Earthquake Engineering Chapter 4-6 PDF

CHAPTER 4 RAPID VISUAL SCREENING (STRUCTURAL AND NON- STRUCTURAL COMPONENTS OF A BUILDING) Y Rapid Visual Screening (RVS) of Buildings...

CHAPTER 4 RAPID VISUAL SCREENING (STRUCTURAL AND NON- STRUCTURAL COMPONENTS OF A BUILDING) Y Rapid Visual Screening (RVS) of Buildings P Rapid Visual Screening (RVS) is a preliminary method used to quickly assess the potential seismic vulnerability of buildings. This method involves a visual inspection of the structural and non-structural components of a building to identify features that may contribute O to or mitigate damage during an earthquake. The primary goal of RVS is to prioritize buildings for further, more detailed seismic evaluations, particularly in regions with high seismic activity. C RVS is often conducted by trained personnel who use standardized forms and checklists to evaluate buildings based on specific criteria. The process is designed to be quick, typically taking less than an hour per building, and does not require detailed structural analysis. T N Structural Components E Structural components are the elements of a building that bear loads and are integral to the building’s overall stability. In the context of RVS, the following structural components are commonly assessed: D 1. Building Material and Type: U ◦ Reinforced Concrete: Buildings constructed with reinforced concrete are evaluated for the presence of proper T reinforcement, concrete quality, and construction methods. Poor construction practices can lead to vulnerabilities. S ◦ Steel Frame: Steel-framed buildings are assessed for the condition of connections, potential corrosion, and whether the frame is adequately braced. ◦ Masonry: Unreinforced masonry buildings are particularly vulnerable to seismic activity. The RVS process identifies if the masonry is unreinforced or poorly bonded. 2. Height and Number of Stories: ◦ Taller buildings or those with many stories are more likely to experience severe shaking and require more detailed analysis. Low-rise buildings (1-3 stories) are generally less vulnerable, but exceptions exist depending on the construction quality. CE 116-EARTHQUAKE ENGINEERING PANGASINAN STATE UNIVERSITY RIZALYN C. ILUMIN, MSME, MSCE URDANETA CAMPUS (1st Sem, AY 2024-2025) Instructor Page 1 of 22  ◦ Older buildings might not adhere to modern seismic codes and are often more vulnerable. Buildings constructed before the implementation of stringent seismic design standards are flagged during RVS. 4. Configuration: ◦ The overall shape and design of the building are evaluated. Buildings with irregular shapes, soft stories (e.g., ground floors with fewer walls or columns), or large openings are considered more vulnerable. 5. Foundation: ◦ The type and condition of the building’s foundation are reviewed. Buildings on poor soil conditions or slopes may be more at risk. Y P Non-Structural Components O Non-structural components are elements of a building that do not carry significant loads but can still pose hazards during an earthquake. These include: C 1. Exterior Cladding and Facades: T ◦ Loose or poorly attached exterior elements can fall during an earthquake, posing significant risks to people and property. N 2. Interior Partitions: E ◦ Interior walls that are not properly braced or connected to the structural frame can collapse, especially in older buildings. D 3. Mechanical, Electrical, and Plumbing (MEP) Systems: U ◦ Equipment and systems like HVAC units, water heaters, and electrical panels should be securely anchored to prevent tipping or falling. T S 4. Ceilings and Lighting Fixtures: ◦ Suspended ceilings, light fixtures, and other overhead elements need proper bracing to avoid collapse during shaking. 5. Contents and Furnishings: ◦ Items such as bookshelves, cabinets, and heavy furniture can become dangerous projectiles if not anchored properly. FEMA P-154: Rapid Visual Screening of Buildings for Potential Seismic Hazards CE 116-EARTHQUAKE ENGINEERING PANGASINAN STATE UNIVERSITY RIZALYN C. ILUMIN, MSME, MSCE URDANETA CAMPUS (1st Sem, AY 2024-2025) Instructor Page 2 of 22 Key Features of FEMA P-154: 1. Screening Forms: ◦ FEMA P-154 includes standardized screening forms that assess both structural and non-structural components. These forms guide the evaluator through a series of observations and checkboxes, helping to identify features that may increase a building's seismic risk. 2. Scoring System: Y ◦ The method uses a scoring system to assign a seismic risk score to each building. This score helps prioritize buildings for further evaluation or retrofitting. P Photographic Examples: O 3. ◦ C The guide includes numerous photographic examples of different building types and vulnerabilities to help evaluators make accurate assessments. T 4. Application to Various Building Types: N ◦ FEMA P-154 is applicable to a wide range of buildings, including residential, commercial, and institutional structures. The guidelines are designed to be flexible enough to be used across different regions and building codes. E Examples Applicable in the Philippines D 1. Schools: U ◦ Scenario: A public elementary school building in Manila built in the 1970s, made of reinforced concrete but with minimal T seismic detailing. S ◦ RVS Findings: The school may be at risk due to inadequate reinforcement, potential soft stories (ground floor with large open spaces), and aging concrete. Non-structural hazards could include unanchored classroom cabinets and ceiling fans. ◦ Action: Prioritize this school for a detailed seismic evaluation and consider retrofitting, such as adding shear walls and bracing non-structural elements. 2. Residential Houses: ◦ Scenario: A two-story unreinforced masonry house in Baguio City, built on a sloping site. ◦ RVS Findings: High seismic risk due to unreinforced masonry, potential slope instability, and lack of proper bracing in the upper story. Non-structural risks include unanchored water tanks on the roof. CE 116-EARTHQUAKE ENGINEERING PANGASINAN STATE UNIVERSITY RIZALYN C. ILUMIN, MSME, MSCE URDANETA CAMPUS (1st Sem, AY 2024-2025) Instructor Page 3 of 22  3. Commercial Buildings: ◦ Scenario: A three-story commercial building in Cebu City with a large glass facade and unreinforced interior partitions. ◦ RVS Findings: The large glass facade could shatter during an earthquake, posing a risk to occupants. The unreinforced interior partitions may collapse, leading to internal damage and injuries. ◦ Action: Suggest upgrading the glass to laminated or reinforced glass, bracing interior partitions, and securing heavy equipment and furnishings. These examples and guidelines demonstrate how RVS and FEMA P-154 can be applied to assess the seismic vulnerability of buildings Y in the Philippines, particularly in schools, houses, and commercial buildings, ensuring better preparedness for earthquakes. P References: O Federal Emergency Management Agency. (2015). FEMA P-154: Rapid Visual Screening of Buildings for Potential Seismic C Hazards: A Handbook. 3rd Edition. https://www.fema.gov/sites/default/files/2020-07/fema_p-154.pdf Department of Public Works and Highways (DPWH). (2010). National Structural Code of the Philippines Vol. 1. 6th Edition. T DPWH. N Philippine Institute of Volcanology and Seismology. (2018). Earthquake preparedness guide. https://www.phivolcs.dost.gov.ph/ index.php/earthquake/earthquake-preparedness E D U T S CE 116-EARTHQUAKE ENGINEERING PANGASINAN STATE UNIVERSITY RIZALYN C. ILUMIN, MSME, MSCE URDANETA CAMPUS (1st Sem, AY 2024-2025) Instructor Page 4 of 22  DYNAMICS OF VIBRATION; ATTENUATION Vibration in Earthquake Engineering Vibration in Earthquake Engineering refers to the oscillatory motion of structures and the ground during seismic events. Earthquakes generate seismic waves that propagate through the Earth's crust, causing ground motion. These ground motions induce vibrations in buildings, bridges, dams, and other structures, leading to potential damage or even collapse if the structures are not designed to Y withstand such forces. P Key Concepts in Earthquake-Induced Vibrations 1. O Seismic Waves: Earthquakes generate different types of seismic waves, including P-waves (primary waves), S-waves (secondary waves), and surface waves. These waves cause the ground and structures to vibrate in various ways. C 2. Natural Frequency: Every structure has a natural frequency, which is the frequency at which it naturally tends to vibrate. If the T frequency of the ground motion matches the structure's natural frequency, resonance occurs, amplifying the vibrations and potentially causing severe damage. N E 3. Damping: Damping is the process of energy dissipation in a vibrating structure. In earthquake engineering, designing structures with adequate damping helps reduce the amplitude of vibrations and prevent catastrophic failures. D U 4. Mode Shapes: Structures can vibrate in different patterns, known as mode shapes, depending on the frequency and characteristics of the seismic waves. Understanding these mode shapes is crucial for predicting how a structure will behave T during an earthquake. S Real-Life Examples 1. Mexico City Earthquake (1985): Mexico City is built on a former lakebed with soft, water-saturated soils. During the 1985 earthquake, the natural frequency of the ground matched the frequency of the seismic waves, leading to resonance. This caused severe amplification of vibrations, resulting in the collapse of many buildings, especially those between 6 and 15 stories tall, which had similar natural frequencies to the ground motion. 2. Kobe Earthquake (1995): The Kobe Earthquake in Japan highlighted the importance of understanding the dynamic response of structures. Many older buildings and bridges that lacked adequate seismic design experienced significant damage due to the intense vibrations caused by the earthquake. The Akashi Kaikyō Bridge, a modern structure with advanced seismic design, survived the earthquake without significant damage, demonstrating the effectiveness of proper engineering. 3. Northridge Earthquake (1994): In Los Angeles, the Northridge Earthquake caused significant ground shaking that led to the collapse of several freeway overpasses. The failure was partly due to inadequate design considerations for the high-frequency CE 116-EARTHQUAKE ENGINEERING PANGASINAN STATE UNIVERSITY RIZALYN C. ILUMIN, MSME, MSCE URDANETA CAMPUS (1st Sem, AY 2024-2025) Instructor Page 5 of 22 Teaching Implications Using these real-life examples, students can understand the importance of considering vibrations in earthquake engineering. By analyzing how different structures responded to past earthquakes, students can learn about the critical factors that influence a structure's ability to withstand seismic forces, such as natural frequency, damping, and resonance. References Bozorgnia, Y., & Bertero, V. V. (2004). Earthquake Engineering: From Engineering Seismology to Performance-Based Engineering. CRC Press. Y Chopra, A. K. (2020). Dynamics of Structures: Theory and Applications to Earthquake Engineering (5th ed.). Pearson. P Kanamori, H., & Brodsky, E. E. (2004). The physics of earthquakes. Reports on Progress in Physics, 67(8), 1429-1496. https:// doi.org/10.1088/0034-4885/67/8/R03 O Naeim, F. (Ed.). (2001). The Seismic Design Handbook. Springer Science & Business Media. C These references provide further reading and detailed discussions on the topic of vibrations in earthquake engineering. T Dynamics of Vibration N Vibration refers to the oscillatory motion of a mechanical system about an equilibrium position. This can occur in various forms, E including translational, rotational, or complex motion. Vibrations are typically characterized by the following: D 1. Amplitude: The maximum displacement from the equilibrium position. U 2. Frequency: The number of oscillations per unit time, typically measured in Hertz (Hz). T 3. Period: The time taken for one complete cycle of vibration. S 4. Phase: The relative position of the waveform at the start of the vibration. Attenuation in Vibrations Attenuation refers to the gradual reduction in the amplitude of a vibration as it propagates through a medium. This decrease in amplitude can be caused by several factors: 1. Material Damping: The inherent property of materials to dissipate vibrational energy as heat. 2. External Damping: Energy dissipation due to friction, air resistance, or other external forces acting on the system. 3. Geometric Spreading: The decrease in amplitude as the vibration spreads over a larger area. Attenuation is crucial in designing structures to ensure they do not experience excessive vibrations, which could lead to fatigue or failure. CE 116-EARTHQUAKE ENGINEERING PANGASINAN STATE UNIVERSITY RIZALYN C. ILUMIN, MSME, MSCE URDANETA CAMPUS (1st Sem, AY 2024-2025) Instructor Page 6 of 22  Here is the updated illustration of a Y mass-spring system representing free vibrations of undamped systems. The P image clearly shows the key components and the sinusoidal motion O curve, providing a modern and scientific representation. C T N E D U T S Free vibrations occur when a system oscillates without any external force acting on it after being initially disturbed. In an undamped system, there is no energy loss over time, meaning the system continues to oscillate indefinitely with a constant amplitude. CE 116-EARTHQUAKE ENGINEERING PANGASINAN STATE UNIVERSITY RIZALYN C. ILUMIN, MSME, MSCE URDANETA CAMPUS (1st Sem, AY 2024-2025) Instructor Page 7 of 22  Mass-Spring System: The simplest example of a free vibration system is a mass attached to a spring. When the mass is displaced from its equilibrium position and then released, it oscillates back and forth around this position. Y P O C T N 7. Real-World Applications E D Seismology: Understanding the natural frequencies of buildings and bridges helps engineers design structures that can withstand earthquakes. U Mechanical Engineering: Vibration analysis is crucial in designing engines, machinery, and vehicles to prevent resonance and failure. T S References Chopra, A. K. (2020). Dynamics of Structures: Theory and Applications to Earthquake Engineering (5th ed.). Pearson. Rao, S. S. (2017). Mechanical Vibrations (6th ed.). Pearson. Inman, D. J. (2013). Engineering Vibration (4th ed.). Pearson. These references provide a deeper exploration into the theory and applications of free vibrations of undamped systems. In free vibrations, the system oscillates without any external forces acting after the initial disturbance. If the system is undamped, it means there is no energy loss, and the system will continue to vibrate indefinitely at its natural frequency. The key characteristics of such a system are: CE 116-EARTHQUAKE ENGINEERING PANGASINAN STATE UNIVERSITY RIZALYN C. ILUMIN, MSME, MSCE URDANETA CAMPUS (1st Sem, AY 2024-2025) Instructor Page 8 of 22  ). The frequency at which the system naturally oscillates without external forces 2. Simple Harmonic Motion: The motion is sinusoidal, with displacement, velocity, and acceleration varying sinusoidally with time 3. Equation of Motion: For a simple undamped system, the equation of motion is given by mx¨+kx= 1. where ◦ m is the mass ◦ k is the stiffness ◦ x is the displacement ◦ x¨ is the acceleration ¨ The solution to this di erential equation is: The solution to this differential equation is Y x(t)=A cos(ωn t+ P where A is the amplitude ϕ is the phase angle, O C T Why is it important to study free vibrations of undamped systems N Studying free vibrations of undamped systems is fundamental in understanding the basic principles of mechanical and structural E dynamics. Here are some key reasons and real-world applications: D 1. Foundation for Understanding Complex Systems U Conceptual Clarity: Free vibrations of undamped systems serve as a simplified model to understand how structures and mechanical systems behave under vibratory motion without external forces or damping effects. This foundational knowledge is T essential before delving into more complex scenarios involving damping, external forces, or non-linear behavior. S 2. Natural Frequency Identification Resonance Avoidance: In real-world engineering, it’s crucial to determine the natural frequency of a structure or component. If the frequency of external forces matches the natural frequency, resonance can occur, leading to catastrophic failure. Understanding free vibrations helps engineers design structures that avoid these dangerous resonant conditions. 3. Design and Safety Considerations Structural Integrity: Engineers use the principles of free vibrations to ensure that buildings, bridges, and other structures can withstand environmental forces such as wind, earthquakes, and machinery-induced vibrations. By analyzing the natural frequencies, engineers can design structures to be robust and safe. 4. Mechanical Systems Design CE 116-EARTHQUAKE ENGINEERING PANGASINAN STATE UNIVERSITY RIZALYN C. ILUMIN, MSME, MSCE URDANETA CAMPUS (1st Sem, AY 2024-2025) Instructor Page 9 of 22. : : 0 , , ff 𝜙 , ) , : :. 5. Vibration Isolation Noise and Vibration Control: In industries such as automotive, aerospace, and manufacturing, reducing unwanted vibrations is critical for comfort, safety, and precision. Knowledge of free vibrations helps in designing systems that isolate or mitigate these vibrations effectively. 6. Testing and Calibration Modal Analysis: Free vibration analysis is used in experimental modal analysis to identify the dynamic characteristics of structures. This information is vital for validating computational models and for designing structures that behave predictably under dynamic loads. Y Real-World Application Example P Earthquake Engineering: In earthquake-prone regions, buildings and bridges are designed considering their natural O frequencies to avoid resonance with seismic waves. By studying the free vibrations of undamped systems, engineers can predict how structures will respond to different types of ground motion and design accordingly. C In summary, studying free vibrations of undamped systems equips engineers with the knowledge to design safer, more efficient, and reliable structures and mechanical systems, ensuring they perform optimally under various conditions without falling into resonance or T excessive vibration. N E How to determine the natural frequency of the structure? D U Determining the natural frequency of a structure is a critical aspect of structural and mechanical engineering. The natural frequency is the frequency at which a structure tends to vibrate when disturbed and then allowed to vibrate freely without external forces or damping. T Here’s a step-by-step guide on how to determine the natural frequency: S 1. Simplified Model Approach Single-Degree-of-Freedom (SDOF) System: For many structures, especially simple ones like a cantilever beam, the system can be approximated as a single-degree-of-freedom (SDOF) system. The natural frequency for an SDOF system can be calculated using the following formula: 2. Multi-Degree-of-Freedom (MDOF) Systems Mass and Stiffness Matrices: For more complex structures, which cannot be approximated as an SDOF system, you need to consider the structure as a multi-degree-of-freedom (MDOF) system. This involves formulating mass and stiffness matrices and solving the eigenvalue problem: Eigenvalue Analysis: Solving the eigenvalue problem gives you the natural frequencies of the system. This is typically done using numerical methods and software tools like MATLAB, ANSYS, or other nite element analysis (FEA) programs. CE 116-EARTHQUAKE ENGINEERING PANGASINAN STATE UNIVERSITY RIZALYN C. ILUMIN, MSME, MSCE URDANETA CAMPUS (1st Sem, AY 2024-2025) Instructor Page 10 of 22 fi  Y P O C Modal Testing: In practice, the natural frequency can also be determined experimentally using modal testing. This involves: ◦ Impact Testing: A structure is struck with a hammer equipped with a force sensor, and the resulting vibrations are T measured using accelerometers. N ◦ Frequency Response Function (FRF): The data from the sensors is analyzed to obtain the frequency response function, which shows peaks at the natural frequencies. E D Shaker Testing: A shaker is used to apply a controlled, sinusoidal force to the structure at varying frequencies. The response of the structure is measured, and the natural frequencies are identified where resonance occurs (maximum response). U T 4. Analytical Solutions for Simple Structures S Continuous Systems: For some simple continuous structures like beams or plates, there are well-established analytical solutions. For example, the natural frequency of a simply supported beam can be calculated as: CE 116-EARTHQUAKE ENGINEERING PANGASINAN STATE UNIVERSITY RIZALYN C. ILUMIN, MSME, MSCE URDANETA CAMPUS (1st Sem, AY 2024-2025) Instructor Page 11 of 22 To determine the natural frequency of a structure: 1. Simplified models like SDOF systems are used for basic calculations. 2. MDOF systems require solving mass and stiffness matrices. 3. Experimental methods like modal testing provide practical verification. 4. Analytical solutions are available for simple, continuous structures. The method used depends on the complexity of the structure and the desired accuracy of the natural frequency determination. Y Determining the natural frequency of earthquakes, or more accurately, the natural frequency of structures in relation to earthquake P activity in the Philippines, involves various methods. The natural frequency of a structure is critical in assessing its response to seismic events, particularly in areas like the Philippines, which is seismically active due to its location along the Pacific Ring of Fire. Methods for Determining Natural Frequency O C 1. Analytical Methods T ◦ Mathematical Modeling: This involves creating a mathematical model of the structure using its physical parameters like mass, stiffness, and damping. The natural frequency can be calculated using the formula: N E D U T S 2. Experimental Methods ◦ Ambient Vibration Testing (AVT): This non-destructive testing method involves measuring the structure's response to ambient vibrations (such as wind or traffic). The recorded vibrations are analyzed using spectral analysis to determine the natural frequencies. This method is widely used because it does not require any external force to be applied to the structure. ◦ Forced Vibration Testing: This method involves applying a known force to the structure and measuring its response. The natural frequency is determined by analyzing the structure's vibration response to the applied force. This method is more controlled but can be more invasive than AVT. ◦ Seismic Instrumentation: For regions like the Philippines, monitoring actual earthquake events using seismic sensors installed in buildings can help determine the natural frequency of those structures. The data from seismic events is analyzed to identify the dominant frequencies at which the structure vibrates. CE 116-EARTHQUAKE ENGINEERING PANGASINAN STATE UNIVERSITY RIZALYN C. ILUMIN, MSME, MSCE URDANETA CAMPUS (1st Sem, AY 2024-2025) Instructor Page 12 of 22  ◦ Code-based Methods: Building codes, such as the National Structural Code of the Philippines (NSCP), provide empirical formulas to estimate the natural frequency based on the building's height and construction material. These formulas are derived from statistical data and provide a quick estimate of the natural frequency. Application to the Philippines In the Philippines, due to the high seismic activity, determining the natural frequency of structures is essential for earthquake-resistant design. The methods mentioned above are used in combination to ensure that buildings and infrastructure can withstand seismic forces. For example, Finite Element Analysis (FEA) is often used in the design phase, while Ambient Vibration Testing (AVT) is employed to verify the natural frequency of existing structures. References Y Chopra, A. K. (2012). Dynamics of Structures: Theory and Applications to Earthquake Engineering (4th ed.). Prentice Hall. P Rao, S. S. (2011). Mechanical Vibrations (5th ed.). Pearson. O National Structural Code of the Philippines (NSCP). (2015). ASEP. C Kelly, J. M. (1997). Earthquake-Resistant Design with Rubber. Springer. T Stewart, J. P., & Fenves, G. L. (1998). System Identification for Evaluating Seismic Response of Buildings. Journal of Structural N Engineering, ASCE. E D How to Determine if Resonance Will Occur U 1. Identify the Natural Frequency of the Structure: T ◦ Analytical Calculation: As discussed earlier, the natural frequency of a structure can be calculated using the formula: S 2. Determine the Frequency Content of the Ground Motion: ◦ Seismic Hazard Analysis: This involves analyzing historical earthquake data and local seismological studies to understand the range of frequencies that are likely to affect the site. The Philippine Institute of Volcanology and Seismology (PHIVOLCS) provides data on past earthquakes, which can be used to assess the frequency content of expected ground motions. CE 116-EARTHQUAKE ENGINEERING PANGASINAN STATE UNIVERSITY RIZALYN C. ILUMIN, MSME, MSCE URDANETA CAMPUS (1st Sem, AY 2024-2025) Instructor Page 13 of 22  3. Compare the Natural Frequency with the Frequency of Ground Motion: ◦ Frequency Matching: If the natural frequency of the structure is within the range of frequencies generated by the earthquake, there is a potential for resonance. This comparison can be visualized using a plot of the building’s natural frequency against the response spectrum of the anticipated earthquake. 4. Evaluate the Risk of Resonance: ◦ Damping Consideration: Damping in the structure can reduce the risk of resonance. Structures with higher damping ratios are less susceptible to resonance because damping dissipates vibrational energy. Y ◦ Mode Shapes and Participation Factors: Higher modes (second, third, etc.) can also resonate with the earthquake P frequencies, not just the fundamental mode. Engineers evaluate these modes using modal analysis and consider the participation factors, which indicate how much a particular mode contributes to the overall response. O C References Chopra, A. K. (2012). Dynamics of Structures: Theory and Applications to Earthquake Engineering (4th ed.). Prentice Hall. T Clough, R. W., & Penzien, J. (2003). Dynamics of Structures (3rd ed.). McGraw-Hill. N National Structural Code of the Philippines (NSCP). (2015). ASEP. Kelly, J. M. (1997). Earthquake-Resistant Design with Rubber. Springer. E Kramer, S. L. (1996). Geotechnical Earthquake Engineering. Prentice Hall. D PHIVOLCS. (n.d.). Earthquake Information. Philippine Institute of Volcanology and Seismology. U T 5.2. Free Vibrations of Damped Systems S 1. Introduction to Damped Systems Free vibrations of damped systems refer to the vibratory motion that occurs in a system when it is disturbed from its equilibrium position and allowed to vibrate freely, but with the presence of a damping force that gradually reduces the amplitude of the oscillations. Unlike undamped systems, where vibrations continue indefinitely, damped systems experience a loss of energy over time due to resistance forces such as friction, air resistance, or material hysteresis. 2. Mathematical Representation The equation of motion for a damped system can be described by a second-order differential equation: CE 116-EARTHQUAKE ENGINEERING PANGASINAN STATE UNIVERSITY RIZALYN C. ILUMIN, MSME, MSCE URDANETA CAMPUS (1st Sem, AY 2024-2025) Instructor Page 14 of 22  Y P O Studying damped vibrations is crucial for several reasons: C Predicting System Behavior: Understanding how damping affects a system's response allows engineers to predict how quickly a system will stop vibrating after being disturbed. This is essential for designing systems that are both stable and responsive. T N Avoiding Resonance: In real-world applications, damping plays a critical role in mitigating the effects of resonance. A properly damped system can avoid catastrophic failures due to resonance by dissipating energy more effectively. E D Enhancing Comfort and Safety: In structures like buildings, bridges, or vehicles, controlling vibrations through damping improves comfort and safety. For example, in automotive engineering, dampers (shock absorbers) are designed to reduce U vibrations, providing a smoother ride. T Design Optimization: Engineers use damping to optimize the performance of mechanical systems. In many cases, the right S amount of damping can extend the life of a component by reducing the amplitude of oscillations and minimizing stress. 5. Real-World Applications Civil Engineering: In earthquake engineering, damping is incorporated into building designs through the use of materials and systems that absorb seismic energy. Base isolators and tuned mass dampers are examples of devices used to control vibrations and enhance the earthquake resilience of structures. Automotive Engineering: Shock absorbers in vehicles are designed with specific damping characteristics to absorb road impacts and vibrations, providing a comfortable and controlled ride. Without adequate damping, vehicles would experience excessive bouncing, leading to loss of control and discomfort. CE 116-EARTHQUAKE ENGINEERING PANGASINAN STATE UNIVERSITY RIZALYN C. ILUMIN, MSME, MSCE URDANETA CAMPUS (1st Sem, AY 2024-2025) Instructor Page 15 of 22  Machinery and Equipment: In rotating machinery, such as turbines and motors, damping is applied to reduce vibrations that could lead to mechanical failure, noise, and reduced efficiency. References Chopra, A. K. (2017). Dynamics of structures: Theory and applications to earthquake engineering (5th ed.). Pearson. Clough, R. W., & Penzien, J. (2003). Dynamics of structures (3rd ed.). McGraw-Hill. Y Rao, S. S. (2017). Mechanical vibrations (6th ed.). Pearson. P Thomson, W. T., & Dahleh, M. D. (1998). Theory of vibration with applications (5th ed.). Prentice Hall. O In summary, studying the free vibrations of damped systems is essential for understanding how systems dissipate energy and stabilize over time. The knowledge gained from this study is applied across various engineering disciplines to design safer, more efficient, and C reliable systems. T N SDOF (Single-Degree-of-Freedom System) Definition: An SDOF system is a simplified model of a structure that assumes all the mass and stiffness are concentrated in a E single point, and the system can move in only one direction (degree of freedom). D Relevance: SDOF systems are widely used to represent basic structures (such as a simple mass on a spring) and are the first step in understanding more complex dynamic behavior. U Applications: SDOF systems are used to model simple structures like a single-story building, or to approximate certain aspects T of more complex systems for basic dynamic analysis. S MDOF (Multi-Degree-of-Freedom System) Definition: An MDOF system is a more complex model where the structure can move in multiple directions or exhibit different types of movement (e.g., translation and rotation). This is a more realistic representation of how actual buildings and bridges behave under dynamic loads. Relevance: MDOF systems are essential for analyzing real-world structures, which have many interconnected components that move differently in response to dynamic forces like earthquakes. Applications: MDOF systems are used to model multi-story buildings, bridges, or any structure that requires a more detailed dynamic analysis. Topic Relevance These systems belong to topics such as: CE 116-EARTHQUAKE ENGINEERING PANGASINAN STATE UNIVERSITY RIZALYN C. ILUMIN, MSME, MSCE URDANETA CAMPUS (1st Sem, AY 2024-2025) Instructor Page 16 of 22  2. Vibration Analysis: SDOF and MDOF systems are fundamental for analyzing the natural frequencies, modes of vibration, and damping properties of structures. 3. Earthquake Engineering: Time history analysis and response spectrum analysis often use MDOF models to predict how a structure will respond to seismic activity. In earthquake engineering, studying SDOF systems allows for understanding fundamental dynamic principles, while MDOF systems are necessary for analyzing the more complex behavior of real structures under earthquake loads. Y P O C T N E D U T S CE 116-EARTHQUAKE ENGINEERING PANGASINAN STATE UNIVERSITY RIZALYN C. ILUMIN, MSME, MSCE URDANETA CAMPUS (1st Sem, AY 2024-2025) Instructor Page 17 of 22  TIME HISTORY Overview of Time History in Earthquake Engineering In earthquake engineering, time history analysis is a critical tool used to study and predict the behavior of structures under seismic loading. A time history represents how a physical quantity such as ground acceleration, velocity, or displacement changes over time during an earthquake. It captures the dynamic nature of ground shaking, providing engineers with detailed information about the seismic forces that buildings and infrastructure may experience during an earthquake. Y 1. Definition of Time History P A time history is essentially a sequence of data points measured at regular intervals, recording the variation of ground motion over the O duration of an earthquake. These records are typically obtained from seismometers or accelerometers positioned at various locations. The data can include: C Acceleration time histories: The most common form, showing how ground acceleration varies over time during an earthquake. T Velocity time histories: Derived from acceleration data, representing the speed of ground movement over time. N Displacement time histories: Representing how far the ground moves during the earthquake. E 2. Purpose and Importance of Time History in Earthquake Engineering D Time history analysis allows engineers to understand how structures respond dynamically to seismic events. Unlike static analysis, which only considers constant forces, time history analysis evaluates how structures respond to varying forces over time. This approach U is crucial for seismic design and retrofitting because earthquakes involve complex, time-dependent motions that generate significant inertia forces within a building. T Key reasons for the importance of time history analysis in earthquake engineering include: S Dynamic Response Evaluation: Time history analysis helps in evaluating how different parts of a structure react to time-varying seismic forces. This includes identifying critical points where maximum stress or displacement occurs. Performance-Based Design: Engineers can use time histories to predict how buildings will perform during earthquakes of various magnitudes, enabling the design of structures that meet performance objectives (e.g., safety, functionality) under specific seismic scenarios. Nonlinear Behavior Analysis: Time history data is essential for studying the nonlinear behavior of structures during intense ground shaking, where materials may yield or fail. Nonlinear time history analysis is critical for capturing these effects, which linear models cannot. CE 116-EARTHQUAKE ENGINEERING PANGASINAN STATE UNIVERSITY RIZALYN C. ILUMIN, MSME, MSCE URDANETA CAMPUS (1st Sem, AY 2024-2025) Instructor Page 18 of 22 3. Types of Time History Analysis Linear Time History Analysis: Assumes that the structural behavior remains within the elastic range (no permanent deformations). It is typically used for smaller earthquakes or initial design phases. Nonlinear Time History Analysis: Takes into account the inelastic (nonlinear) behavior of structures, including yielding and energy dissipation mechanisms. It is crucial for understanding how buildings behave during larger, more damaging earthquakes. Y 4. Applications of Time History Analysis P In earthquake engineering, time history analysis is used for several purposes: O Design of New Structures: Engineers use time history analysis to simulate how a proposed building or structure will respond to C expected seismic events. By inputting time history data from past earthquakes, engineers can predict whether the design will perform satisfactorily. T Seismic Retrofitting of Existing Structures: Time history analysis helps identify weaknesses in existing structures and N determine the appropriate retrofit measures to improve their seismic performance. E Structural Health Monitoring: After an earthquake, time history data collected from sensors installed in buildings can be D analyzed to assess the structural health and identify any areas that may require repair or reinforcement. U 5. Selection of Time History Records T For accurate and realistic results, it is important to choose or generate time history records that represent the seismic hazard at a given S site. The selection of appropriate time histories depends on factors such as: Magnitude and duration of expected earthquakes. Distance from the fault line. Soil conditions that can amplify or dampen seismic waves. Time histories can be derived from real earthquake recordings or generated synthetically to simulate worst-case scenarios for a given region. Time history analysis is a vital tool in earthquake engineering, providing detailed insights into the dynamic behavior of structures under seismic loading. It allows engineers to design buildings and infrastructure that can withstand the unpredictable forces generated during an earthquake, improving safety, resilience, and performance. By studying time histories, engineers can also develop more effective seismic mitigation strategies and ensure that structures comply with modern building codes. CE 116-EARTHQUAKE ENGINEERING PANGASINAN STATE UNIVERSITY RIZALYN C. ILUMIN, MSME, MSCE URDANETA CAMPUS (1st Sem, AY 2024-2025) Instructor Page 19 of 22 Time history refers to the representation of the variation of a physical quantity (such as acceleration, velocity, or displacement) over time. In the context of earthquake engineering, a time history is the record of ground motion data during an earthquake, typically presented as acceleration, velocity, or displacement versus time. This data is crucial for analyzing the dynamic response of structures subjected to seismic activity. Each earthquake event produces unique time histories for ground motion at different locations, which captures the intensity and characteristics of seismic waves, including peak acceleration, frequency content, and duration. Time histories can be derived from actual earthquake records or generated artificially to simulate possible future seismic events. 2. Importance of Studying Time History Y Time history analysis is critical in earthquake engineering and the construction of buildings for the following reasons: P Dynamic Response of Structures: Earthquake ground motions are dynamic, and time history analysis helps in understanding O how a structure will respond over time to the changing forces generated by the earthquake. C Designing for Seismic Resilience: By analyzing time history data, engineers can design structures to resist the dynamic effects of seismic forces. This analysis ensures that buildings can withstand the expected ground motion, reducing the risk of collapse or major damage. T N Validation of Structural Models: Time history is used to validate and calibrate computational models that predict how buildings behave during earthquakes. These models rely on accurate time histories to simulate real-world conditions. E D Assessment of Structural Vulnerabilities: By subjecting structures to different earthquake time histories, engineers can identify weaknesses in design or construction that could lead to failure during an earthquake. U T 3. How Time History is Used in Earthquake Engineering S Time history analysis plays a vital role in the design, construction, and safety evaluation of buildings and infrastructure: Linear and Nonlinear Time History Analysis: ◦ Linear Time History Analysis assumes that the structural behavior remains linear (i.e., stress is proportional to strain) throughout the earthquake event. This method is often used for small-to-moderate seismic intensities. ◦ Nonlinear Time History Analysis is required for more significant earthquakes, where structural elements may undergo plastic deformation. This method allows engineers to capture the actual behavior of the structure, including yielding and possible failure mechanisms. Performance-Based Design: Performance-based seismic design (PBSD) often uses time history analysis to predict how buildings will perform during different levels of earthquake intensity. The analysis helps set performance objectives such as life safety, damage control, and immediate occupancy. CE 116-EARTHQUAKE ENGINEERING PANGASINAN STATE UNIVERSITY RIZALYN C. ILUMIN, MSME, MSCE URDANETA CAMPUS (1st Sem, AY 2024-2025) Instructor Page 20 of 22  Selection of Ground Motion Records: Engineers select earthquake ground motion time histories that match the seismic hazard expected at a specific site. This ensures that the design accounts for the appropriate intensity, duration, and frequency content of potential earthquakes. 4. Using Time History in Constructing Buildings Time history analysis is applied during various stages of building design and construction, particularly in earthquake-prone areas: Y Foundation and Structural Design: Engineers use time history data to design foundations and structural elements (such as columns, beams, and walls) that can absorb and dissipate seismic energy without collapsing. By analyzing different time P histories, the building’s dynamic response is evaluated for worst-case scenarios. O Tall Building Design: Time history analysis is especially important for tall buildings, where the structure's response to earthquake-induced vibrations is more complex. Engineers ensure that the building’s natural frequencies do not resonate with C the earthquake’s predominant frequencies, which could amplify the shaking. T Damping Systems: Time history analysis helps design and optimize damping systems (e.g., tuned mass dampers, base isolators) that reduce the building’s seismic response by dissipating energy. The effectiveness of these systems is tested by N subjecting the building to different seismic time histories. E Construction Codes and Guidelines: Many building codes (e.g., ASCE 7-16, Eurocode 8) require that structures be designed D to withstand specific seismic forces, and these forces are often determined by time history analysis. Engineers must demonstrate that the building can endure multiple earthquake scenarios derived from time histories. U T 5. Tools and Software for Time History Analysis S Various software packages facilitate time history analysis, allowing engineers to simulate how a building will respond to earthquake ground motions: ETABS: Widely used for modeling and analyzing the seismic response of buildings. Time history data can be imported to simulate the response of structural models. SAP2000: Used for time history analysis of both linear and nonlinear structural models. It offers tools to define and apply earthquake time histories. OpenSees: An open-source software used for advanced nonlinear time history analysis of structures. CE 116-EARTHQUAKE ENGINEERING PANGASINAN STATE UNIVERSITY RIZALYN C. ILUMIN, MSME, MSCE URDANETA CAMPUS (1st Sem, AY 2024-2025) Instructor Page 21 of 22 Consider a 10-story building designed in a high-seismic region. Engineers select ground motion time histories from previous earthquakes similar to the seismic hazard at the building site. Using software, they subject the building to these time histories in both linear and nonlinear analyses. The results highlight specific floors and columns that are vulnerable to excessive displacements or forces, guiding adjustments in the design to prevent failure. Conclusion Time history analysis is an essential tool in earthquake engineering, offering valuable insights into the dynamic response of structures during seismic events. By studying time histories, engineers can design buildings that are safer and more resilient to earthquakes, ensuring compliance with building codes and reducing the risk of catastrophic failure. Y References: P Chopra, A. K. (2017). Dynamics of structures: Theory and applications to earthquake engineering (5th ed.). Pearson. O Clough, R. W., & Penzien, J. (2003). Dynamics of structures (3rd ed.). Computers and Structures, Inc. C Naeim, F., & Kelly, J. M. (1999). Design of seismic isolated structures: From theory to practice. John Wiley & Sons. T American Society of Civil Engineers (ASCE). (2016). Minimum design loads and associated criteria for buildings and other structures N (ASCE/SEI 7-16). E D U T S CE 116-EARTHQUAKE ENGINEERING PANGASINAN STATE UNIVERSITY RIZALYN C. ILUMIN, MSME, MSCE URDANETA CAMPUS (1st Sem, AY 2024-2025) Instructor Page 22 of 22