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General principles of rigid body mechanics, problems solving, statics terminology, and resolving resultant forces

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EGN 3310 Statics Chaps 1 & 2 Fall 2013 Handout 1
DFiller
Chap. 1 General Principles
What is Mechanics? What is
Statics
?
Mechanics
RRiiggiidd--bbooddyy
MMeecchhaanniiccss
Deformable-body
Mechanics
Fluid Mechanics
SSttaattiiccss
Deals with equilibrium of bodies at rest or at constant velocity
Dynamics
Deals with bodies under accelerated motion
Design & Analysis of:
Structural systems
Mechanical systems
Electrical systems
Rigid-body mechanics is based on Newton’s 3 Laws of Motion:
Law
Name
Description
1
st
Law of Equilibrium A particle at rest or at constant velocity will remain so unless subjected to an unbalanced force.
2
nd
Law of Acceleration A particle subjected to an unbalanced force accelerates.
3
rd
Law of Mutual Attraction Mutual action-reaction forces between two particles are equal, opposite and collinear.
Steps to Effective Problem Solving:
1. Understand the problem 2. Tabulate the known data and draw a free-body diagram (FBD) 3. Apply mathematical principles 4. Solve the problem with units check 5. Evaluate your result (Make sense of your solution – is it reasonable?)
Problem Formatting is an organizational skill!
On engineering paper……
1.
D
efine problem (in your own words is best) 2. Diagram (if appropriate) – FBD 3. Analysis (step-by-step method) 4. Solution (report to 2-3 significant figures and underline or box)
EGN 3310 Statics Chaps 1 & 2 Fall 2013 Handout 1
DFiller
EGN 3310 Statics Chaps 1 & 2 Fall 2013 Handout 1
DFiller
Chap. 2 Force Vectors Terminology -
Learn the lingo! Stick with convention!
Scalar (number) Vector
(→ magnitude, direction, and sense)
Collinear (forces or vectors) (sharing the same line, or alignment) Orthogonal axes (form right angles) Parallelogram Law (parallel sides of equal length, with equal opposite angles; used with orthogonal and non-orthogonal axes) Free Body Diagram (FBD) Drawing/illustration Resultant force (or vector) (2 force vectors added together form a
resultant
force vector) Force triangle (Triangle Rule, Law of Sines, Law of Cosines) Rectangular components (2D, rectify force as
xy
components using trig.) Cartesian vector (3D,
xyz
axes; rectify force as
ijk
components) Unit vector (u) (specifies direction) Position vector (r) (orients force between two points) Coordinate direction angles (
α, β, γ
orients force wrt xyz axes) Concurrent force system (multiple forces acting at/from the same point) Dot product Multiplication of two vectors together yields a scalar Conventions:
x z
+ + +
EGN 3310 Statics Chaps 1 & 2 Fall 2013 Handout 1
DFiller
Finding and resolving resultant forces.
2-4.
Determine
the
magnitude
of the
resultant
forc
e
F
R
=
F
1
+
F
2
and its
direction, measured
clockwise
from
the positive
u
axis.
2-5
.
Resolve the force
F
1
into
components
acting
along
the
u
and
v
axes and
determine
the
magnitudes
of
the components.
2-6.
Resolve
the force F
2
into
components
acting a
long
the
u
and
v
axes and
determine
the
magnitudes
of t
h
e
compo
n
ents.

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