Principles of statics - principles of moments

free body diagram

a sketch of the isolated body which shows only the forces acting upon the body

center of moments

axis of moments which is perpendicular to the plane of forces, appears as the point commonly called -the intersection of the axis of moments with the plane of forces

magnitude position of its line of action the direction or sense in which the force acts along its line of action

characteristics of a forc

external effects of forces

considered in engineering mechanics

internal effects of forces

considered in strength of materials

statics

considers the effects and distribution of forces on rigid bodies which are and remain at rest

dynamics

considers the motion of rigid bodies caused by the forces acting upon them

engineering mechanics

defined as the science which considers the effects of forces on rigid bodies

internal effect of the force

dependent on its point of application

statics dynamics

engineering mechanics is divided into two parts

concurrent

forces whose line of action pass through a common point

parallelogram law two forces are in equilibrium only when equal in magnitude, opposite in direction, and collinear in action a set of forces are in equilibrium may be added to any system of forces without changing the effect of the original system action and reaction forces are equal but oppositely directed

fundamental axioms of mechanics

Triangle Law

if two forces are represented by their free vectors placed tip to tail, their resultant vector is the third side of the triangle, the direction of the resultant being from the tail of the first vector to the tip of the last vector

force system

is any arrangement where two or more forces act on a body or on a group of related bodies

study of strength of materials

is based on the deformation of such bodies

rigid body

is defined as a definite amount of matter the parts of which are fixed in position relative to each other. -solid bodies are never rigid they deform under the action of applied forces.

moment of a force about an axis or line

is the measure of its ability to produce turning or twisting about the axis

internal effect of a force

is to produce stress and deformation in the body on which the force acts.

parallel force system

line of action are parallel

non-concurrent force system

lines of action neither are parallel nor intersects in a common point

force

may be defined as that which changes or tends to change, the state of motion of a body -external effect

parallelogram law

method of vector addition -cannot be proved and can only be demonstrated by experiment - the resultant of two forces is the diagonal of the parallelogram formed on the vectors of these forces

Varignon's Theorem

moment of force is equivalent to the sum of the moments of its components

vectors

quantities that posses direction as well as magnitude -can be combined only by geometric addition/ vector addition

scalar

quantities which possess magnitude only and can be added arithmetically

principle of transmissibility of a force

states that the external effort of a force on a bofy is the same for all points of application along its line of action, independent of the point of application

action forces or applied forces

the forces acting on the free body

moment arm of the force

the perpendicular distance from the force's line of action to the axis of rotation

coplanar

when the lines of action all the forces in a force system line in one plane, otherwise, its called non-coplanar

up to right

++

down to right

+-

up to left

-+

down to left

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