ES Reviewer

Mechanics

science which describes and predicts the conditions of rest or motion of bodies under the action of forces

categories of mechanics

rigid bodies, deformable bodies, fluids

mechanics

foundation of most engineering sciences and is an indispensable prerequisite to their study

length

needed to locate the position of a point in space.

Distance

is described in terms of a standard unit of length

SI unit of length

meter (m)

english unit of length

foot (ft)

space

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

coordinates

x,y,z

time

definition of an event requires specification of the time and position at which it occurred

SI and english unit of time

seconds (s)

mass

used to characterize and compare bodies, e.g., response to earth's gravitational attraction and resistance to changes in translational motion

SI unit of mass

kilogram (kg)

english unit of mass

slug (sl)

force

represents the action of one body on another. It is characterized by its point of application, magnitude, and direction

SI unit of force

N (Newton)

english unit of force

pound (lb)

1 lb is equal to _N

4.4482N

1 slug is equal to _kg

14.5983kg

1ft is equal to _m

0.3048m

Weight

expressed in Newton since it is also a force

Weight formula

W = mg (mass x gravity) gravity = 9.81m/s² (32.2ft/s²) mass = mass of the body in kg

Force Formula

F = ma (mass x acceleration)

Classification of forces on rigid bodies

external force, internal force, applied force, reaction force, and distributed force

external force

force generated outside the body

internal force

force generated inside the body (to keep the body together)

applied force

is 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

free-body diagram (FBD)

1st step of solving

space diagram

A sketch showing the physical conditions of the problem.

Free Body Diagram (FBD)

A sketch showing only the forces on the selected particle

external forces

shown in a free-body diagram

Force systems according to the line of action

concurrent forces, parallel forces, non-concurrent forces

concurrent forces

forces whose lines of action pass through a common point

parallel forces

forces whose lines of actions are parallel

non-concurrent forces

forces whose lines of actions are neither parallel nor intersect in a common point

Newton's First Law

If the resultant force on a particle is zero, the particle 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 nonzero resultant applied force

Newton's Third Law

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

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

scalar

A quantity that has only magnitude

vector

A quantity that has magnitude and direction

scalar

mass, speed, volume, temperature

vector

dorce, displacement, velocity, acceleration

Fixed or Bound Vectors

have well defined points of application that cannot be changed without affecting an analysis.

free vector

may be freely moved in space without changing their effect on an analysis

sliding vectors

may be applied anywhere along their line of action without affecting an analysis.

equal vectors

have the same magnitude and direction

negative vectors

same magnitude and the opposite direction.

sign convention of components

QUADRANT = X COMPONENT | Y COMPONENT 1st = + | + 2nd = - | + 3rd = - | - 4th = + | -

components of the resultant

equal to the sum of the corresponding scalar components of the given forces

direction of the resultant formula

θ= tan-1 (Ry / Rx)

magnitude of the resultant formula

R = √(R²x + R²y)

resultant

is equivalent to the diagonal of a parallelogram which contains the two forces in adjacent legs

Law of Cosines Formula

R² = P² + Q² - 2PQcosB

Law of Sines Formula

sinA/a = sinB/b = sinC/c

X and Y component Formula

Fx= FCosθ Fy= Fsinθ

Moment of a Force

e measure of the tendency of a force F to make the rigid body rotate about a fixed axis perpendicular to the plane of the force F

Moment arm

larger the force or the longer the moment arm (d) , the greater the moment or turning effect

Magnitude formula

M = Fd M= moment F = force d= moment arm perpendicular to line of action of force F

Varignon's Theorem

moment about a given point O of the resultant of several concurrent forces is equal to the sum of the moments of the various forces about the same point O.

couples

Sometimes the resultant of a force system will be zero in magnitude and yet have a resultant moment sum

couples

s made up of two equal, parallel, oppositely directed forces

statics

deals primarily with the calculation of external forces which act on rigid bodies in equilibrium

rigid body

combination of a large number of particles occupying fixed positions with respect to each other

force is developed if..

If a support prevents the translation of a body in a given direction

a couple moment is exerted on a body if..

If rotation is prevented

cables

no. of unknown= 1

contacting surface

no. of unknown= 1

roller support

no. of unknown= 1

pin support

no. of unknown= 2

pin connections allow..

it allows rotation

considered as FORCES not moments

reactions at pins

slider / constrained pin

no. of unknown= 1

fixed support

no. of unknown= 3

∑Fx and ∑Fy

represent sums of x and y components of all the forces

∑Mo

represents the sum of the couple moments and moments of the force components

truss

a structure composed of slender members joined together at their end points.

planar trusses

lie in a single plane and are often used to support roofs and bridges

truss members

connected at their extremities only; thus no member is continuous through a joint.

Plane Truss assumptions

1. the weight of the members are negligible

2. all joints are smooth pins

3. the applied forces act at the joints

tension

member reaction due to pulling forces at both ends and is denoted by (T); lengthening force

compression

member reaction due to pushing forces at both ends denoted by (C); shortening force

members of a truss

are slender and not cappable of supporting large lateral loads. Loads must be applied at the joints

method of joints

To calculate the forces in the members of a truss, the equilibrium equations are applied to individual joints (or pins) of the truss

method of sections

Consist of cutting a truss into two sections at a point where the bar force is required.

Rigid truss

will not collapse under the application of a load

simple truss

constructed by successively adding two members and one connection to the basic triangular truss

m = 2n-3

Trusses are statically determinant, rigid, and completely constrained

m > 2n-3

Truss contains a redundant member and is statically indeterminate

Joints Under Special Loading Conditions

1. Forces in opposite members intersecting in two straight lines at a joint are equal

2. forces in two opposite members are equal when a load is aligned with a third member. The third member force is equal to the load (including zero load)

3. The forces in two members connected at a joint are equal if the members are aligned and zero otherwise

Compound trusses

are statically determinant, rigid, and completely constrained

2 members are zero force members if..

If a joint has only two non-collinear members and there is no external load or support reaction at that joint

third noncollinear member is a zero force member if..

If three members form a truss joint for which two of the members are collinear and there is no external load or reaction at that joint, then the third noncollinear member is a zero force member

strength of materials

aka mechanics of materials

strength of materials

the study of the internal effect of external forces applied to structural members

stress

internal loads cause ______ in a body/material

deform

stresses cause a body to ____

stress

defined as the strength of a material per unit area