The Basic Principles of Statics
Statics is the study of forces acting on a rigid body. Statics is often in calculating loads and stability in structures (ie. bridges, buildings, or airplanes).
For base level Statics, several assumptions are made:
- The bodies in the system are rigid and cannot deform
- The system is in equilibrium
- There is no motion within the system
Vectors are mathematical quantities that have both a magnitude and direction.
Example of a vector:
A car traveling down the highway. In this example, you could consider
the speed of the car to be the magnitude and the car's direction to be the direction.
For Statics, the most common vectors are Forces and Moments.
Newton's Three Laws of Motion
-
A body continues in its state of rest,
or in uniform motion in a straight line,
unless acted upon by a force
-
A body acted upon by a force moves in such
a manner that the time rate of change of
momentum equals the force.
-
If two bodies exert forces on each other,
these forces are equal in magnitude and
opposite in direction.
Isaac Newton's laws of motion are often considered the foundation of classical mechanics and physics.
Statics can be considered as a sub-set of mechanics.
Consider Newton's Second Law of Motion
The equation form of this law is as follows:
F = ma
F - force
m - mass
a - acceleration
In colloquial terms, force is often thought
of as the pushing or pulling of an object.
Consider pushing pulling a box attached to rope
across an ice rink (frictionless).
Every time you pull (aka apply a force), the box will accelerate.
The box will then continue at its velocity until another force is applied.
Most of our actions that apply a force are counteracted by opposing forces
such as friction and gravity. Imagine pulling that same box across a friction
heavy surface such as sandpaper. As soon as the box begins moving, friction will
reduce its decelerate the box by applying a force in the opposite direction.
Moment refers to rotational forces about an axis
M = Fd
M - Moment
F - perpendicular Force
d - perpendicular distance from axis
Alternatively, moments can be calculated by taking the cross product between the Force and the distance from the axis to any point on the line of action of the force.
M = r x F
M - Moment
r - distance in Cartesian Components
F - Force in Cartesian Components
A colloquial example of moments would be to swing a door. As you get closer to the hinge (axis), the force required to move the door increases. Conversely, apply force at the opposite end, the force required is minimal. Also note that applying force along the door (ex. pushing in the direction of the hinge) does not effect the door if we hold to the assumption that the door is completely rigid and cannot deform.
So far, we have discussed forces and moments in terms of motion. However, recall that one of our assumptions is that there is no motion within our system. This is accomplished by having counteracting forces and moments to reduce the acceleration (both linear and angular) to 0.
ΣF=ma, where a=0
ΣF=0
ΣM=Fd, where F=ma & a=0
ΣM=0
At its core, Statics is solving these two equations
ΣF=0, ΣM=0
Here is a list of additional topics that fall within the realm of statics or are related.