1. Mahmoud SAYED-AHMED
Introducing
N-M INTERACTION FOR STEEL JACKET
RETROFITTING RC BRIDGE COLUMN
DUE TO EARTHQUAKE

2. Arrangement of the presentation
Literature Parametric Results and
Review Study Conclusions
A bridge is a structure built to span physical obstacles

3. Literature Review
Earthquake, Failure; Buildings & Substructures, Steel Jacketing

4. Earthquakes
Tectonic plate movement

5. Cont.,
Source: http://www.atcouncil.org/pdfs/bp1a.pdf

6. Cont.,
0.8
0.7
Spectral Response Acceleration,S
0.6
0.5
Toronto
0.4
Alexandria
0.3
White River
0.2
0.1
0
0 0.5 1 1.5 2 2.5
Period, T
• Seismic map in Canada
• The four Sa 0.2, 0.5, 1.0 and
2.0 seconds (equivalent to
frequencies of 5, 2, 1, and 0.5
Hertz)

7. Failure due to base shear in Moment Resisting Frame (MFR)
Inflection point
Plastic hinge

8. Cont.,
13-story building is part of the
Lotus Riverside complex in
suburban Shanghai.

9. Failure due to base shear in Bridge substructures
http://www.youtube.com/watch?v=qIiuDUgvZpY
http://www.youtube.com/watch?v=KytqmPKYNSE

10. Steel Jacketing;
I-5 - South Seattle Vic. Seismic Retrofit - Complete Dec 2008

11. Cont.,
Source: http://www.wsdot.wa.gov/Projects/I5/SSeattleSeismic/Photos

12. Know-How?
N-M interaction diagrams are generated for major and minor
axes of the column shape subjected to bending moment and
axial compression or tension.
Research Significance
In biaxial bending the
section is subjected to
double compression
and double tension.
Retrofitting for biaxial bending in columns The coupled moment
shifts the neutral axis
with an angle

13. Column Analysis and Design
The computation of the failure envelope for
the column shape subjected to biaxial
bending and to an axial force, at the ultimate
limit state.
Due to the non linearity of the constitutive
laws for both steel and concrete, it is
practically impossible to find the exact
analytical solution

14. Parametric Study
Specifications, Earthquake and Results

15. Reinforced Concrete Box Girder Bridge
Deck Section – Concrete Box Girder
- Slab and Girder Thickness
- Fillet Horizontal Dimension Data
- Fillet Vertical Dimension Data
- Left Overhang Data
- Right Overhang Data
- Parametric Variation
- Prestress Tendons
Others
- Diaphragm
- Abutment
CL-625 Truck
- BentCap & BentColumn (Frame)
- Lane & Vehicle class

16. Earthquake
Los Angeles Century City
Acceleration
Time, Seconds
== LACC0 ==
Acceleration
Time, Seconds
== LACC90 ==

17. Mode 1
Mode 3
Modal deformation
Mode 4 Mode 2

18. Mode 5 Cont.,
Mode 6

19. It’s not just about the visuals, but strengthening
SERVICE LIFE DESIGN

20. Design procedures
Load combination
Str-I1 = 1.25 Dead Load + 1.25 Nonlinear Modal History + 1.75 Moving Load
+ 1.00 Prestress
50, 125, 125, 175, 150
Section design CL-625 Truck
𝑃 𝑓 ≤ 𝑃𝑟,𝑚𝑎𝑥 = 0.8𝐴 𝑔 [𝛼1 𝜙 𝑐 𝑓𝑐′ 1 + 𝜌 𝑔 + 𝜙 𝑠 𝑓 𝑦 𝜌 𝑔 ]
𝑀
𝐾𝐿 𝑢 25 − 10 𝑀1
2
≤
𝑟
𝑃𝑓
𝑓𝑐′ 𝐴 𝑔
CSiCOL
N-M Interaction
𝑁 𝑛 = 𝑁 𝑅𝐶 + 𝑁 𝑆𝐽
𝑀 𝑛 = 𝑀 𝑅𝐶 + 𝑀 𝑆𝐽
𝑀 𝑢𝑥 𝑀 𝑢𝑦 𝑃 𝑢 , 𝑀 𝑢𝑥𝑦
𝐶𝑟 = + ≤ 1 @ 𝑁𝑢 𝐶𝑟 = ≤1
𝑀 𝑛𝑥 𝑀 𝑛𝑦 𝑃 𝑛 , 𝑀 𝑛𝑥𝑦

21. Columns Load, SAP2000
Load Type Load-Pu Mux-Bot Muy-Bot Mux-Top Muy-Top
[kN] [kN-m] [kN-m] [kN-m] [kN-m]
Modal 1 -1,826.825 -14,446.2809 3,719.2717 11,907.2437 -4,259.2954
Modal 2 3,532.885 -16,441.1208 4,572.981 23,321.6435 -5,746.9539
Modal 3 -14,092.555 -6,420.4581 27,669.2224 -6,296.0268 -30,473.8426
Modal 4 9,121.627 2,808.6831 383.325 -4,377.3631 -220.5096
Modal 5 33,246.646 3,565.5988 9,986.6942 -7,261.6253 -15,918.000
Str – I1, Max -4,595.054 1.6875 168.8998 -517.3525 -63.9742
Str – I1, Min -9,195.481 -173.7267 69.3186 -1,160.2619 -170.2266

22. Biaxial Bending Effects
Conventional RC column & stresses for rebars
Steel Jacket RC column & stresses for rebars
Stress view of RC column – Str-I1, Max Stress view of Steel Jacket retrofitted RC column – Model 1

23. N-M Interaction
8.00E+04
6.00E+04
4.00E+04
Load, kN
2.00E+04
0.00E+00
0.00E+00 5.00E+03 1.00E+04 1.50E+04 2.00E+04 2.50E+04
-2.00E+04
RC Column
-4.00E+04
Steel Jacket
-6.00E+04
Moment, kN-m

24. Lateral Deflection
Load Direction Height, [m]
combination 0.00 2.44 4.88 7.32
Modal 1 1 0.00 -5.88909 -16.90164 -25.0389
Vertical and Horizontal Deflection, mm
2 0.00 0.09305 0.58337 1.69961
3 0.00 -0.09825 -0.19648 -0.29467
Modal 2 1 0.00 -6.43437 -15.75635 -16.24604
2 0.00 -0.08266 -0.40561 -1.04655
3 0.00 0.19000 0.37991 0.56967
Modal 3 1 0.00 -0.34759 -0.71758 -0.32963
2 0.00 -10.95762 -29.22599 -37.63029
3 0.00 -0.75790 -1.51530 -2.27169
Modal 4 1 0.00 0.9684 2.21186 1.8010
2 0.00 -0.41871 -1.07300 -1.25985
3 0.00 0.49056 0.98072 1.47008
Modal 5 1 0.00 0.27061 0.16327 -1.35564
2 0.00 -3.86040 -8.31792 -5.40400
3 0.00 1.78801 3.57097 5.34386
Str – I1 1 0.00 -0.11573 -0.62268 -1.68916
2 0.00 -0.03847 -0.02648 0.20260
3 0.00 -0.48749 -0.96088 -1.42019

25. Want to jump to a
bookmark in your video?
Hover over the video and
you’ll be pleasantly surprised.
Did we mention you can add
bookmarks, include fades, and
trim your videos now?
BentColumn

26. Results & Conclusions
Results, Conclusions, and Discussions

27. RESULTS
» Lateral deflection
𝑤𝐻4 𝑉ℎ3 𝑉ℎ2
𝛥𝑢 = + +
8(𝐸𝐼) 𝑐 12𝐸 𝐼 𝑐 12𝐸 𝐼𝑏
𝐿
µ= 𝛥𝑢 𝛥𝑦

28. Based on the theoretical findings, the following conclusions can be drawn:
• Pushover analysis is able to determine the column capacity but not under the
seismic demands.
• Steel jacketing enhance the ultimate compressive strain of concrete for the
spalling strain of unconfined concrete.
• Steel jacketing enhances the column capacity ratio, its resistant to lateral
deflection and its ductility.

29. ?
But wait…
There’s More!
New applications for bridges!

30. Water Bridge
This is a channel-bridge
over the River Elbe and
joins the former East and
West Germany, as part of
the unification project. It is
located in the city
of Magdeburg, near Berlin.
http://www.youtube.com/watch?v=y_xHKKGHV8I&feature=related
Bay Bridge in an Earthquake
http://www.youtube.com/watch?v=WvAIivBaxso

31. Your Questions?
Thanks