statics chapter 2

particle

mathematical model of an object as a mass point. has mass but no size or shape

rigid body

mathematical model of a material body or system of particles in which the distance btw them is constant NO DEFORMATION

w=mg

weight=mass*9.81m/s^2

mass

the amount of material in a body, scalar, same in all gravitational fields and is a measure of inertia

weight

the effect of gravity on body, vector, varies with gravitational pull and is a measure of force

scalar

quantity that only has magnitude and no direction.

scalar examples (5)

mass, distance, speed, time, temp

vector

quantity with both magnitude and direction

vector examples (5)

displacement, velocity, acceleration, momentum, force

free vector

vector with definite magnitude and direction but no specific location in space (think moment vector of couple)

sliding vector

vector that can be moved along a line that is collinear with itself

bound vector

vector that has a specific point of application

force

the action on one body to another that has magnitude, direction and LOA, effect is push or pull

body force

force due to attraction of two bodies - no contact

surface/contact force

force btwn two bodies due to contact

concentrated force

force acting on a specific point, not an area

distributed force

force spread over an area uniformly or non uniformly

external forces

force acting outside of a structure set in equilibrium - not altered by a load applied on external force LOA

internal forces

force effect within the entity or any part of a structure set in equilibrium - altered by loads

collinear force

act on the same LOA

coplanar force

act on same plane (parallel or general)

concurrent force

all intersect at a common point

M=Fd

moment=force*perp distance from LOA to moment center

M= r x F

moment vector = position vector from moment center to force X force vector

moment

measure of the tendency of a force to cause an object to rotate about a point or axis

free body diagram

diagram used to identify all forces

parallelogram rule

head to tail addition of vectors, when half of the gram is used its triangle construction

equilibrium

state where no net external forces are acting on a particle and the body remains at rest or continues at a constant velocity. newtons 1st law

varignon's theorem

the moment of any force is equal to the algebraic sum of the moments of the components of that force M=Mx+My+Mz

equivalence

all systems can be reduced to a single force and moment, sometimes reduce to only a single force at a known location THINK LOADS

transmissibility

doesn't matter if we push or pull, as long as LOA is maintained the results are same

lateral transfer theorem

if we move a force laterally (NOT along LOA) we must add moment couple

newtons third law

for every action there is an equal and opposite reaction

superposition

if there is a linearity, a complex problem can be broken down smaller and summed (think review shape 2.67)

friction

coulomb's law of dry friction which are empirical (cannot prove) in nature, not derived but observed

area moment of inertia

stiffness parameter based on shape

components of a vector

resolution of a vector into its x, y, and z … that all sum to the original vector

unit vector

magnitude of 1, has no units only direction, ijk

equal

same magnitude and direction

equivalent

same effect on body, same moment

resultant

sum of vectors, also has same net external effects as the original force system

resolution

the replacement of a single force into two forces acting along a set of axes

3D direction cosines

cos(theta x) = Fx/F - same for y and z

1 ft in meter

0.3048m

1 lb in kg

0.4536kg

1 lb in N

4.448N

1 slug in kg

14.59kg

1 slug units

1 lb/ (ft/s^2)

1 kip to lb

1000lb

unit of N

mass(kg) / acc(m/s^2)

unit of lb

mass (slug) * acc(ft/sec^2)

ln(xy)

lnx + lny

ln(x/y)

lnx - lny

ln(x)^c

c ln(x)

right hand coordinate system

fingers on x, curl towards y, thumb is z

3 ways to give info in 3d

directional angles, double projection, distances(position vector)

3d cosine direction identity

1 = cos²(alpha) + cos²(beta) + cos²(gamma)