Statics Concepts

Force Classifications

1. Contact (push/pull)

2. Body (gravitation, magnetic)

Force Application

1. Concentrated

2. Distributed

Force Location

1. External - change motion or develop reactions

2. Internal - cause deformations

Force Characteristics

Magnitude + Direction + Point of Application + Unit

Transmissibility

Either force has the same external effect

Force Systems

1. Concurrent - LOAs intersect at a point —> can replace with on force (Fr = F1 + F2 + F3)

2. Non-concurrent: LOAs don’t intersect

Mo in scalar and vector notation

1. Scalar: Mo = Fd

2. Vector: Mo = r x F

Varignon’s Theorem

The forces along a same LOA create the same moment

Characteristics of a Moment of a Couple

1. Equal magnitude

2. Opposite direction

3. Parallel LOAs

4. Non-collinear

Newton’s First Law

An object remains at rest if there is no unbalanced force acting on it

Equations of Equilibrium (Concurrent)

ΣFx = 0

ΣFy = 0

Equations of Equilibrium

ΣFx = 0

ΣFy = 0

ΣM_{Any Point} = 0

Required Items of a Free Body Diagram

1. Body detached from its surroundings

2. Coordinate axis system

3. Reactions & applied forces

4. Dimensions and number labels

Support Conditions

1. Roller (positive-y)

2. Pin (positive-y and positive-x)

3. Fixed (positive-x, positive-y, and positive-z)

4. Cable (tension)

5. Frictionless Slot (positive-y)

Fr (in terms of a resulting force in centroid problems)

Equivalent concentrated force/area under the load curve

x_c

Distance to centroid of load curve

Centroid

Geometric center of a line, area, or volume

Conditions of a centroid

1. Same as center of mass/gravity for homogenous material

2. Not necessarily on the shape

3. Always located on the axis/axes of symmetry

Fluid Pressure

p = ρgh *valid only for incompressible fluids

Two-Force Members

Member with forces applied only at its ends

Characteristics of Two-Force Members

1. Neglect self-weight

2. No applied moments or couples

3. Frictionless pins at the ends

4. Positive = tension; Negative = compression

5. The forces are

   1. Equal

   2. Opposite

   3. Collinear (same LOA)

Truss

structure composed of two-force members joined at their ends by frictionless pins (basically interlocking triangles)

Assumptions of trusses

1. Members connected at the ends only

2. Loads are applied only to truss joints

3. Self-weight neglected or placed at joints