Static of Rigid Bodies \\ ES 1

Based from online tutorials of CE Box, this flashcards outline major concepts and terms in ES1.

Rigid Body

is a solid body in which deformation is zero or negligible, when a deforming pressure or deforming force is applied on it.

Force

refers to an applied or internal resistance or physical movement, motion, or formation.

Statics

Word meaning “at rest”

Dynamics

Word meaning “movement”

Coplanar

A type of force system where all forces are acting upon a common geometric plane.

Non-coplanar

A type of force system where all forces are acting upon multiple geometric planes.

Concurrent

A type of force system where all lines of action meet at a singular point.

Non-concurrent

A type of force system where lines of action do not meet at a singular point.

Parallel

A type of force system where two lines of action that never meet has a set distance perpendicular to both lines. This can be vertical, horizontal, or inclined.

Free Body Diagram

A type of diagram used to isolate parts of a whole structure in order to derive forces from each part.

Resultant

Refers to the overall effect of forces in a body

Equilibrium Condition

Refers to the resultant in statics where R = 0

Dynamics

Refers to the resultant when R is not equal to 0

Rsinθx

An equation used to express the vertical force with respect to the x-axis multiplied with the inclined resultant force.

Rcosθx

An equation used to express the horizontal force with respect to the x-axis multiplied with the inclined resultant force.

tan⁻¹(Py/Px)

An equation used to find a missing angle using the vertical and horizontal forces given in an inclined resultant force.

R(Opp./Hyp.)

An equation used to express the vertical force with respect to a given slope multiplied with the inclined resultant force.

R(Adj./Hyp.)

An equation used to express the horizontal force with respect to a given slope multiplied with the inclined resultant force.

Normal force

A type of force perpendicular to the plane

Tangential force

A type of force parallel to the plane

Opposite Angles

A pair of equal angles that are diagonally connected and non-adjacent to each other.

Tensile Force

A balanced outward stretching force that acts upon the rigid body

Compressive Force

A balanced inward force that acts upon the rigid body

Shear Force

A force directed so as to displace layers of the material parallel to each other.

Structure

A combination of different structural members or elements to support loading.

Truss

Consists of slender elements that support or carries roofs and bridges.

Frames

Combination of column and beams usually made in reinforced concrete or steel for buildings.

Cables & Arches

Two other forms of structures used to span long distances for bridges.

Determinate Structure

When the unknown forces in a structure can be determined simply by using equilibrium conditions.

Indeterminate Structure

When the unknown forces in a structure is more than the required equations to be used in the analysis.

Unstable

When the unknown forces in a structure is lesser than the required equation to be used in the analysis.

Method of Joints

This method of structural analysis accounts for each joint in its computations, requiring only two unknown forces.

Method of Sections

This method of structural analysis cuts through a specific joint, requiring at least three unknown forces.

1. Summation of horizontal forces (ZFh = 0)

2. Summation of vertical forces(ZFv = 0)

3. Summation of moment(ZM = 0)

Three formulas used in a structural analysis of a truss

Steel Roof Truss

Often used as part of an industrial building frame.

Bridge Truss

Is the main structural element in a typical bridge.

Friction

Is a contact resistance exerted by one body to another body.

Friction

Is an opposite force that is retarded due to the roughness of a surface.

Maximum Available Friction

Limit or threshold where P ≥ F, and motion is impending.

Kinetic Friction

Known as motion occurrence when P>F

Angle of Friction

Angle created by the resultant force between the normal force.

b(h)

Equation for the area of a rectangular polygon

b/2

Equation for the x̅ with respect to the y-axis in a rectangular polygon

h/2

Equation for the ȳ with respect to the x-axis in a rectangular polygon

½ b(h)

Equation for the area of a triangular polygon

1/3 b

Equation for the x̅ with respect to the y-axis in a triangular polygon

1/3 h

Equation for the ȳ with respect to the x-axis in a triangular polygon

πr²/2

Equation for the area of a semi-circle

0 or = radius

Value of x̅ with respect to the y-axis in a semi-circle

4r/3π

Equation for the ȳ with respect to the x-axis in a semi-circle

πr²/4

Equation for the area of a quarter circle

4r/3π

Equation for the x̅ with respect to the y-axis in a quarter circle

4r/3π

Equation for the ȳ with respect to the x-axis in a semi-circle

r²α

Equation for the area of a circular sector

2/3 [rsinx/α]

Equation for the x̅ with respect to the y-axis in a circular sector

0

Value of ȳ with respect to the x-axis in a circular sector

1/n+1 bh

Equation for the area of a slope

1/n+2 b

Equation for the x̅ with respect to the y-axis in a slope

n+1/4n+2 h

Equation for the ȳ with respect to the x-axis in a semi-circle

Centroid

Is the geometric center of a plane or solid figure is the arithmetic mean position of all the points in the surface of a figure.

Mechanics

An aplied science which describes and predicts the condition of rest or motion of bodies under the act of forces.

Length

A physical quantity of a geometric measurement between two points.

Space

Associated with the notion of a position of the point, P, given in terms of three coordinates measured from a reference point or origin.

Time

Definition of an event requires specification of the time and position at which it occured.

Mass

Amount of matter an object contains.

Force

Represents the action of one body on another.

W = mg

Weight is a force expressed in terms of:

External force

Force generated outside the body

Internal force

Force generated inside to keep the body together.

Applied force

An external force on the body that tries to change the state of movement of the body

Reaction force

An external force that inhibits change in the state of movement of a body when acted on by an applied force.

Distributed force

Is a force density (N/m)

Principle of transmissibility

The external effect of a force on a body is the same for all points of application along its line of action.

Newton’s First Law

If the resultant force on a particle is zero, the particlr will remain at rest or continue to move in a straight line.

Newton’s Second Law

A particle will have an acceleration proportional to a non- zero resultant applied force.

Newton’s Third Law

The forces of action and reaction between two particles have the samr magnitude and line of action with opposite sense.