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4.0 Introduction to Dynamic Theory

Updated: Oct 10

Most of the loads discussed to this point in these Pipe Stress Analysis Notes have been static loads (or in some cases, dynamic loads modeled as static loads). Static loads are those which are applied slowly enough that the piping system has time to react and internally distribute the loads, thus remaining in equilibrium. Once in equilibrium, all forces and moments are resolved (i.e. the sum of the forces and moments are zero), so the pipe doesn't move.

With a dynamic load — a load which changes quickly with time — the piping system may not have time to internally distribute the loads, so forces and moments are not always resolved — resulting in unbalanced loads, and therefore pipe movement. Since the sum of the forces and moments are not necessarily equal to zero, the internally induced loads can be different — either higher or lower — than the applied loads.

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Pipe Stress Analysis Notes

4.1 Characteristics of Dynamic Loads

4.1.1 Variation of Load Versus Time — Load Types 4.1.2 System Response Time Versus Timing of Load Change 4.1.3 Lack of System Equilibrium 4.1.4 Movement of Dynamically Loaded System 4.1.5 Relation of Induced System Loads to Applied Loads

4.2 The Dynamic Equation of Motion

4.2.1 Evaluation of a Single Degree-of-Freedom System 4.2.2 The Dynamic Load Factor

4.3 Evaluation of Multi-Degree-of-Freedom Systems

4.3.1 Modal Analysis 4.3.2 Modal Response Multipliers — Participation Factors and DLFs

4.4 Eigensolver Algorithm 4.5 Accuracy of The Dynamic Model

4.5.1 Mass Point Spacing

4.6 Types of Analysis

4.6.1 Time History Analysis 4.6.2 Seismic Spectrum Analysis 4.6.2.1 Generation of the Response Spectrum 4.6.2.2 Application to a Multi-Degree-of Freedom System 4.6.2.3 Modal Results Summation Methods 4.6.2.4 Combination of Spatial Components 4.6.2.5 Missing Mass Correction 4.6.3 Force Spectrum Analysis (for Impulse Loadings) 4.6.3.1 Generation of the Response Spectrum 4.6.3.2 Application to a Multi-Degree-of Freedom System 4.6.3.3 Summation of Responses 4.6.4 Harmonic Analysis

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