21
7.78
7.42
7.11
6.88
33.14
30.48
28.09
25.98
24.15
22.59
21.30
20.29
82.49
76.05
70.28
65.18
60.73
56.96
53.85
51.40
149.26
137.06
126.13
116.46
108.05
100.89
95.00
90.37
269.62
248.23
229.06
212.09
197.33
184.78
174.44
166.31
𝑀
(kN.m)
1.99
1.94
1.90
1.87
1.83
1.80
1.78
1.76
15.58
15.09
14.65
14.24
13.87
13.55
13.28
13.07
60.46
58.20
56.09
54.15
52.41
50.88
49.59
48.55
144.30
139.28
134.62
130.37
126.55
123.20
120.38
118.11
253.37
244.60
236.46
229.01
222.33
216.49
211.56
207.60
437.89
423.80
410.76
398.87
388.23
378.95
371.12
364.85
𝑀
𝑀
1.007
1.014
1.017
1.018
1.017
1.017
1.019
1.023
1.045
1.048
1.037
1.025
1.016
1.011
1.012
1.016
0.989
1.006
0.998
0.983
0.976
0.970
0.970
0.975
1.018
1.030
1.029
1.018
1.009
1.005
1.004
1.007
0.965
0.985
0.986
0.983
0.976
0.971
0.968
0.972
0.952
0.978
0.976
0.971
0.965
0.961
0.960
0.962
Effect of steel beam length (𝐋) on the proposed
equation for the elastic moment capacity
Table (7) shows the ratio between the finite element results
and the proposed equation's results for different spans
under a uniform bending moment with simply supported
end conditions. This study is conducted on IPE200 with
four batten plates per span of a thickness (𝑇 ) and located
at a distance 0.1L from both beams ends. The studied
spans are (6, 8, 10 and 12m). The batten plates width is (
L/30 ). The results of the finite element results show an
excellent agreement with the proposed design procedure,
with an average ratio for (𝑀 / 𝑀 ) equals to 1.016 and a
standard deviation of 1.78 %.
4.3
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TABLE 7
COMPARISON BETWEEN THE PROPOSED
EQUATION'S RESULTS AND THE FEM RESULTS FOR
DIFFERENT BEAM LENGTHS
10
12
𝑀
𝑀
0.0289
9.90
26.66
1.044
27.25
0.0236
9.27
25.87
1.053
0.2
26.08
0.0188
8.71
25.15
1.037
0.25
24.88
0.0145
8.21
24.49
1.016
0.3
23.92
0.0108
7.78
23.90
1.001
0.35
23.16
0.0077
7.42
23.38
0.990
0.4
22.61
0.0051
7.11
22.95
0.985
0.45
22.28
0.0031
6.88
22.61
0.985
0.1
20.54
0.0289
9.90
19.64
1.046
0.15
20.06
0.0236
9.27
19.04
1.054
0.2
19.19
0.0188
8.71
18.48
1.038
0.25
18.36
0.0145
8.21
17.98
1.022
0.3
17.67
0.0108
7.78
17.53
1.008
0.35
17.12
0.0077
7.42
17.13
1.000
0.4
16.77
0.0051
7.11
16.80
0.998
0.45
16.55
0.0031
6.88
16.54
1.001
0.1
16.27
0.0289
9.90
15.58
1.045
0.15
15.81
0.0236
9.27
15.09
1.048
0.2
15.18
0.0188
8.71
14.65
1.037
0.1
27.83
0.15
𝐹
14
0.1
11.11
0.0289
9.90
11.04
1.006
0.15
10.82
0.0236
9.27
10.70
1.012
0.2
10.48
0.0188
8.71
10.37
1.010
0.25
10.14
0.0145
8.21
10.08
1.006
0.3
9.85
0.0108
7.78
9.81
1.004
0.35
9.62
0.0077
7.42
9.58
1.003
0.4
9.46
0.0051
7.11
9.39
1.007
0.45
9.36
0.0031
6.88
9.24
1.013
Effect of batten plate width (𝑾 ) on the proposed
equation for elastic moment capacity
The effect of change batten plate width is studied in this
section on beam stiffened with 4 batten plates. This study
is conducted on different standard IPE profiles with a span
of 10 meters and batten plates of a thickness (𝑇 ) located
at a distance 0.1L from both beams ends. The batten
plates width is defined relative to the beam span (L). The
studied ratios for the width are (L/50, L/40, L/30, L/20, L/10)
Table (8) shows the ratio between the finite element results
and the proposed equation's results for different batten
plate width. The results of the finite element results show
an excellent agreement with the proposed design
procedure, with an average ratio for (𝑀 / 𝑀 ) equals to
1.012 and a standard deviation of 5.03 %. Moreover, we
can figure out from the table that the effect of batten plate
width for the same IPE profile is extremely significant on
the flexural strength of laterally unsupported simply
supported I-beams.
4.4
TABLE 8
COMPARISON BETWEEN THE PROPOSED
EQUATION'S RESULTS AND THE FEM RESULTS FOR
DIFFERENT BATTEN PLATE WIDTH
186.2
𝐿 x1
0
(mm
)
200
900
186.2
100
1.62
2.08
1.2
933
186.2
66.7
1.48
1.99
1.96
1.2
950
186.2
50
1.41
1.94
1.019
1.93
1.2
960
186.2
40
1.37
1.91
12.52
1.024
20.86
6.98
800
1754.4
200
15.69
19.51
8.71
12.14
1.017
17.67
6.98
900
1754.4
100
11.34
16.64
0.0145
8.21
11.80
1.009
16.28
6.98
933
1754.4
66.7
9.88
15.57
11.54
0.0108
7.78
11.49
1.004
15.46
6.98
950
1754.4
50
9.16
15.00
0.35
11.24
0.0077
7.42
11.22
1.002
14.93
6.98
960
1754.4
40
8.72
14.65
0.4
11.03
0.0051
7.11
11.00
1.003
85.73
20.1
800
7453.2
200
59.03
79.21
0.45
10.92
0.0031
6.88
10.82
1.009
67.18
20.1
900
7453.2
100
39.56
65.62
profil
e
𝑀
(kN.m
)
𝐽 x10
4
0.25
14.59
0.0145
8.21
14.24
1.025
0.3
14.09
0.0108
7.78
13.87
1.016
2.38
(mm
)
1.2
0.35
13.70
0.0077
7.42
13.55
1.011
2.09
1.2
0.4
13.44
0.0051
7.11
13.28
1.012
2.00
0.45
13.27
0.0031
6.88
13.07
1.016
0.1
13.16
0.0289
9.90
12.92
0.15
12.81
0.0236
9.27
0.2
12.35
0.0188
0.25
11.91
0.3
IPE 100
8
𝑀
(kN.m)
𝑀
(kN.m)
IPE 200
6
𝐽 x104
(mm4)
𝑍
L
IPE
300
L
(m)
ISSN 2277-8616
4
𝐿 x1
0
(mm
)
800
𝐽 x104
(mm4)
𝐽 x104
(mm4)
𝑀
(kN.m
)
2.03
2.33
𝑀
𝑀
1.02
1
1.00
5
1.00
8
1.00
8
1.00
7
1.06
9
1.06
2
1.04
6
1.03
0
1.01
9
1.08
2
1.02
4
338
IJSTR©2021
www.ijstr.org
66.7
33.08
60.41
55.92
20.1
950
7453.2
50
29.83
57.63
53.72
20.1
960
7453.2
40
27.89
55.90
213.4
2
164.2
1
146.9
0
138.2
3
132.9
6
359.8
9
273.1
7
244.4
9
230.8
9
224.0
3
600.5
8
462.2
8
416.7
8
394.0
5
383.6
8
51.1
800
200
51.1
900
100
144.8
3
97.97
51.1
933
66.7
82.34
51.1
950
50
74.53
51.1
960
40
69.85
89.3
800
200
89.3
900
89.3
933
89.3
950
89.3
960
165
800
165
900
165
933
165
950
165
960
18038.
8
18038.
8
18038.
8
18038.
8
18038.
8
34166.
2
34166.
2
34166.
2
34166.
2
34166.
2
59936.
4
59936.
4
59936.
4
59936.
4
59936.
4
268.3
3
178.8
1
148.9
8
134.0
6
125.1
1
477.3
9
321.1
9
269.1
3
243.1
0
227.4
8
186.0
0
155.6
9
144.1
8
138.0
7
134.2
7
326.8
8
273.4
7
253.1
7
242.3
8
235.6
8
556.4
7
470.1
2
437.5
7
420.3
5
409.6
7
100
66.7
50
40
200
100
66.7
50
40
0.99
0
0.97
0
0.96
1
1.14
7
1.05
5
1.01
9
1.00
1
0.99
0
1.10
1
0.99
9
0.96
6
0.95
3
0.95
1
1.07
9
0.98
3
0.95
2
0.93
7
0.93
7
Effect of batten plate thickness (𝑻 ) on the
proposed equation for elastic moment capacity
The effect of change batten plate thickness is studied in
this section on a beam stiffened with 4 batten plates. This
study is conducted on different standard profiles with a
span of 10 meters and stiffened with four batten plates of
a width (L/30) and located at a distance 0.1L from both
beams ends. The studied batten plate thicknesses are (4,
6, 8, 10 and 12 mm). Table (9) shows the ratio between
the finite element results and the proposed equation's
results for different batten plate thickness. The results of
the finite element results show an excellent agreement
with the proposed design procedure, with an average
ratio for (𝑀 / 𝑀 ) equals to 0.995 and a standard
deviation of 4.82%. Moreover, we can figure out from the
table that the flexural capacity for the same IPE profile is
slightly increased with increasing the batten plate
thickness of laterally unsupported simply supported Ibeams.
4.5
TABLE 9
COMPARISON BETWEEN THE PROPOSED
EQUATION'S RESULTS AND THE FEM RESULTS FOR
DIFFERENT BATTEN PLATE THICKNESS
IPE 100
profile
𝑇
(mm)
𝑀
(kN.m
)
4
6
8
2.0
2.0
2.0
𝐽 x10
4
(mm
)
1.2
1.2
1.2
4
𝐽 x104
(mm4)
𝐽 x104
(mm4)
𝑀
(kN.m
)
182.5
250.5
309.1
1.47
1.60
1.71
2.0
2.1
2.1
𝑀
𝑀
1.010
0.972
0.942
IPE 200
7453.2
IPE 300
933
IPE 400
20.1
IPE 500
59.80
IPE 600
IPE 600
IPE 500
IPE 400
INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH VOLUME 10, ISSUE 01, JANUARY 2021
10
12
4
6
8
10
12
4
6
8
10
12
4
6
2.0
2.0
16.2
16.3
16.4
16.6
16.7
58.8
59.5
60.1
60.9
61.8
143.6
145.1
1.2
1.2
7.0
7.0
7.0
7.0
7.0
20.1
20.1
20.1
20.1
20.1
51.1
51.1
8
146.5
51.1
10
148.0
51.1
12
149.7
51.1
4
237.6
89.3
6
239.9
89.3
8
242.0
89.3
10
244.3
89.3
12
246.8
89.3
4
403.0
165.0
6
406.7
165.0
8
409.9
165.0
10
413.2
165.0
12
416.8
165
360.7
407.1
1319.7
1856.6
2334.6
2765.5
3157.9
4577.8
6487.0
8205.0
9764.9
11192.7
9174.2
13218.
4
16966.
3
20456.
3
23720.
7
14577.
6
21254.
5
27577.
8
33582.
1
39297.
3
21571.
0
31714.
5
41471.
8
50870.
8
59936.
4
ISSN 2277-8616
1.81
1.90
9.05
10.08
11.00
11.83
12.58
27.55
31.22
34.52
37.52
40.26
65.32
73.08
2.2
2.3
14.9
15.7
16.4
17.0
17.5
55.6
58.8
61.6
64.0
66.2
130.5
136.9
0.918
0.898
1.083
1.037
1.003
0.976
0.956
1.058
1.010
0.976
0.951
0.934
1.101
1.060
80.28
142.6
1.027
86.99
147.7
1.002
93.26
152.3
0.983
111.35
225.0
1.056
124.1
7
136.3
2
147.8
5
158.8
3
195.4
3
214.9
2
233.6
6
251.7
2
269.1
3
235.0
1.021
244.1
0.992
252.4
0.968
260.0
0.949
386.8
1.042
400.9
1.014
413.9
0.990
426.1
0.970
437.6
0.952
5 SUMMARY AND CONCLUSIONS
A finite element model is performed to investigate the
increase in the elastic moment capacity of steel beams
strengthened with batten plates. Verification is performed to
the finite element model with previous research works. The
effects of using different standard IPE profiles, span of
beam, batten plate centerline location ratio to the beam
total length, batten plate width and thickness on the elastic
moment capacity were studied. A design procedure is
proposed to predict the elastic moment capacity of beams
strengthened with batten plates of different configurations.
The conclusions of this paper can be summarized as
follows:
1- The location of batten plates has a major effect on
the elastic moment capacity and it is found that the
best location for batten plates is at 0.1L. On the
other hand, installing batten plates at the mid-span
of the beam is not effective.
2- The proposed design equations proved to be
efficient and in very good agreement with the finite
element results for standard IPE steel beam
strengthened with batten plates taking into
consideration the change of I-beam section, batten
plate width and thickness.
3- The effect of batten plate width is very significant and
leads to a higher increase in the flexural strength
than increasing the batten plates thickness.
339
IJSTR©2021
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INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH VOLUME 10, ISSUE 01, JANUARY 2021
ISSN 2277-8616
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