Statics & Machine Design
UC A–G / Advanced Engineering Course Proposal
Course Length: Year-long (3 Trimesters)
Target Grade Level: 11–12
Department: Physics / Engineering
Prerequisite: Successful completion of High School Physics (Honors or AP Physics recommended)
Course Overview
Statics & Machine Design is a rigorous, year-long engineering course designed for high school students who have completed a full physics course and are ready to apply physics and mathematics to real-world engineering systems. This course introduces students to foundational concepts traditionally taught in first- and second-year undergraduate mechanical engineering programs, with an emphasis on analytical reasoning, engineering judgment, and design principles.
Students will study forces in two and three dimensions, moments and equilibrium, structural analysis, stress and strain, torsion, failure theories, and the design of mechanical components. The course blends theoretical problem solving with applied design challenges, enabling students to understand not only how systems behave, but why they fail and how engineers design against failure.
By the end of the course, students will be able to analyze and design basic mechanical systems using statics principles and machine design methodologies, preparing them for college-level engineering, physics, or robotics programs.
Course Goals
By the end of this course, students will:
🔹 Apply statics principles to analyze forces and moments in engineering systems
🔹 Solve equilibrium problems in two and three dimensions
🔹 Analyze trusses, frames, and machines
🔹 Understand stress, strain, and material behavior under load
🔹 Perform torsion and bending analyses of mechanical components
🔹 Evaluate failure using common engineering failure criteria
🔹 Design simple mechanical components with safety and performance constraints
🔹 Develop engineering problem-solving, documentation, and teamwork skills
Instructional Methods
🔹 Direct instruction with worked engineering examples
🔹 Analytical problem-solving sessions
🔹 Engineering-style homework and design calculations
🔹 Hands-on demonstrations and physical models
🔹 Design-based projects and case studies
🔹 Technical reports and design reviews
Trimester Breakdown & Units of Study
Trimester 1 – Engineering Statics Fundamentals
Unit 1: Forces, Vectors, and Equilibrium in 2D
Topic Description:
Students are introduced to force vectors, free-body diagrams, and equilibrium analysis in two dimensions.
Objectives:
Represent forces as vectors
🔹 Draw accurate free-body diagrams
🔹 Apply equilibrium equations in 2D
🔹 Solve problems involving concurrent and non-concurrent forces
Sample Assignment:
Students analyze a suspended sign supported by cables, drawing free-body diagrams and calculating cable tensions required for static equilibrium.
Unit 2: Forces and Equilibrium in 3D
Topic Description:
This unit extends equilibrium analysis into three-dimensional systems.
Objectives:
🔹 Resolve forces in three dimensions
🔹 Analyze spatial force systems
🔹 Apply equilibrium equations in 3D
Sample Assignment:
Students calculate the forces in 3D support cables holding a platform using vector methods.
Unit 3: Moments, Couples, and Rigid Body Equilibrium
Topic Description:
Students examine rotational effects of forces and rigid body equilibrium.
Objectives:
🔹 Calculate moments about a point and axis
🔹 Analyze couples and torque
🔹 Solve rigid body equilibrium problems
Sample Assignment:
Students analyze a beam with multiple loads and supports to determine reaction forces and moments.
Trimester 2 – Structural Analysis & Mechanics of Materials
Unit 4: Trusses, Frames, and Machines
Topic Description:
Students analyze internal forces in truss structures and mechanical frames.
Objectives:
🔹 Identify two-force members
🔹 Use method of joints and sections
🔹 Analyze internal member forces
Sample Assignment:
Students determine the internal forces in a planar truss bridge and identify members in tension or compression.
Unit 5: Stress, Strain, and Material Behavior
Topic Description:
This unit introduces how materials deform and fail under load.
Objectives:
🔹 Define normal and shear stress
🔹 Calculate strain and elastic deformation
🔹 Interpret stress–strain curves
🔹 Apply Hooke’s Law
Sample Assignment:
Students analyze stress–strain diagrams and select materials appropriate for a structural component.
Unit 6: Torsion of Circular Shafts
Topic Description:
Students study torsional loading in mechanical shafts.
Objectives:
🔹 Calculate shear stress due to torsion
🔹 Analyze angle of twist
🔹 Design shafts for allowable stress
Sample Assignment:
Students design a circular shaft to transmit a specified torque without exceeding material limits.
Trimester 3 – Machine Design & Failure Analysis
Unit 7: Bending, Combined Loading, and Deflection
Topic Description:
Students analyze bending stresses and combined loading scenarios.
Objectives:
🔹 Calculate bending stress using flexure formula
🔹 Analyze combined axial, bending, and torsional loads
🔹 Estimate deflection in beams
Sample Assignment:
Students analyze a cantilever beam supporting a load and calculate maximum bending stress and deflectio
Unit 8: Failure Criteria and Factor of Safety
Topic Description:
Students evaluate mechanical failure using engineering criteria.
Objectives:
🔹 Understand yielding vs fracture
🔹 Apply failure theories (e.g., maximum normal stress, von Mises – qualitative)
🔹 Select appropriate factors of safety
Sample Assignment:
Students evaluate whether a mechanical component will fail under a given load using a selected failure criterion.
Unit 9: Capstone Machine Design Project (Final Exam)
Topic Description:
Students complete a comprehensive engineering design project integrating statics and machine design concepts.
Project Examples:
🔹 Design of a load-bearing bracket or support structure
🔹 Design of a shaft and gear system for torque transmission
🔹 Structural analysis of a small bridge or robotic frame
Deliverables:
🔹 Engineering calculations and free-body diagrams
🔹 Component drawings or CAD sketches
🔹 Failure analysis and safety justification
🔹 Written technical report and oral presentation
Assessment Methods
🔹 Analytical problem sets
🔹 Quizzes and tests on statics and mechanics concepts
🔹 Design assignments and technical reports
🔹 Trimester projects
🔹 Final capstone design project
Resources / References
• Hibbeler, R. C. Engineering Mechanics: Statics
• Gere & Goodno. Mechanics of Materials
• Norton, R. L. Machine Design: An Integrated Approach
• FIRST Robotics engineering resources
• Engineering simulations and physical demonstrations
Conclusion
Statics & Machine Design provides students with a deep and authentic engineering experience grounded in physics and mathematics. By completing this course, students gain analytical and design skills aligned with undergraduate mechanical engineering curricula, preparing them for success in engineering, robotics, physics, and other advanced STEM pathways.
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