# Structural Analysis

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## structural analysis

[′strək·chə·rəl ə′nal·ə·səs]## Structural analysis

## Structural Analysis

the determination of stresses and strains in structural elements, of displacements, and of conditions for the strength, rigidity, and stability of the elements under, for example, dead loads, live loads, and temperature effects. The principal objective of structural analysis is to ensure the reliability and durability of structures, given an economically sound expenditure of materials.

Various methods are used, depending on the type of structure. Elements for which all three dimensions—width, length, and thickness—are of the same order of magnitude are calculated on the basis of the laws of the mathematical theory of elasticity. The principles of the applied theory of elasticity are used in calculating plates and shells, for which one dimension—the thickness—is smaller than the other two, and thin-walled bars, for which all three dimensions are different. Trusses and frames are designed in accordance with the laws and principles of structural mechanics and of the strength of materials. Problems of the analysis of structures that are subject to dynamic loads are considered in the dynamics of structures.

In the majority of cases, the methods of structural analysis are based on the conception of a structure as an ideal elastic body. A more accurate analysis of the structure takes into account the plastic deformation of the material; this approach permits the actual safety margins of the structure—in particular, the parameters of the structure’s limit state—to be found. In a number of cases, such as for reinforced-concrete structures and elements and the beddings of structures, methods of the theory of creep are used, with the rheological properties of the materials being taken into account. Statistical methods are used in the analysis of structures that are subject to the action of random, for example, seismic, loads.

L. V. KASAB’IAN

## Structural analysis

A detailed evaluation intended to assure that, for any structure, the deformations will be sufficiently below allowable values that structural failure will not occur. The deformations may be elastic (fully recoverable) or inelastic (permanent). They may be small, with an associated structural failure that is cosmetic; for example, the deflection of a beam supporting a ceiling may cause cracking of the plaster. They may be large, with an associated structural failure that is catastrophic; for example, the buckling of a column or the fracture of a tension member causes complete collapse of the structure.

Structural analysis may be performed by tests on the actual structure, on a physical model of the structure to some scale, or through the use of a mathematical model. Tests on an actual structure are performed in those cases where many similar structures will be produced, for example, automobile frames, or where the cost of a test is justified by the importance and difficulty of the project, for example, a lunar lander. Physical models are sometimes used where subassemblages of major structures are to be investigated. The vast majority of analyses, however, are on mathematical models, particularly in the field of structural engineering which is concerned with large structures such as bridges, buildings, and dams. *See* Bridge, Buildings, Dam, Structure (engineering)

The advent of the digital computer made it possible to create mathematical models of great sophistication, and almost all complex structures are now so analyzed. Programs of such generality have been written as to permit the analysis of any structure. These programs permit the model of the structure to be two- or three-dimensional, elastic or inelastic, and determine the response to forces that are static or dynamic. Most of the programs utilize the stiffness method, in which the stiffnesses of the individual elements are assembled into a stiffness matrix for the entire structure, and analysis is performed in which all behavior is assumed to be linearly elastic. *See* Digital computer, Elasticity

The structural engineer's function continues to require training and experience in conceptualizing the structure, choosing the appropriate model, estimating the loads that will be of importance, coding the information for the program, and interpreting the results. The analyst usually enters the process after the conceptualization. Most structures consist of assemblies of members connected at joints. While all real members transmit axial, torsional, and bending actions, the majority of buildings and bridges are analyzed as trusses, beams, and frames with either axial or bending forces predominant. *See* Beam, Engineering design, Stress and strain, Structural design, Truss

Whether the model selected is detailed or simplified, one extremely important part of the analysis consists of the estimate of the loads to be resisted. For bridges and buildings, the primary vertical loads are gravity loads. These include the weight of the structure itself, and such appurtenances as will be permanent in nature. These are referred to as dead loads. The loads to be carried, the live loads, may consist of concentrated loads (heavy objects occupying little space, for example, a printing press), or loads distributed over relatively large areas (such as floor and deck coverings). Horizontal loads on buildings are produced by wind and by the inertia forces created during earthquakes. In seismic analysis, computers are used to simulate the dynamic characteristics of the structure. The accelerations actually measured during earthquakes are then used to determine the response of the structure. *See* Loads, dynamic, Loads, transverse