Statics: Wikis

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Example of a beam in static equilibrium. The sum of force and moment is zero.

Statics is the branch of mechanics concerned with the analysis of loads (force, torque/moment) on physical systems in static equilibrium, that is, in a state where the relative positions of subsystems do not vary over time, or where components and structures are at a constant velocity. When in static equilibrium, the system is either at rest, or its center of mass moves at constant velocity. The study of moving bodies is known as dynamics, and in fact the entire field of statics is a special case of dynamics[1].

By Newton's first law, this situation implies that the net force and net torque (also known as moment of force) on every body in the system is zero. From this constraint, such quantities as stress or pressure can be derived. The net forces equalling zero is known as the first condition for equilibrium, and the net torque equalling zero is known as the second condition for equilibrium. See statically determinate.

Contents

Solids

Statics is used in the analysis of structures, for instance in architectural and structural engineering. Strength of materials is a related field of mechanics that relies heavily on the application of static equilibrium. A key concept is the center of gravity of a body at rest: it represents an imaginary point at which all the mass of a body resides. The position of the point relative to the foundations on which a body lies determines its stability towards small movements. If the center of gravity exists outside the foundations, then the body is unstable because there is a torque acting: any small disturbance will cause the body to fall or topple. If the center of gravity exists within the foundations, the body is stable since no net torque acts on the body. If the center of gravity coincides with the foundations, then the body is said to be metastable.

Fluids

Hydrostatics, also known as fluid statics, is the study of fluids at rest. This analyzes bodies of fluid in static equilibrium. The characteristic of any fluid at rest is that the force exerted on any particle of the fluid is the same at all points at the same depth (or altitude) within the fluid. If the net force is greater than zero the fluid will move in the direction of the resulting force. This concept was first formulated in a slightly extended form by the French mathematician and philosopher Blaise Pascal in 1647 and would be later known as Pascal's Law. This law has many important applications in hydraulics. Archimedes, Abū Rayhān al-Bīrūnī, Al-Khazini[2] and Galileo Galilei were also major figures in the development of hydrostatics.

See also

References

  • Beer, F.P. and Johnston Jr, E.R. (1992). Statics and Mechanics of Materials. McGraw-Hill, Inc.  
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Notes

  1. ^ Hibbeler, R.C. Engineering Mechanics: Statics 12th ed. (Pearson Prentice Hall Publishing (C) 2010) ISBN 0-13-607790-0
  2. ^ Mariam Rozhanskaya and I. S. Levinova (1996), "Statics", p. 642, in (Morelon & Rashed 1996, pp. 614-642):
    "Using a whole body of mathematical methods (not only those inherited from the antique theory of ratios and infinitesimal techniques, but also the methods of the contemporary algebra and fine calculation techniques), Arabic scientists raised statics to a new, higher level. The classical results of Archimedes in the theory of the centre of gravity were generalized and applied to three-dimensional bodies, the theory of ponderable lever was founded and the 'science of gravity' was created and later further developed in medieval Europe. The phenomena of statics were studied by using the dynamic apporach so that two trends - statics and dynamics - turned out to be inter-related withina single science, mechanics. The combination of the dynamic apporach with Archimedean hydrostatics gave birth to a direction in science which may be called medieval hydrodynamics. [...] Numerous fine experimental methods were developed for determining the specific weight, which were based, in particular, on the theory of balances and weighing. The classical works of al-Biruni and al-Khazini can by right be considered as the beginning of the application of experimental methods in medieval science."

External links


Study guide

Up to date as of January 14, 2010

From Wikiversity

Part of the Division of Applied Mechanics and the School of Engineering

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Contents

Content summary

The study of Statics is the fundamental examination of the effects of Forces upon objects. Often referred to as the primary discipline within the field of Engineering Mechanics, statics explores the behavior of bodies moving at a constant velocity. Dynamics is the subsequent study of the forces acting upon bodies moving with a non-constant velocity (i.e accelerating).

Prerequisites

A Force System

Mathematics

Physics

Projects, courses, lessons, lectures, and so forth

Learning Materials

A Free Body Diagram of a Loaded Truss

Texts

Statics Lessons

Assignments

Preliminary Study guide

  1. Wikipedia article:Statics
  2. Wikipedia article:Force
  3. Wikipedia article:Particle
  4. Wikipedia article:Rigid Body
  5. Wikipedia article:Vector
  6. Wikipedia article:Newtons laws
  7. Wikipedia article:Units
  8. Wikipedia article:Free Body Diagram

Readings

  • Peruse the appropriate sections of b:Statics

Activities

References

Additional helpful readings include:

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See also


1911 encyclopedia

Up to date as of January 14, 2010
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From LoveToKnow 1911

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Wikibooks

Up to date as of January 23, 2010

From Wikibooks, the open-content textbooks collection

Welcome to the Wikibook of

Statics

The Eads Bridge over the Mississippi River under construction in St. Louis, Missouri, in 1874 or earlier.

Objective

By the end of this course, you should understand the fundamentals of forces and moments, and be able to solve equilibrium problems for rigid (non-deformable) bodies in both two and three dimensions.

What You Should Already Know

In order to completely comprehend the material in this course, you should have a firm understanding of all math leading up to Calculus III. Also, an understanding of basic physics as well as technical sketching is useful.

Contents

Introduction

Preliminary Principles

Forces

Resultants of Force Systems

Rigid Body Equilibrium

Structural Analysis

Internal Forces

Moment of Inertia

Center of Gravity and Centroid

Quizzes and Tests

  • Quizzes Development stage: 25% (as of {{{2}}})
  • Tests Development stage: 25% (as of {{{2}}})

References

Acknowledgements and Further Reading

Printable Version

There is a printable version of this book.


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