STATICS OF RIGID BODIES

Engineering Mechanics

a branch of physics that deals with forces and effects of these forces to the body

Force

It is the push or pull caused by interactions of bodies

Forces and Effects

what does engineering mechanics study?

Rigid Body

a body that does not deform

Magnitude

number or value that shows the intensity or extent of the force

Direction

the path where the force is applied to or going to

Line of Action

the path where the force is or the line in which the force may be considered to act

Components

parts of the force acting on the x,y,z axes.

Equilibrium

opposing forces or effects of forces are balanced

Newton or KiloNewton

which unit measures force in the metric system

Force Direction

what does the arrowhead of a force represent

Principle of Transmissibility

an applied force can be moved anywhere along its line of action without changing the external reaction of a rigid body

Force system

a body that has two or more applied forces

Resultant

vector summation of all forces

Magnitude and Direction

two properties that characterizes a vector

Displacement, Motion, Accelerate, Deformations, Reaction

Effects of Force

Reaction

is the force that counters the effect of the applied force. It is exerted/produced by the support of the body and the body itself.

Magnitude of Applied Force

what is the magnitude of the reaction equal to?

1st Law of Motion

a body at rest will remain at rest, and a body in motion will remain in motion unless acted upon by an external force.

2nd law of motion

force acting on an object is equal to the mass of the object times its acceleration

3rd Law of Motion

for every action there is an equal and opposite reactoin.

Angle of Inclination

an acute angle or right angle whose initial side is horizontal

Coplanar force system

applied forces on the body are in one plane. Not all force are in the same plane, some are in other plane

Collinear Force System

applied forces are in one line. Line of action coincide with one another

Concurrent Force System

all forces have a common point of intersectionP

Parallel Force System

are non concurrent force system where forces are parallel with eachother but line of action never intersect.

Parallelogram Method

The diagonal from the point of intersection of the two forces to the intersection of the projected lines is the resultant of the two forces

Triangle Method

Rearrange the forces in head-tail fashion

Cosine Law

determines the resultant magnitude in the triangle method

Sine Law

helps determine the resultant angle in the triangle method

x and y

what are the tqo components of a 2D force?

x y and z

what are the components of a 3D force

Component Method

solve for the x and y components of the forces where fy= fsin(0) and fx=fcos(0)

System

combination of two or more body carrying loads and forces.

Free Body Diagram

a diagram that shows the force acting on the body

Centroid

geometric center of any closed figure

Equilibrium

moment = 0
resultant = 0
fx and fy = 0
acceleration = 0

Loads

are weights that machine and structures are carrying

Dead Loads

loads that fixed and permanent loads such as the weight of the structure itself

Superimposed Dead Loads

weights of permanent fixtures, fittings and partitions

Live loads

weights of living and non living things that are not permanent (e.g people, chairs, tables, etc.)

Point load

occupies a small portion of the structure that it is assumed to be acting on just a point on the structure

Uniformly Distributed Load

load that is acting on a considerable length of the structure

Uniformly Varying load

also acting on considerable length, however, its magnitude varies at constant rate (decreasing or increasing). Can be represented by triangle or trapezoid

Varignon’s Theorem

what theorem related total moment to individual moments

Inertia

is the resistance to change

Loads and Reactions

what is the primary purpose of supports

Tensile Force

what type of force acts along a cable

Surface

a support that has two reactions at the same time (Normal and Friction force)

Cable

a support that has 1 reaction (Tensile force (t)

Rod

a support that has one reaction at the same time (compressive or tensile force)

Hinge

a support that has two reactions at the same time (Verical and horizontal components) -perpendicular to the surface and parallel to the surface

Roller

a support that has one reaction at the same time (vertical and horizontal components)

Pin

a support that has two reactions at the same time (vertical and horizontal components)

Fixed

a support that has three reactions at the same time (vertical and horizontal components and moment reaction)

Column

a vertical structural member that carries the beam

Beam

horizontal bearing member of a machine or structure that supports slab, board or roof

Overhanging Beam

A beam supported by hinge and roller but one support is not at the end of the beam.

Double Overhanging Beam

A beam supported by hinge and roller but the supports are not at the ends of the beam

Cantilever Beam

A beam supported by fixed support at one end and unsupported at the other end.

Fixed Beam

A beam supported by fixed supports at both ends of the beam.

Continuous Beam

A beam supported by hinge and roller at both ends and hinges in between

Semi Continuous Beam

A beam supported by hinge and roller at both ends and one hinge in between

Circular Motion

the motion o the body in circular path

Coefficient of Friction

describes the roughness or smoothness of the surface

0 to 1

range of coefficient of frictions

Impending Motion

motion that is about to happen. body with this motion is considered stationary

Rectilinear Motion

motion of the body in linear or straight line path

Friction Force

one of reactions of surface support.

TRUE

if there is no motion (actual or impending), friction is not active.
acts along the surface
always perpendicular to normal force.

Friction Force

coefficient of friction times normal force

0

this means that the surface is smooth

1

this means the surface is rough

Normal Force

maximum value of friction of friction force

Zero

minimum value of friction force

Static Friction

friction between surfaces while the body is still stationary with impending motion

Kinetic Friction

is the friction between surfaces while the body is moving

Static Friction

which is greater? coefficient of static friction or coefficient of kinetic friction

Normal Force

reaction of the surface against the weight of the body and other loads that are being carried but the surface support.
perpendicular to the surface.

Angle of Friction

angle between the resultant and normal force.
equal to arctan(coefficient of friction)

Moment

is the measure of the tendency of the force to rotate part of the body or the whole body about an axis of rotation

Moment Arm

distance which is perpendicular to the applied force from the force to center of moment

Center of Moment

axis of rotation of the moment which is the reference point/axis of the applied force

Couple

two forces parallel w eachother, equal in magnitude and opposite in direction

Simply Supported Beam

hinge and roller supported and has support at both ends