1. Bentley RM Bridge Seismic Design and Analysis
How many of you (structural) engineers remember the devastating images that results of a major earthquake over our infrastructure?
Bentley RM Bridge Seismic Design and Analysis
Alexander Mabrich, PE, Msc 1

2. Earthquake in the Chilean mountains.
If you have not experience the force of a seismic event, this could give you an idea….
It is amazing that we as civil engineers have to design structural facilites that can withstand these kind of forces.
Click on video and turn your speaker really loud. Engage the audience in how an earthquake sounds like.

3. AGENDA
This is Kobe, Japan, 1995, on a Tuesday, January 17, at 5:46 a.m. an entire elevated freeway section collapses…
Even though great advances have been made on the field of seismic analysis….there is much more to learn. !!!
Kobe, Japan (1995)

4. Loma Prieta, California (1989)
AGENDA
Loma Prieta, 1989, October, 17th – in black and white it looks like a long time ago
Seismicity is a recurring phenomena with probability over the time… Northridge quake in 1994, also in California, but;…
How many of you are aware that Arkansas, Missouri, Washington, Nevada, Idaho, Montana, Hawaii, and Alaska also had major seismic events?
Loma Prieta, California (1989)

5. RM Bridge Seismic Design and Analysis
Critical infrastructures require:
Sophisticated design methods
Withstand collapse in earthquake occurrences
Bentley RM Bridge can perform from the simple to the most sophisticated earthquake load simulation to design our bridges, from static to non linear dynamic analysis.
Bridges, highways and critical infrastructures require design methods that ensure that they withstand collapse in earthquake occurrences - not only saving lives, but reducing post-event disruptions. Major links should stand even when we have a disaster.

6. RM Bridge Seismic Design and Analysis
The Bentley BrIM vision
RM Bridge Seismic Design Methods
Earthquake simulations in Bentley RM Bridge
In order to clarify how wide is our concept of facilitating the seismic design in your company day job we will separate it in three main ideas:
1 – First we are going to talk about the Bentley BrIM Concept: Share of information. Not going to another program to do seismic design, or compute loads.
2 – Second I will present you the Bentley RM Bridge analysis, design and verification philosophy for earthquake analysis
3 – Third you will understand how to deal with earthquake load simulations in Bentley RM Bridge.

7. RM Bridge Seismic Design and Analysis
AASTHO, Simple Seismic Load
Basic concepts for Dynamic Analysis:
- Eigenvalues
- Eigenshapes
Two non-linear dynamic options:
- Response Spectrum
- Time-History
In order to clarify how wide is our concept of facilitating the seismic design in your company day job we will separate it in three main ideas:
1 – First: the AASTHO considerations and the Simple Seismic Load
2 – Second: the Basic concepts involved in Systems Vibrations and the Eigenvalues with corresponding Eigenshapes
3 – Third: the two non-linear options: a Response Spectrum or a Time-History,
At the end of this presentation you will discover how RM Bridge seismic design and analysis tools provide measurable benefits for these labor intensive, computing and modeling processes. Then we can plan the implementation of this amazing tool in your bridge design office.
So… Let’s get started?

8. AASHTO Bridge Design Specifications
7% probability of exceedence in 75years
Seismic Design Categories
Soil
Site / location
Importance
Earthquake Resistant System
Demand/Capacity
According to AASHTO LRFD Bridge Design Specifications, we will consider a 7% probability of exceedence in 75 years to permit minimal, moderate and significant damage
At the very beginning of our Seismic Analysis we have to classify our bridge according to the Seismic Design Categories; SDC,
Soil classification, with site (6 miles) or location (Map) classification and Importance Classification: critical, essential or normal.
This Seismic Classification will define the Analysis Requirements,
Mathematically our bridge can be divided into frames and this will be our analytical “global” models
assure we are using one of the options of Earthquake Resistant System
At the end we go back to the ration between Component Demand/Capacity

9. AASHTO Bridge Design Specifications
Site Location

10. AASHTO Bridge Design Specifications
Type of Seismic Analysis Required
SM = single model analysis
UL= uniform load
MM = multimode analysis
TH = time history

11. Static Seismic Load
First we will see the simple approach of simulating the seismic load with ESA: Equivalent Static Analysis
but even for this we have to start with our Seismic Classification first

12. Equivalent Static Analysis
Uniform Load Analysis
Orthogonal Displacements
Simultaneously
Fundamental mode
Simple Seismic load is an equivalent static analysis procedure.
This assumes that the seismic load can be considered as an equivalent static horizontal force applied to an individual frame in either longitudinal or transverse direction. This causes orthogonal displacements and also this can happen Simultaneously applying combination with coefficients.

13. Equivalent Static Analysis
Direction, Factor
Equivalent static analysis procedure with Uniform Load: It is mostly related to Self-weight,
we just change the vectors directions from global Y to Z and X…and we can apply a mutltiplication factor to that loads directly, or apply a constant factor of 1 and enable the needed load combinations in the Combination table.
The Orthogonal displacements can happen Simultaneously and we use to apply combination with coefficients

14. Fundamental Mode
Regular bridges, with response on their FUNDAMENTAL or FIRST MODE of vibration

15. Results

16. Basic Concepts used in Dynamic Analysis
So in the simplified analysis we ignore many of the basic characteristics of earthquake loads, there are huge simplifications
Let’s take a look on what are they and why we can start using
Eigenvalues and corresponding Eigenshapes as initial step for our dynamic calculations in RM BRIDGE
You have seen that even for simple bridge it is a good idea to check if the first mode of vibration, or natural deformed shape is representative

17. Basic Concepts Vibration of Systems with one or more DOF
Eigen values and Eigen modes
Forced Vibration
Harmonic and Stochastic Simulation
Linear and Non-linear behavior of the structure
We are all the time talking about Vibration of Systems with one or more degrees of freedom. For those we use the natural signatures of our structures:
Eigen value: vibration frequency of a structure
Eigen mode: the different shapes or vibration modes that a structure can deforme. E.g : move to the left, right, up, down, shake, twist, etc
Into those we can apply a Forced Vibration thru a harmonic and stochastic(random in nature) stimulation.
RMBRIDGE will calculate this values and modes, then used for the basis of its dynamic calculations.
A stochastic process is one whose behavior is non-deterministic in that a state's next state is determined both by the process's predictable actions and by a random element. In a stochastic or random process there is some indeterminacy in its future evolution described by probability distributions.
Classical examples of this are medicine: a doctor can administer the same treatment to multiple patients suffering from the same symptoms, however, the patients may not all react to the treatment the same way.
And this will be our final analysis with
Linear: analysis in the elastic range
Non-linear : analysis in the plastic, inleastic range behaviour of the structure

18. Dynamic Vibration
Any Dynamic Vibration (an earthquake) is an Oscillation movement with a maximum Amplitude that could be measured by deflection, velocity or acceleration
We use the common variable Angular speed (w), Frequency(f) and Period (T).
w = angular speed. Oscillations per second. Natural circular frequency of vibration
K = stiffness of structure
M= mass of structure
F = frequency of the structure
T = natural period of vibration. Time to complete one cycle.

19. Damped Vibration
Introducing Damping considerations we start considering the natural characteristics of our structure materials and system
We have the same movement but now with a dissipation of energy that changes the movement over the time.
In RM bridge we also take that into account….while doing the modal or time-history, RM Bridge requieres only the damping coefficient or damping degree value or even a damping table !
. Go to next slide

20. Rayleigh Damping
our structures while doing a time-history calculations we have the option to use Rayleigh Damping. This method assumes that the damping is proportional to the mass and stiffnes of the structure
If doing a time-step, time history analysis, then RM only requieres the Raleigh coefficients (alfa and beta) to be entered as global parameters (Recal > Dynamics)

21. Single Mass Oscillator
spring constant k
damping constant c x F
mass m
external Force F(t)
amplitude x(t)
EQUILIBRIUM
Anyway what we have to resolve is the same equation of a Single Mass Oscillator
M= mass
X.. = acceleration
c= damping ratio. Characteristics of the structure to dissipate energy
x. = velocity
X = displacement
First term in the equation is the acceleration of mass
Second term is the damping force on the mass related to velocity across the damper
Thrid term is the force on mass and displacement between the mass and the ground.
EQUATION OF MOTION

22. Damping Ratio
c0:
The damping ratio is a system characteristic together with material properties.
Characteristics of the structure to dissipate energy. E.g. Opening and closing microcracks on a concrete structure, stressing non structural elements, and friction at the conection of steel structures.
We can have: not damped, below critic damping, critic damping and above critic damping
In structures and bridges we are normally dealing with below critic damping
Steel 2% ratio
Prestress concrete 2 to 5%
Concrete 4 to 7%` ratio
To characterize the amount of damping in a system a ratio called the damping ratio (also known as damping factor and % critical damping) is used. This damping ratio is just a ratio of the actual damping over the amount of damping required to reach critical damping.

23. Free Vibration Solution: …no damping…and dividing by m… But..
If it is a free vibration…. this the equation for the movement
You might remember from your dynamic classes
Solution:

24. Multi Degree of Freedom System
A multi degree system is represented by the matrix.
The same equation as before, but now it is addressing multiple modes of vibration…in a matrix form
For a software this means computation power and time which are getting cheaper and more accessible
With a very power solver inside RM you don´t need a special computer for complex analysis.

25. Numerical Methods for Dynamic Analysis
Calculation of Eigen frequency
Modal Analysis
Direct Time integration, linear and non-linear
Eigen : calculation of frequencies and vibration modes
Modal analysis is the response spectrum. RM can do any number of modes as the user specified the number of vibration shapes he wants to analysis. It is just a little more of computing time. This analysis is also called….an analysis done in the frequency domain. It evaluates different frequencies. !
Direct Time integration is another name for time-history analysis. This is done in the time domain. Analysis the structure on intervals of time. !
Linear and no linear analysis. Check for structures behaving in the elastic range. Meaning that after the earthquake they come back to the original form. Non linear means the plastic range. Structure gets deformed, dissipating energy, does NOT come back to the original form…get some damage but structure does not collapse.

26. Modal Analysis System of dynamic equations : Free vibration motion:
If damping matrix and applied loads are omitted  evaluation for assumed free vibration motion comes to the second equation in the powerpoint: FREE VIBRATION OF MOTION
This is a Classical Eigenvalue problem.
As we solve the 3rd equation, where K is the stiffness matrix and M is the mass matrix...then the unknown are the wn (frequencies) values as many modes of vibration we are considering. After we solved the wn matrix, we replace the wn values in the second equation . Then we will solve and obtain a new matrix for the phi n values. These are the eigenshapes...or deformations of the structures.
Example:
If we are analyzing a structure for 3 modes of vibration only....then...
K will be a 3x3 matrix
M will be a 3x3 matrix
w is an scalar, single value that represents each vibration frequency
We will obtain 3 values for w...3 frequencies
That will finish the calculation of the 3rd equation of the powerpoint
As we replace the first w value in the 2nd equation, we will get a 3x3 matrix....in which the unknown will be the 3 deflections for the first frequency w. Therefore, 3 equations with 3 unknowns. Then, we can solve the phi values for that. We just got the eigenshape for one mode of vibration
We repeat the procedure for each value of w obtained (remember 3 frequencies...!!)....then 3 eigenshapes.
So we will assemble a matrix of 3x3, where each column represents the phi values obtained per frequency or 3 eigenshapes.
W = is the matrix of eigen values...it contains the N natural frequencies of the system....then with the w matrix solved we can compute the phi matrix of deflections or eigenshapes.
Non trivial solution:

27. Eigen Calculation Eigen values Eigen shapes Unique nature
Differential equations
Eigen calculation is a linear transformation. It is the study of vibrations.
In any Dynamic problem we have a vibration produced by machine, traffic, wind or earthquake
In any case the first step is to investigate the natural frequencies and deformed shapes of our structure
The well known Eigen calculation results in the 
Eigen values, the characteristic root, gives us the natural frequencies of vibration while the
Eigen shapes determine the shapes of these vibrational modes.
Unique nature …"own", "peculiar to", "characteristic", or "individual" — emphasizing how important eigenvalues are to defining the unique nature of a specific transformation
Differential Equations: Solves the equantion of motion. RM calculates the eigen values and finally the eigen modes of the bridge as a basis of calculation for its dynamic analysis. It can analyze any number of modes, as the bridge can vibrate, “move” in a lot of different shapes …as shown in the avi.

28. Eigen Shapes
VIBRATIONAL MODES Eigen shapes Eigen vectors Eigen space Eigen formes
The orthogonality properties of the eigenvectors allows decoupling of the differential equations so that the system can be represented as linear summation of the eigenvectors.
RM can give you graphical and numerical reports of its eigen calculations. !!!!

29. MASS PARTICIPATION FACTORS [%]
MODE phi*M*phi X Y Z SUM-X SUM-Y SUM-Z HERTZ E E E E E E E E E E E E E E E E E E E E E E E E E
In RM we produce a report to check for the mass participation factors in each direction, x, y, z for all modes
Particular modes and the sum until this n number of modes are available for evaluate the results and decide if we need more modes and deeper analysis.
As a good practice we should be requesting different MODEs of vibration until we achieve a mass participation (amount of mass of the structure that contributes in the vibration mode being analyzed) of above 90% of the total mass in the relevant direction.
E.g. Check mode 2 in the report....if we are analyzing the X direction...then we are fine with 90.68% of mass participation). There is no need to request more modes of vibration. !!

30. Response Spectrum Modal Decomposition
AASHTO Seismic Classification and Analysis Requirement
Multi-modal spectral.
According to AASHTO, the modes should be at least 3 times the number of spans in the bridge
The number of degrees of freedom and the number of modes considered in the analysis shall be sufficient to capture at least 90% mass participation in both the longitudinal and transverse directions
Elastic Dynamic Analysis (EDA)

31. Response Spectrum Combination of natural modes One mass oscillator
Oscillating loads
Intensity factor
Single contribution
Synchronization by Stochastic Calculation Rules: ABS,SRSS,CQC, etc
Combination of natural modes represents response of the structure
Each contribution is equivalent to „one mass oscillator” having same frequency. As theory says, it liberates one node, fixes the others and computes the vibration, then it continues to the next node, etc…
Oscillating loads investigated – just small increasing
For each frequency the design standard provides the intensity factor for the maximum deflection
Single Contribution = Factor times eigen oscillation mode
Problem: Single Contributions (Max.Values) are not synchronised. Therefore Superposition due to Stochastic Calculation Rules:
ABS
SRSS
CQC : Complete cuadratic combination. By AASHTO. Art

32. Spectral Response Acceleration
Inside RM we can create a table that will represent the design spectra we are going to use.
AASHTO recomends the creation of the spectra using values like peak acceleration, soil conditions, proximity to eathquake faults, etc. These values are placed in the curve type shown in the powerpoint. Then in RM, we have to tabulate these values and place it into a table….on the Variables part of RM.
And this way we can create a spectrum for our Response Analysis
A RESPONSE SPECTRUM is a diagram describing the relationship between the angular velocity (OMEGA, X axis) and the related ground motion amplitude (y-value). This response spectra is given by the design standards of a particular region, and given in the form of x=period y=acceleration factors.
In the lower picture, it shows the LRFD code guidelines on how to define a response spectra for a particular region.
AASHTO Definition

33. Solution in Frequency Domain
Solution by combining the contributions of the eigenvectors
Superposition of eigenvectors
Loading has lost information about correlation during conversion
Solution has no information on phase differences between the contributions of different eigenvectorsUse Stochastic methodology
Use Stochastic methodology
Response Spectra or multimodal analysis assumes that member forces, moments and displacements due to seismic load can be estimated by combining the repsonses of individual modes using some combination methos like CQC, ABS, etc.... AASHTO recomends CQC
All solutions will end combining the contributions of the eigenvectors in the total result
Difficulties for the superposition of factorised eigenvectors:
The loading has lost information about loading correlation during the mathematical conversion from time-domain to frequency domain. During the calculation it has isolated one deformation of the structure...forgetting the rest.
Solution has no information on phase differences between the contributions of different eigenvectors in total result. As the isolation happens...it does not know the effects it has caused on the other shapes...therefore...they have to be combined using the CQC, ABS, etc...rules.

34. Combination Rules Max/Min results with different rules available:
ABS – Rule (Sum of absolute values)
SRSS – Rule (Square root of sum of sqaures)
DSC – Rule (Newmark/Rosenblueth)
CQC – Rule (Complete quadratic combination)
GENERAL : a lot of other rules exist
To predict Max/Min results different rules are available:
ABS – Rule  (Sum of absolute values)
SRSS – Rule  (Square root of sum of sqaures)
DSC – Rule  (Newmark/Rosenblueth)
CQC – Rule  (Complete quadratic combination)
GENERAL  a lot of other rules exist

35. CQC-RULE
More complex theory, modelling the correlation between different eigenfrequencies
Good results if the duration of the event is 5 times higher than the longest considered period of vibration
AASHTO preferred by art

36. ABS-RULE
Total response computed by adding the absolute values of all individual contributions
Full correlation between the different eigenfrequencies
All maxima are reached at the same time
ABS-rule is suitable for structures where relevant eigenvalues are situated close to each other

37. Individual eigenfrequencies are completely uncorrelated
SRSS-RULE
Individual eigenfrequencies are completely uncorrelated
Eigenfrequencies are added in `Pythagorean` manner
Good results if considered eigenfrequencies are over a wide range
They are not situated too close one to each other

38. DSC-RULE
Correlation between the contributions of individual eigenfrequencies must exist
Different damping for different eigenfrequencies can be taken into account
Additional information specifiying the frequency dependency of damping must be available

39. Earthquake Load Earthquake Load Item specific in RM Bridge
We have special load functions related to earthquake loads
It is a different Load Definition that allows to simply create Response Spectral Analysis just by defining:
Eigen values and respective shapes to be loaded
Spectra to be used
load duration in seconds
direction vectors
damping ratio
….and the type of response spectrum: in term of displacements, velocities or accelerations

40. Response Spectrum in RM Bridge
Click on VIDEO icon

41. Time-History Time Integration
According to AASHTO Seismic Classification and Analysis Requirement
a more rigorous methods of analysis could be required for certain classes of important bridges
which are considered to be critical or essential structures,
and/or for those that are geometrically complex or close to active earthquake faults
Procedure 3, Non-linear Time History Analyses are generally recommended for these bridges
What is behind this time history? A integration in time

42. Time History Direct Time Integration Linear and Non-Linear analysis
Standard event is defined: time-histories of ground acceleration are site specific
Probability of bearable damage
Most accurate method to evaluate structure response under earthquake event.
Direct Time Integration. It still satisfies the equation of motion but it allows us to find the response of the system at every time interval selected. Now the equation of motion is solved taken a look at time….then it is called a solution in the Time Domain.
With this method we can update the stiffness and damping matrix of the system over time (remember that the properties of the material can change since they are sustaining some damage during the earhquake)…

43. What Can Be Non-Linear in RM Bridge?
Structure-stiffness
- Springs
- Connections
- Materials
- Interaction between the substructure and bridge
- Large deformations
- Cables
Mass of structure
- Moving vehicle traffic
Structure-damping
- Raleigh damping effect
- Viscous damping
Load dependent on time
- Change of position, intensity or direction
- Time delay of structural elements
Structure-stiffness: Non linear springs, wrenched connections, non linear material Interaction between substructure and bridge, eccentric loads, large deformation, cables, ...
Mass of Structure: moving vehicle traffic
Structure-damping:Raleigh damping: C =  * M +  * K
Viscous damping
Load dependent on time: Change of Position, Intensity or direction
Time delay of structural elements

44. Comparison MODAL ANALYSIS TIME-HISTORY
Solution of uncoupled differential equations
Each eigenmode as single mass oscillator
Coupled system of differential equations
Time domain approximated
Static starting condition
Analysis of secondary systems: vehicles, equipment, extra bridge features
All Non-Linearities possible
TIME-HISTORY
Response Spectrum. Modal Analysis
solution of uncoupled differential equations
analogy of each eigenmode with single mass oscillator
just linear analysis…Response spectra method does NOT allow the change of the stiffness matrix..therefore Non-linearities are impossible. It is a restriction in the theory not in RM Bridge.
Time History
solves coupled system of differential equations
time domain approximated by a Taylor series
results of static = starting condition
all non linearity's possible

45. Application Example Click on VIDEO icon Element 105 Element 110

46. Bentley RM Bridge Seismic Analysis
Conclusions

47. As you can see with the different methods of calculations presented to you...and day by day new research is being published and applied...the destructive effects of earthquakes can be prevented or at least minimized....for example....see next slide
Kobe, Japan (1995)

48. Akashi-Kaikyo – “Pearl Bridge”
During the Kobe 95 earthquake ….its epicenter was right between this two towers, still under construction, moving them apart by almost a meter…3 feet !!!
The bridge was planned to withstand over two meters longitudinal displacements! Only geometry adjustments were necessary…
The bridge towers contain tuned mass dampers in order to diminish the vibrations in the structure during earthquakes and typhoons.
Bentley RM Bridge can simulate and superimpose in only one envelope all involved phenomena: large deflections, cables, dampers, Computational Fluid Dynamics, Time-history seismic and wind dynamic events.
Akashi-Kaikyo,opened April5th, 1998, the longest main span in the world is locally known as Marcus Bridge.
The Akashi Straits is four miles wide at the bridge site with sea depths of one hundred metres and currents averaging fourteen kmph. The Akashi Straits is one of the busiest sea lanes in the world with over a thousand ships per day travelling through it. Furthermore, the bridge is in a typhoon region in which winds can reach speeds of 290 kmph.

49. RM Bridge Benefits Bentley BrIM vision Bentley portfolio
Intuitive step-by-step calculation
One tool for all: static, modal, time-history
Integrated reports and drawings
Bentley BrIM vision: means interoperability, data-reuse and managing, error reducing
Bentley portfolio: signify you keep using the same tool, we try to keep the learning at a minimum level, specific tool for the jobs
Intuitive step-by-step calculation: one line, one data, simple commands. User has full control of the calculations
One tool for all: RM Bridge is Finite Element specific solution for all bridge problems: from analysis, thru design with construction, fabrication, erection control and verification
Integrated reports: code checking and further connection for detailing

50. Bentley RM Bridge Seismic Design and Analysis
Questions
Who has the first question?
How much time to learn using the software advanced capabities?
Let´s start NOW, don´t wait to learn when you have a HUGE project in your hands.
How many times have you simplified your seismic analysis?
How many times have you ignored any seismic event possibility?
Is it a problem of having the right tool to do it?
What if you could do it with the same tool that is integrated with all others software solutions in your company job workflow?

51. Thank you for your attention!
You know how Bentley BrIM, the Bridge Information Modeling Group has the tools to help your company to work even better, easier and faster.
Shall we begun?
Thank you very much for your time and attention!
Thank you for your attention! 1