1: Principles of Statics
- Page ID
- 102498
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Introduction
Statics is a branch of Mechanics, which is a subset of Physical Sciences. It involves the study of bodies that are at rest or move with constant velocity. Unlike Dynamics, which deals with bodies in motion, Statics focuses on mechanical systems in equilibrium.
The fundamental concept in Statics is the equilibrium of forces. This means that for a system to be in equilibrium, the net force and the net torque (moment of force) acting on it must be zero. This is based on Newton’s First Law of Motion, which states that an object at rest tends to stay at rest, and an object in motion tends to stay in motion, unless acted upon by an external force.
Statics is used in many fields of engineering, especially in the design of structures and machines. Engineers use the principles of statics to calculate forces in structures like bridges, buildings, and mechanical devices, ensuring they can withstand the forces they encounter.
Statics is the foundation for future courses like Strength of Materials. In Statics, when we solve problems, all bodies are considered ridged and do not deform. When we get to Strength of Materials, then we will study the relationships between external forces acting on bodies at rest and the internal responses generated. In Strength of Materials, bodies are assumed to be deformable (real world deformation).
In summary, Statics is a crucial area of study in physics and engineering that helps us understand and predict the behavior of stationary objects and structures. It provides the foundation for designing safe and efficient structures and machines. Understanding statics can also give us insights into the natural world, helping us understand how objects and structures, from the smallest machine to the largest skyscraper, withstand the forces they experience.
- 1.1: Right Triangles
- Explanation of the six trigonometric function values of an angle in a right triangle.
- 1.2: Oblique Triangles
- Trigonometry literally means 'measuring triangles', we are more than prepared to do just that. The main goal of this section is to develop theorems which allow us to 'solve' triangles -- that is, find the length of each side of a triangle and the measure of each of its angles.
- 1.3: Calculations, Units, and Unit Conversion
- A review of SI base units, derived units, prefixes, and unit conversions.
- 1.4: Forces
- Definition of a force. Quantities of interest of a force: magnitude, direction, points of application.
- 1.5: Moments
- Definition and vector representation of moments. Brief overview of how to calculate moments. Lecture video covering topics from this section can be found at bottom of this page.
- 1.6: Free Body Diagrams
- The process for drawing free body diagrams, and an overview of the types of forces commonly encountered in problems involving these diagrams. Contains multiple worked examples.