Vibration Analysis of Gantry Structures · Tacoma Narrows Bridge • Mode Shapes – the shape of which a structure oscillates at its natural frequency Modal Superposition: Method-Mass
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Seth Weber KDOT Bridge Design Engineer (785) 296-6946 [email protected]Dr. Hayder Rasheed Ph.D., P.E., F.ASCE Professor, Kansas State University (785) 532-1589 [email protected]Vibration Analysis of Gantry Structures KSU Bridge Design Workshop October 13 th , 2017
Dr. Hayder RasheedPh.D., P.E., F.ASCEProfessor, Kansas State University(785) [email protected]
Vibration Analysis of GantryStructures
KSU Bridge Design Workshop
October 13th, 2017
Presenter
Presentation Notes
Introductions: Performed a dynamic analysis of Overhead sign gantry structures for the Kansas Turnpike Authority. Worked in conjunction with Dr. Rasheed to perform the analysis
• Project Description and Task• Method of Analysis• Summary of Findings
Presenter
Presentation Notes
Here’s a quick outline of today’s presentation. First, I’m going to give a short description of the project and the tasks given to us. Then, I’ll talk through the method I used to perform the vibration analysis Dr. Rasheed will then talk a little on the theory of dynamic analysis And then lastly, we will conclude the presentation with a summary of our findings
Project Description3
• The KTA has a goal for open road tolling at their three largest toll plazas: Eastern Terminal, East Topeka, and Southern Terminal
• Open road tolling▫ Allows for vehicle traffic to pass through toll roads at high speeds
without stopping with use of a KTAG▫ Provides tollbooths to the right of the main roadway to allow for
customers without KTAG’s to pay ▫ Implements video reinforcement to ensure payment of tolls
• KDOT was tasked to design the structures that will hold the technology for open road tolling
Presenter
Presentation Notes
The KTA is currently building infrastructure to move toward Open Road tolling. For those that don’t know, Open road tolling is a form of tolling that is used to increase the functionality through a toll plaza. Those with an appropriate TAG, in our case the KTAG, will be able to drive through the toll plaza at high speeds,60-65MPH as a ball park number, without stopping. The appropriate infrastructure includes an overhead gantry structure outfitted with cameras sensitive to vibrational movement. KDOT was tasked to design these structures such that the vibration criteria of the equipment would be met.
Task4
• Perform a dynamic analysis and check that structures fulfill the following criteria:▫ Vibration should be limited to excursions no greater than 0.001”
above 20Hz▫ No combined movement greater than 1” per millisecond▫ Overall sway should be less than 6”
• Performed analysis for Spans of:▫ 50’ gantries▫ 63’ gantries▫ 86’ gantries
▫ Some held signs, others did not
Presenter
Presentation Notes
The criteria specified by the manufacturer of the equipment is as follows: Vibrations should be limited to excursions no greater than 0.001” above 20 Hz This means that when the structure is oscillating at a frequency above 20 HZ the total displacement can be no greater than 0.001” No combined movement greater than 1” per millisecond This is with respect to the equipment. Therefore, no point at which a camera is located can the total distance of the traveled path within a millisecond be greater than 1” Overall sway due to forces must be less than 6”
Method-Overview5
• Research▫ Code: Standard Specification For Structural Supports For
Highway Signs, Luminaires, and Traffic Signals (11.7.4) to determine the amplitude of truck gust forces Truck Gust = 18.8*C*I = 18.8*1.2*1.0 = 22.56 (PSF) Static Pressure used for Fatigue
▫ STAAD analysis and limitations Can only vary nodal loads w.r.t. time Can only have up to 136 different forcing functions
• Utilized STAAD Finite Element Models to analyze the structures▫ Performs a response time history analysis by modal superposition Uses mass modeling to determine the natural frequencies and
mode shapes The natural frequencies and eigen values are then used to solve
for displacements under the effects of forcing functions using modal superposition
• Utilized excel to organize and synthesize STAAD output
Presenter
Presentation Notes
To start the discussion of the method I utilized to analyze the structure, I’m going to give an overview of the whole process. The first thing I did was do some research. I researched the code and found that there were two primary forces to consider for dynamic analysis of sign structures. Natural Wind Gusts Truck Gusts Calculated the truck gust to be 22.56 PSF Based on code for fatigue analysis Assumed this to be an appropriate amplitude for dynamic loading I then researched our 3D Finite Element Analysis program, STAAD Pro, to understand how it will find deflections due to the dynamic loads. I found that: The program can only apply time varying loads at nodes The program can only store 136 different forcing function types After researching, I then utilized STAAD Pro. to build my model STAAD performs a response time history analysis by using mass modeling and modal superposition Lastly, I utilized excel to synthesize STAAD output and compare the deflections with the given criteria
• Natural Frequencies – the frequency at which a system oscillates when not subjected to a continuous or repeated external force
Resonance: Tacoma Narrows Bridge
• Mode Shapes – the shape of which a structure oscillates at its natural frequency
Modal Superposition:
Method-Mass Modeling6
Presenter
Presentation Notes
I’ll start the discussion on our method of analysis by introducing the primary factors that contribute to forcing functions. The first are the natural frequencies of the structure. This is defined as the frequency at which a system oscillates when not subjected to a continuous or repeated external force A great example of what happens when a forcing function oscillates at the same frequency as a structure’s natural frequency is the case of the Tocoma Narrows Bridge. This event is called resonance and can be detrimental to structures without damping devices The second factor is the mode shape which is defined as the shape of which a structure oscillates at its natural frequency. A structure will have many mode shapes and can best be described as a combination of the modes that have the highest participation factors.
Method-STAAD Model7
• Used in house program to build gantry structure model.• Used model’s loads for natural wind, and input truck gust loads• Assumptions:▫ Truck Gust will act vertically along the bottom chord of the
structure directly above the two 12 ft lanes. Applied as a pressure load.
▫ The frequency of the wind gust is equal to the length of the truck, 44 ft, divided by the truck speed, 65mph. ω= 0.46 HZ
Harmonic Behavior Sinusoidal Wave
Presenter
Presentation Notes
With this in mind the first step was to find the frequencies of our forcing functions: First we built our STAAD model using an in-house program. Then we idealized the truck and natural wind gusts to be harmonic and sinusoidal Natural Wind Gusts Is rather random based on weather conditions Assumed a value near the truck gust frequency to produce the most critical condition The natural wind gust acts in the horizontal plane directly perpendicular to the face of the gantry structure. Truck Gusts We idealized the wave of the truck gust forcing function as a sinusoidal and harmonic wave Assumed the wave of the forcing function would be correlated to the length and speed of the truck. Omega = Length divided by Speed Defined the truck gust to act on the bottom of the structure along the two 12 foot lanes
Method-STAAD Model
• Used tributary area to idealize the structure such that all wind loads were represented as point loads▫ This allowed us to vary the
wind load w.r.t. time• Placed nodes at each of the
camera locations and analyzed the structure’s deflections at those points
#8
Presenter
Presentation Notes
With the approximate frequencies found, we then applied the forces as point loads using tributary areas. Then we defined the frequencies at which the loads would oscillate and input an arbitrary number of cycles. We used 500 cycles Then lastly we placed nodes at the camera locations and used STAAD’s time history analysis functions to analyze the structure.
State Bridge Office
STAAD Model of Gantry Structure
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Presenter
Presentation Notes
Here is a picture of the model we built in STAAD. Comprised of beam elements and signs are modeled as loads placed on the structure. Boundary Conditions: Fixed Releases where appropriate for structure
State Bridge Office
Loading of Gantry Structure for Vibration Analysis
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Presenter
Presentation Notes
Here is a picture of the mass modeling and time history analysis loading. We took the mass loads of the structure and applied them in all directions of movement (one in the x, y, and z planes for each load) then we applied the forcing functions developed by the wind loads and applied those loads where appropriate.
State Bridge Office
STAAD Model of Gantry Structure
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Mode Shape of Gantry Structure
Presenter
Presentation Notes
And then here is a picture of one of the mode shapes the structure has. This mode shape shows movement primarily in the z direction, but each mode is comprised of movement in all three directions.
State Bridge Office
•
SDOF System – Forced Motion12
MC
K
Graph courtesy of Chopra
State Bridge Office
MDOF System -Modal Superposition13
•
State Bridge Office
Summary of Findings-STAAD Output• Post-processing feature allowed us to see the overall sway of the structure
(maximum deflection). All were less than 6”.• The gantry structures had few to no natural frequencies above 20 HZ.
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Mode FrequencyHz
PeriodSeconds
Part. X%
Part. Y%
Part. Z%
Type
1 1.581 0.632 97.806 0.003 0 Elastic
2 4.038 0.248 0 0 89.939 Elastic
3 5.410 0.185 0.003 75.588 0.006 Elastic
4 8.688 0.115 0.001 0.004 0.159 Elastic
5 10.834 0.092 0.000 0.382 0.000 Elastic
6 14.716 0.068 0.005 0.000 0.004 Elastic
Presenter
Presentation Notes
In the post-processor, we were able to export the results into excel and synthesize the data. The sway criteria was met for all structures and could easily be viewed in the post-processor The gantries rarely had natural frequencies above 20 Hz and if they did the participation factors for these modes were very low. Thus we could conclude that the structure will not oscillate above 20 Hz and the criteria is met. The table is a typical format of one of the data tables given by STAAD’s post-processor. In it you can see the different modes and the participation factors for each direction of movement. Thus we can conclude that the behavior of the structure is primarily a combination of modes 1, 2, and 3
State Bridge Office
Summary of Findings-STAAD Output• The post-processer in STAAD allows
you to graphically select nodes and then draws the dynamic displacement in three different graphs (x,y,z).
• Defined the time step to be 1 millisecond so that the data from the graphs could be easily compared with the criteria specifying that excursions be less than 1” per millisec
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1
1
1
1
2
2
2
2
3
3
3
3
10 20 30
2.51
25.1
-2.56
0.059
X-Disp.(E-3 in) - Node: 48
Time - Displacement
Time Displacement X Displacement Y Displacement Z RESULTANT MAX X 0.01836 IN0 0 -0.000009 0.00002 2.19317E-05 MAX Y 0.055424 IN
In STAAD’s post-processor, we were able to create graphs of a nodes displacement vs. time for each direction of movement and export the data into excel. When defining our forcing functions, we chose to have calculations done every millisecond. This enabled us to find how much the structure moves every millisecond. After finding the maximum resultant displacement, we could compare with the criteria. We found that all the structures met the given criteria The table below is an example of our excel spreadsheet calculations
State Bridge Office
Summary of Findings-Conclusions• 50’ Structures▫ No excursions above 20 HZ▫ Maximum displacement in 1
millisecond = 0.9”▫ Maximum sway = 3.2”
• 63’ Structures▫ No excursions above 20 HZ▫ Maximum displacement in 1
millisecond = 0.006”▫ Maximum sway = 2.5”
• 86’ Structures▫ No excursions above 20 HZ▫ Maximum displacement in 1
millisecond = 0.3”▫ Maximum sway = 3.6”
• All structures were found to meet the criteria specified by the KTA equipment
• The forcing functions used represents truck pairs running in a train while natural wind gust is applied perpendicularly to the sign with a frequency close to that of the truck gust frequency. This situation is highly unlikely to occur, so we conclude that the structures will perform exceptionally for normal traffic and weather conditions.
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Presenter
Presentation Notes
In conclusion, we found that for all the structures, the criteria is met at the locations of the cameras. We concluded that our results were representative of an unlikely worst case scenario and that the structure would function exceptionally under normal traffic and weather conditions.
