Mechanics of Deformable Structures: Part 1 from edX

Many natural and man-made structures can be modeled as assemblages of interconnected structural elements loaded along their axis (bars), in torsion (shafts) and in bending (beams). In this course you will learn to use equations for static equilibrium, geometric compatibility and constitutive material response to analyze structural assemblages.

This course provides an introduction to behavior in which the shape of the structure is permanently changed by loading the material beyond its elastic limit (plasticity), and behavior in which the structural response changes over time (viscoelasticity).

This is the second course in a 3-part series. In this series you will learn how mechanical engineers can use analytical methods and “back of the envelope” calculations to predict structural behavior. The three courses in the series are:

Part 1 – 2.01x: Elements of Structures. (Elastic response of Structural Elements: Bars, Shafts, Beams).Part 2 – 2.02.1x Mechanics of Deformable Structures: Part 1. (Assemblages of Elastic, Elastic-Plastic, and Viscoelastic Bars in axial loading).Part 3 – 2.02.2x Mechanics of Deformable Structures: Part 2. (Assemblages of bars, shafts, and beams. Multi-axial Loading and Deformation. Energy Methods).

These courses are based on the first subject in solid mechanics for MIT Mechanical Engineering students. Join them and learn to rely on the notions of equilibrium, geometric compatibility, and constitutive material response to ensure that your structures will perform their specified mechanical function without failing.

What's inside

Learning objectives

Use free body diagrams to formulate equilibrium equations in structural assemblages
Identify geometric constraints to formulate compatibility equations in structural assemblages

Understand the formulation of thermo-elastic, elastic-perfectly-plastic and linear viscoelastic models for the material response
Analyze and predict the mechanical behavior of statically determinate and statically indeterminate assemblages with deormable bars in axial loading.

Use free body diagrams to formulate equilibrium equations in structural assemblages
Identify geometric constraints to formulate compatibility equations in structural assemblages
Understand the formulation of thermo-elastic, elastic-perfectly-plastic and linear viscoelastic models for the material response
Analyze and predict the mechanical behavior of statically determinate and statically indeterminate assemblages with deormable bars in axial loading.

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Provides a foundation in solid mechanics, which is essential for mechanical engineering students and professionals working with structural analysis and design

Based on the first subject in solid mechanics for MIT Mechanical Engineering students, offering a curriculum aligned with a top-tier engineering program

Explores thermo-elastic, elastic-perfectly-plastic, and linear viscoelastic models, which are crucial for understanding material behavior under various loading conditions

Requires students to take this course in serial with others as part of a series, which may be a barrier to some students

Presented by the Massachusetts Institute of Technology, which is known for its engineering programs and research

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Mechanics of Deformable Structures: Part 1 with these activities:

Review Statics and Mechanics of Materials

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Reinforce your understanding of fundamental concepts like stress, strain, and equilibrium, which are essential for analyzing deformable structures.

Browse courses on Mechanics of Materials

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Review your notes and textbooks from previous statics and mechanics courses.
Work through practice problems focusing on stress, strain, and free body diagrams.
Identify any areas where your understanding is weak and seek out additional resources.

Read 'Mechanics of Materials' by James M. Gere and Barry J. Goodno

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Use this book as a reference to deepen your understanding of the underlying principles of deformable structures.

View Mechanics of Materials on Amazon

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Read the chapters relevant to axial loading, stress, and strain.
Work through the example problems in the book.
Compare the book's approach to the course materials.

Solve Statically Indeterminate Problems

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Practice solving problems involving statically indeterminate structures to improve your ability to apply compatibility equations.

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Find practice problems involving statically indeterminate bars under axial loading.
Draw free body diagrams and write equilibrium equations.
Formulate compatibility equations based on geometric constraints.
Solve the system of equations to determine the unknown forces and displacements.

Four other activities

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Create a Material Property Database

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Compile a database of material properties for common structural materials to aid in future design and analysis projects.

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Research material properties such as Young's modulus, Poisson's ratio, and yield strength for various materials.
Organize the data into a spreadsheet or database.
Include sources for each material property.
Add notes on the limitations of each material property value.

Create a Free Body Diagram Guide

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Solidify your understanding of free body diagrams by creating a visual guide with examples relevant to deformable structures.

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Gather examples of structural elements under different loading conditions.
Draw free body diagrams for each example, clearly showing all forces and moments.
Write a brief explanation of how to create each free body diagram.
Share your guide with other students for feedback.

Analyze a Simple Truss Structure

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Apply your knowledge to analyze a simple truss structure, calculating member forces and displacements.

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Select a simple truss structure with known geometry and loading conditions.
Draw free body diagrams of the joints and members.
Apply the method of joints or method of sections to determine the member forces.
Calculate the displacements of the joints using compatibility equations.
Verify your results using structural analysis software.

Read 'Advanced Mechanics of Materials' by Arthur P. Boresi and Richard J. Schmidt

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Expand your knowledge of advanced topics in mechanics of materials to gain a deeper understanding of structural behavior.

View Advanced Mechanics of Materials on Amazon

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Read chapters on topics not covered in the course, such as fatigue or fracture.
Compare the book's treatment of topics to the course materials.
Consider how these advanced topics relate to real-world structural design.

Career center

Learners who complete Mechanics of Deformable Structures: Part 1 will develop knowledge and skills that may be useful to these careers:

Mechanical Engineer

Mechanical engineers design, develop, and manufacture mechanical devices and systems. A course like this one is useful for a mechanical engineer who is interested in the analysis and design of structures. This course will help one who wishes to become a mechanical engineer to understand how to use equations for static equilibrium, geometric compatibility, and constitutive material response to analyze structural assemblages. In addition, the course provides an introduction to plasticity and viscoelasticity, important concepts for those working with materials under various conditions. This course is particularly useful because it is based on the first subject in solid mechanics for MIT Mechanical Engineering students.

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Structural Engineer

A structural engineer designs and analyzes structures such as buildings and bridges, ensuring they can withstand various loads. This course helps a structural engineer understand how to analyze structural assemblages by using equations for static equilibrium, geometric compatibility, and constitutive material response. It also provides an introduction to material behavior when a structure is loaded beyond its elastic limit or when the structural response changes over time. A person interested in the field of structural engineering should take this course to learn how to predict structural behavior and design structures that are safe, reliable, and function as intended.

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Civil Engineer

Civil engineers plan, design, and oversee the construction of infrastructure projects such as roads, buildings, and bridges. This course provides a civil engineer with an understanding of how to analyze structural assemblages by using equations for static equilibrium, geometric compatibility, and constitutive material response. It discusses how mechanical engineers can use analytical methods and calculations to predict structural behavior. It also provides an introduction to plasticity and viscoelasticity. The course will help a civil engineer ensure that design choices are safe and effective, and that structures can withstand the forces they are expected to experience.

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Aerospace Engineer

Aerospace engineers design, test, and oversee the manufacturing of aircraft and spacecraft. This course helps an aerospace engineer learn to analyze structural assemblages using equations for static equilibrium, geometric compatibility, and constitutive material response. This is an important part of the design process for aerospace structures. The course also introduces the concepts of plasticity and viscoelasticity, which are critical for understanding how materials used in aircraft and spacecraft behave under different conditions. An aerospace engineer should take this course to learn how to predict and ensure the structural integrity of aircraft and spacecraft.

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Materials Scientist

Materials scientists research and develop new materials, as well as study the properties of existing ones. This course, which discusses the formulation of thermo-elastic, elastic-perfectly-plastic and linear viscoelastic models for material response, is relevant for materials scientists. A materials scientist should take this course to gain a stronger understanding of material behavior under various conditions.

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Automotive Engineer

Automotive engineers design and develop vehicles and their components. This course helps an automotive engineer understand how to analyze structural assemblages by using equations for static equilibrium, geometric compatibility, and constitutive material response. It also provides an introduction to material behavior when a structure is loaded beyond its elastic limit or when the structural response changes over time. This is important for designing safe, reliable, and high-performing vehicles. This course is helpful to learn more about the mechanical behavior of different materials and the structural integrity of components.

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Engineering Consultant

Engineering consultants provide expert advice to clients on various engineering-related projects. This course may help an engineering consultant who works in the field of structural analysis, providing a basis for understanding how to analyze structural assemblages with equations for static equilibrium, geometric compatibility, and constitutive material response. It will also introduce the concepts of plasticity and viscoelasticity, which are useful in assessing the behavior of structures under various loads. By understanding how mechanical engineers predict structural behavior, the consultant can provide sound advice to clients.

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Design Engineer

Design engineers create technical drawings and specifications for products and infrastructure. The analysis of structural assemblages using equations for static equilibrium, geometric compatibility, and constitutive material response taught in this course is useful to a design engineer who wishes to ensure that designs are structurally sound. The concepts of plasticity and viscoelasticity are also relevant to this role. This course may help a design engineer understand the mechanical behavior of materials, which will allow for more precise and robust designs.

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Product Development Engineer

Product development engineers are involved in the design, development, and testing of new products. This course may be useful to a product development engineer working with products that are mechanical in nature, specifically when predicting the behavior of those products under load. Gaining insight from this course, which examines equations for static equilibrium, geometric compatibility, and constitutive material response will allow the product development engineer to analyze structural assemblages, as well as gain an understanding of plasticity and viscoelasticity. This may help to ensure that products perform according to their specifications.

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Research Engineer

Research engineers conduct studies and investigations to develop new technologies and improve existing ones. This course may help a research engineer working on research related to the mechanical behavior of structures. This course will introduce the analysis of structural assemblages by using equations for static equilibrium, geometric compatibility, and constitutive material response. The course also introduces key concepts related to material behavior such as plasticity and viscoelasticity. These concepts can be important when developing new technologies.

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Test Engineer

Test engineers plan, design, and oversee tests of products and systems to ensure they meet quality and performance standards. This course may help a test engineer understand mechanical behavior, specifically when structures are loaded. This course introduces the analysis of structural assemblages through the use of equations for static equilibrium, geometric compatibility, and constitutive material response. It also introduces material behavior concepts like plasticity and viscoelasticity. Therefore, the test engineer could make more informed decisions in regards to testing and evaluation.

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Project Engineer

Project engineers oversee and coordinate engineering projects, ensuring they are completed on time and within budget. This course may be helpful for a project engineer working on projects involving structural components. It introduces the analysis of structural assemblages using equations for static equilibrium, geometric compatibility, and constitutive material response. In addition, it introduces key material concepts such as plasticity and viscoelasticity. In this way, a project engineer can better understand and manage the technical aspects of these projects.

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Academic Researcher

An academic researcher, often holding an advanced degree such as a master's or a doctorate, conducts research in a university setting. The content of this course, in that it focuses on the analysis of structural assemblages, the use of equations for static equilibrium, geometric compatibility, and constitutive material response, may be useful for an academic researcher who studies mechanics. The content of this course also provides an introduction to plasticity and viscoelasticity. This course may be useful for building a base for further study.

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Quality Control Engineer

Quality control engineers develop and implement quality control procedures within a manufacturing process. This course, which introduces the analysis of structural assemblages through equations for static equilibrium, geometric compatibility, and constitutive material response, may be helpful for a quality control engineer. The course also introduces the concepts of plasticity and viscoelasticity. These concepts may be useful for the design of quality control measures.

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Technical Writer

A technical writer is responsible for creating documentation that helps people understand how to use a product or perform a technical task. While a technical writer may not need to perform structural analysis, this course may help them understand the underlying principles of mechanics. This course will introduce the use of equations for static equilibrium, geometric compatibility, and constitutive material response to analyze structural assemblages. In addition, this course introduces plasticity and viscoelasticity. This is all helpful for writing accurate and informative documentation.

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Mechanics of Deformable Structures

Part 1

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