Response spectrum

A response spectrum is a plot of the peak or steady-state response (displacement, velocity or acceleration) of a series of oscillators of varying natural frequency, that are forced into motion by the same base vibration or shock. The resulting plot can then be used to pick off the response of any linear system, given its natural frequency of oscillation. One such use is in assessing the peak response of buildings to earthquakes. The science of strong ground motion may use some values from the ground response spectrum (calculated from recordings of surface ground motion from seismographs) for correlation with seismic damage.

If the input used in calculating a response spectrum is steady-state periodic, then the steady-state result is recorded. Damping must be present, or else the response will be infinite. For transient input (such as seismic ground motion), the peak response is reported. Some level of damping is generally assumed, but a value will be obtained even with no damping.

Response spectra can also be used in assessing the response of linear systems with multiple modes of oscillation (multi-degree of freedom systems), although they are only accurate for low levels of damping. Modal analysis is performed to identify the modes, and the response in that mode can be picked from the response spectrum. These peak responses are then combined to estimate a total response. A typical combination method is the square root of the sum of the squares (SRSS) if the modal frequencies are not close. The result is typically different from that which would be calculated directly from an input, since phase information is lost in the process of generating the response spectrum.

The main limitation of response spectra is that they are only universally applicable for linear systems. Response spectra can be generated for non-linear systems, but are only applicable to systems with the same non-linearity, although attempts have been made to develop non-linear seismic design spectra with wider structural application. The results of this cannot be directly combined for multi-mode response.

A series of mixed vertical oscillators
A plot of the peak acceleration for the mixed vertical oscillators

Seismic response spectra

Response spectra are very useful tools of earthquake engineering for analyzing the performance of structures and equipment in earthquakes, since many behave principally as simple oscillators (also known as single degree of freedom systems). Thus, if you can find out the natural frequency of the structure, then the peak response of the building can be estimated by reading the value from the ground response spectrum for the appropriate frequency. In most building codes in seismic regions, this value forms the basis for calculating the forces that a structure must be designed to resist (seismic analysis).

As mentioned earlier, the ground response spectrum is the response plot done at the free surface of the earth. Significant seismic damage may occur if the building response is 'in tune' with components of the ground motion (resonance), which may be identified from the response spectrum. This was observed in the 1985 Mexico City Earthquake[1] where the oscillation of the deep-soil lake bed was similar to the natural frequency of mid-rise concrete buildings, causing significant damage. Shorter (stiffer) and taller (more flexible) buildings suffered less damage.

In 1941 at Caltech, George W. Housner began to publish calculations of response spectra from accelerographs.[1] In the 1982 EERI Monograph on "Earthquake Design and Spectra",[2] Newmark and Hall describe how they developed an "idealized" seismic response spectrum based on a range of response spectra generated for available earthquake records. This was then further developed into a design response spectrum for use in structural design, and this basic form (with some modifications) is now the basis for structural design in seismic regions throughout the world (typically plotted against structural "period", the inverse of frequency). A nominal level of damping is assumed (5% of critical damping).

For "regular" low-rise buildings, the structural response to earthquakes is characterized by the fundamental mode (a "waving" back-and-forth), and most building codes permit design forces to be calculated from the design spectrum on the basis of that frequency, but for more complex structures, combination of the results for many modes (calculated through modal analysis) is often required. In extreme cases, where structures are either too irregular, too tall or of significance to a community in disaster response, the response spectrum approach is no longer appropriate, and more complex analysis is required, such as non-linear static or dynamic analysis like in seismic performance analysis technique.

See also


  1. Report on 1985 Mexico City Earthquake from "EQ Facts & Lists: Large Historical Earthquakes", USGS.
  2. ^ "Historic Developments in the Evolution of Earthquake Engineering", illustrated essays by Robert Reitherman, CUREE, 1997, p10.
  3. ^ Newmark, N. M., and Hall, W. J. 1982. “Earthquake Spectra and Design,” Engineering Monographs on Earthquake Criteria, Structural Design, and Strong Motion Records, Vol 3, Earthquake Engineering Research Institute, Oakland, CA.
  1. ^ "Earthquake Hazards Program: Michoacan, Mexico 1985 September 19 13:17:47 UTC, Magnitude 8.0". Archived from the original on 6 February 2007.

External links


An accelerograph can be referred to as a strong-motion instrument or seismograph, or simply an earthquake accelerometer. They are usually constructed as a self-contained box, which previously included a paper or film recorder (an analogue instrument) but now they often record directly on digital media and then the data is transmitted via the Internet.Accelerographs are useful for when the earthquake ground motion is so strong that it causes the more sensitive seismometers to go off-scale. There is an entire science of strong ground motion, that is dedicated to studying the shaking in the vicinity of earthquakes (roughly within about 100 km of the fault rupture).

Accelerographs record the acceleration of the ground with respect to time. This recording is often called an accelerograms, strong-motion record or acceleration time-history. From this record strong-motion intensity measures (IMs, also called parameters) can be computed. The simplest of which is peak ground acceleration (PGA). Other IMs include Arias intensity, peak ground velocity (PGV), for which the accelerogram needs to be integrated once, peak ground displacement (PGD), for which double integration is required. Often a response spectrum is computed to show how the earthquake would affect structures of different natural frequencies or periods. These observations are useful to assess the seismic hazard of an area.

As well as their engineering applications, accelerograms are also useful for the study earthquakes from a scientific viewpoint. For example, accelerograms can be used to reconstruct the detailed history of rupture along a fault during an earthquake, which would not be possible with seismograms from standard instruments because they would be too far away to resolve the details. An example of an accelerograph array that was established to improve knowledge of near-source earthquake shaking as well as earthquake rupture propagation is the Parkfield Experiment, which involved a massive set of strong motion instrumentation.Within the accelerograph, there is an arrangement of three accelerometer sensing heads. In recent low-cost instruments these are usually micro-machined (MEMS) chips that are sensitive to one direction. Thus constructed, the accelerometer can measure full motion of the device in three dimensions.

Unlike the continually recording seismometer, accelerometers nearly always work in a triggered mode. That means a level of acceleration must be set which starts the recording process. For analogue and older digital instruments this makes maintenance much more difficult without a direct Internet connection (or some other means of communication). Many trips have been made to accelerometers after a large earthquake, only to find that the memory was filled with extraneous noise, or the instrument was malfunctioning.

Accelerometers are used to monitor the response of structures to earthquakes. Analysis of these records along with the shaking recorded at base of the structure can improve building design, through earthquake engineering.


A borehole is a narrow shaft bored in the ground, either vertically or horizontally. A borehole may be constructed for many different purposes, including the extraction of water, other liquids (such as petroleum) or gases (such as natural gas), as part of a geotechnical investigation, environmental site assessment, mineral exploration, temperature measurement, as a pilot hole for installing piers or underground utilities, for geothermal installations, or for underground storage of unwanted substances, e.g. in carbon capture and storage.

Campbell diagram

A Campbell diagram plot represents a system's response spectrum as a function of its oscillation regime. It is named for Wilfred Campbell, who introduced the concept.

It is also called an interference diagram.


Clay is a finely-grained natural rock or soil material that combines one or more clay minerals with possible traces of quartz (SiO2), metal oxides (Al2O3 , MgO etc.) and organic matter. Geologic clay deposits are mostly composed of phyllosilicate minerals containing variable amounts of water trapped in the mineral structure. Clays are plastic due to particle size and geometry as well as water content, and become hard, brittle and non–plastic upon drying or firing. Depending on the soil's content in which it is found, clay can appear in various colours from white to dull grey or brown to deep orange-red.

Although many naturally occurring deposits include both silts and clay, clays are distinguished from other fine-grained soils by differences in size and mineralogy. Silts, which are fine-grained soils that do not include clay minerals, tend to have larger particle sizes than clays. There is, however, some overlap in particle size and other physical properties. The distinction between silt and clay varies by discipline. Geologists and soil scientists usually consider the separation to occur at a particle size of 2 µm (clays being finer than silts), sedimentologists often use 4–5 μm, and colloid chemists use 1 μm. Geotechnical engineers distinguish between silts and clays based on the plasticity properties of the soil, as measured by the soils' Atterberg limits. ISO 14688 grades clay particles as being smaller than 2 μm and silt particles as being larger.

Mixtures of sand, silt and less than 40% clay are called loam. Loam makes good soil and is used as a building material.

Extreme response spectrum

The Extreme Response Spectrum (ERS) (or Maximum Response Spectrum (MRS)) is defined as a curve giving the value of the highest peak of the response of a linear Single Degree of Freedom System (SDOF system) to vibration, according to its natural frequency, for a given damping ratio. The response is described here by the relative movement of the mass of this system in relation to its support. The x-axis refers to the natural frequency and the y-axis to the highest peak multiplied by the square of the quantity (2 π x natural frequency), by analogy with the relative displacement shock response spectrum.

The severity of a vibration can be evaluated by calculating the stresses on a mathematical or finite element model of the structure and, for example, comparison with the ultimate stress of the material. This is the method used to dimension the structure. Generally, however, the problem is instead to evaluate the relative severity of several vibrations (vibrations measured in the real environment, measured vibrations with respect to standards, establishment of a specification etc.). This comparison would be difficult to carry out if one used a fine model of the structure and besides, this is not always available, in particular at the stage of the development of the specification of dimensioning.

A solution consists of applying the vibration under consideration to a “standard” mechanical system, which thus does not claim to be a model of the real structure, composed of a support and N linear one-degree-of-freedom resonators, each one comprising a mass, a spring and a damping device.

A vibration A is considered as more severe than a vibration B if it produces a highest relative displacement (i.e. a highest stress) on this SDOF system than the vibration B.

An ERS is generated from a vibration signal using the following process:

1. Choose a damping ratio for the ERS to be based on;

2. Assume a hypothetical Single Degree of Freedom System, with a given natural frequency (Hz);

3. Calculate (by time base simulation or from a Power Spectral Density (PSD) of the vibratory signal) the highest instantaneous relative displacement experienced by the mass element of this SDOFs at any time during exposure to the vibration in question. Plot this value multiplied by the square of (2 π x natural frequency) against the natural frequency of the hypothetical system;

4. Repeat steps 2 and 3 for other values of the natural frequency.

The resulting plot is called an Extreme response spectrum.


Gravel is a loose aggregation of rock fragments. Gravel is classified by particle size range and includes size classes from granule- to boulder-sized fragments. In the Udden-Wentworth scale gravel is categorized into granular gravel (2 to 4 mm or 0.079 to 0.157 in) and pebble gravel (4 to 64 mm or 0.2 to 2.5 in). ISO 14688 grades gravels as fine, medium, and coarse with ranges 2 mm to 6.3 mm to 20 mm to 63 mm. One cubic metre of gravel typically weighs about 1,800 kg (or a cubic yard weighs about 3,000 pounds).

Gravel is an important commercial product, with a number of applications. Many roadways are surfaced with gravel, especially in rural areas where there is little traffic. Globally, far more roads are surfaced with gravel than with concrete or asphalt; Russia alone has over 400,000 km (250,000 mi) of gravel roads. Both sand and small gravel are also important for the manufacture of concrete.

IEEE 802.11w-2009

IEEE 802.11w-2009 is an approved amendment to the IEEE 802.11 standard to increase the security of its management frames.

Maurice Anthony Biot

Maurice Anthony Biot (May 25, 1905 – September 12, 1985) was a Belgian-American applied physicist. He made contributions in thermodynamics, aeronautics, geophysics, earthquake engineering, and electromagnetism. Particularly, he was accredited as the founder of the theory of poroelasticity.Born in Antwerp, Belgium, Biot studied at Catholic University of Leuven in Belgium where he received a bachelor's degrees in philosophy (1927), mining engineering (1929) and electrical engineering (1930), and Doctor of Science in 1931. He obtained his Ph.D. in Aeronautical Science from the California Institute of Technology in 1932 under Theodore von Kármán.

In 1930s and 1940s Biot worked at Harvard University, the Catholic University of Leuven, Columbia University and Brown University, and later for a number of companies and government agencies, including NASA during the Space Program in the 1960s. Since 1969, Biot became a private consultant for various companies and agencies, and particularly for Shell Research and Development.

Biot's early work with von Kármán and during the World War II working for the US Navy Bureau of Aeronautics led to the development of the three-dimensional theory of aircraft flutter. During the period between 1932 and 1942, he conceived and then fully developed the response spectrum method (RSM) for earthquake engineering. For irreversible thermodynamics, Biot utilized the variational approach and was the first to introduce the dissipation function and the minimum dissipation principle to account for the dissipation phenomenon, which led to the development of thermoelasticity, heat transfer, viscoelasticity, and thermorheology. Biot’s interest in the non-linear effects of initial stress and the inelastic behavior of solids led to his mathematical theory of folding of stratified rocks. In the period between 1935 and 1962 Biot published a number of scientific papers that lay the foundations of the theory of poroelasticity (now known as Biot theory), which describes the mechanical behaviour of fluid-saturated porous media.

Biot is a recipient of the Timoshenko Medal (1962) and the von Kármán Medal (1967). He was an Honorary Fellow of the Acoustical Society of America, a member of the US National Academy of Engineering [37, 46], and was elected a Fellow of the American Academy of Arts and Sciences. He died in his Brussels apartment aged 80.

To honor Biot’s pioneering contributions, a Maurice A. Biot Medal was established by the Engineering Mechanics Institute of American Society of Civil Engineers. A Biot Conference on Poromechanics was established and was held at Université catholique de Louvain, Belgium (1998), Universite Joseph Fourier, France (2002), University of Oklahoma, USA (2005), Columbia University, USA (2009), and Technical University of Vienna, Austria (2013).


STAAD or (STAAD.Pro) is a structural analysis and design software application originally developed by Research Engineers International in 1997. In late 2005, Research Engineers International was bought by Bentley Systems.STAAD.Pro is one of the most widely used structural analysis and design software products worldwide. It supports over 90 international steel, concrete, timber & aluminium design codes.

It can make use of various forms of analysis from the traditional static analysis to more recent analysis methods like p-delta analysis, geometric non-linear analysis, Pushover analysis (Static-Non Linear Analysis) or a buckling analysis. It can also make use of various forms of dynamic analysis methods from time history analysis to response spectrum analysis. The response spectrum analysis feature is supported for both user defined spectra as well as a number of international code specified spectra.

Additionally, STAAD.Pro is interoperable with applications such as RAM Connection, AutoPIPE, SACS and many more engineering design and analysis applications to further improve collaboration between the different disciplines involved in a project. STAAD can be used for analysis and design of all types of structural projects from plants, buildings, and bridges to towers, tunnels, metro stations, water/wastewater treatment plants and more.

Seismic analysis

Seismic analysis is a subset of structural analysis and is the calculation of the response of a building (or nonbuilding) structure to earthquakes. It is part of the process of structural design, earthquake engineering or structural assessment and retrofit (see structural engineering) in regions where earthquakes are prevalent.

As seen in the figure, a building has the potential to 'wave' back and forth during an earthquake (or even a severe wind storm). This is called the 'fundamental mode', and is the lowest frequency of building response. Most buildings, however, have higher modes of response, which are uniquely activated during earthquakes. The figure just shows the second mode, but there are higher 'shimmy' (abnormal vibration) modes. Nevertheless, the first and second modes tend to cause the most damage in most cases.

The earliest provisions for seismic resistance were the requirement to design for a lateral force equal to a proportion of the building weight (applied at each floor level). This approach was adopted in the appendix of the 1927 Uniform Building Code (UBC), which was used on the west coast of the United States. It later became clear that the dynamic properties of the structure affected the loads generated during an earthquake. In the Los Angeles County Building Code of 1943 a provision to vary the load based on the number of floor levels was adopted (based on research carried out at Caltech in collaboration with Stanford University and the U.S. Coast and Geodetic Survey, which started in 1937). The concept of "response spectra" was developed in the 1930s, but it wasn't until 1952 that a joint committee of the San Francisco Section of the ASCE and the Structural Engineers Association of Northern California (SEAONC) proposed using the building period (the inverse of the frequency) to determine lateral forces.[1]The University of California, Berkeley was an early base for computer-based seismic analysis of structures, led by Professor Ray Clough (who coined the term finite element[2]). Students included Ed Wilson, who went on to write the program SAP in 1970,[3] an early "finite element analysis" program.

Earthquake engineering has developed a lot since the early days, and some of the more complex designs now use special earthquake protective elements either just in the foundation (base isolation) or distributed throughout the structure. Analyzing these types of structures requires specialized explicit finite element computer code, which divides time into very small slices and models the actual physics, much like common video games often have "physics engines". Very large and complex buildings can be modeled in this way (such as the Osaka International Convention Center).

Structural analysis methods can be divided into the following five categories.

Seismic hazard

A seismic hazard is the probability that an earthquake will occur in a given geographic area, within a given window of time, and with ground motion intensity exceeding a given threshold. With a hazard thus estimated, risk can be assessed and included in such areas as building codes for standard buildings, designing larger buildings and infrastructure projects, land use planning and determining insurance rates. The seismic hazard studies also may generate two standard measures of anticipated ground motion, both confusingly abbreviated MCE; the simpler probabilistic Maximum Considered Earthquake (or Event ), used in standard building codes, and the more detailed and deterministic Maximum Credible Earthquake incorporated in the design of larger buildings and civil infrastructure like dams or bridges. It is important to clarify which MCE is being discussed.

Calculations for determining seismic hazard were first formulated by C. Allin Cornell in 1968 and, depending on their level of importance and use, can be quite complex. The regional geology and seismology setting is first examined for sources and patterns of earthquake occurrence, both in depth and at the surface from seismometer records; secondly, the impacts from these sources are assessed relative to local geologic rock and soil types, slope angle and groundwater conditions. Zones of similar potential earthquake shaking are thus determined and drawn on maps. The well known San Andreas Fault is illustrated as a long narrow elliptical zone of greater potential motion, like many areas along continental margins associated with the Pacific ring of fire. Zones of higher seismicity in the continental interior may be the site for intraplate earthquakes) and tend to be drawn as broad areas, based on historic records, like the 1812 New Madrid earthquake, since specific causative faults are generally not identified as earthquake sources.

Each zone is given properties associated with source potential: how many earthquakes per year, the maximum size of earthquakes (maximum magnitude), etc. Finally, the calculations require formulae that give the required hazard indicators for a given earthquake size and distance. For example, some districts prefer to use peak acceleration, others use peak velocity, and more sophisticated uses require response spectral ordinates.

The computer program then integrates over all the zones and produces probability curves for the key ground motion parameter. The final result gives a 'chance' of exceeding a given value over a specified amount of time. Standard building codes for homeowners might be concerned with a 1 in 500 years chance, while nuclear plants look at the 10,000 year time frame. A longer-term seismic history can be obtained through paleoseismology. The results may be in the form of a ground response spectrum for use in seismic analysis.

More elaborate variations on the theme also look at the soil conditions. Higher ground motions are likely to be experienced on a soft swamp compared to a hard rock site. The standard seismic hazard calculations become adjusted upwards when postulating characteristic earthquakes. Areas with high ground motion due to soil conditions are also often subject to soil failure due to liquefaction. Soil failure can also occur due to earthquake-induced landslides in steep terrain. Large area landsliding can also occur on rather gentle slopes as was seen in the Good Friday earthquake in Anchorage, Alaska, March 28, 1964.

Shock (mechanics)

A mechanical or physical shock is a sudden acceleration caused, for example, by impact, drop, kick, earthquake, or explosion. Shock is a transient physical excitation.

Shock describes matter subject to extreme rates of force with respect to time. Shock is a vector that has units of an acceleration (rate of change of velocity). The unit g (or g) represents multiples of the acceleration of gravity and is conventionally used.

A shock pulse can be characterised by its peak acceleration, the duration, and the shape of the shock pulse (half sine, triangular, trapezoidal, etc.). The Shock response spectrum is a method for further evaluating a mechanical shock.

Shock mount

In a variety of applications, a shock mount or isolation mount is a mechanical fastener that connects two parts elastically. They are used for shock and vibration isolation.

Isolation mounts allow a piece of equipment to be securely mounted to a foundation and/or frame and, at the same time, allow it to float independently from the substrate.

Shock response spectrum

A Shock Response Spectrum (SRS) is a graphical representation of a shock, or any other transient acceleration input, in terms of how a Single Degree Of Freedom (SDOF) system (like a mass on a spring) would respond to that input. The horizontal axis shows the natural frequency of a hypothetical SDOF, and the vertical axis shows the peak acceleration which this SDOF would undergo as a consequence of the shock input.


Silt is granular material of a size between sand and clay, whose mineral origin is quartz and feldspar. Silt may occur as a soil (often mixed with sand or clay) or as sediment mixed in suspension with water (also known as a suspended load) and soil in a body of water such as a river. It may also exist as soil deposited at the bottom of a water body, like mudflows from landslides. Silt has a moderate specific area with a typically non-sticky, plastic feel. Silt usually has a floury feel when dry, and a slippery feel when wet. Silt can be visually observed with a hand lens, exhibiting a sparkly appearance. It also can be felt by the tongue as granular when placed on the front teeth (even when mixed with clay particles).

Spectral acceleration

Spectral acceleration (SA) is a unit measured in g (the acceleration due to Earth's gravity, equivalent to g-force) that describes the maximum acceleration in an earthquake on an object – specifically a damped, harmonic oscillator moving in one physical dimension. This can be measured at (or specified for) different oscillation frequencies and with different degrees of damping, although 5% damping is commonly applied. The SA at different frequencies may be plotted to form a response spectrum.

Spectral acceleration, with a value related to the natural frequency of vibration of the building, is used in earthquake engineering and gives a closer approximation to the motion of a building or other structure in an earthquake than the peak ground acceleration value, although there is normally a correlation between [short period] SA and PGA.Some seismic hazard maps are also produced using spectral acceleration.


A trench is a type of excavation or depression in the ground that is generally deeper than it is wide (as opposed to a wider gully, or ditch), and narrow compared with its length (as opposed to a simple hole).In geology, trenches are created as a result of erosion by rivers or by geological movement of tectonic plates. In the civil engineering field, trenches are often created to install underground infrastructure or utilities (such as gas mains, water mains or telephone lines), or later to access these installations. Trenches have also often been dug for military defensive purposes. In archaeology, the "trench method" is used for searching and excavating ancient ruins or to dig into strata of sedimented material.

Visible spectrum

The visible spectrum is the portion of the electromagnetic spectrum that is visible to the human eye. Electromagnetic radiation in this range of wavelengths is called visible light or simply light. A typical human eye will respond to wavelengths from about 380 to 740 nanometers. In terms of frequency, this corresponds to a band in the vicinity of 430–770 THz.

The spectrum does not contain all the colors that the human eyes and brain can distinguish. Unsaturated colors such as pink, or purple variations like magenta, for example, are absent because they can only be made from a mix of multiple wavelengths. Colors containing only one wavelength are also called pure colors or spectral colors.

Visible wavelengths pass largely unattenuated through the Earth's atmosphere via the "optical window" region of the electromagnetic spectrum. An example of this phenomenon is when clean air scatters blue light more than red light, and so the midday sky appears blue. The optical window is also referred to as the "visible window" because it overlaps the human visible response spectrum. The near infrared (NIR) window lies just out of the human vision, as well as the medium wavelength infrared (MWIR) window, and the long wavelength or far infrared (LWIR or FIR) window, although other animals may experience them.

Retaining walls
Numerical analysis


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