Introduction to Structural Analysis

A structure comprises several components that are connected to one another and function to transfer the loads to the soil successfully. The structure is a collection of elements linked together in such a way that serves a meaningful purpose. Thus, a structure is an arrangement and organization of interrelated elements in an object or system, with the load affecting structural components vertically or laterally. Different types of structures are concrete, framed, shell, membrane, truss, cables and arches, surface structure, etc. 

In other terms “structure” refers to a building or any other artificial object designed to support a load in construction. Structures can be made of various materials such as wood, steel, concrete or brick and can range from simple structures such as a shed or fences to complex structures such as bridges, skyscrapers or dams. 

Structural engineering is the field of engineering that deals with the design, analysis and construction of structures. A properly designed and constructed structure must resist various forces and loads such as gravity, wind, earthquakes and other external factors to ensure the safety of the structure.

Structural analysis is the prediction of the performance of a given structure under prescribed loads and/or other external effects, such as support movements and temperature changes. The performance characteristics commonly used in the design of structures are

1. Stress or stress resultant, such as axial force, shear force and bending moment
2. Deflection
3. Support reaction

Thus, the analysis of a structure usually involves determination of these quantities as caused by a given loading condition. 

History of Structural Engineering

Since the dawn of history, structural engineering has been an essential part of human endeavor. However, it was not until about the middle of the seventeenth century that, engineers began applying the knowledge of mechanics (mathematics and science) in designing structures. Earlier engineering structures were designed by trial and error and by using rules of thumb based on past experience. The fact that some of the magnificent structures from earlier eras, such as Egyptian pyramids (about 3000 BC), Greek temples (500–200 BC), Roman coliseums and aqueducts (200 BC–AD 200), and Gothic cathedrals (AD 1000–1500), still stand today is a testimonial to the ingenuity of their builders.

Galileo Galilei (1564–1642) is generally considered to be the originator of the theory of structures. In his book entitled ‘Two New Sciences’, which was published in 1638, Galileo analyzed the failure of some simple structures, including cantilever beams. Although Galileo’s predictions of strengths of beams were only approximate, his work laid the foundation for future developments in the theory of structures and ushered in a new era of structural engineering, in which the analytical principles of mechanics and strength of materials would have a major influence on the design of structures.

Following Galileo’s pioneering work, the knowledge of structural mechanics advanced at a rapid pace in the second half of the seventeenth century and into the eighteenth century. Among the notable investigators of that period were Robert Hooke (1635–1703), who developed the law of linear relationships between the force and deformation of materials (Hooke’s law); Sir Isaac Newton (1642–1727), who formulated the laws of motion and developed calculus; John Bernoulli (1667–1748), who formulated the principle of virtual work; Leonhard Euler (1707–1783), who developed the theory of buckling of columns; and C. A. de Coulomb (1736–1806), who presented the analysis of bending of elastic beams. In 1826 L. M. Navier (1785–1836) published a treatise on elastic behavior of structures, which is considered to be the first textbook on the modern theory of strength of materials.

The development of structural mechanics continued at a tremendous pace throughout the rest of the nineteenth century and into the first half of the twentieth, when most of the classical methods for the analysis of structures described in this text were developed. The important contributors of this period included B. P. Clapeyron (1799–1864), who formulated the three-moment equation for the analysis of continuous beams; J. C. Maxwell (1831–1879), who presented the method of consistent deformations and the law of reciprocal deflections; Otto Mohr (1835–1918), who developed the conjugate-beam method for calculation of deflections and Mohr’s circles of stress and strain; Alberto Castigliano (1847–1884), who formulated the theorem of least work; C. E. Greene (1842–1903), who developed the moment-area method; H. Muller-Breslau (1851–1925), who presented a principle for constructing influence lines; G. A. Maney (1888–1947), who developed the slope-deflection method, which is considered to be the precursor of the matrix stiffness method; and Hardy Cross (1885–1959), who developed the moment-distribution method in 1924.

The moment-distribution method provided engineers with a simple iterative procedure for analyzing highly statically indeterminate structures. This method, which was the most widely used by structural engineers during the period from about 1930 to 1970, contributed significantly to their understanding of the behavior of statically indeterminate frames. Many structures designed during that period, such as high-rise buildings, would not have been possible without the availability of the moment-distribution method. The availability of computers in the 1950s revolutionized structural analysis. Because the computer could solve large systems of simultaneous equations, analyses that took days and sometimes weeks in the precomputer era could now be performed in seconds.