Earthquake Engineering Lecture Notes PDF

BICOL UNIVERSITY COLLEGE OF ENGINEERING LEGAZPI CITY CE 413 EARTHQUAKE ENGINEERING LESSON 4 – 5: DYNAMICS OF VIBRATION, ATTE...

BICOL UNIVERSITY COLLEGE OF ENGINEERING LEGAZPI CITY CE 413 EARTHQUAKE ENGINEERING LESSON 4 – 5: DYNAMICS OF VIBRATION, ATTENUATION & TIME HISTORY PART 1 “This presentation is not for distribution outside this subject and to be used solely for this course subject – CE 413.” PREPARED BY: ANNA G. BILARO, MSCE Faculty ANNA G. BILARO, MSCE FACULTY CE 413 – EARTHQUAKE ENGINEERING Slide No. 1 OBJECTIVES: After the discussion in this chapter, the student will be able to: 1. Learn and describe the effects of earthquakes. 2. Describe the earthquake characteristics, basic site characteristics and structural characteristics. 3. Review the topics about dynamics in relation to earthquake engineering. 4. Explain the dynamics of vibration/ ground motion and attenuation. 5. Introduction about structural dynamics. ANNA G. BILARO, MSCE FACULTY CE 413 – EARTHQUAKE ENGINEERING Slide No. 2 INTRODUCTION: Seismic waves arise from sudden movements in a rupture zone in the Earth’s crust. Waves of different types and velocities travel different paths before reaching a building’s site, where the local ground is subjected to various motions. The ground moves rapidly back and forth in all directions. The upper part of the building remains in delay in respect to the foundation moving, due to its mass. This causes strong vibrations of the structure with Source, waves and building resonance phenomena between the structure and the ground and hence large inertial force arise. Gioncu, Victor and Mazzolani, Federico M. 2011. Earthquake Engineering for Structural Design. Spon Press, imprint of Taylor and Francis. ANNA G. BILARO, MSCE FACULTY CE 413 – EARTHQUAKE ENGINEERING Slide No. 3  Building's weight: Due to its weight, the soil is overloaded, becoming stiffer, hence producing change in its behavior. For stiff soils, the weight effect is to reduce the acceleration peak. But for soft soils, possible to observe a relative increasing in acceleration peaks due to the presence of a building. Soil effect: Part of the vibrating energy of buildings is released into soil through waves produced Influence of building’s weight by buildings. Gioncu, Victor and Mazzolani, Federico M. 2011. Earthquake Engineering for Structural Design. Spon Press, imprint of Taylor and Francis. ANNA G. BILARO, MSCE FACULTY CE 413 – EARTHQUAKE ENGINEERING Slide No. 4  Effect of earthquakes on structures Engineers must understand the behaviors of structures when subjected to various loads, including seismic loads. The severity of shaking is controlled primarily by two (2) factors: a. Attenuation of ground motion. b. Earthquake characteristics Estrada, Hector and See, Luke S. 2017. Introduction to Earthquake Engineering. CRC Press, Taylor and Francis Group, Florida. ANNA G. BILARO, MSCE FACULTY CE 413 – EARTHQUAKE ENGINEERING Slide No. 5  Effect of earthquakes on structures a. Attenuation of ground motion → The dissipation of seismic energy as seismic waves move through layers of varying soil and rock strata. → Characterized as the decrease in amplitude of the seismic waves with distance from source. It results from geometric spreading of propagating waves, energy absorption and scattering of waves. → Attenuation of ground motion through rock over a large distance can be significant. Estrada, Hector and See, Luke S. 2017. Introduction to Earthquake Engineering. CRC Press, Taylor and Francis Group, Florida. ANNA G. BILARO, MSCE FACULTY CE 413 – EARTHQUAKE ENGINEERING Slide No. 6  Effect of earthquakes on structures b. Earthquake characteristics During earthquake, different structures will behave differently. Seismic waves can be modified by site characteristics, earthquake characteristics and structural performance. Estrada, Hector and See, Luke S. 2017. Introduction to Earthquake Engineering. CRC Press, Taylor and Francis Group, Florida. ANNA G. BILARO, MSCE FACULTY CE 413 – EARTHQUAKE ENGINEERING Slide No. 7  Earthquake characteristics Other important earthquake measurement parameters are the measured ground motions at the ground surface. These are: Peak Ground Acceleration (PGA) Peak Ground Velocity (PGV) Peak Ground Displacement (PGD) PGA has become the most popular parameter to denote the measure of an earthquake and has been related to the magnitude through several empirical relationship. Estrada, Hector and See, Luke S. 2017. Introduction to Earthquake Engineering. CRC Press, Taylor and Francis Group, Florida. ANNA G. BILARO, MSCE FACULTY CE 413 – EARTHQUAKE ENGINEERING Slide No. 8  Typical processed record for strong motion. The velocity was produced by integrating the acceleration. The displacement was produced by integrating the velocity. Estrada, Hector and See, Luke S. 2017. Introduction to Earthquake Engineering. CRC Press, Taylor and Francis Group, Florida. ANNA G. BILARO, MSCE FACULTY CE 413 – EARTHQUAKE ENGINEERING Slide No. 9  Ground Motion Parameters Ground motion parameters are essential for describing the important characteristics of strong ground motion in compact, quantitative form. Amplitude Parameters: The most common way of describing a ground motion is with time history. The motion parameter may be acceleration, velocity or displacement. Estrada, Hector and See, Luke S. 2017. Introduction to Earthquake Engineering. CRC Press, Taylor and Francis Group, Florida. ANNA G. BILARO, MSCE FACULTY CE 413 – EARTHQUAKE ENGINEERING Slide No. 10  Earthquake characteristics The PGA at a site depends not only on the magnitude and epicentral distance of the earthquake, but also on the regional geological characteristics. Therefore, the empirical constants are derived from the measured earthquake data in the region. As the PGA value decreases with the epicentral distance, these empirical relationships are also called attenuation laws. Although the primary factor controlling an earthquake’s effect on structural behavior at a site is the PGA, the largest PGA earthquakes do not always cause the most damage from shaking. Shaking depends on duration and frequency content, and to factors such as length of fault rupture, focal depth, orientation of the fault, speed of rupture. Estrada, Hector and See, Luke S. 2017. Introduction to Earthquake Engineering. CRC Press, Taylor and Francis Group, Florida. ANNA G. BILARO, MSCE FACULTY CE 413 – EARTHQUAKE ENGINEERING Slide No. 11  Large PGA earthquakes do not always create the most damage. In fact, a large PGA earthquake would produce little damage to some structures if it only occurs for a short time, whereas a relatively small earthquake that continues for several seconds can be devastating to some structures. Estrada, Hector and See, Luke S. 2017. Introduction to Earthquake Engineering. CRC Press, Taylor and Francis Group, Florida. ANNA G. BILARO, MSCE FACULTY CE 413 – EARTHQUAKE ENGINEERING Slide No. 12  Site characteristics The strength of shaking diminishes as waves travel away from the focus because of attenuation. This results in smaller shaking for sites at greater distances from the epicenter. Shaking can be strengthen depending on the geologic conditions along the path of the wave between the focus and the site, same as the soil conditions and topography. Soil condition and topography greatly affect the characteristics of the input motion in terms of the amplitude and natural period of the shaking at site. The inherent stiffness of the ground beneath a site is a function of its shear-wave velocity and thickness of the sediment above the bedrock. Shear wave velocity is faster for hard rock than for soft soil; seismic waves travel faster through hard rock than soft soil. So when seismic waves pass from rock into soil, they slow down. This slower speed must be accompanied by an increase in wave amplitude (amplifying the ground shaking). Estrada, Hector and See, Luke S. 2017. Introduction to Earthquake Engineering. CRC Press, Taylor and Francis Group, Florida. ANNA G. BILARO, MSCE FACULTY CE 413 – EARTHQUAKE ENGINEERING Slide No. 13  Local site characteristics greatly influence the seismic wave frequency and amplitude. Six ground types based on shear-wave velocity to establish amplification effects for design purposes: 1. Type A – hard rock (igneous rock) 2. Type B – rock (volcanic rock) 3. Type C – very dense soil and soft rock (sandstone) 4. Type D – stiff soil (mud) 5. Type E – soft soil (artificial fill) 6. Type F –soils requiring site-specific evaluations Type A has the largest stiffness and generates the smallest amplifications, while Type E is the softest and generates the largest amplifications. Estrada, Hector and See, Luke S. 2017. Introduction to Earthquake Engineering. CRC Press, Taylor and Francis Group, Florida. ANNA G. BILARO, MSCE FACULTY CE 413 – EARTHQUAKE ENGINEERING Slide No. 14  NSCP 2015 Soil Profile Types (Table 208-2). National Structural Code of the Philippines. 2015. page 2-186 (Chapter 2 – Minimum Design Loads). ANNA G. BILARO, MSCE FACULTY CE 413 – EARTHQUAKE ENGINEERING Slide No. 15  National Structural Code of the Philippines. 2015. page 2-186 (Chapter 2 – Minimum Design Loads). NSCP 2015 Soil Profile Types (Table 208-2). ANNA G. BILARO, MSCE FACULTY CE 413 – EARTHQUAKE ENGINEERING Slide No. 16  NSCP 2015 Seismic Zone Factor Z (Table 208-3). National Structural Code of the Philippines. 2015. page 2-186 (Chapter 2 – Minimum Design Loads). ANNA G. BILARO, MSCE FACULTY CE 413 – EARTHQUAKE ENGINEERING Slide No. 17  Structural characteristics Once seismic waves have been modified for ground conditions at the site of structure, the structure responds to ground excitation based on its inherent characteristics, as well as the age of the structure and the quality of its construction. The characteristics of a structure that have the largest influence on its response include weight and stiffness. Damping can play a significant role when structures remain within the elastic limit, but remains a much smaller effect for structures that deform into inelastic behavior. Although these characteristics affect the displacement amplitude and natural period of a structure, stiffness has the greatest effect on structural response. The age and construction of structures play a major role in their performance during an earthquake. Older and/ or poorly constructed structures are at a greater risk of failure during an earthquake because of inadequate ductility, which is the ability of a structure to absorb the seismic energy. Estrada, Hector and See, Luke S. 2017. Introduction to Earthquake Engineering. CRC Press, Taylor and Francis Group, Florida. ANNA G. BILARO, MSCE FACULTY CE 413 – EARTHQUAKE ENGINEERING Slide No. 18  REVIEW: Mechanics – branch of physics subdivided into statics. Static refers to the fact that the state of the system and the applied forces do not vary in time; they are time- independent. Chen, W.F. and Scawthorn, C.. 2003. Earthquake Engineering Handbook. CRC Press LLC. ANNA G. BILARO, MSCE FACULTY CE 413 – EARTHQUAKE ENGINEERING Slide No. 19  Dynamics is the study of systems subject to time-varying applied forces. As a consequence of the time variability of the applied forces, the system’s internal forces and its state (displacement/ deformation) also vary Time varying with time – the system’s response motion. The inclusion of inertia effects associated with mass in motion is another key distinction of dynamic problems. Chen, W.F. and Scawthorn, C.. 2003. Earthquake Engineering Handbook. CRC Press LLC. Structural response (u, F, ) ANNA G. BILARO, MSCE FACULTY CE 413 – EARTHQUAKE ENGINEERING Slide No. 20  Structural response: → structural analysis of static loading will be extended to deal with dynamic loading. Basic difference between static and dynamic loads: (a) static loading; (b) dynamic loading. Clough, R and Penzien, J. 2003. Dynamics of Structures, 3rd Ed. Berkeley, USA.. ANNA G. BILARO, MSCE FACULTY CE 413 – EARTHQUAKE ENGINEERING Slide No. 21  Approaches to Structural response: Solutions can be: a) deterministic (prescribed dynamic loading, time variation of loading is known wherein the output provides displacement time history) or b) non-deterministic (random dynamic loading, uses statistical approach and provide statistical solution for displacement). Chen, W.F. and Scawthorn, C.. 2003. Earthquake Engineering Handbook. CRC Press LLC. ANNA G. BILARO, MSCE FACULTY CE 413 – EARTHQUAKE ENGINEERING Slide No. 22 Dynamic Loadings: Jimenez, Guillermo Alfonso Lopez. 2016. Static and Dynamic Behavior of Pile Supported Structures in Soft Soils. Universite Grenoble Alpes. Characteristics and sources of typical dynamic loadings: a) Harmonic load, b) Complex periodic load, c) Transient load, and d) Earthquake load ANNA G. BILARO, MSCE FACULTY CE 413 – EARTHQUAKE ENGINEERING Slide No. 23 Dynamic solution: → Varies with time. a. time consuming and complex. b. solution is needed at each time step. → Inertia forces a. Static condition – equilibrium condition is due to external force only (a = 0) b. Dynamic condition – equilibrium condition is due to external and inertial forces (a ≠ 0). Note: Recall about the topics on the Newton’s Law of Motion. Jimenez, Guillermo Alfonso Lopez. 2016. Static and Dynamic Behavior of Pile Supported Structures in Soft Soils. Universite Grenoble Alpes. ANNA G. BILARO, MSCE FACULTY CE 413 – EARTHQUAKE ENGINEERING Slide No. 24  Structural dynamics – considered as the study of a body or structure in dynamic equilibrium and the mathematical expression of this equilibrium is the equation of motion. The equation of motion expresses the equilibrium of internal and external force terms and the mass inertia and damping effects. The inertia term involves the second derivative and the damping term the first derivative of the displacement with respect to time. The equation of motion is a second-order differential equation with constant coefficients. Chen, W.F. and Scawthorn, C.. 2003. Earthquake Engineering Handbook. CRC Press LLC. ANNA G. BILARO, MSCE FACULTY CE 413 – EARTHQUAKE ENGINEERING Slide No. 25  Theory of Vibration Essential Characteristics of a vibrating system: All bodies possessing inertia (mass) and elasticity (degree of stiffness) are capable of vibration. A time – dependent displacement of a particle or a system with respect to its equilibrium position. CE226 Lectures of Prof. Ignacio. Institute of Civil Engineering , University of the Philippines, Diliman, Quezon City ANNA G. BILARO, MSCE FACULTY CE 413 – EARTHQUAKE ENGINEERING Slide No. 26  Theory of Vibration Types of Vibration Free Vibration – a system put out of its equilibrium position and vibrates a. Free, undamped vibration under the action of forces inherent in b. Free, damped vibration the system, and in the absence of external forces, is under free c. Forced, undamped vibration vibration. d. Forced, damped vibration Forced Vibration – a vibration that takes place under the action of external forces. CE226 Lectures of Prof. Ignacio. Institute of Civil Engineering , University of the Philippines, Diliman, Quezon City ANNA G. BILARO, MSCE FACULTY CE 413 – EARTHQUAKE ENGINEERING Slide No. 27  BASIC DEFINITIONS Examples of Single Degree of Degree of Freedom Freedom Systems (SDOF) (DOF) – the number of degree of freedom is equal to the number of independent coordinates necessary to describe the motion of a system. CE226 Lectures of Prof. Ignacio. Institute of Civil Engineering , University of the Philippines, Diliman, Quezon City ANNA G. BILARO, MSCE FACULTY CE 413 – EARTHQUAKE ENGINEERING Slide No. 28  Examples of Multiple Degree of Freedom Systems (SDOF) CE226 Lectures of Prof. Ignacio. Institute of Civil Engineering , University of the Philippines, Diliman, Quezon City ANNA G. BILARO, MSCE FACULTY CE 413 – EARTHQUAKE ENGINEERING Slide No. 29  Examples of Multiple Degree of Freedom Systems (MDOF) ◦ 3 DOF – 3 masses are fully concentrated and are constrained so that the corresponding mass points translate only in vertical direction. ◦ 6 DOF – if the 3 masses are not fully concentrated and they possess finite rotational inertia, the rotational displacements of the 3 Idealization of the simple beam. points will be considered. ◦ 9 DOF – if axial distortions of the beam are significant and will result to translation displacement parallel with the beam axis. ◦ 18 DOF – if the structure’s mas deforms in 3D space. Clough, R and Penzien, J. 2003. Dynamics of Structures, 3rd Ed. Berkeley, USA. ANNA G. BILARO, MSCE FACULTY CE 413 – EARTHQUAKE ENGINEERING Slide No. 30  Period (Tn) →Or the natural period of vibration in units of seconds. →The time required for the system to complete one cycle of the vibration. Free vibration response. Frequency (fn) Circular (Angular) Frequency (n) →Or the natural cyclic of vibration in units of hertz (Hz) →Or the natural circular frequency of vibration in units of radians per second. →The number of cycles per unit time (cycles per second) Clough, R and Penzien, J. 2003. Dynamics of Structures, 3rd Ed. Berkeley, USA. ANNA G. BILARO, MSCE FACULTY CE 413 – EARTHQUAKE ENGINEERING Slide No. 31 Reference 1. Association of Structural Engineers of the Philippines, Inc. (ASEP). (2015). National Structural Code of the Philippines Volume I: Buildings, Towers and Other Vertical Structures (NSCP C101-15). 7th Edition. 2. American Concrete Institute (ACI). (2019). Building Code Requirements for Structural Concrete (ACI 318-19). 3. McCormac, J., & Brown, R., (2016). Design of Reinforced Concrete. Wiley 10th Edition. 4. Darwin, D., Dolan, C., & Nilson, A., (2016). Design of Concrete Structures. McGraw Hill 15th Edition. 5. Wang, C., Salmon, C., & Pincheira, J. Reinforced Concrete Design. 7th Edition. 6. Pictures in google. ANNA G. BILARO, MSCE FACULTY CE 413 – EARTHQUAKE ENGINEERING Slide No. 32  THANK YOU FOR LISTENING! ANNA G. BILARO, MSCE FACULTY CE 413 – EARTHQUAKE ENGINEERING Slide No. 33