Difference Between Static And Dynamic Analysis Of Structures Pdf

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Structural dynamics is a type of structural analysis which covers the behavior of a structure subjected to dynamic actions having high acceleration loading. Dynamic loads include people, wind, waves, traffic, earthquakes , and blasts. Any structure can be subjected to dynamic loading.

The difference between static and dynamic analysis

Your email address will not be published. Overview In static structural analysis, it is possible to describe the operation of MSC Nastran without a detailed discussion of the fundamental equations. Due to the several types of dynamic analyses and the different mathematical form of each, some knowledge of both the physics of dynamics and the manner in which the physics is represented is important to using MSC Nastran effectively and efficiently for dynamic analysis.

You should become familiar with the notation and terminology covered in this chapter. This knowledge will be valuable to understand the meaning of the symbols and the reasons for the procedures employed in later chapters.

References and Bibliography, provide a list of references for structural dynamic analysis. Two basic aspects of dynamic analysis differ from static analysis.

First, dynamic loads are applied as a function of time or frequency-. Second, this time or frequency-varying load application induces time or frequency-varying response displacements, velocities, accelerations, forces, and stresses. These time or frequency-varying characteristics make dynamic analysis more complicated and more realistic than static analysis.

This chapter introduces the equations of motion for a single degree-of-freedom dynamic system see Equations of Motion, 3 , illustrates the dynamic analysis process see Dynamic Analysis Process, 13 , and characterizes the types of dynamic analyses described in this guide see Dynamic Analysis Types, Those who are familiar with these topics may want to skip to subsequent chapters.

The basic types of motion in a dynamic system are displacement u and the first and second derivatives of displacement with respect to time. These derivatives are velocity and acceleration, respectively, given below:.

Velocity is the rate of change in the displacement with respect to time. Velocity can also be described as the slope of the displacement curve.

Similarly, acceleration is the rate of change of the velocity with respect to time, or the slope of the velocity curve. The most simple representation of a dynamic system is a single degree-of-freedom SDOF system see Figure In an SDOF system, the time-varying displacement of the structure is defined by one component of motion u t.

Mass and damping are associated with the motion of a dynamic system. Degrees-of-freedom with mass or damping are often called dynamic degrees-of-freedom; degrees-of-freedom with stiffness are called static degrees-of-freedom.

It is possible and often desirable in models of complex systems to have fewer dynamic degrees-of-freedom than static degrees-of-freedom. The four basic components of a dynamic system are mass, energy dissipation damper , resistance spring , and applied load. As the structure moves in response to an applied load, forces are induced that are a function of both the applied load and the motion in the individual components.

The equilibrium equation representing the dynamic motion of the system is known as the equation of motion. This equation, which defines the equilibrium condition of the system at each point in time, is represented as.

The equation of motion accounts for the forces acting on the structure at each instant in time. Typically, these forces are separated into internal forces and external forces. Internal forces are found on the left-hand side of the equation, and external forces are specified on the right-hand side. The resulting equation is a second-order linear differential equation representing the motion of the system as a function of displacement and higher-order derivatives of the displacement.

An accelerated mass induces a force that is proportional to the mass and the acceleration. The energy dissipation mechanism induces a force that is a function of a dissipation constant and the velocity.

The damping force transforms the kinetic energy into another form of energy, typically heat, which tends to reduce the vibration. The final induced force in the dynamic system is due to the elastic resistance in the system and is a function of the displacement and stiffness of the system.

This force is called the elastic force or occasionally the spring force ku t. The applied load p t on the right-hand side of Eq. This load is independent of the structure to which it is applied e. The primary task for the dynamic analyst is to determine the type of analysis to be performed. The nature of the dynamic analysis in many cases governs the choice of the appropriate mathematical approach. The extent of the information required from a dynamic analysis also dictates the necessary solution approach and steps.

Dynamic analysis can be divided into two basic classifications: free vibrations and forced vibrations. Free vibration analysis is used to determine the basic dynamic characteristics of the system with the right-hand side of Eq. If damping is neglected, the solution is known as undamped free vibration analysis. The quantity u t is the solution for the displacement as a function of time t. As shown in Eq. In systems having more than one mass degree of freedom and more than one natural frequency, the subscript may indicate a frequency number.

For an SDOF system, the circular natural frequency is given by. The circular natural frequency is specified in units of radians per unit time. The natural frequency is often specified in terms of cycles per unit time, commonly cycles per second cps , which is more commonly known as Hertz Hz. This characteristic indicates the number of sine or cosine response waves that occur in a given time period typically one second.

The period of the response defines the length of time needed to complete one full cycle of response. In the solution of Eq. These constants are determined by considering the initial conditions in the system. These initial value constants are substituted into the solution, resulting in. Graphically, the response of an undamped SDOF system is a sinusoidal wave whose position in time is determined by its initial displacement and velocity as shown in Figure If damping is included, the damped free vibration problem is solved.

If viscous damping is assumed, the equation of motion becomes. The solution form in this case is more involved because the amount of damping determines the form of the solution. The three possible cases for positive values of b are.

Critical damping occurs when the value of damping is equal to a term called critical damping b cr. The critical damping is defined as.

Under this condition, the system returns to rest following an exponential decay curve with no oscillation. In this case, the solution has the form. Again, A and B are the constants of integration based on the initial conditions of the system. This term is related to the undamped circular natural frequency by the following expression:. The damping ratio is commonly used to specify the amount of damping as a percentage of the critical damping.

In the underdamped case, the amplitude of the vibration reduces from one cycle to the next following an exponentially decaying envelope. This behavior is shown in Figure The amplitude change from one cycle to the next is a direct function of the damping. Vibration is more quickly dissipated in systems with more damping. The damping discussion may indicate that all structures with damping require damped free vibration analysis. This result is significant because it avoids the computation of damped natural frequencies, which can involve a considerable computational effort for most practical problems.

Therefore, solutions for undamped natural frequencies are most commonly used to determine the dynamic characteristics of the system see Real Eigenvalue Analysis, However, this does not imply that damping is neglected in dynamic response analysis.

Damping can be included in other phases of the analysis as presented later for frequency and transient response see Frequency Response Analysis, and Transient Response Analysis, Forced vibration analysis considers the effect of an applied load on the response of the system.

Forced vibrations analyses can be damped or undamped. Since most structures exhibit damping, damped forced vibration problems are the most common analysis types. The type of dynamic loading determines the mathematical solution approach. From a numerical viewpoint, the simplest loading is simple harmonic sinusoidal loading. In the undamped form, the equation of motion becomes. Again, A and B are the constants of integration based on the initial conditions.

The third term in. This portion of the solution is a function of the applied loading and the ratio of the frequency of the applied loading to the natural frequency of the structure.

The numerator and denominator of the third term demonstrate the importance of the relationship of the structural characteristics to the response. In addition, to obtain the steady state solution, the static displacement is scaled by the denominator. The denominator of the steady-state solution contains the ratio between the applied loading frequency and the natural frequency of the structure.

This term scales the static response to create an amplitude for the steady state component of response. The response occurs at the same frequency as the loading and in phase with the load i. Numerically, this condition results in an infinite or undefined dynamic amplification factor. Physically, as this condition is reached, the dynamic response is strongly amplified relative to the static response. This condition is known as resonance.

The resonant buildup of response is shown in Figure It is important to remember that resonant response is a function of the natural frequency and the loading frequency. Resonant response can damage and even destroy structures.

The dynamic analyst is typically assigned the responsibility to ensure that a resonance condition is controlled or does not occur. Solving the same basic harmonically loaded system with damping makes the numerical solution more complicated but limits resonant behavior. With damping, the equation of motion becomes. In this case, the effect of the initial conditions decays rapidly and may be ignored in the solution.

The difference between static and dynamic analysis

Whether in dynamic and transient analysis need to use the inertia. Static and quasi static both refer to models where there is no dependency on time. Quasi static might be for a mechanism that is moving so slowly, that it is practically static. Both Dynamic and Transient analysis requires the material have a density so that acceleration loads on the mass of the bodies can be calculated. A Static analysis also needs material with density if you apply a gravity or acceleration load, but it doesn't need density if you are only applying forces. In a static problem, we assume acceleration is zero. Quasi-static means that at a given instant in time we can assume the problem is static.

When I was doing my first civil engineering design I hardly thought about dynamics. And to some degree, it might have been even justified back then. Now, when I understand a bit more, I would like to take you on a trip! We will learn about the differences between statics and dynamics! The main difference between static and dynamic analysis is TIME! But of course, there is implicit and explicit, and all the exciting stuff!

Whether in dynamic and transient analysis need to use the inertia. Static and quasi static both refer to models where there is no dependency on time. Quasi static might be for a mechanism that is moving so slowly, that it is practically static. Both Dynamic and Transient analysis requires the material have a density so that acceleration loads on the mass of the bodies can be calculated. A Static analysis also needs material with density if you apply a gravity or acceleration load, but it doesn't need density if you are only applying forces. In a static problem, we assume acceleration is zero.

analysis. The pertaining structure of 20 stories residential building. has been modeled. The storey plan is changing in the different. floors.

Fundamentals of Dynamic Analysis | MSC Nastran

Purchase the latest bound copy of the book at CSIberkeley. Or, Read Parts of the Book Here. It is not possible, due to the limited website storage, to place the complete book online. Chapter 1. Material Properties - click and wait to download an PDF file.

Structural dynamics

Static analysis involves going through the code in order to find out any possible defect in the code. Dynamic analysis involves executing the code and analyzing the output. While coding there may be a lot of typing errors, syntax error, loop structure, code termination etc etc. This should be fixed by inspecting thorough reading of your code. You program will run only after clearing all the coding defects by static analysis. Dynamic analysis : Now you need to check your program output whether it is the desired output or not.

Your email address will not be published. Overview In static structural analysis, it is possible to describe the operation of MSC Nastran without a detailed discussion of the fundamental equations. Due to the several types of dynamic analyses and the different mathematical form of each, some knowledge of both the physics of dynamics and the manner in which the physics is represented is important to using MSC Nastran effectively and efficiently for dynamic analysis.

Mahajan, R. However, there is no precise method available for modelling rock masses as they contain natural discontinuities and joints. Thus, a practical equivalent continuum approach is used in which properties are assigned to the rock mass in such a way as to represent the contributions of the intact rock and joints towards its overall response. This paper presents the outcome of static and dynamic study carried out on the underground Nathpa Jhakri hydro power cavern in India using FLAC2D software using this approach. The advantage of this approach is that it estimates the properties of jointed rock mass from the properties of intact rock and a joint factor Jf , which is the integration of the properties of joints to take care of the effects of frequency, orientation, and strength of joint. The results are compared for three different material models i.

As the world move to the accomplishment of Performance Based Engineering philosophies in seismic design of Civil Engineering structures, new seismic design provisions require Structural Engineers to perform both static and dynamic analysis for the design of structures. This paper also deals with the effect of the variation of the building height on the structural response of the shear wall building. This paper highlights the accuracy and exactness of Time History analysis in comparison with the most commonly adopted Response Spectrum Analysis and Equivalent Static Analysis.

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