Statics

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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.

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 equaling zero is known as the first condition for equilibrium, and the net torque equaling zero is known as the second condition for equilibrium. See statically determinate.

Contents

Vectors

A scalar is a quantity like mass or temperature which only has a magnitude. A vector is a quantity that has both a magnitude and a direction, which is denoted by a bold faced character, an underlined character, or a character with an arrow on it. Vectors can be added using the parallelogram law. Vectors contain components in orthogonal bases. Unit vectors i, j, and k are along the x, y, and z directions.

Equilibrium Equations

The static equilibrium of a particle is an important concept in Statics. A particle is in equilibrium only if the resultant of all forces acting on the particle is equal to zero. In a rectangular coordinate system the equilibrium equations can be represented by three scalar equations, where the sum of forces in all three directions are equal to zero. An engineering application of this concept is determining the tensions of up to three cables under load, for example the forces exerted on each cable of a hoist lifting an object or of guy wires restraining a hot air balloon to the ground.[1]

Moment of a Force

The magnitude of the moment of a force at a point O, is equal to the perpendicular distance from O to the line of action of F, multiplied by the magnitude of the force. The direction of the moment is given by the right hand rule, where counter clockwise (CCW) is out of the page, and clockwise (CW) is into the page. Moments can be added together as vectors.

Trusses

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