STRUCTURE ANALYSIS-1 structural elements.pptx
- 1. STRUCTURAL ANALYSIS 1 Structural system (Classification, types of structures), support conditions, determinacy, stability Instructor: Engr. Hajrah Nosheen
- 2. Week Contents Relevance w Weekly Break Up Field Application CLO 1. Introduction to structural supports, types of beam redundancy and stability of structure Structural safety CLO1 2. Shear force and bending moment diagram of VDL beam Structural design CLO2 3. Determination of Member forces of truss by method of joint Truss analysis for structures CLO1,2 P 4. Determination of Member forces of truss by method of section CLO1,2 P 5. Axial force, shear force and bending moment diagram of frame Structural Frame design CLO1,2 P 6. Axial force, shear force and bending moment diagram of frame CLO2 7. Influence line Diagram for reactions and shear of beam under moving loads Bridge design, design of beams & trusses used in crane rails, conveyor belts, floor girders, etc. CLO1,2 P 8. Influence line Diagram for shear and bending of beam under moving loads CLO2 9. Analysis of cables Analyzing suspension bridges, transmission lines and power cables CLO1,2 P 10. Analysis of Arches Force and deformation analysis of arches CLO1,2 P 11. Rotation and deflection by conjugate Beam method (Simply supported Beam) Analysis of beam for any type of structure, buckling, rotation and deformation behavior CLO1,2 P 12. Rotation and deflection by conjugate Beam method (Cantilever Beam) CLO1,2 P 13. Rotation and deflection by moment area method (Simply supported Beam) CLO1,2 P 14. Rotation and deflection by moment area method (Cantilever Beam) CLO1,2 P 15. Rotation and deflection by principle of virtual work method (Simply supported Beam) CLO1,2 P 16. Rotation and deflection by principle of virtual work method (Cantilever Beam) CLO1,2 P
- 3. Structural system • The combination of structural elements and the materials from which they are composed is referred to as a structural system. • A structure refers to a system of connected parts used to support a load. Important examples related to civil engineering include buildings, bridges, and towers; and in other branches of engineering, ship and aircraft frames, tanks, pressure vessels, mechanical systems, and electrical supporting structures are important. • When designing a structure to serve a specified function for public use, the engineer must account for its safety, esthetics, 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
- 4. 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, Fig. 1–1.
- 5. 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, as indicated in Fig. 1–2. • 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 aluminum, the cross section is most efficient when it is shaped as shown in Fig. 1–3. This cross section is commonly referred to as a “wide flange,” and it is normally formed as a single unit in a rolling mill in lengths up to 75 ft (23 m). • 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 togetherat 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 solid sections of wood, which are fastened together using high- strength glues.
- 6. • Columns. • Members that are generally vertical and resist axial compressive loads are referred to as columns, Fig. 1–4. • 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.
- 7. Types of Structures • 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 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. • Economically feasible to use a truss to cover spans ranging from 30 ft(9 m) to 400 ft (122 m).
- 8. • Cables and Arches. • Cables are usually flexible and carry their loads in tension. They are commonly used to support bridges, Fig. 1–6a, 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. • 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 structures, Fig. 1–6b, dome roofs, and for openings in masonry walls.
- 9. • Frames. • Frames are often used in buildings and are composed of beams and columns that are either pin or fixed connected, Fig. 1–7. • 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 of analysis.
- 10. Surface Structures • A surface structure is made from a material having a 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 structure. In both cases the material acts as a membrane that is subjected to pure tension. • Surface structures may also be made of rigid material such as reinforced concrete. As such they may be shaped as folded plates, cylinders, 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 structures are generally very difficult to analyze, due to the three-dimensional geometry of their surface.
- 11. Loads • Loads are specified in codes such as the ASCE 7-10 code. • Dead loads are fixed and refer to the weights of members and materials. • Live loads are movable and consist of uniform building floor loads, traffic and train loads on bridges, impact loads due to vehicles and machines, wind loads, snow loads, earthquake loads, and hydrostatic and soil pressure.
- 12. Support Connections • Structural members are joined together in various ways depending on the intent of the designer. • The three types of joints most often specified are the pin connection, the roller support, and the fixed joint. • A pin-connected joint and a roller support allow some freedom for slight rotation, whereas a fixed joint allows no relative rotation between the connected members and is consequently more expensive to fabricate. • Examples of these joints, fashioned in metal and concrete, are shown in Figs. 2–1 and 2–2, respectively
- 15. Principle of superposition • The principle of superposition forms the basis for much of the theory of structural analysis. It may be stated as follows: The total displacement or internal loadings (stress) at a point in a structure subjected to several external loadings can be determined by adding together the displacements or internal loadings (stress) caused by each of the external loads acting separately. • For this statement to be valid it is necessary that a linear relationship exist among the loads, stresses, and displacements. • Two requirements must be imposed for the principle of superposition to apply: 1. The material must behave in a linear-elastic manner, so that Hooke’s law is valid, and therefore the load will be proportional to displacement. 2. The geometry of the structure must not undergo significant change when the loads are applied, i.e., small displacement theory applies.
- 16. Determinacy • The equilibrium equations provide both the necessarymand sufficient conditions for equilibrium. • When all the forces in a structure can be determined strictly from these equations, the structure is referred to as statically determinate. • Structures having more unknown forces than available equilibrium equations are called statically indeterminate. • As a general rule, a structure can be identified as being either statically determinate or statically indeterminate by drawing free-body diagrams of all its members, or selective parts of its members, and then comparing the total number of unknown reactive force and moment components with the total number of available equilibrium equations. • For a coplanar structure there are at most three equilibrium equations for each part, so that if there is a total of n parts and r force and moment reaction components, we have
- 18. • Stability. To ensure the equilibrium of a structure or its members, it is not only necessary to satisfy the equations of equilibrium, but the members must also be properly held or constrained by their supports. Two situations may occur where the conditions for proper constraint have not been met. • Partial Constraints. In some cases a structure or one of its members may have fewer reactive forces than equations of equilibrium that must be satisfied. The structure then becomes only partially constrained. For example, consider the member shown in Fig. 2–22 with its corresponding free-body diagram. Here the equation will not be satisfied for the loading conditions and therefore the member will be unstable. • Improper Constraints. In some cases there may be as many unknown forces as there are equations of equilibrium; however, instability or movement of a structure or its members can develop because of improper constraining by the supports. This can occur if all the support reactions are concurrent at a point. Another way in which improper constraining leads to instability occurs when the reactive forces are all parallel
- 21. Shear force and bending moment diagrams of beams Field application: Used in structural design to find maximum loads so that we can optimize the design to prevent failure and reduce weight and cost of overall structure. Shear on a member allow the ripping of a member in opposite direction. Force V is resisting shear. Bending moment is a reaction induced in a structural member when an external force or moment is applied to member, causing it to bend. Couple M is resisting or applied moment.
- 22. Types of Loading • Loads applied to the beam may consist of a concentrated load (load applied at a point), uniform load, uniformly varying load, or an applied couple or moment. These loads are shown in the following figures.