Engineering Mechanics: Statics - ENG2008

Engineering Mechanics: Statics - ENG2008

• Course lecturer/tutors: Vaughn Brown
• Email: [email protected]
• Office hours: Monday 10:00 AM - 12:00 PM (Mechanical Office)

Module Description

• The module studies the effects of forces on particles and rigid bodies in mechanical equilibrium
• Focuses on sharpening mathematical skills in vector and linear algebra
• Covers active and reactive forces (concentrated and distributed)
• Includes trusses, beams, composites, friction, and inertia

Major Topics

• Vector Operations and the Cartesian System
  • Unit Vector
  • Coordinate Angles
  • Dot Product
• 2D and 3D Particle Equilibrium
• 2D and 3D Moments about a point and axis
• 3D Rigid Body Equilibrium
• Trusses and Internal Forces
• Centroids and Center of Gravity
• Moments of Inertia

Recommended Text

• Hibbeler, R.C. "Engineering Mechanics: Statics", SI ed. Prentice Hall, 2010

Assessment Breakdown

• Quizzes (best 4 of 6): 15%
• Test 1 and 2: 15%
• Assignment: 10%
• Design Project: 10%
• Exam: 50%

Access to Module Content

• Moodle
• Search: Engineering Mechanics: Statics SEM 2 AY 2023/2024
• Includes: Textbook, syllabus, module outline, lectures, and tutorials
• Also review proposed course schedule.

Today's Objectives

• Identify mechanics/statics
• Work with two types of units
• Round final answers appropriately
• Apply problem-solving strategies

In-Class Activities

• What is mechanics?
• System of units
• Numerical calculations
• Problem-solving strategy
• Sample quiz questions

What is Mechanics?

• Study of what happens to a "body" under the application of forces
• Forces can range from large (e.g., rocket launch) to small

Branches of Mechanics

• Mechanics
  • Particle
    • Statics: Study of rigid bodies in mechanical equilibrium (at rest or constant velocity)
    • Dynamics: Study of rigid bodies in motion
  • Rigid Bodies (Solids): (Things that do not change shape)
  • Deformable Bodies (e.g. Elastics): (Things that change shape)
  • Fluids (Liquids and Gases)
    • Fluid Mechanics
    • Fluid Dynamics
      • Incompressible Flow
      • Compressible Flow

What May Happen if Statics is Not Applied Properly?

• Illustrated by an image of a truck in an unsafe position.

Fundamental Concepts - Quantities

• Length (Units: m): Used to locate points and describe size.
• Time (Units: s): Conceived as a succession of events.
• Mass (Units: kg): Measures the amount of matter in a body.
• Force (Units: N = kg⋅m/s²): A push or pull exerted by one body on another.

Fundamental Concepts - Idealizations

• Particle: Mass exists, but size is negligible
• Rigid Body: A large collection of points that maintain fixed distances.
• Concentrated Force: A force acting at a point
• Distributed Force: To be defined

Newton's Laws of Motion

• First Law: A body at rest or moving with constant velocity remains so unless acted upon by an unbalanced force.
• Second Law: A body acted upon by an unbalanced force experiences acceleration in the direction of the force, proportional to the force.
• Third Law: For every action, there is an equal and opposite reaction.
• Law of Gravitational Attraction: The force of attraction between two bodies is directly proportional to the product of their masses and inversely proportional to the square of the distance between them (F = G*(m1*m2)/r^2).

Systems of Units

• Four fundamental physical quantities: length, mass, time, force
• F = m * a is used to develop systems of units.

Unit Systems

• Define three units as base units
• Derive the fourth unit using F= m * a
• Focus on SI and US customary systems.

Common Conversion Factors

• Various conversions between feet, inches, pounds, slugs, and meters, Newtons
• Work problems using given units unless otherwise instructed
• Example conversion for torque

Rules for Using SI Symbols

• No plural units (e.g. kg not kgs)
• Separate units with a multiplication sign
• Use lower-case symbols, except for some exceptions (e.g., N, Pa, M, and G)
• Exponential powers apply to units (e.g. cm² = cm * cm)
• Apply algebraic operations to both numerical characters and unit symbols

Numerical Calculations

• Calculations must exhibit dimensional homogeneity (same dimensions on both sides of the equation)
• Use appropriate significant figures (3 for answers and at least 4 for intermediate calculations
• Consistent rounding rules (rounding up or down based on the digit after the digit you round to, with rules for if the digit equals 5)

Concept Quiz

• Historical use of slide rules limited significant figures
• Original data typically has accuracy under 1%

Problem Solving Strategy

• 3-step approach
  • Interpretation: Identify knowns, unknowns, and assumptions.
  • Planning: Outline steps and consider alternative solutions.
  • Execution: Apply formulas, diagrams, and estimate answers. Reflect/revise work and remember units

General Procedure for Analysis

• 6-step approach for problem presentation.
  • Understand the problem
  • Tabulate given info
  • Identify assumptions and relevant equations
  • Solve the equation correctly (maintaining dimensional homogeneity)
  • Report answer with relevant accuracy
  • Consider the reasonableness of the answer
  • Review and suggest alternative methods

Sample Reading Quiz

• Mechanics deals with forces (not magnetic fields, heat, neutrons, or lasers)
• Newtonian Mechanics is the basis for many modern engineering concepts (not relativistic, euclidean, or greek mechanics)

Sample Attention Quiz

• Write final answers in a proper format, showing correct units
• "P" in the three-step problem-solving approach stands for "Plan"

Group Work

• Includes evaluating units; metric conversions

Additional Information

• Provide weights, and solve for the mass, using conversion factors and other given information.

This quiz covers the principles of Engineering Mechanics, focusing on the effects of forces on particles and rigid bodies in mechanical equilibrium. You'll sharpen your mathematical skills in vector and linear algebra through various topics, including equilibrium and the analysis of trusses and beams.