Structural Analysis and Design of Structural Elements of A Building

1.1 General Engineering is a professional art of applying science to the efficient conversion of natural resources for the benefit of man. Engineering therefore requires above all creative imagination to innovative useful application for natural phenomenon. The design process of structural planning and design requires not only imagination and conceptual thinking but also sound knowledge of science of structural engineering besides the knowledge of practical aspects, such as recent design codes, bye laws, backed up by ample experience, intuition and judgment. The purpose of standards is to ensure and enhance the safety, keeping careful balance between economy and safety.


General
Engineering is a professional art of applying science to the efficient conversion of natural resources for the benefit of man. Engineering therefore requires above all creative imagination to innovative useful application for natural phenomenon. The design process of structural planning and design requires not only imagination and conceptual thinking but also sound knowledge of science of structural engineering besides the knowledge of practical aspects, such as recent design codes, bye laws, backed up by ample experience, intuition and judgment. The purpose of standards is to ensure and enhance the safety, keeping careful balance between economy and safety.
The process of design commences with planning of the structure, primarily to meet its functional requirements. Initially, the requirements proposed by the client are taken into consideration. They may be vague, ambiguous or even unacceptable from engineering point of view because he is not aware of the various implications involved in the process of planning and design, and about the limitations and intricacies of structural science.
It is emphasized that any structure to be constructed must satisfy the need efficiently for which it is intended and shall be durable for its desired life span. Thus, the design of any structure is categorized into the following two main types 1) Functional design 2) Structural design. @ IJTSRD | Available Online @ www.ijtsrd.com | Volume -2 | Issue -3 | Mar-Apr 2018 professional art of applying science to the efficient conversion of natural resources for the benefit of man. Engineering therefore requires above all creative imagination to innovative useful tural planning and design requires not only imagination and conceptual thinking but also sound knowledge of science of structural engineering besides the knowledge of practical aspects, such as recent design codes, bye laws, backed intuition and judgment. The purpose of standards is to ensure and enhance the safety, keeping careful balance between economy and The process of design commences with planning of the structure, primarily to meet its functional requirements. Initially, the requirements proposed by the client are taken into consideration. They may be vague, ambiguous or even unacceptable from ng point of view because he is not aware of the various implications involved in the process of planning and design, and about the limitations and It is emphasized that any structure to be constructed eed efficiently for which it is intended and shall be durable for its desired life span. Thus, the design of any structure is categorized into

Functional design
The structure to be constructed should be primarily serve the basic purpose for which it is to be used and must have a pleasing look. The building should provide happy environment inside as well as outside. Therefore, the functional planning of a building must take proper arrangements of rooms / halls to satisfy the need of the client, good ventilation, lighting, acoustics, unobstructed view in the case of community halls, cinema halls, etc.. sufficient head room, proper water supply and drainage arrangements, planting of trees etc. bearing all these aspects in mind the architect/engineer has to decide whether it should be a load bearing structure or R.C.C framed structure or a steel structure etc..

Structural design
Structural design is an art and science of understanding the behavior of structural members subjected to loads and designing them with economy and elegance to give a safe, serviceable and durable structure. re to be constructed should be primarily serve the basic purpose for which it is to be used and The building should provide happy environment inside as well as outside. Therefore, the functional planning of a building must take into account the proper arrangements of rooms / halls to satisfy the need of the client, good ventilation, lighting, acoustics, unobstructed view in the case of community halls, cinema halls, etc.. sufficient head room, proper water supply and drainage angements, planting of trees etc. bearing all these aspects in mind the architect/engineer has to decide whether it should be a load bearing structure or R.C.C framed structure or a steel structure etc.. Structural design is an art and science of understanding the behavior of structural members subjected to loads and designing them with economy and elegance to give a safe, serviceable and durable To make a study about the analysis and design of To make a study about the guidelines for the design of principle elements of a R.C building frame according to IS code. To analyze manually the problem frame, using Substitute Frame method under vertical loading Hardy cross method is application of continuity of flow and continuity of potential in which flow is equal in all directions. He accomplished the task by distributing unbalanced moments known as CROSS METHOD.
Galileo Galilei (1564-1642) has worked on theory of structures. In his book entitled Two New Science which was published in 1638, Galileo analyzed the failure of some simple structures, including cantilever beams. Although Galileo's predictions on 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.
Leonhard Euler (1707-1783) has investigated on the theory of buckling of columns. He was the first person to realize that the failure of slender columns takes place because of buckling. He formulated his famous equation in 1744 for predicting the buckling load of columns which are not stressed above the proportional limits and proposed that buckling involves parameters such as shaft section& elastic properties, coupling strength & stiffness, soil strength& stiffness and the eccentricity of applied load. He solved the question of critical compression load with = components are carried out in a single line diagram of the structure. His method is convenient for multistoried building frames in vertical and lateral loading conditions as it is self correcting.
Claude-Louis Navier has worked out on the elastic behavior of structures in mathematical form in 1821 making it available to the field of construction with sufficient accuracy in 1826 as elastic formed as a basic until World War II when bombs damaged buildings was unpredictable. Navier is considered as a founder of modern structure analysis. He published elastic theory of beams in 1826 along with three methods for analyzing forces in trusses.
Daniel Bernoulli has investigated on the structural technology such as beams and columns. In 1705, he proposed a paper that the curvature of beams is directly proportional to its bending moment and used this theory to address the transverse vibrations of beams. Euler following Bernoulli introduced the concept of strain energy per unit length of beam is directly proportional to the beam curvature.

CHAPTER-3 STRUCTURAL ANALYSIS AND GUIDELINES FOR REINFORCEMENT 3.1 Structural analysis
A structure refers to a system of two or more connected parts use to support a load. It is an assemblage of two or more basic components connected to each other so that they serve the user and carry the loads developing due to the self and superimposed loads safely without causing any serviceability failure. Once a preliminary design of a structure is fixed, the structure then must be analyzed to make sure that it has its required strength and rigidity. To analyze a structure a structure correctly, certain idealizations are to be made as to how the members are supported and connected together. The loadings are supposed to be taken from respective design codes and local specifications, if any. The forces in the members and the displacements of the joints are found using the theory of structural analysis. The whole structural system and its loading conditions might be of complex nature so to make the analysis simpler, we use certain simplifying assumptions related to the quality of material, member geometry, nature of applied loads, their distribution, the type of connections at the joints and the support conditions. This shall help making the process of structural analysis simpler to quite an extent.

Methods of structural analysis
When the number of unknown reactions or the number of internal forces exceeds the number of equilibrium equations available for the purpose of analysis, the structure is called as a statically indeterminate structure. Most of the structures designed today are statically indeterminate.
While analyzing any indeterminate structure, it is essential to satisfy equilibrium, compatibility, and force-displacement requisites for the structure. When the reactive forces hold the structure at rest, equilibrium is satisfied and compatibility is said to be satisfied when various segments of a structure fit together without intentional breaks or overlaps. Two fundamental methods to analyze the statically indeterminate structures are discussed below.

Force methods
Originally developed by James Clerk Maxwell in 1864, later developed by Otto Mohr and Heinrich Muller-Breslau. As compatibility is the basis for this method, it is sometimes also called as compatibility method or the method of consistent displacements. In this method, equations are formed that satisfy the compatibility and force-displacement requirements for the given structure in order to determine the redundant forces. Once these forces are determined, the remaining reactive forces on the given structure are found out by satisfying the equilibrium requirements.

Displacement methods
In these methods, we first write load-displacement relations for the members of the structure and then satisfy the equilibrium requirements for the same. In here, the unknowns in the equations are displacements. Unknown displacements are written in terms of the loads (i.e. forces) by using the loaddisplacement relations and then these equations are solved to determine the displacements. As the displacements are determined, the loads are found out from the compatibility and load-displacement equations. Some classical techniques used to apply the displacement method are discussed.

Slope deflection method
This method was devised by Heinrich Manderla and Otto Mohr to study the secondary stresses in trusses.
The basic assumption of this method is to consider the deformations caused only by bending moments. It's assumed that the effects of shear force or axial force The fundamental slope-deflection equation expresses the moment at the end of a member as the superposition of the end moments caused due to the external loads on the member, while the ends being assumed as restrained, and the end moments caused by the displacements and actual end rotations. A structure comprises of several members, slopedeflection equations are applied to each of the member. Using appropriate equations of equilibrium for the joints along with the slope-deflection equations of each member we can obtain a set of simultaneous equations with unknowns as the displacements. Once we get the values of these unknowns i.e. the displacements we can easily determine the end moments using the slope-deflection equations.

Moment distribution method
This method of analyzing beams and multi-storey frames using moment distribution was introduced by Prof. Hardy Cross in 1930, and is also sometimes referred to as Hardy Cross method. It is an iterative method in which one goes on carrying on the cycle to reach to a desired degree of accuracy. To start off with this method, initially all the joints are temporarily restrained against rotation and fixed end moments for all the members are written down. Each joint is then released one by one in succession and the unbalanced moment is distributed to the ends of the members, meeting at the same joint, in the ratio of their distribution factors. These distributed moments are then carried over to the far ends of the joints. Again the joint is temporarily restrained before moving on to the next joint. Same set of operations are performed at each joints till all the joints are completed and the results obtained are up to desired accuracy. The method does not involve solving a number of simultaneous equations, which may get quite complicated while applying large structures, and is therefore preferred over the slope-deflection method.
Kani's method This method was first developed by Prof. Gasper Kani of Germany in the year 1947. The method is named after him. This is an indirect extension of slope deflection method. This is an efficient method due to simplicity of moment distribution. The method offers an iterative scheme for applying slope deflection method of structural analysis. Whereas the moment distribution method reduces the number of linear simultaneous equations and such equations needed are equal to the number of translator displacements, the number of equations needed is zero in case of the Kani's method. This method may be considered as a further simplification of moment distribution method wherein the problems involving sway were attempted in a tabular form thrice (for double story frames) and two shear coefficients had to be determined which when inserted in end moments gave us the final end moments. All this effort can be cut short very considerably by using this method. Frame analysis is carried out by solving the slope−deflection equations by successive approximations. Useful in case of side sway as well. Operation is simple, as it is carried out in a specific direction. If some error is committed, it will be eliminated in subsequent cycles if the restraining moments and distribution factors have been determined correctly.

Method of substitute frames
A substitute frame consists of a small portion of the multistory, multi-bay frame generally comprising of the floor beams, with the columns above and below the floor assumed to be fixed at the far ends as shown in figure 1.
It is sufficient to consider the loads on the two nearest spans on each side of the joint under consideration. The continuous beam is analyzed for vertical loads by moment distribution to compute the maximum span and support moments using the following criterion:

Slabs
Minimum reinforcement: The minimum reinforcement in either direction in slabs should not be less than 0.15% of total cross-sectional area using mild steel reinforcement & 0.12% of total crosssectional area using high strength deformed reinforcement or welded wire fabric. The maximum diameter of reinforcing bars should not exceed 1/8 th of total thickness of slab.

Columns
There are two types of reinforcements in columns: longitudinal reinforcement and transverse reinforcement.
The purpose of transverse reinforcement is to hold vertical bars in position providing lateral supports so that individual bars cannot buckle outwards and split the concrete. Transverse reinforcement doesn't contribute to strength of a column directly.
Longitudinal reinforcement 1. The minimum area of cross-section of longitudinal bars must be less atleast 0.8% nor more than 6% of the gross-sectional area of the column. 2. In any column that has a larger cross-sectional area more than the required to support the load, the minimum steel % is based on the area of concrete required to resist the direct stress and not upon the actual area.

The minimum number of longitudinal bars
provided a column shall be 4 in rectangular columns & 6 in circular columns. 4. The bars shall not be less than 12mm in diameter. 5. A reinforced concrete column having helical reinforcement shall have atleast 6 bars of longitudinal reinforcement. 6. In a helically reinforced column, the longitudinal bars shall be in contact with the helical reinforcement and equidistant around its inner circumference. 7. Spacing of longitudinal bars measured along the periphery of the column shall not exceed 300mm. 8. In case of pedestals in which longitudinal reinforcement isn't taken into account in strength calculations, nominal longitudinal reinforcement not less than 0.15% of the cross sectional area shall be provided. longitudinal bars in between these bars are to be tied in one direction by open ties. 3. Where the longitudinal reinforcing bars in a compression members are placed in more than one row, effective lateral supports to the longitudinal bars in the inner rows may be assumed to have been provided if: i. Transverse reinforcement is provided for the outer-most row. ii.
No bar of the inner row is closer to the nearest compression face than 3times the diameter of the largest bar in the inner row. 4. Where the longitudinal bars in a compression member are grouped such that they are not in contact and each group is adequately tied with transverse reinforcement.
lateral ties 1. The diameter of the polygonal links or lateral ties should not be less than 1/4 th of the diameter of the largest longitudinal bar, and in no case less than 6mm. 2. The pitch of the lateral ties should not exceed the following distances: i. The least lateral dimension of the compression member. ii.
16 times the smallest diameter of the longitudinal reinforcement bar to be tied, and iii. 300mm.

CHAPTER-4 ANALYSIS AND DESIGN 4.1 Approximate analysis for vertical loads / Substitute frame method:
Consider a building frame as shown in figure 5. Any typical beam in this building frame is subjected to axial force, bending moment and shear force.      Slabs are plane structural members forming floors and roofs of building whose thickness is quite small compared to their other dimensions. When the ratio of the length to the width of a slab is more then 2, and then most of the load is carried by shorter span and in such a case is known as one-way in case the ratio is less than 2 then it is called a twoway slab.