4 ce elec2 earthquake dynamic lateral force procedure

CE ELEC2 EARTHQUAKE ENGINEERING

MARK ELSON C. LUCIO, MSCE (Structures)Association of Structural Engineers of the Philippines (ASEP)

Philippine Institute of Civil Engineers (PICE)American Society of Civil Engineers (ASCE)

American Concrete Institute (ACI)

EARTHQUAKE Dynamic Lateral Force Procedure

• Structural damage during an earthquake is caused by the response of the structure to the ground motion input at its base.• The dynamic forces produced in the structure are due to the inertia of its vibrating elements.• The magnitude of the effective peak acceleration reached by the ground vibration directly affects the magnitude of the dynamic forces observed in the structure.


Accelerograph-An instrument that records the acceleration of the ground during an

earthquake, also commonly called an accelerometer


Accelerogram- graphical output of an accelerograph

Peak Ground Acceleration (PGA)


• The response of the structure exceeds the ground motion and the dynamic magnification depends on the following:

a. Ground vibrationb. Soil properties at the sitec. Distance from the epicenterd. Dynamic characteristics of the structure


Response SpectraA response spectrum is simply a plot of the peak or steady-state response(displacement, velocity or acceleration) of a series of oscillators ofvarying natural frequency, that are forced into motion by the samebase vibration. The resulting plot can then be used to pick off the response ofany linear system, given its natural frequency of oscillation.


Response Spectra – NSCP 2010

So TT 2.0=

EARTHQUAKE Structural Dynamics

Dynamic ModelA dynamic model of the structure consists of a single column with stiffness ksupporting a mass of magnitude m to give the inverted pendulum, or lollipopstructure shown.If the mass is subjected to an initial displacement and released, with noexternal forces acting, free vibration occur about the static position.


Undamped Free Vibration• Oscillations continue forever and the idealized structure will never come torest• The same maximum displacement occurs oscillations after oscillations• Intuition suggests that this is unrealistic.


Damped Free Vibration• The process by which vibration steadily diminishes in amplitude is calleddamping.• In damping, the energy of the vibrating system is dissipated by variousmechanisms.• In a vibrating building these includes friction at steel connections, openingand closing of microcracks in concrete, friction between the structure itselfand nonstructural elements such as partition walls.


Dampers


Equation of Motion : External Force• The external force applied on the structure is resisted by the inertia force,elastic force, and damping force.

Where: - the velocity or the first derivative of dispalcement u- the acceleration or the second derivative of dispalcement u


Equation of Motion : Earthquake Excitation• The relative displacement or deformation of the structure due to groundacceleration will be identical to the displacement of the structure if its basewas stationary and was subjected to an external force.

Where: - ground acceleration


Equation of Motion : Undamped Free Vibration• The equation of motion for systems without damping

The solution to the homogeneous differential equation is

Natural circular frequency of vibration = in radians/sec


Equation of Motion : Undamped Free Vibration

The time required for the undamped system to complete one cycle of free vibration is the natural period of vibration of the system, which we denote as Tn , in units of seconds. It is related to ωn whose unit is in radians per second.

The natural cyclic frequency of vibration is 1/Tn

The units of fn are hertz (Hz) [cycles per second (cps)]; fn is related to ωn


Example: Determine the natural period of vibration and the natural cyclic frequency for the industrial building shown.

Total Weight, W = 187.5 kips

North-South (Moment Frames) Stiffness:k = 231.6 kips/in.

East-West (Braced Frames) Stiffness:k = 358.7 kips/in.


Solution:

rad/sec 8.21485.0

1.236===

mk

nω

North-South Direction:

inkipsin

kipsg

Wm

/sec485.0 sec/4.386

5.187

2

2

−=

==

.sec287.08.21

22===

πωπ

nnT

HzT

fn

48.31==


Solution:

rad/sec 2.27485.0

7.358===

mk

nω

East-West Direction:

.sec23.02.27

22===

πωπ

nnT

HzT

fn

3.41==


Modal Analysis

• A technique used to determine a structure’s vibration characteristics:Natural frequenciesMode shapesMode participation factors (how much a given mode participates in a given direction)

• Gives engineers an idea of how the design will respond to different types of dynamic loads.


Mode Shape

• A mode shape is a specific pattern of vibration executed by a structuralsystem at a specific frequency.• Different mode shapes will be associated with different frequencies. Theexperimental technique of modal analysis discovers these mode shapes andthe frequencies.


Modal AnalysisGeneral equation of motion:

Assume free vibrations and ignore damping:

Assume harmonic motion:

The roots of this equation are ωi2, the eigenvalues, where i ranges from 1 to

number of DOF. Corresponding vectors are {φ}i, the eigenvectors. The eigenvectors {φ}i represent the mode shapes - the shape assumed by the structure when vibrating at frequency fi.

[ ]{ } [ ]{ } [ ]{ } ( ){ }tFuKuCuM =++

[ ]{ } [ ]{ } { }0uKuM =+

[ ] [ ]( ){ } { }0uMK 2 =ω−


Mode Shape – 3D

Mode 1: T = 1.82s• Translational


Mode Shape -3D

Mode 2: T = 1.59s• Translational


Mode Shape - 3D

Mode 3: T = 1.08s• Torsional


Mode Shape - 3D

Mode 1: T = 1.82s Mode 4: T = 0.48s


Mode Shape - 3D

Mode 2: T = 1.59s Mode 5: T = 0.34s


Mode Shape - 3D

Mode 3: T = 1.08s Mode 6: T = 0.25s


Modal Analysis

• Usually the lower modes are significant.


Modal Analysis


Modal Analysis

• Results from each mode are combined statistically using methods such as

SRSS – Square Root of the Sum of SquaresCQC - Complete Quadratic Combination


Scaling of Results

staticdynamic VV 90.0≥




Scaling of Results


Example: Determine the base shear from modal analysis of the seven storey building.

Spectral Acceleration from Response Spectrum:


Solution:


Static vs. Dynamic

• Static analysis are used for regular and irregular structures with height less than 20m.

• The base shear may be equal but the distribution of storey forces will vary.

• The structural response from dynamic analysis is from the combination of response from several modes. In static analysis, only the fundamental mode is used.

• Dynamic analysis, being the more general approach, can be used for all types of structures.

Thank You!

4 ce elec2 earthquake dynamic lateral force procedure

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