Automation in Structural Analysis & Design
What is a Structure?
A structure is anything that you see around you from buildings to your own body. Everything has a structure, when we say structure we are referring to a system with connected parts that supports a load. There are two key distinctions when referring to a structure:
They must be capable of carrying the loads without collapsing.
They must support the various parts of the external load in the correct relative position.
When dealing with structure analysis we will always see simple and complex structures. We will be focusing on the structural efficiency and the economic efficiency of a design. To take this one step further, we will be adhering to matrix methods, but we will be using a simple computation tool to understand how the structure responds.
To understand any structure, we must first look at the building blocks. Structural members are subjected to a tensile force. Due to the nature of the load, these members are slender and are often chosen from rods, bars, angles, or channels.
A beam is the simplest 2-D structure that you will learn in this course. Another common example of a structural element that you see in everyday life is a beam. These are straight horizontal members designed to carry vertical loads. Beams may be designed from several elements and materials such as concrete or metal, and they have different cross-sections. When you see a complex structure you can break it down to simple elements, like beams.
They are generally vertical and resist compressive loads. Columns are elements similar to the tie rods but they carry vertical loads and axial loads. Columns support beams and transfers loads from the beam to the ground.
Trusses are an assembly of beams and other elements. In this course, you will learn about how to write simple automation codes to solve for the value of Trusses. They are composed of slender rods usually arranged in a triangular fashion. Trusses are suitable for constructions with large spans when the depth is not an important criterion for design. Plane trusses are composed of members that lie in the same plane, this truss can be extended to a complex called 3-Dimensional plane and the top beams or columns of the Truss are in compression and the bottom beams or columns are in tension. The interior part of a Truss is called a web and the area between the webs is called a panel. Trusses are frequently used for bridge and roof support.
This composite structure is a simple determinate frame used generally as a base element for complicated frame structures; they are mostly used as a covering structure. Most three-hinged frames are statically determinate structures. Three-hinged frames are the easiest to solve for using automation script, they are simple and can be determined by using the equilibrium reactions.
They are often used in buildings and are composed of beams and columns which are with a hinge or rigid connections, which determines how the load is shared. These structures are usually indeterminate and the load causes bending of its members. Frames also serve as support and shape for the structure, usually as a connection between beams and columns.
A common example in civil engineering is wall framing, including vertical and horizontal members of exterior walls and interior partitions - studs, wall-plates, serving as a nailing base for covering material, and support the upper floors, ceiling, and roof.
Whereas in mechanical engineering, a frame has to support a vehicles mechanical components and body to deal with static and dynamic loads without undue deflection or distortion.
These structures can be made from a flexible or rigid material and have a three-dimensional shape like a cylinder hyperbolic paraboloid. The analysis of these structures is also aimed at the theory of elasticity. This is because these structures are also subjected to tension or compression forces. A common example of this structure is folded plates.
The way Surface structures differ from 2-D structures are they in which they transfer the load - membrane stresses. They have relatively smaller thickness and are quite susceptible to buckling failure where the loads are static in nature.
In order to analyze a structure, we must first understand how the structure responds to certain actions. One way to introduce an action is by adding a load to the structure. We will be looking at different types of structural loads, such as concentrated forces, concentrated moments, and distributed loads.
Structural loads are forces, deformations, or accelerations applied to structural components.
We will be discussing how the input to a structure produces a response, and this response acts as an input to another structure frame. This is where breaking down a complex structure into simpler frames comes into the picture, we will be analyzing how a response becomes an input to a structure. When we receive a response we need to understand whether the structure is in a serviceable state, or undergoes failure, and what nature of failure does the structure experience.
Once the dimensional requirements for a structure have been defined, it becomes necessary to determine the loads the structure must support. Structural design, therefore, begins with specifying loads that act on the structure. The design loading for a structure is often specified in building codes. There are two types of codes: general building codes and design codes, engineers must satisfy all of the code's requirements in order for the structure to remain reliable.
Some loads you may have heard of include dead loads, live loads, impact loads, cyclic loads. Dead loads consist of the weights of the various structural members and the weights of any objects that are permanently attached to the structure. Live loads are moving loads.
For example, columns, beams, girders, the floor slab, roofing, walls, windows, plumbing, electrical fixtures, and other miscellaneous attachments.
Live loads vary in their magnitude and location. There are many different types of live loads like building loads, highway bridge loads, railroad bridge loads, impact loads, wind loads, snow loads, earthquake loads, and other natural loads.
Some other loads we see are terminal loads and fire loads. In recent times we have seen different structures undergoing accidents. And if you see the response to these structures after these accidents, you will see the failure of structure members; for example, columns and beams. So, we will be looking at finding limit loads and taking it towards safety.
Determinate Structures are analyzed just by using basic equilibrium equations. By this analysis, the unknown reactions are found for the further determination of stresses.
Some examples of determinate structures would include: simply supported beams, cantilever beams, single and double overhanging beams, three-hinged arches, etc.
Redundant or Indeterminate Structures are not capable of being analyzed by mere use of equilibrium equations. Along with the basic equilibrium equations, some extra conditions are required to be used like compatibility conditions of deformations, etc. to get the unknown reactions for drawing bending moment and shear force diagrams.
Some examples of indeterminate structures include fixed beams, continuous beams, fixed arches, two hinged arches, portals, multistoried frames, etc.
Indeterminate and determinate structures cannot be solved by using equilibrium equations, by developing a general script, we can simplify this complex method of analysis - the force method and the displacement method
The force method is used to calculate the response of statistically indeterminate structures to loads and/or imposed deformations. The method is based on transforming a given structure into a statistically determinate primary system and calculating the magnitude of the statistically redundant forces required to restore the geometric boundary conditions of the original structure. The force method (also called the flexibility method or the method of consistent deformation) is used to calculate reactions and internal forces statistically indeterminate structures due to loads and imposed deformations.
The force method expresses the relationship between displacement and forces that exist in a structure. The primary objective of the force method is to determine the chosen set of unknown forces and couple redundance. The number of redundancies is equivalent to the static indeterminacy of the structure, so that's where the degree of freedoms comes into place. When we deal with the concept of degree of indeterminacy we will also think about how to arrive at the degree of indeterminacy of a structure. Most of you might be using different formulas to calculate the degree of indeterminacy for a portal frame, three hinge, truss, etc. We will be combining everything to a simple form, a single formula. When you input your structure or the boundary conditions to this program, we will be arriving with a degree of indeterminacy that will help you to proceed with the force method that sets up their force matrix and displacement matrix to arrive at the response of the structures.
In the displacement method of analysis, the primary unknowns are the displacements. In this method, force-displacement relations are computed initially, and subsequently, equations are written satisfying the equilibrium conditions of the structure. After determining the unknown displacements, the other forces are calculated satisfying the compatibility conditions and force-displacement relations. The displacement-based method is amenable to computer programming and hence the method is being widely used in the modern-day structural analysis.
It works by satisfying the equilibrium equations for the structure, to do this the unknown displacements are returned. So previously the forces were the unknown terms, and now the displacements become the unknown terms by using the load-displacement relations, and these equations are solved for the displacements. Once the displacements are obtained, we get the unknown loads from the compatibility equations using the load-displacement relation.
But you might be wondering, why do we need to know about both the methods when developing a general script?
In the industry, there is no permeance given to any one method, all you need to know is basic fundamentals to arrive at a solution to respond to the structure, so it’s good to know both. Also, all the displacement methods follow a general procedure and are the same with the force methods.
Why should you learn this?
When you enter an organization, chances are that you will have to work with a design software that is of considerable sophistication.
MASTAN2 is an interactive structural analysis program that provides preprocessing, analysis, and post-processing capabilities. It’s used as a tool to analyze how different structures will react under specific loading conditions. It does this by using the MATLAB engine to do its calculations, it can do a wide range of analyses that are cumbersome or impossible on paper.
Preprocessing options include the definition of structural geometry, support conditions, applied loads, and element properties. The analysis routines provide the user the opportunity to perform first or second-order elastic or inelastic analysis of two or three-dimensional frames and trusses subjected to static loads.
Working With MASTAN
In order to analyze a structure, you must input it into the program. The most relevant components that you must know are as follows:
Connections (fixed/pinned, frame/truss)
Sections (Define and Attach)
A: cross-sectional area of each beam
I: second moment of area
L: torsion constant
Materials (Define and Attach)
E: modulus of elasticity
V: Poisson’s ratio
Fixities (physical restraints on the structure)
Loads (also, Moments and Distributed Loads)
This course will focus on the analyses and design of structures and writing automation scripts for them, therefore it is important to first understand the definition of a structure.
The course structure is focused on structural analysis and design. It is a fundamental concept for any Mechanical or Civil Engineer. By the end of this course, you will have learned how to analyze complex space frame structures in simple methods, how to create simulations of matrix methods using the post-processing features of MATLAB, and Parametric Design Optimization.
This is not only to refresh your skills in engineering, but also to prepare you for future projects. Once a student completes this course, they can, for example, look at a structure and understand how it will react to different loads acting on it.
You will also gain valuable knowledge over concepts, as well as tools such as::
SAP 2000, REVIT, Abaqus - for Civil Engineers
Solidworks, Ansys, Cosmol - for Mechanical Engineers.
Throughout this course, we will be using different computation tools to help us analyze structures. This is to prepare you for the coursework you will receive in higher education. You will also gain strong fundamentals for GATE and IES examinations.
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