Structural Theory PDF

STRUCTURAL THEORY TYPES OF STRUCTURES AND LOADS INTRODUCTION A structure refers to a system of connected parts used to support a load. When designing a structure to serve a specified function for public use, the engineer must account for its safety, aesthetics, and serviceability, while taking int...

STRUCTURAL THEORY TYPES OF STRUCTURES AND LOADS INTRODUCTION A structure refers to a system of connected parts used to support a load. When designing a structure to serve a specified function for public use, the engineer must account for its safety, aesthetics, and serviceability, while taking into consideration economic and environmental constraints. Often this requires several independent studies of different solutions before final judgment can be made as to which structural form is most appropriate. This design process is both creative and technical and requires a fundamental knowledge of material properties and the laws of mechanics which govern material response. Once a preliminary design of a structure is proposed, the structure must then be analyzed to ensure that it has its required stiffness and strength. To analyze a structure properly, certain idealizations must be made as to how the members are supported and connected together. The loadings are determined from codes and local specifications, and the forces in the members and their displacement are found using the theory of structural analysis. The result of this analysis then can be used to redesign structure, accounting for a more accurate determination of the weight of the members and their size. Structural design, therefore, follows a series of successive approximations in which every cycle requires a structural analysis. CLASSIFICATION OF STRUCTURES It is important for a structural engineer to recognize the various types of elements composing a structure and to be able to classify structures as to their form and function. STRUCTURAL ELEMENTS. Some of the more common elements from which structures are composed are as follows: TIE RODS Structural members subjected to a tensile force are often referred to as tie rods or bracing struts. Due to the nature of this load, these members are rather slender, and are often chosen from rods, bars, angles, or channels. BEAMS Beams are usually straight horizontal members used primarily to carry vertical loads. Quite often they are classified according to the way they are supported (simply supported beam, cantilevered beam, fixed-supported beam, continuous beam). In particular, when the cross section varies, the beam is referred to as tapered or haunched. Beam cross sections may also be “built up” by adding plates to their top and bottom. Beams are primarily designed to resist bending moment; however, if they are short and carry large loads, the internal shear force may become quite large and this force may govern their design. When the material used for a beam is a metal such as steel or alumina, the cross section is most efficient when it is shaped as shown in figure. Here the forces developed in the top and bottom flanges of the beam form the necessary couple used to resist the applied moment M, whereas the web is effective in resisting the applied shear V. This cross section is commonly referred to as “wide flange,” and it is normally formed as a single unit in a rolling mill in lengths up to 75 ft (23 m). If shorter lengths are needed, a cross section having tapered flanges is sometimes selected. When the beam is required to have a very large span and the loads applied are rather large, the cross section may take the form of a plate girder. This member is fabricated by using a large plate for the web and welding or bolting plates to its ends for flanges. The girder is often transported to the field in segments, and the segments are designed to be spliced or joined together at points where the girder carries a small internal moment. Concrete beams generally have rectangular cross sections, since it is easy to construct this form directly in the field. Because concrete is rather weak in resisting tension, steel “reinforcing rods” are cast into the beam within regions of the cross section subjected to tension. Precast concrete beams or girders are fabricated at a shop or yard in the same manner and then transported to the job site. Beams made from timber may be sawn from a solid piece of wood or laminated. Laminated beams are constructed from slid sections of wood, which are fastened together using high-strength glues. COLUMNS Members that are generally vertical and resist axial compressive loads are referred to as columns. Tubes and wide-flange cross sections are often used for metal columns, and circular and square cross sections with reinforcing rods are used for those made of concrete. Occasionally, columns are subjected to both an axial load and a bending moment as shown in the figure. These members are referred to as beam columns. TYPES OF STRUCTURES. The combination of structural elements and the materials from which they are composed is referred to as a structural system. Each system is constructed of one or more of four basic types of structures. Ranked in order of complexity of their force analysis, they are as follows: TRUSSES When the span of a structure is required to be large and its depth is not an important criterion for design, a truss may be selected. Trusses consist of slender elements, usually arranged in triangular fashion. Planar Trusses are composed of members that lie in the same plane and are frequently used for bridge and roof support, whereas Space Trusses have members extending in three dimensions and are suitable for derricks and towers. Due to the geometric arrangement of its members, loads that cause the entire truss to bend are converted into tensile or compressive forces in the members. Because of this, one of the primary advantages of a truss, compared to a beam, is that it uses less material to support a given load. CABLES AND ARCHES Two other forms of sructures used to span long distances are the cable and the arch. Cables are usually flexible and carry their loads in tension. They are commonly used to support bridges, and building roofs. When used for these purposes, the cable has an advantage over the beam and the truss, especially for spans that are greater than 150 ft (46 m). Because they are always in tension, cables will not become unstable and suddenly collapse, as may happen with beams or trusses. Furthermore, the truss will require added costs for construction and increased depth as the span increases. Use of cables, on the other hand, is limited onl by their sag, weight, and methods of anchorage. The arch achieves its strength in compression, since it has a reverse curvature to that of the cable. The arch must be rigid, however, in order to maintain its shape, and this results in secondary loadings involving shear and moment, which must be considered in its design. Arches are frequently used in bridge structure, dome roofs, and for openings in masonry walls. FRAMES Frames are often used in buildings and are composed of beams and columns that are either pin or fixed connected. Like trusses, frames extend in two or three dimensions. The loading on a frame causes bending of its members, and if it has rigid joint connections, this structure is generally “indeterminate” from a standpoint o analysis. The strength of such a frame is derived from the moment interactions between the beams and the colmns at the rigid joints. SURFACE STRUCTURES A Surface structure is made from a material having very small thickness compared to its other dimensions. Sometimes this material is very flexible and can take the form of a tent or air-inflated strucure. In both cases the material acts as a membrane that is subjected to pure tension. Some structures may also be made of rigid material such as reinforced concrete. As such they may be shape as folded plates, cylinder, or hyperbolic paraboloids, and are referred to as thin plates or shells. These structures act like cables or arches since they support loads primarily in tension or compression, with very little bending. In spite of this, plate or shell strucures are generally very difficult to analyze,due to the three-dimensional geometry of their surface. The roof of the “Georgia Dome” in Atlanta, Georgia can be considered as a thin membrane. LOADS Once the dimensional requiremenys for a structure have been defined, it becomes necessary to determine the loads the structure must support. Often, it is the anicipation of the various loads that will be imposed on the structure that provides the basic type of structure that will be chosen for design. For examples, high-rise structures must endure large lateral loadings caused by wind, and so shear walls and tubular frame systems are selected, whereas buildings located in areas prone to earthquakes must be designed having ductile frames and connections. Once the structural form has been determined, the actual design begins with those elements that are subjected to the primary loads the structure is intended to carry, and proceeds in sequence to the various supporting members until the foundation is reaced. Thus, a building floor slab would be designed first, followed by the supporting beams, columns, and last, the foundation footing. In order to design a structure, it is therefore necessary to first specify the loads that act on it. The design loading for a structure is often specified in codes. In general, the structural engineer works with two typesof codes: general building codes and design building codes. General building codes specify the requirements of governmental bodies for minimum design loads n structures and minimum standards for construction. Design codes provide detailed technical standards and are used to establish the requirements for the actual structural design. The following list are some of the important codes used in practice: GENERAL BUILDING CODES -Minimum Design Loads for Buildings and Other Structures, ASCE/SEI 7-10, American Society of Civil Engineers (ASCE) – International Building Code DESIGN CODES -Building Code Requirement for Reinforced Concrete, American Concrete Institute (ACI) -Manual of Steel Construction, American Institute of Steel Construction (AISC) -Standard Specifications for Highway Bridges, American Association of State Highway and Transportation Officials (AASHTO) -National Design Specification for Wood Construction, American Forest and Paper Association (AFPA) -Manual for Railway Engineering, American Railway Engineering Association (AREA) ✓ IN THE PHILIPPINES -National Building Code of the Philippines, Department of Public Works and Highways (DPWH) -National Structural Code of the Philippines, Association of Structural Engineers of the Philppines (ASEP) DEAD LOADS Dead Loads consist of the weights of the various structural members and the weights of any object that are permanently attached to the structure. Hence, for a building, the dead loads include the weights of the columns, beams, and girders, the floor slab, roofing, walls, windows, plumbing, electrical fixtures, and other miscellaneous attachments. In some cases, a structural dead load can be estimated satisfactorily from simple formulas based n the weights and sizes of similar structures. Through experience one can also derive a “feeling” for the magnitude of these loadings. The densities of typical materials used in construction are listed in the code and a portion of a table listing the weights of typical building components is given. Although calculation of dead loads based on the use of tabulated data is rather straightforward, it should be realized that in many respects these loads will have to be estimated in initial phase design. These estimates include nonstructural materials such as prefabricated façade panels, electrical and plumbing systems, etc. Futhermore, even if the material is specified, the unit weights of elements reported n codes may vary from those given by manufacturers, and later use of the building may include some changes in dead loading. As a result, estimates of dead loadings can be in error by 15% to 20% or more. Normally, the dead load is not large compared to the design load for simple structures such as a beam or a single-storey frae; however, for multistorey buildings it is important to have an accurate accounting of all the dead loads in order to properly design the columns, especially for the lower floors. LIVE LOADS Live loads can vary both in their magniude and location. They may be caused by the weghts of objects temporarily placed on a structure, moving vehicles, or natural forces. The minimum live loads specified in codes are determined from studying the history of their effects on existing structures. Usually, these loads include additional protection against excessive deflection or sudden overload. In future discussons we will develop techniques for specifying the proper location of live loads on the structure so that they cause the greatest stress or deflection of the members. Various types of live loads will now be discussed. BUILDING LOADS The floors of buildings are assumed to be subjected to uniform live loads, which depend on the purpose for which the building is designed. These loadings are generally tabulated in local, state, or national codes. A representative sample of such minimum live loadings, taken from the NSCP 2015 Chapter 2 is shown in Table 205-1 Minimum Uniform and Concentrated Live Loads. The values are determined from a history of loading various buildings. They include some protection against the possibility of overload due to emergency situations, construction loads, and serviceability requirements due to vibration. In addition to uniform loads, some codes specify minimum concentrated live loads, caused by hand carts, automobiles, etc., which must also be applied anywhere to the  floor system. For example, both uniform and concentrated live loads must be considered in the design of an automobile parking deck. HIGHWAY BRIDGE LOADS The primary live loads on bridge spans are those due to traffic, and the heaviest vehicle loading encountered is that caused by a series of trucks. Specifications for truck loadings on highway bridges are reported in the LRFD Bridge Design Specifications of the American Association of State and Highway Transportation Officials (AASHTO). RAILROAD BRIDGE LOADS The loadings on railroad bridges are specified in the Specifications for Steel Railway Bridges published by the American Railroad Engineers Association (AREA). IMPACT LOADS Moving vehicles may bounce or sidesway as they move over a bridge, and therefore they impart an impact to the deck. The percentage increase of the live loads due to impact is called impact factor, I. This factor is generally obtained from formulas developed from experimental evidence. WIND LOADS When the speed of the wind is very high, it can cause massive damage to a structure. The reason is that the pressure created by the wind is proportional to the square of the wind speed. The destruction due to the wind is increased if the building hs an opening, if the opening is at the front, then the pressure within the building is increased and this intensifies the xternal suction on the back, side wals, and the roof. If the opening is on a sie wall, then the opposite effect occurs. Air wll be sucked out of the building, lowering its inside pressure, and intensifying the pressure acting externally on the front of the building. For high-rise building, the wind loading can be quite complex, and so these structures are often designed based on the behavior of a model of the building, tested in a wind tunnel. When doing so, it is important to consider the wind striking the structure from any direction. The effects of lateral loadings developed by wind, can cause racking, or leaning of a building frame. To resist this effect, engineers often use cross bracing, knee or diagonal bracing, or shear walls. SNOW LOADS In some parts of the world, roof loading due to snow can be quite severe, and therefore protection against possible failure is of primary concern. Design loadings typically depend on the building’s general shape and roof geometry, wind exposure, location, its importance, and whether or not it is heated. Like wind, snow loads in the ASCE 7-10 Standard are generally determined from a zone map reporting 50-year recurrence intervals of an extreme snow depth. EARTHQUAKE LOADS Earthquakes produce lateral loadings on a structure through the structure’s interaction with the ground. The magnitude of an earthquake load depends on the amount and type of ground accelerations and the mass and stiffness of the structure. In order to show how earthquake loads occur, consider the simple structural model in the figure. This model may represent a single-storey building, where the block is the “lumped” mass of the roof, and the column has a total stiffness representing all the building’s columns. During an earthquake, the ground vibrates both horizontally and vertically. The horizontal accelerations create shear forces in the column that put the block in sequential motion with the ground. If the column is stiff and the block has a small mass, the period of vibration of the block will be short and the block will accelerate with the same motion as the ground and undergo only slight relative displacements. For an actual structure that is designed to have large amounts of bracing and stiff connections, this can be beneficial, since less stress is developed in the members. On the other hand, if the column in the figure is very flexible and the block has a large mass, then earthquake-induced motion will cause small accelerations of the lock and large relative displacements. Some codes require that specific attention e given to earthquake design, especially in areas of th country where strong earthquakes predominate. OTHER NATURAL LOADS Several other types of live loads may also have to be considered in the design of a structure, depending on its location or use. These include the effect of blast, temperature changes, and differential settlement of the foundation. STRUCTURAL DESIGN Whenever a structure is designed, it is important to give consideration to both material and load uncertainties. These uncertainties include a possible variability in mmaterial properties, residual stress in materials, intended measurements being different from fabricated sizes, loadings due to vibration or impact, and material corrosion or decay. ALLOWABLE STRESS DESIGN (ASD) Allowable Stress Design (ASD) or Working Stress Design (WSD) methods include both the material and load uncertainties into a single factor of safety. The many types of loads discussed previously can occur simultaneously on a structure but it is very unlikely that the maximum of all these loads will occur at the same time. For example, both maximum wind and earthquake loads normally do not act simultaneously on a structure. For allowable-stress design the computed elastic stress in the material must not exceed the allowable stress for each of various load combinations. LOAD AND RESISTANCE FACTOR DESIGN (LRFD) Since uncertainty can be considered using probability theory, there has been an increasing trend to separate material uncertainty from load uncertainty. This method is called strength design or LRFD (Load and Resistance Factor Design). For example, to account for the uncertainty of loads, thismethod uses load factors applied to the loads or combinations of loads. The combination of loads is thought to provide a maximum, yet realistic loading on the structure.