Structural Theory - History and Analysis PDF

STRUCTURAL THEORY 1.1 HISTORICAL BACKGROUND 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 17th century that engineers began applying the knowle...

STRUCTURAL THEORY 1.1 HISTORICAL BACKGROUND 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 17th 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. Some of the magnificent structures from earlier eras such as Egyptian Pyramids (about 3000 B.C.) Greek temples (500 – 200 B.C.), Roman coliseums and aqueducts (200 B.C. –A.D.200), and Gothic cathedrals (A.D. 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, he 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 17th century and into the 18th century. Among the notable investigators of that period were Robert Hooke ( 1635-1703), who developed the law of linear relationships between the force and the 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 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 19th century and into the first half of the 20th century when most of the classical methods for the analysis of structures 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 1950’s revolutionized structural analysis. Because the computer could solve large systems of simultaneous, analyses that took days and sometimes weeks in precomputer era could be performed in seconds. The development of the current computer-oriented methods of structural analysis can be attributed to among others J. H. Argyris, R. W. Clough, S. Kelsey, R. K. Livesley, H. C. Martin, M. T. Turner, E. L. Wilson, and O. C. Zienkiewicz. 1.2 INTRODUCTION TO STRUCTURAL ANALYSIS The word structure has various meanings. An engineering structure means something constructed or built. The principal structures of concern to civil engineers are bridges, buildings, walls, dams, towers, and shell structures. Structures as such are composed of one or more solid elements so arranged that the whole structures as well as their components are capable of holding themselves without appreciable geometric change during loading and unloading. Structural Analysis is the prediction of performance of a given structure under prescribed loads and/or other external effects such as support movements and temperature changes. The performance characteristics commonly of interest in the design of structures are stresses or stress resultants such as axial forces, shear forces and bending moments, deflections and support reactions. Thus, analysis of structures usually involves determination of these quantities as caused a given loading condition. Structural Engineer usually acts in a service capacity to the functional design engineer, who normally provides the leadership in carrying out an engineering project. In the civil engineering field, he assists the transportation engineer, hydraulic engineer or sanitary engineer by providing the structures needed to implement their projects. In building construction, he is one of the architect’s principal collaborators. In a similar way, the structural engineer assists mechanical, chemical or electrical engineers in designing the heavy machinery or facilities required for their projects. He may shift his entire activity into naval architectural architecture or aeronautical engineering and become a specialist in the design of ship or airplane structures. Beams are straight members that are loaded perpendicular to their longitudinal axis. Rigid Frames are composed of straight members connected together either by rigid (moment-resisting) connections or by hinged connections to form stable configuration. Unlike trusses, which are subjected only to joint loads, the external loads on frames may be applied on the members as well as on the joints. The members of a rigid frame are in general, subjected to bending moment, shear and axial compression or tension under the action of external loads. However, the design of horizontal members or beams of rectangular frames is often governed by bending and shear stresses only since the axial forces in such members are usually small. Frames are among the most commonly used types of structures. Structural steel and reinforced concrete frames are commonly used in multistory buildings, bridges and industrial plants. Frames are also used as supporting structures in airplanes, ships, aerospace vehicles and other aerospace and mechanical applications. Reinforced concrete slabs are flat plates that are supported at its sides by reinforced concrete beams, walls, columns, steel beams or by the ground. Structural Engineering is the science and art of planning, designing, and constructing safe and economical structures that will serve their intended purposes. The following are the phases of typical structural engineering project: 1. Planning Phase: involves a consideration of the various requirements and factors that affect the general layout and dimensions of the structure and leads to the choice of one or several alternative types of structures that offer the best general solution. The primary consideration is the function of the structure, whether it is to enclose or house, to convey, or to support in space. Many secondary considerations are also involved, including aesthetic, sociological, legal, financial, economic, environmental, or resource-conservation factors. In addition, there are structural and constructional requirements and limitations that may also affect the structural type selected. 2. Design Phase: involves a detailed consideration of the alternative solutions evolved in the planning phase and leads to the determination of the most suitable proportions, dimensions, and details of the structural elements and connections for constructing each alternative structural arrangement being considered. Usually, before the final design stage is reached, the best solution has been identified, and final construction plans are prepared for this selection. Occasionally, the choice is dependent on economic and constructional features that can not be accurately evaluated except by competitive bidding, so final bid plans have to be prepared for the competitive alternatives. 3. Construction Phase: involves procurement of materials, equipment, and personnel; shop fabrication of the members and subassemblies and their transportation to the site; and the actual field construction and erection. During this phase, some redesign may be required if unforeseen foundation difficulties develop or if specified materials cannot be procured, or for any number of other issues. Classifications of Structures Depending on the Type of Primary Stresses That May Develop in Their Members Under Major Design Loads: 1. Tension Structures: subjected to pure tension under the action of external loads. Because the tensile stress is distributed uniformly over the cross-sectional area of the members, the material of such a structure is utilized in the most efficient manner. Flexible steel cables supporting bridges and long-span roofs are tension structures. Vertical rods used as hangers (for example, to support balconies or tanks) and membrane structures such as tents and roofs of large-span domes are also examples of tension structures. 2. Compression Structures: develop mainly compressive stresses under the action of external loads. Two common examples of such structures are columns and arches. Columns are straight members subjected to axially compressive loads and bending moments. Arches are curved structures with shape similar to that of an inverted cable. Such structures are frequently used to support bridges and long-span roofs. Arches develop mainly compressive stresses when subjected to loads and are usually designed so that they will develop compression under major design loading. Because compression structures are susceptible to buckling or instability, the possibility of such failure should be considered in their design. If necessary, adequate bracing must be provided to avoid such failures. 3. Trusses: composed of straight members connected at the ends by hinged connections to form stable configuration. The members of an ideal truss are always either in uniform tension or uniform compression. Real trusses are usually constructed by connecting members to gusset plates by bolted or welded connections. Although the rigid joints thus formed cause some bending in the embers of a truss when it is loaded, in most cases such secondary bending stresses are small, and the assumption of hinged joints yields satisfactory designs. Trusses are among the most commonly used type of structures because of their light weight and high strength. Such structures are used in a variety of applications ranging from supporting roofs of buildings to serving as support structures in space stations and sports arenas. 4. Bending Structures: develop mainly bending stresses under the action of external loads. In some structures, the shear stresses associated with the changes in bending moments may also be significant and should be considered in their designs. Some of the most commonly used structures such as beams, rigid frames, slabs and plates can be classified as bending structures. 5. Shear Structures: used in multistory buildings to reduce lateral movements due to wind and earthquake loads. They develop mainly in-plane shear with relatively small bending stresses under the action of external loads. Shear wall is an example of shear structure. LOADS ON STRUCTURES: 1. Dead Loads: gravity loads of constant magnitudes and fixed positions that act permanently on the structure. Such loads consist of the structural system itself and of all other materials and equipment permanently attached to the structural system. The dead loads for a building structure include the weights of the frames, framing and bracing systems, floors, roofs, ceilings, walls, stairways, heating and air-conditioning systems, plumbing, electrical systems and others. 2. Live Loads: loads of varying magnitudes and/or positions caused by the use of the structure. The magnitudes of design live loads are usually specified in building codes. The position of live loads may change so each member of the structure must be designed for the position of the load that causes the maximum stress in that member. 3. Impact: When live loads are applied rapidly to a structure, they cause larger stresses than those that would be produced if the same loads would have been applied gradually. The dynamic effect of the load that causes this increase in stress in the structure is referred to as impact. To account for increase in stress due to impact, the live loads expected to cause such a dynamic effect on structures are increased by a certain impact percentage or impact factors. The impact percentages of factors which are usually based on past experience and/or experimental results are specified in the building codes. For example, the ASCE7 standard specifies that all elevator loads for buildings be increased by 100 % to account for impact. For highway bridges, the AASHTO specification gives the expression for the impact factor as I = (50/(L + 125)) ≤ 3 in which L is the length in feet of the portion of span loaded to cause the maximum stress in the member under consideration. 4. Wind Loads: produced by the flow of wind around the structure. The magnitudes of wind that may act on the structure depend on the geographical location of the structure, obstructions in its surrounding terrain such as nearby buildings and the geometry of the vibrational characteristics of the structure itself. Although the procedures described in the various codes for the estimation of wind loads usually vary in detail, most of them are based on the same basic relationship between the wind speed V and the dynamic pressure q induced on flat surface normal to the wind flow, which can be obtained by applying Bernoulli’s principle and is expressed as q = ½pV2 in which p is the mass density of the air. 5. Earthquake Loads: An earthquake is the sudden undulation of a portion of the earth’s surface. Although the ground surface moves in both horizontal and vertical directions during an earthquake, the magnitude of the vertical component of ground motion is usually small and does not have significant effect on most structures. It is the horizontal component of ground motion that causes structural damage and that must be considered in designs of structures located in earthquake-prone areas. During an earthquake, as the foundation of the structure moves with the ground, the above-ground portion of the structure, because of the inertia of its mass, resists the motion, thereby causing the structure to vibrate in the horizontal direction. These vibrations produce horizontal shear forces in the structure. For an accurate prediction of the stresses that may develop in the structure in the case of an earthquake, a dynamic analysis, considering the mass and stiffness characteristics of the structure must be performed. However for low- to-medium-height rectangular buildings, most codes employ equivalent static force design for earthquake resistance. In this empirical approach, the dynamic effect of the earthquake is approximated by a set of lateral (horizontal) forces applied to the structure and static analysis is performed to evaluate stresses in the structure. 6. Hydrostatic and Soil Pressures: Structures such as dams and tanks as well as coastal structures partially or fully submerged in water must be designed to resist hydrostatic pressure. Hydrostatic pressure acts normal to the submerged surface of the structure with its magnitude varying linearly with height. The pressure at a point located at a depth h below the surface of the liquid is expressed as p = wh where w is the unit weight of the liquid. Underground structures, basement walls and floors and retaining walls must be designed to resist soil pressure. The vertical soil pressure is given by the same equation above with w now representing the unit weight of the soil. The lateral soil pressure depends on the type of soil and is usually considerably smaller than the vertical pressure. For the portions of structures below the water table, the combined effect of the hydrostatic pressure and soil pressure due to the weight of the soil reduced for buoyancy must be considered. 7. Thermal and Other Effects: Statically indeterminate structures may be subjected to stresses due to temperature changes, shrinkage of materials, fabrication errors and differential settlement of supports. These may cause significant stresses in the structures and should be considered in their designs.