STRUCTURAL ANALYSIS

Table of Contents 1.1 INTRODUCTION 1 1.2 What is STRUCTURAL ANALYSIS 1 1.3 Objectives of report 1 2.1 Indeterminate Structure 2 2.2 Determinate Structure 3 2.3 Difference between Determinate and Indeterminate Structures 3 2.4 Classification of Structures 4 2.4.1 Structural Elements 4 2.4.2 Tie Rods 4 2.4.3 Beams 4 2.4.4 Columns 5 2.5 Types of Structures 5 2.5.1 Trusses 5 2.5.2 Cables and Arches. 6 2.5.3 Frames 8 2.6 Support Connections: 8 2.7 Determinacy and Stability 10 2.7.1 Determinacy 10 2.7.2 Stability 11 2.8 DETERMINATE STRUCTURES 12 2.8.1 Fan 12 2.8.2 Bulb Holder 12 2.8.3 Merry-Go-Round 12 12 2.8.4 Electric Pole 13 2.8.5 Column 13 2.9 INDETERMINATE STRUCTURE 14 2.9.1 Swing 14 2.9.2 Sign Board 14 2.9.3 Bench 15 2.9.4 Pipe Rod 15 3. FORCE MATHOD AND DISPLACEMENT METHOD OF ANALYSIS 17 3.1 Force Method 17 3.3 Application of Displacement Method 17 3.3.1 Slope-Deflection Method 17 4 COMPUTER BASED ANALYSIS OF INDETERMINATE STRUCTURE 19 4.1 About Software Used 19 4.1.1 SAP 2000 19 4.1.2 Microsoft Excel 20 4.2 Discussion and Comparison Long Hand Calculation Result with SAP200 20 4.3 Generate Excel Sheet for Analysis of the Given Problem 53 Problem 4.3.1 53 Problem 4.3.2 54 Problem 4.3.3 55 Problem 4.3.4 55 5 CALCULATIONS AND DISCUSION 57 5.1 What Have You Learned From the Report 57 5.2 Which Technique Is Preferable? Long Hand Calculation or Software Simulation for Analysis of Indeterminate Structure. And Why? 57 5.3 Suggestion for the Future Lab Report for Lab Work of SA-II 57 References: 57 Table of Figures Figure 2. 1: Indeterminate Structure 2 Figure 2. 2 (b): Types of Beams 4 Figure 2. 3: Typical cross section 4 Figure 2. 4: Columns 5 Figure 2. 5: Truss Member 6 Figure 2. 6: Arch & Cable 8 Figure 2. 7: Frame 8 Figure 2. 8: Connections 9 Figure 2. 9: Connections 9 Figure 2. 10: Supports & Joints 10 Figure 2. 11: Forces criteria according to supports 11 Figure 2. 12: Fan 12 Figure 2. 13: Bulb 12 Figure 2. 14: Merry-Go-Round 12 Figure 2. 15: Electrical Pole 13 Figure 2. 16: Column 13 Figure 2. 17: Swing 14 Figure 2. 18: Sign board 14 Figure 2. 19: Bench 15 Figure 2. 20: Pipe Rod 15 Figure 2. 21: Electric Transmission Pole 16  INTRODUCTION 1.1 INTRODUCTION In this report we discuss all work in lab and assignments of STRUCTURAL ANALYSIS given by ENGR NAJAM ABBAS. 1.2 What is STRUCTURAL ANALYSIS Structural analysis is the determination of the effects of loads on physical structures and their components. Structures subject to this type of analysis include all that must withstand loads, such as buildings, bridges, vehicles, machinery, furniture, attire, soil strata, prostheses and biological tissue. 1.3 Objectives of report Reports communicate information which has been compiled as a result of research and analysis of data and of issues. Reports can cover a wide range of topics, but usually focus on transmitting information with a clear purpose, to a specific audience. Good reports are documents that are accurate, objective and complete. They should also be well-written, clearly structured and expressed in a way that holds the reader's attention and meets their expectations. The true value of the research may be assessed through a report since the written report may be the "only tangible product of hundreds of hours of work. Rightly or wrongly, the quality and worth of that work are judged by the quality of the written report - its clarity, organization and content"  2 INDETERMINATE STRUCTURE In this chapter we will present some of the approximate methods used to analyze statically indeterminate trusses and frames. These methods were developed on the basis of structural behavior, and their accuracy in most cases compares favorably with more exact methods of analysis. Although not all types of structural forms will be discussed here, it is hoped that enough insight is gained from the study of these methods so that one can judge what would be the best approximations to make when performing an approximate force analysis of a statically indeterminate structure. 2.1 Indeterminate Structure In statics, a structure is statically indeterminate (or hyper static) when the static equilibrium equations are insufficient for determining the internal forces and reactions on that structure. Σ H = 0: the sum of the horizontal components of the forces equals zero; Σ V = 0: the sum of the vertical components of forces equals zero; Figure 2. 1: Indeterminate Structure 2.2 Determinate Structure Statically determinacy is a term used in structural mechanics to describe a structure where force and moment equilibrium conditions alone can be utilized to calculate internal member actions. Descriptively, a statically determinate structure can be defined as a structure where, if it is possible to find internal actions in equilibrium with external loads, those internal actions are unique. 2.3 Difference between Determinate and Indeterminate Structures Table 2.1: S. No. Determinate Structures Indeterminate Structures 1 Equilibrium conditions are fully adequate to analyze the structure. Conditions of equilibrium are not adequate to fully analyses the structure. 2 Bending moment or shear force at any section is independent of the material property of the structure. Bending moment or shear force at any section depends upon the material property. 3 The bending moment or shear force at any section is independent of the cross-section or moment of inertia. The bending moment or shear force at any section depends upon the cross-section or moment of inertia. 4 Temperature variations do not cause stresses. Temperature variations cause stresses. 5 No stresses are caused due to lack of fit. Stresses are caused due to lack of fit. 6 Extra conditions like compatibility of displacements are not required to analyze the structure. Extra conditions like compatibility of displacements are required to analyze the structure along with the equilibrium equations. 2.4 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. We will introduce some of these aspects now and expand on them at appropriate points throughout the text. 2.4.1 Structural Elements Some of the more common elements from which structures are composed are as follows. 2.4.2 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. 2.2 2.4.3 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. 2.3. 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 Figure 2. 2 (b): Types of Beams Figure 2.2 Typical cross section Figure 2. 3: Typical cross section Figure 2.4 Columns Figure 2. 4: Columns 2.4.4 Columns Members that are generally vertical and resist axial compressive loads are referred to as columns, Fig. 2.4. 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. These members are referred to as beam columns. 2.5 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. 2.5.1 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, Fig. 2.5. Also, a truss is constructed from long and slender elements, which can be arranged in various ways to support a load. Most often it is economically feasible to use a truss to cover spans ranging from 30 ft. (9 m) to 400 ft. (122 m), although trusses have been used on occasion for spans of greater lengths. Figure 2.5: Truss Member Figure 2. 5: Truss Member Fig 2.5 Loading causes bending of truss, which develops compression in top members, tension in bottom members. 2.5.2 Cables and Arches. Two other forms of structures 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, Fig. 2–6a, 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. 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 only 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 structures, Fig. 2–6b, dome roofs, and for openings in masonry walls.  Figure 2. 6: Arch & Cable Cables support their loads in tension. (a) Arches support their loads in compression. (b) 2.5.3 Frames Frames are often used in buildings and are composed of beams and columns that are either pin or fixed connected, Fig. 2.7. 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. The strength of such a frame is derived from the moment interactions between the beams and the columns at the rigid joints. Figure 2. 7: Frame 2.6 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 Figure 2. 8: Connections Joints, fashioned in metal and concrete, are shown in Figs. 2.8 and 2.9, respectively. For most timber structures, the members are assumed to be pin connected, since bolting or nailing them will not sufficiently restrain them from rotating with respect to each other. Idealized models used in structural analysis that represent pinned and fixed supports and pin-connected and fixed-connected joints are shown in Figs. 2.10a and 2.10b. In reality, however, all connections exhibit some stiffness toward joint rotations, owing to friction and material behavior. In this case a more appropriate model for a support or joint might be that shown in Fig. 2.9c. If the torsional spring constant the joint is a pin, and if k: q, the joint is fixed. Figure 2. 9: Connections Figure 2. 10: Supports & Joints 2.7 Determinacy and Stability Before starting the force analysis of a structure, it is necessary to establish the determinacy and stability of the structure. 2.7.1 Determinacy The equilibrium equations provide both the necessary and 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 r = 3n, statically determinate r > 3n, statically indeterminate Figure 2. 11: Forces criteria according to supports 2.7.2 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. 2.8 DETERMINATE STRUCTURES 2.8.1 Fan Figure 2. 12: Fan Because the member of reaction is equal to the number of equilibrium condition that’s why beam is determinate. 2.8.2 Bulb Holder Figure 2. 13: Bulb Because the member of reaction is equal to the number of equilibrium condition that’s why beam is determinate. 2.8.3 Merry-Go-Round Figure 2. 14: Merry-Go-Round 2.8.4 Electric Pole Figure 2. 15: Electrical Pole Because the member of reaction is equal to the number of equilibrium condition that’s why beam is determinate. 2.8.5 Column Figure 2. 16: Column Because the member of reaction is equal to the number of equilibrium condition that’s why beam is determinate. 2.9 INDETERMINATE STRUCTURE Figure 2. 17: Swing 2.9.1 Swing Because the number of reaction is more than the equilibrium condition and degree of indeterminacy is “3” that’s why frame is indeterminate. 2.9.2 Sign Board Figure 2. 18: Sign board Because the number of reaction is more than the equilibrium condition and degree of indeterminacy is “3” that’s why frame is indeterminate. 2.9.3 Bench Figure 2. 19: Bench Because the number of reaction is more than the equilibrium condition and degree of indeterminacy is “3” that’s why frame is indeterminate. 2.9.4 Pipe Rod Figure 2. 20: Pipe Rod Because the number of reaction is more than the equilibrium condition and degree of indeterminacy is “3” that’s why frame is indeterminate. 2.9.5 Electrical Transmission Pole Figure 2. 21: Electric Transmission Pole Because the number of reaction is more than the equilibrium condition and degree of indeterminacy is “3” that’s why frame is indeterminate.  3. FORCE MATHOD AND DISPLACEMENT METHOD OF ANALYSIS 3.1 Force Method The force method was originally developed by James Clerk Maxwell in 1864 and later refined by Otto Mohr and Heinrich Müller-Breslau. This method was one of the first available for the analysis of statically indeterminate structures. Since compatibility forms the basis for this method, it has sometimes been referred to as the compatibility method or the method of consistent displacements. This method consists of writing equations that satisfy the compatibility and force-displacement requirements for the structure in order to determine the redundant forces. Once these forces have been determined, the remaining reactive forces on the structure are determined by satisfying the equilibrium requirements. 3.2 Displacement Method The displacement method of analysis is based on first writing force-displacement relations for the members and then satisfying the equilibrium requirements for the structure. In this case the unknowns in the equations are displacements. Once the displacements are obtained, the forces are determined from the compatibility and force displacement equations. 3.3 Application of Displacement Method 3.3.1 Slope-Deflection Method As indicated previously, the method of consistent displacements studied in Point 3 is called a force method of analysis, because it requires writing equations that relate the unknown forces or moments in a structure. Unfortunately, its use is limited to structures which are not highly indeterminate. This is because much work is required to set up the compatibility equations, and furthermore each equation written involves all the unknowns, making it difficult to solve the resulting set of equations unless a computer is available. By comparison, the slope-deflection method is not as involved. As we shall see, it requires less work both to write the necessary equations for the solution of a problem and to solve these equations for the unknown displacements and associated internal loads. Also, the method can be easily programmed on a computer and used to analyze a wide range of indeterminate structures. The slope-deflection method was originally developed by Heinrich Manderla and Otto Mohr for the purpose of studying secondary stresses in trusses. Later, in 1915, G.A. Maney developed a refined version of this technique and applied it to the analysis of indeterminate beams and framed structures.  4 COMPUTER BASED ANALYSIS OF INDETERMINATE STRUCTURE 4.1 About Software Used There are two software used are following. 4.1.1 SAP 2000 Sap 2000 founded about 30 years ago and is the most widely used structural software in Latin America, Portugal, Italy and Spain. It is also very popular in Asia and UK as well. In parallel the second most widely used software are StaadPro, ETABS and Risa 3D.However, the grids provided in SAP makes it easier to create the geometric input than with the StaadPro or any other software of the same kind. Dynamic analysis is stronger in SAP2000 for example earthquake force applied in any direction, automatic lumping of masses for earthquake, live load reduction, bridges transient loads, eigen modes and ritz modes, etc. it has facilities for creep and shrinkage of concrete. Its ability to solve heterogeneous soil-structure interaction clearly differentiates it from others. 4.1.2 Microsoft Excel There is no need to explain that how important this software is. It is obvious that none of the person can start his professional career especially office work without knowing the importance and usability of Microsoft Office products like MS Word, MS Excel, MS PowerPoint and list goes on. If you want to become a good Civil Engineer your top most choice for software should be Microsoft Office. 4.2 Discussion and Comparison Long Hand Calculation Result with SAP200 Advantages, Disadvantages, and Conclusion Advantages and Disadvantages to the Client There are a number of advantages to the proof of concept (POC) for the client including Expectation synchronization with the vendor Improved ownership of the implementation process Identification of functional gaps or overselling Better understanding of investment required. More accurate scoping provides a better understanding of the investment required to complete the implement  4.3 Generate Excel Sheet for Analysis of the Given Problem Problem 4.3.1 Problem 4.3.2 Problem 4.3.3 Problem 4.3.4  5 CALCULATIONS AND DISCUSION 5.1 What Have You Learned From the Report I think it's a good experience for me and now I am so happy for completion of the report. I learn more thing from this report now I can work on Microsoft office easily. Now I am able to compose anything on Microsoft office with complete specification of any document that required. 5.2 Which Technique Is Preferable? Long Hand Calculation or Software Simulation for Analysis of Indeterminate Structure. And Why? I think software simulation is preferable, because the software is more accurate then long hand calculation. The software have very less chance of error, and it’s very fast. We can save time and money through the software. 5.3 Suggestion for the Future Lab Report for Lab Work of SA-II My suggestion is that making of report is very hard work so it should be assign for student after mid-term examination. The report is very help full for the preparation of final year project report.  References: Structural Analysis by “R.C Hibbeler”, Eight edition Notes by “Engineer Najam Abbas” Theory Structures by “Stephen-P-Timoshenko” Basic Structural Analysis by C.S Reddy CHAPTER-1 CHAPTER-2 CHAPTER-3 CHAPTER-4 CHAPTER-5 CALCULATIONS AND DISCUSION References 3 10 19 21 26