1. Presented By:
Ramy Hassan Mohamed Gabr
B.Sc. Ain Shams University, Structural Department
Structural Engineer, Parsons International
Ain Shams University
Faculty of Engineering
Structural Engineering Department
BEHAVIOUR AND STRENGTH OF SINGLY-
SYMMETRIC CONTINUOUS I-BEAMS

2. Supervised By:
Prof. Dr. Adel Helmy Salem
Professor of Steel Structures
Ain Shams University
Dr. Abdel-Rahim Badawy Abdel-Rahim
Assistant Professor of Steel Structures
Ain Shams University
Supervised by:

3. AGENDA
 Introduction
 Literature Review
 Problem Statement
 Objectives
 Finite Element Model
 Verification
 Parametric Study
 Results Discussion
 Proposed Design Model
 Conclusions
 Recommendations for Future Study

4. AGENDA
 Introduction
 Literature Review
 Problem Statement
 Objectives
 Finite Element Model
 Verification
 Parametric Study
 Results Discussion
 Proposed Design Model
 Conclusions
 Recommendations for Future Study

5. Introduction
 Open cross sections such as I-beams, are widely
used in structural applications.
 These sections can be classified as follows:
1. Compact
l < lp
2. Noncompact
lp < l < lr
3. Slender
l > lr

6. Introduction (cont’d)
 Types of failure:
1. Lateral-Torsional Buckling
• Short beams:
non compact or slender section
• Long beams
2. Local Buckling
3. Distortional Buckling
• Slender unstiffened webs

7. AGENDA
 Introduction
 Literature Review
 Problem Statement
 Objectives
 Finite Element Model
 Verification
 Parametric Study
 Results Discussion
 Proposed Design Model
 Conclusions
 Recommendations for Future Study

8. Literature Review
 Trahair, (2008), presented the influence of restraints
on the elastic buckling of monorails, without
distortion, loaded at the bottom flange
 Trahair developed an economical strength design method for determining
the nominal LTB resistance (distortion was not taken into account).
 Trahair, (2009), studied the influence of the elastic
lateral-distortional buckling of single span steel
monorail I-beams on its strength, using the parameter
LD/LTB ratio.
 For beams with bottom flange loading, and unrestrained bottom flange,
smaller LD/LTB ratios were encountered, but they increase when rigid
web stiffeners or top flange torsional restraints were provided at the
supports.

9. Literature Review (cont’d)
 Kitipornchai et. al, (1986) studied the effect of
moment gradient and load position on buckling
capacities of singly-symmetric beams subjected to
different ratios of end moments.
 Traditional moment gradient factors worked reasonably well with singly-
symmetric sections subjected to single-curvature bending.
 For cases with reverse-curvature bending, the study found that the Cb
factors were unsafe when the maximum moment caused compression in
the small flange and overly conservative when the maximum moment
caused compression in the larger flange.

10. Literature Review (cont’d)
 Andrade et. al, (2006), evaluated the elastic critical
moment (Mcr) in doubly and singly-symmetric I-
section cantilevers. Different parameters were
introduced in the paper such as: degree of mono-
symmetry (r), load type and load position with respect
to the shear center.
 The 3-factor formula which was included in the ENV version of the
Eurocode 3 was extended to cantilevers by providing approximate
analytical expression to determine C1, C2 and C3 factors.

11. Literature Review (cont’d)
 Avik and Ashwini, (2005), studied the effect of
distortional buckling of simply supported I-section of
different degrees of mono-symmetry (r).
 For fairly long beams, Cb values obtained from the study agree with
SSRC Guide (1998) recommendations as buckling is guided by flexural-
torsional buckling.
 For short beams, the difference is significant since Cb values dependent
not only on the degree of beam singly-symmetry (r) but on the span to
beam height (L/h) ratio where the distortional buckling is predominant.
 Avik and Ashwini, (2006), extended the investigation
to the case of reverse-curvature bending.
 It was shown from the results presented that the available design
specifications provide over estimated Cb values for the two load
cases (point and distributed) considered

12. Literature Review (cont’d)
 Helwig, et. al, (1997), investigated the lateral-torsional buckling
of singly-symmetric I-beams and some expressions were
suggested for the moment modification factors Cb.
 For single-curvature bending, the finite element results showed that
traditional Cb values can be used.
 For reverse-curvature bending, the Cb factor was modified to agree with the
FEM results.
 Mohsen, et. al, (2007)a, b, c, investigated the behavior and
capacity of over-hanging singly-symmetric I-beams for various
restraint conditions at the tip. The ultimate moment capacities
obtained from the study are compared to those computed
according to AISC specification, (2005), and BS 5950, (2000).
 The comparison shows that the ultimate moment capacities computed
according to the current standards and specifications vary from conservative
to non-conservative, depending on the overhang length, degree of mono-
symmetry and location of load with respect to the height of I-section. A
design model was introduced based on the results developed from the FEM
analysis

13. AGENDA
 Introduction
 Literature Review
 Problem Statement
 Objectives
 Finite Element Model
 Verification
 Parametric Study
 Results Discussion
 Proposed Design Model
 Conclusions
 Recommendations for Future Study

14. Problem Statement
1. The behavior of the singly-symmetric I-beams is not
yet totally investigated.
2. The design of the singly-symmetric I-beams did not
take the same interest in any of the standards and
specifications as the double symmetric simple beam
took.
3. The type of analysis in the previous work took into
consideration the elastic behavior of I-beams and
did not consider the geometric and material
nonlinearities.

15. Problem Statement (cont’d)
4. Design procedures for continuous I-beams are not
yet clear.
5. Different loading positions are not considered in the
current standards and specifications (AISC
specification considered loading and restraining
conditions at centroid only).
6. Discrepancy between current standards and
specifications (AISC vs. BS).

16. AGENDA
 Introduction
 Literature Review
 Problem Statement
 Objectives
 Finite Element Model
 Verification
 Parametric Study
 Results Discussion
 Proposed Design Model
 Conclusions
 Recommendations for Future Study

17. Objectives
1. Study the effect of different parameters on the buckling
behavior and bending capacity of singly-symmetric
continuous I-beams, such as the effect of:
a. Span length of the continuous beams.
b. Loading position along the section height.
c. Degree of mono-symmetry (r).
d. Load case.
e. Section height.
Span Length Span Length

18. Objectives (cont’d)
2. Develop and propose new design models for the
beams in study.
3. Compare the proposed model results to those of the
current standards and specifications.

19. AGENDA
 Introduction
 Literature Review
 Problem Statement
 Objectives
 Finite Element Model
 Verification
 Parametric Study
 Results Discussion
 Proposed Design Model
 Conclusions
 Recommendations for Future Study

20. Finite Element Model
 A finite element model for a continuous I-beam was
developed using ANSYS Program (V.12)
a. This model takes into account both material and
geometry nonlinearities.
i. Non-linear stress-strain curve.
ii. Initial imperfections = L/500
b. 8-Node quadrilateral thin shell element “shell 93”:
i. Include initial imperfection of plates.
ii. Account for plasticity, stress stiffening and large
deformations.
iii. Each node has six degrees of freedom, translations (Ux,
Uy and Uz) in the nodal X, Y and Z directions,
respectively, and rotations (ROT x, ROT y and ROT z)
about the nodal X, Y and Z directions, respectively.0
50
100
150
200
250
300
350
400
450
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07
Strain
Stress(N/mm
2
)
r
t s
N
K
O
L
P
I
M
J

21. AGENDA
 Introduction
 Literature Review
 Problem Statement
 Objectives
 Finite Element Model
 Verification
 Parametric Study
 Results Discussion
 Proposed Design Model
 Conclusions
 Recommendations for Future Study

22. Verification
 The Finite element model verified with past
experimental work developed by Bassem, 2008.
t1
t2
1000 1000
tw
L1 L2
b1
b2
h
150 150

23. Verification (cont’d)
Specimen h tw b1 t1 b2 t2 L1 L2 h/tw b1/2t1 b1/2t2 Tip
OH-1 200 7.4 68 8.2 101 8.4 2000 2000 27.0 4.100 6.010 R
OH-2 200 6.0 60 8.0 100 8.0 2000 2000 33.3 3.750 6.250 T
OH-3 200 5.0 61 8.0 101 8.0 2000 1000 40.0 3.810 6.310 R
OH-4 202 5.5 61 8.0 101 8.0 2000 1000 36.7 3.810 6.310 F
OH-5 200 6.0 60 8.0 101 8.0 2000 2996 33.3 3.750 6.310 R
OH-6 201 6.0 62 8.0 101 8.0 2000 2997 33.5 3.875 6.310 F
R: Laterally and Torsionally Restrained
F: Laterally Free
T: Top Flange Laterally Restrained
b1
b2
twh
t1
t2

24. Verification (cont’d)
 The ultimate loads from FEM are in good agreement with the
experimental results with a range of deviation of + 14%
to -5%, and an average of + 4%.
SPECIMEN
Pu
Experimental
(N)
Pu
FEM
(N)
Pu FEM /
Pu EXP
OH-1 36297 35218 0.97
OH-2 30019 30489 1.02
OH-3 54446 61999 1.14
OH-4 46696 47088 1.01
OH-5 19130 18207 0.95
OH-6 10104 11380 1.13
AVERAGE 1.04

25. AGENDA
 Introduction
 Literature Review
 Problem Statement
 Objectives
 Finite Element Model
 Verification
 Parametric Study
 Results Discussion
 Proposed Design Model
 Conclusions
 Recommendations for Future Study

26. Parametric Study
 Studied parameters:
a. Span Length
b. Load Position
c. Degree of mono-
symmetry (r)
c. Load Case
e. Section Height
Different Loading Positions at Mid Span
Bottom Loading (BT)
Top Loading (TP) CG Loading (CG)
Span Length
3000, 4000, 5000,
6000, 7000 and 8000 mm
Span Length
3000, 4000, 5000,
6000, 7000 and 8000 mm
95 mm
150 mm
122 mm
150 mm 185 mm 240 mm
r = 0.20 r = 0.35 r = 0.50 r = 0.65 r = 0.80
Constant Web
Thickness = 6.0 mm
Constant Flanges
Thickness = 8.0 mm
Web Height = 350,
500 and 650 mm
150 mm 150 mm 150 mm 150 mm Stiffeners
Thickness = 12 mm
 540 models were created to accommodate all
parameters that as follows:

27. AGENDA
 Introduction
 Literature Review
 Problem Statement
 Objectives
 Finite Element Model
 Verification
 Parametric Study
 Results Discussion
 Proposed Design Model
 Conclusions
 Recommendations for Future Study

28. Results Discussion
 Behavior of the beams:
 Lateral Torsional Buckling:
• Degree of mono-symmetry (r) = 0.20 and 0.35.

29. Results Discussion (cont’d)
 Behavior of the beams:
 Lateral Torsional Buckling:
• Degree of mono-symmetry (r) = 0.20 and 0.35.

30. Results Discussion (cont’d)
 Behavior of the beams:
 Lateral Torsional Buckling:
• Degree of mono-symmetry (r) = 0.20 and 0.35.

31. Results Discussion (cont’d)
 Behavior of the beams:
 Tension Flange Yielding:
• Degree of mono-symmetry (r) = 0.50 for short spans.
 Tension Flange Yielding + LTB:
• Degree of mono-symmetry (r) = 0.50 for long spans.

32. Results Discussion (cont’d)
 Behavior of the beams:
 Tension Flange Yielding:
• Degree of mono-symmetry (r) = 0.50 for short spans.
 Tension Flange Yielding + LTB:
• Degree of mono-symmetry (r) = 0.50 for long spans.

33. Results Discussion (cont’d)
 Behavior of the beams:
 Tension Flange Yielding:
• Degree of mono-symmetry (r) = 0.50 for short spans.
 Tension Flange Yielding + LTB:
• Degree of mono-symmetry (r) = 0.50 for long spans.

34. Results Discussion (cont’d)
 Behavior of the beams:
 Local Buckling:
• Degree of mono-symmetry (r) = 0.65 and 0.80 for short
spans.
 Compression Flange Yielding + LTB:
• Degree of mono-symmetry (r) = 0.65 and 0.80 for long
spans.

35. Results Discussion (cont’d)
 Behavior of the beams:
 Local Buckling:
• Degree of mono-symmetry (r) = 0.65 and 0.80 for short
spans.
 Compression Flange Yielding + LTB:
• Degree of mono-symmetry (r) = 0.65 and 0.80 for long
spans.

36. Results Discussion (cont’d)
 Behavior of the beams:
 Local Buckling:
• Degree of mono-symmetry (r) = 0.65 and 0.80 for short
spans.
 Compression Flange Yielding + LTB:
• Degree of mono-symmetry (r) = 0.65 and 0.80 for long
spans.

37. Results Discussion (cont’d)
1. Effect of Load Position on the Ultimate Moment
Capacities
The difference between the ultimate moment capacity of a section with top loading and
a section with bottom loading varies giving 40% for the cases of degree of mono-
symmetry (r) equals to 0.20 and 0.35 and …..
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
40 80 120 160 200 240 280 320 360 400
MU/MP
Lb/rt
BOTTOM
TOP
CENTROID
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
40 80 120 160 200 240 280 320 360 400
MU/MP
Lb/rt
BOTTOMT
TOP
CENTROID
and 80% for (r) equals to 0. 50, 0.65 and 0.80.
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
40 80 120 160 200 240 280 320 360 400
MU/MP
Lb/rt
BOTTOM
TOP
CENTROID
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
40 80 120 160 200 240 280 320 360 400
MU/MP
Lb/rt
BOTTOM
TOP
CENTROID
The ultimate moment capacity for the top flange loading position gives the lowest
values whereas the bottom flange loading position show the highest capacities due to
loading at bottom flange counteract the torsion of the section.

38. Results Discussion (cont’d)
2. Effect of Degree of Mono-Symmetry (r) on the
Ultimate Moment Capacities
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
40 80 120 160 200 240 280 320 360 400
MU/MP
Lb/rt
ρ=0.20
ρ=0.35
ρ=0.50
ρ=0.65
ρ=0.80
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
40 80 120 160 200 240 280 320 360 400
MU/MP
Lb/rt
ρ=0.20
ρ=0.35
ρ=0.50
ρ=0.65
ρ=0.80
The ratio (Mu/MP) is lower for TOP than BOTTOM and CENTROID loading as loading
on top of flange with the presence of geometric imperfection reach lateral-torsional
buckling before its plastic capacity.

39. Results Discussion (cont’d)
3. Effect of Load Case on the Ultimate Moment
Capacities (load at bottom flange)
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
40 80 120 160 200 240 280 320 360 400
MU/MP
Lb/rt
OVER ONE SPAN
OVER TWO SPANS
Ultimate moment capacity of the sections with loading at the bottom flange and loading
case of double (2P) is higher than loading case of a single load (1P) by 20% …
… as the compression flange will tend to freely sway and the same behavior will be
recognized in the second loaded span if combined with the first span it will result in
some stabilization in the section with respect to its lateral move as each span will
balance the compressive and tensile stresses at the top flange with the other span.
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
40 80 120 160 200 240 280 320 360 400
MU/MP
Lb/rt
OVER ONE SPAN
OVER TWO SPANS

40. Results Discussion (cont’d)
3. Effect of Load Case on the Ultimate Moment
Capacities (load at centroid)
Ultimate moment capacity of the sections with loading at the centroid of the section and
loading case of double (2P) is higher than loading case of a single load (1P) by 15%.
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
40 80 120 160 200 240 280 320 360 400
MU/MP
Lu/rt
OVER ONE SPAN
OVER TWO SPANS
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
40 80 120 160 200 240 280 320 360 400
MU/MP
Lu/rt
OVER ONE SPAN
OVER TWO SPANS

41. Results Discussion (cont’d)
4. Effect of Section Height on the Ultimate Moment
Capacities
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
40 80 120 160 200 240 280 320 360 400
MU/MP
Lb/rt
WEB DEPTH = 350 mm
WEB DEPTH = 500 mm
WEB DEPTH = 650 mm
Web 350mm section was the highest although the failure load for the web 650mm was
the highest among all studied sections, higher heights sections fail by LTB giving a
lower ultimate moment capacity with the high plastic capacity of the deeper I beams …
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
40 80 120 160 200 240 280 320 360 400
MU/MP
Lb/rt
WEB DEPTH = 350 mm
WEB DEPTH = 500 mm
WEB DEPTH = 650 mm
… the ratio will end up with values lower than those values from the smaller heights
that have a relatively ultimate moment capacity close to its plastic capacity giving
higher (Mu/MP) ratio

42. AGENDA
 Introduction
 Literature Review
 Problem Statement
 Objectives
 Finite Element Model
 Verification
 Parametric Study
 Results Discussion
 Proposed Design Model
 Conclusions
 Recommendations for Future Study

43. Proposed Design Model
Compact Nonompact
Load on One Span
BT
Load
CG
Load
TP
Load
BT
Load
CG
Load
TP
Load
BT
Load
CG
Load
TP
Load
BT
Load
CG
Load
TP
Load
Load on Two Spans Load on One Span Load on Two Spans
130 ≤ Lb/rt ≤ 360
40 ≤ Lb/rt < 130
200 ≤ Lb/rt ≤ 400
80 ≤ Lb/rt < 200

44. Proposed Design Model (cont’d)
 The general form of the equation derived for the
current study is represented as follow:
   2
2
rr ed
r
L
c
r
L
ba
M
M
t
b
t
b
p
u







yxp FZM 
bL is the length between points that are either braced against lateral displacement
of compression flange or braced against twist of the cross section
tr is the radius of gyration of the flange components in flexural compression plus
one-third of the web area in compression
r is the degree of mono-symmetry which is calculated as the ratio of the moment
of inertia about the minor axis of the compression flange to the moment of
inertia about the minor axis of the whole cross section

45. Proposed Design Model (cont’d)
 Factors a, b, c, d and e are as follows:
Lb/rt a b c d e
Comapct
1P
BOTTOM
40-130 0.738 2.18E-03 -2.25E-05 0.254 -2.59E-01
130-360 1.352 -5.95E-03 9.28E-06 -0.192 1.10E-01
TOP
40-130 0.912 -4.90E-03 -6.80E-07 0.077 -3.17E-02
130-360 0.665 -3.75E-03 7.20E-06 0.082 -1.73E-01
CENTROID
40-130 0.859 -9.40E-04 -1.80E-05 0.105 -3.08E-02
130-360 0.999 -5.13E-03 9.09E-06 0.006 -9.61E-02
2P
BOTTOM
40-130 0.900 1.97E-03 -1.82E-05 -0.274 3.18E-01
130-360 1.443 -5.63E-03 8.30E-06 -0.045 -6.52E-02
TOP
40-130 1.012 -5.36E-03 4.12E-06 -0.312 2.00E-01
130-360 0.584 -2.54E-03 4.11E-06 0.009 -1.56E-01
CENTROID
40-130 0.826 6.55E-03 -6.23E-05 -0.252 2.34E-01
130-360 1.358 -6.81E-03 1.01E-05 0.146 -5.01E-01
NonCompact
1P
BOTTOM
80-200 1.052 -5.20E-03 8.78E-06 0.290 -3.65E-01
200-400 0.598 -5.65E-04 -1.48E-07 -0.585 7.94E-01
TOP
80-200 0.878 -7.43E-03 1.83E-05 0.256 -3.59E-01
200-400 0.111 5.43E-04 -1.16E-06 -0.058 -5.35E-03
CENTROID
80-200 1.105 -8.63E-03 2.06E-05 0.394 -5.17E-01
200-400 0.337 1.63E-04 -9.59E-07 -0.408 4.54E-01
2P
BOTTOM
80-200 0.548 6.16E-04 -5.00E-06 0.283 -3.36E-02
200-400 0.898 -2.36E-03 2.36E-06 -0.042 6.92E-02
TOP
80-200 0.909 -7.89E-03 2.07E-05 0.180 -3.01E-01
200-400 0.036 1.24E-03 -2.63E-06 -0.130 9.78E-02
CENTROID
80-200 1.045 -6.67E-03 8.90E-06 1.235 -1.85E+00
200-400 0.545 -1.33E-03 1.43E-06 -0.317 2.46E-01

46. Proposed Design Model (cont’d)
 Accuracy of the derived equations
a. The predicted moment capacity are close enough to the
corresponding values obtained from the FEM which
validates the current design equations.
b. The proposed formulae produce results within the ±15%
deviation lines with a maximum deviation 13%.
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
Mu(proposedmodel)/Mp
Mu(FE) / Mp
Y=X Line
+15%
Deviation
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
Mu(proposedmodel)/Mp
Mu(FE) / Mp
Y=X Line
+15%
Deviation

47. Proposed Design Model (cont’d)
 Validity of the equations on other sections in range
(reliability)
Span
Web
Height
Top
Flange
Lu/rt (r)
Compact
ness
Load
Config.
Load Pos.
Mu/Mp
FEM
Mu/Mp
Prop.
Model
% Error
6200 520 215 113.24 0.746 Compact 1P Bottom 0.737 0.741 0.559
4500 400 110 173.77 0.283 Compact 1P Bottom 0.532 0.554 3.958
6200 390 175 138.75 0.614 Compact 1P Top 0.293 0.269 -9.135
3500 195 620 73.17 0.687 Compact 1P CG 0.700 0.751 6.818
6800 480 130 221.18 0.394 Compact 1P CG 0.257 0.297 13.354
6200 520 215 113.24 0.746 Compact 2P Bottom 0.880 0.862 -2.093
4500 400 110 173.77 0.283 Compact 2P Bottom 0.742 0.698 -6.272
3500 620 195 73.17 0.687 Compact 2P CG 0.805 0.908 11.348
3800 635 175 90.57 0.614 Noncompact 1P Bottom 0.749 0.694 -7.982
8200 550 110 334.46 0.283 Noncompact 1P Bottom 0.283 0.290 2.468
6500 530 130 214.84 0.394 Noncompact 1P Top 0.154 0.150 -2.701
7450 570 155 201.76 0.525 Noncompact 1P CG 0.265 0.241 -9.857
3800 635 175 90.57 0.614 Noncompact 2P Bottom 0.822 0.724 -13.59
3900 395 100 168.56 0.229 Noncompact 2P CG 0.405 0.360 -12.70
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
Mu(proposedmodel)/Mp
Mu(FE) / Mp
Y=X Line
+15% Error
-15% Error

48. Proposed Design Model (cont’d)
 Comparison Between Standards and Specifications
a. Case of Single Span Loading:
 As the degree of mono-symmetry (r) increases, the AISC (2010)
results move from being the most conservative for the case of
degree of mono-symmetry (r) = 0.20 to the least conservative
results at the degree of mono-symmetry (r) = 0.80, compared to the
parametric study, where failure takes place at the plastic stage.
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
40 80 120 160 200 240 280 320 360 400
MU/MP
Lb/rt
FEM, BOTTOM FEM, TOP
FEM, CENTROID AISC
BS DESIGN MODEL, BOTTOM
DESIGN MODEL, TOP DESIGN MODEL, CENTROID
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
40 80 120 160 200 240 280 320 360 400
MU/MP
Lb/rt
FEM, BOTTOM FEM, TOP
FEM, CENTROID AISC
BS DESIGN MODEL, BOTTOM
DESIGN MODEL, TOP DESIGN MODEL, CENTROID
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
40 80 120 160 200 240 280 320 360 400
MU/MP
Lb/rt
FEM, BOTTOM FEM, TOP
FEM, CENTROID AISC
BS DESIGN MODEL, BOTTOM
DESIGN MODEL, TOP DESIGN MODEL, CENTROID

49. Proposed Design Model (cont’d)
 Comparison Between Standards and Specifications
a. Case of Single Span Loading:
 BS (5950-1:2000) show reasonable agreement with the loading of:
 Bottom flange case for (r) = 0.20 and 0.35 at all span lengths studied.
 Top flange case for (r) = 0.50, 0.65 and 0.80 at spans 3000 and 4000 mm
 Centroid case for (r) = 0.50, 0.65 and 0.80 at span 5000mm.
 Bottom flange case for (r) = 0.50, 0.65 and 0.80 at spans 6000, 7000 and
8000mm.
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
40 80 120 160 200 240 280 320 360 400
MU/MP
Lb/rt
FEM, BOTTOM FEM, TOP
FEM, CENTROID AISC
BS DESIGN MODEL, BOTTOM
DESIGN MODEL, TOP DESIGN MODEL, CENTROID
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
40 80 120 160 200 240 280 320 360 400
MU/MP
Lb/rt
FEM, BOTTOM FEM, TOP
FEM, CENTROID AISC
BS DESIGN MODEL, BOTTOM
DESIGN MODEL, TOP DESIGN MODEL, CENTROID

50. Proposed Design Model (cont’d)
 Comparison Between Standards and Specifications
a. Case of Single Span Loading:
 AISC specification give lower results than the BS code for (r) =
0.20 and 0.35 and higher results for (r) = 0.80
 The comparison between AISC and BS for (r) = 0.50 and 0.65
depends mainly on the ratio (Lb/rt) where AISC give results higher
than the BS code for spans 3000, 4000 and 5000 and lower results
for spans 6000, 7000 and 8000
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
40 80 120 160 200 240 280 320 360 400
MU/MP
Lb/rt
FEM, BOTTOM FEM, TOP
FEM, CENTROID AISC
BS DESIGN MODEL, BOTTOM
DESIGN MODEL, TOP DESIGN MODEL, CENTROID
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
40 80 120 160 200 240 280 320 360 400
MU/MP
Lb/rt
FEM, BOTTOM FEM, TOP
FEM, CENTROID AISC
BS DESIGN MODEL, BOTTOM
DESIGN MODEL, TOP DESIGN MODEL, CENTROID

51. Proposed Design Model (cont’d)
 Comparison Between Standards and Specifications
b. Case of Two-Span Loading:
 The results calculated for both the AISC (2010) and the BS (5950-
1:2000) for this case are identical to single span loading case,
because the capacity of the beam depends on the cross section
properties rather than the loading case.
 BS (5950-1:2000) results lie in between the results of the bottom
and top flange loading of the proposed model results unlike the case
of single span loading for (r) = 0.20 and 0.35.
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
40 80 120 160 200 240 280 320 360 400
MU/MP
Lb/rt
FEM, BOTTOM FEM, TOP
FEM, CENTROID AISC
BS DESIGN MODEL, BOTTOM

52. AGENDA
 Introduction
 Literature Review
 Problem Statement
 Objectives
 Finite Element Model
 Verification
 Parametric Study
 Results Discussion
 Proposed Design Model
 Conclusions
 Recommendations for Future Study

53. Conclusions
1. 540 models were analyzed to study the behavior of
mono-symmetric continues I-beams after being verified.
2. Beams with degree of mono-symmetry (r) = 0.20 and
0.35 failed by Lateral Torsional Buckling.
3. Beams with degree of mono-symmetry (r) = 0.50 for
short spans failed by Tension Flange Yielding.
4. Beams with degree of mono-symmetry (r) = 0.50 for
long spans failed by interaction of Tension Flange
Yielding and Lateral Torsional Buckling.
5. Beams with degree of mono-symmetry (r) = 0.65 and
0.80 for short spans failed by Local Buckling.
6. Beams with degree of mono-symmetry (r) = 0.65 and
0.80 for long spans failed by interaction of Compression
Flange Yielding and Lateral Torsional Buckling.

54. Conclusions (cont’d)
7. Handy design model, based on the parametric study, was
developed using a normalized equation to cover all
studied cases.
8. Span lengths and degrees of mono-symmetry (r) were
incorporated in the design model.
9. The effect of load position and load case was introduced
in the design model; top flange, bottom flange or
centroid.
10. The design model was verified against other sections in
the range with maximum deviation of 13%.
11. The difference between the ultimate moment capacity of
a section with top loading and a section with bottom
loading varies from 40% for (r) = 0.20 and = 0.35 to
80% for (r) = 0.50, 0.65 and 0.80.

55. Conclusions (cont’d)
12. The AISC results are most conservative at (r) = 0.20 and
least conservative at (r) = 0.80.
13. BS (5950-1:2000) show reasonable agreement with the
loading of:
 Bottom flange case for (r) = 0.20 and 0.35 at all span lengths studied.
 Top flange case for (r) = 0.50, 0.65 and 0.80 at spans 3000 and 4000 mm
 Centroid case for (r) = 0.50, 0.65 and 0.80 at span 5000mm.
 Bottom flange case for (r) = 0.50, 0.65 and 0.80 at spans 6000, 7000 and
8000mm.
14. AISC specification give lower results than the BS code
for (r) = 0.20 and 0.35 and higher results for (r) = 0.80.

56. Conclusions (cont’d)
15. The comparison between AISC and BS for (r) = 0.50
and 0.65 depends mainly on the ratio (Lb/rt) where AISC
give results higher than the BS code for spans 3000,
4000 and 5000 and lower results for spans 6000, 7000
and 8000.
16. The effect of loading case and position is not captured in
the calculation of the specifications in study as the beam
is depending on the cross section properties which are
the same in both loading cases.

57. AGENDA
 Introduction
 Literature Review
 Problem Statement
 Objectives
 Finite Element Model
 Verification
 Parametric Study
 Results Discussion
 Proposed Design Model
 Conclusions
 Recommendations for Future Study

58. Recommendations for Future Study
1. Consider different cases of loading (moving and
distributed loads).
2. The effect of different mechanical properties of the
material.
3. The effect of different span ratio of a continuous beam
on the ultimate moment capacity of an I-section.
4. The effect of different lateral restraint on the ultimate
moment capacity.
5. The effect of flange curtailment on the ultimate moment
capacity.
6. The effect of web thickness on the ultimate moment
capacity.

59. THANK YOU