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# What is and how to obtain a Shock Response Spectrum

Shock response spectra are used in seismic engineering to assess a structure’s response to an earthquake. How to obtain them

The ability to understand and predict a structure’s behavior during an earthquake plays a crucial role in safeguarding human lives and reducing damage to existing buildings. The key tool enabling structural engineers to evaluate structural response to seismic actions is called the shock response spectrum.

In this article, we aim to provide a comprehensive overview of shock response spectra. We will illustrate the criteria through which these diagrams are generated and examine how they are employed in the design and verification process of constructions in seismic areas.

To enhance structural design in high seismic risk areas (or simplify the assessment of existing structures’ vulnerability), we invite you to explore the capabilities of a structural analysis software, which offers a wide range of advanced functionalities for seismic analysis and design. By using this application, you can conduct detailed analyses based on shock response spectra, allowing you to accurately and efficiently evaluate your structures’ behavior.

## What are Shock Response Spectra?

Shock response spectra are diagrams used in the field of engineering and construction to describe a structure’s response to seismic stress. These graphs play a crucial role in structural design as they provide a clear representation of the structure’s behavior under seismic action by visually illustrating the expected maximum response in terms of acceleration, velocity, or displacement, depending on the specific analysis requirements.

There are three different types of shock response spectra, each correlated to one of the aforementioned variables:

• acceleration response spectrum: represents the maximum acceleration a structure would experience during a seismic event, based on its natural vibration period. The vibration period is the time taken by a structure to complete one full cycle of oscillation after being disturbed by an earthquake. This type of spectrum is commonly used in structural design to assess a building’s resistance to seismic loads. It shows the maximum expected acceleration on the structure and provides detailed information on the forces the building must be able to withstand;
• velocity response spectrum: describes the maximum velocity a structure would reach during a seismic event. Velocity is an important parameter to consider as it influences the dynamic behavior of the structure. This type of spectrum provides indications of how fast the structure moves in response to seismic oscillations and offers valuable insights into its ability to absorb and dissipate seismic energy;
• displacement response spectrum: illustrates the maximum displacement a structure could undergo during a seismic event. Understanding such displacements is crucial for analyzing the structure’s behavior in terms of deformations. By providing useful details on these displacements, this type of spectrum is usually used to evaluate the deformation and flexibility of various building components.

## Utilization of Shock Response Spectra in Seismic Design

Shock response spectra are used in seismic design to determine design loads and assess the effectiveness of seismic risk mitigation strategies.

They allow engineers to visualize and analyze the relationship between ground acceleration and the corresponding structural response clearly and intuitively.

Elastic spectra can be used in the design of new structures to ensure they can withstand anticipated seismic loads. Additionally, they can be used to assess the seismic vulnerability of existing buildings to identify any weaknesses requiring reinforcement or improvement.

In detail, shock response spectra serve as an indispensable tool for:

• evaluating seismic loads: shock response spectra provide essential data to accurately calculate seismic actions that must be considered in the design of structural elements. Seismic codes often require the use of these tools to determine design seismic loads based on the seismic zone and building category;
• sizing structural elements: based on shock response spectra, it is possible to assess structural response in terms of stresses and deformations. This data is crucial for sizing structural elements such as beams, columns, and foundations. By using shock response spectra, engineers can evaluate the maximum stresses these elements will have to withstand during an earthquake and size them adequately to ensure the safety and durability of the structure;
• verifying structure safety: by analyzing shock response spectra, designers can compare predicted structural stresses with the structure’s resistance capacity. This verification allows determining if the structure meets safety requirements and taking corrective measures, such as adding structural reinforcements and adjusting various components;
• analyzing vulnerability: shock response spectra can also be used to assess the seismic vulnerability of an existing structure. Comparing expected structural response with the building’s resistance capacity allows identifying any critical points and assessing the need for structural reinforcement or improvement;
• enhancing design: shock response spectra enable engineers to evaluate and compare different design solutions to optimize structures’ seismic response. By using these graphs, it is possible to perform various iterations and assess the effect of different structural configurations on seismic response. This optimization process allows developing effective and efficient design solutions from both a structural and seismic point of view.

## The Design Spectrum

Starting from the acceleration response spectrum, it is possible to obtain the design spectrum, a tool used in seismic design to account for the energy dissipation capacity and non-linear behavior of structures. These assumptions allow designing structures for seismic forces lower than those obtained with a purely elastic response.

In other words, to avoid performing complex and nonlinear structural analyses during the design phase, it is possible to consider a structure’s intrinsic capacity to dissipate energy through the ductile behavior of its elements or other dissipation mechanisms. This capacity is taken into account through a linear analysis based on a reduced shock response spectrum consisting precisely of the design spectrum.

The design spectrum is obtained by reducing the ordinates of the elastic spectrum through the application of the “q” behavior factor. This coefficient considers the anelastic dissipative capacities of the structure and allows adapting the shock response spectrum to the specific conditions of the building.

Design Spectrum

## The Importance of Using Advanced Calculation Tools for Seismic Analysis

Seismic analysis based on shock response spectra is a complex process that requires the evaluation of numerous factors to ensure maximum safety and reliability of structures. However, this process can be significantly simplified by using advanced calculation tools.

Structural calculation software allows engineers to simulate and predict the behavior of structures under seismic conditions, identifying potential vulnerabilities and optimizing design to achieve greater resistance. These software offer advanced functionalities for element modeling, application of seismic loads, execution of dynamic analyses, calculation of seismic hazard parameters, and evaluation of structural responses. They also provide more precise and reliable results, reducing margin of error and increasing the safety of designed structures.