Transcript Introductory Material - School of Engineering | Penn State

Introductory Material (ref Ch 1)
MCH T 111
Mechanics for Technologists: Statics
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Perfect
Compliment!!
Consultant:
Instructor:
Robert J. Michael, PhD, PE
Office:
Phone:
Email:
Burke 230
(814) 898-6192
[email protected]
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Elastomer NVH design
Structural Analysis
FEA
Vibration Analysis
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Today…
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Introduction
Website: http://engr.bd.psu.edu/rxm61/
Syllabus
Homework Guidelines
Course Objectives
Math/Trig Review
Print out Handouts from Website!
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SEE Syllabus – Key Points:
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Plan on spending 6
– 8 hrs/ week
outside of class!!
Grade Distribution
Grade Scale
HW Guidelines
Attendance Policy
Makeup Policy
Academic Integrity
Support Services – SEEK TUTORING –
Burke 240 – schedule on board
• COURSE OBJECTIVES
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Course
Title
Page
Name & Date
Chapter &
problem no.
Sketch of
situation
What you are
to find
Always include
UNITS
FBD’s as
necessary
No more than TWO
problems per page
LATE HOMEWORK
NOT ACCEPTED
Engineering
Calculation
Paper
Box or underline
answers
Homework
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61,2
See HO
What is Statics?
• Statics is the branch of engineering
mechanics that studies the forces acting
on bodies that interact with one another in
the absence of acceleration.
• Body is stationary – STATIC
– Forces required for equilibrium
• Reaction forces
• Forces in cables
• 2D force or 3D force
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Branches of Mechanics
Mechanics
Rigid Bodies
(Things that do not change shape)
Statics
Deformable Bodies
(Things that do change shape)
Dynamics
Statics
(MCH T 111)
Dynamics
(M ET 206)
Fluids
Incompressible
Strength of
Materials
(MCH T 213)
Compressible
Industrial
Hydraulics
(MET 432)
ALSO, MCHT 214, Advanced SoM (320) and
FEA courses
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Why is Statics Important??
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Why is Statics Important??
Need to know what the force is in each member so you know how big
to make it! Mechanic vs engineer
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Structures:
scaffolding
burj khalifa
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Middlebury College Library
S-92 Rotor Head
Mechanical
Assemblies
GMT 900 Truck Ft Suspension 13
“Types of Forces”
Small contact area;
treat as a point
FR is
resultant of
w(s) = area
under curve,
acts at
centroid
Acting on
narrow area
Applied
Moment, M
M
One body
acting on
another
One body
acting on
another w/o
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contact
What’s Covered in MCH T 111?
• Fundamental Quantities & Units (ch1)
• Forces (2D and 3D)(ch2)
Draw simple Example!!
– Resultants (FR)
– Components (Fx, Fy, Fz)
• Equilibrium – Particle and Rigid Body (ch3 and 5)
– 2D and 3D
• Rotational Moments & Couples (ch4)
• Reaction Forces and Distributed Loads (ch4)
• Structural Analysis (basically RB Equilibrium) (ch6)
– Trusses and Machine Frames
• Friction (ch8)
• Properties of Plane Areas & Solids (centroids and
inertia) (ch 9 & 10)
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See HO
Table 1-1 in the textbook summarizes these unit systems.
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COMMON CONVERSION FACTORS
• Work problems in the units given unless otherwise instructed!
• Example: Convert a torque value of 47 in • lb into SI units.
– Answer is 5.31026116 N • m?
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THE INTERNATIONAL SYSTEM OF UNITS
(Section 1.4)
• No plurals (e.g., m = 5 kg, not kgs )
• Separate units with a • (e.g., meter second = m • s )
• Most symbols are in lowercase.
• Some exceptions are N, Pa, M and G.
• Exponential powers apply to units, e.g., cm • cm = cm2
• Compound prefixes should not be used.
• Table 1-3 in the textbook shows prefixes used in the SI
system
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Rules & Conventions for SI Units
• Use one prefix so that the number is between 0.1 and
1000. Only use one prefix at a time
• It’s important to use the proper case when using SI
units and prefixes.
• Engineers generally use prefixes that are factors of
1000
• Use a dot between units that represent a product such
as Nm (“newton meters”). Use a slash for units in a
denominator N/m2 (“newtons PER square meter”)
• In calculations use base units and powers of 10 instead
of prefixes
• The prefix becomes part of the name or symbol without
a space. (kN or kilonewton)
• Avoid using a prefix in the denominator.
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SI Unit Prefixes
giga
G
109
1 000 000 000
mega
M
kilo
k
BASE
milli
m
106
103
100
10-3
1 000 000
1 000
1
0.001
m
10-6
0.000 001
micro
Value
Up-LEFT
Symbol
Down-RIGHT
Prefix
When changing the prefix, remember to move the decimal
to the right when switching down the list and to the left
when switching up the list.
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Do example. MPa to N/mm^2
NUMERICAL CALCULATIONS
(Section 1.5)
• Must have dimensional “homogeneity.” Dimensions have
to be the same on both sides of the equal sign, (e.g. distance
= speed  time.)
• Use an appropriate number of significant figures (3 for
answer, at least 4 for intermediate calculations). Why?
• Be consistent when rounding off.
- greater than 5, round up (3528  3530)
- smaller than 5, round down (0.03521  0.0352)
- equal to 5, see your textbook for an explanation.
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Accuracy
• We want answers that are accurate within
0.2 percent. To accomplish this,
– Report 4 significant digits if the answer begins
with a 1,
– Report 3 significant digits if the answer begins
with anything other than a one.
• See handout for significant digit and
rounding rules.
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See HO
Rounding Expected for this Course
• When using the following parameters –
round to a minimum of this many places!!
– Sin / Cos / Tan of an angel – 4 places
• Example – Sin 60° = 0.8660
– Angles – 2 Places
• Example – 65.53°
– Use Common Sense for Other Values
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Newton’s Three Fundamental Laws
• Law #1 – A body at rest will stay at rest and a
body in motion will stay in motion unless acted
upon by an unbalanced force.
• Law #2 – If the resultant force on a particle is not
zero, the particle will have an acceleration
proportional to the magnitude of the resultant
force and in the direction of the force and
inversely proportional to its mass.
• Law #3 – Every action has an equal and
opposite reaction
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Newton’s Second Law of Motion
If a body is acted upon by an unbalancing
force, it will accelerate proportional to and
in the direction of the unbalanced force.
F = m·a
Where,
F = unbalanced force
m = mass
a = acceleration
Newton’s
Law 26
of
Gravitation
al Attraction
Gravity and Weight
• A special case of Newton’s second law to
consider is when the force acting on the
particle is the force of gravity.
• This is a constant acceleration (g) in the
direction of the center of the earth equal to
9.81m/s2 or 32.2 ft/s2
• In this case the force acting on the body is
called Weight (W).
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Weight and Mass
• In statics, we only used forces. Quantities
given as a mass MUST be converted to a
force.
• Based on Newton’s 2nd law of motion:
W = mg
• W = weight of object (force)
• m = mass of object (a scalar, not a force)
• g = gravitational constant
= 32.2 ft/s2 = 9.81 m/s2
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Activity
• An object has a mass of 15 slugs. What is
its weight in pounds?
W=m·g
W = (15 slugs)(32.2 ft/s2)
W = 483 pounds
Side: Kips or K = 1,000 lbs
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Activity
• An object has a mass of 15 kg. What is its
weight in newtons?
W=m·g
W = (15 kg)(9.81 m/s2)
W = 147 N
You will NOT receive any credit for solving
equilibrium equations using mass
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Pounds-mass, lbm
• A pound-mass is a quantity of matter having a
weight of 1 pound-force (lbf).
1 slug = 32.2 lbm
• When using pounds-mass in Newton’s 2nd Law
of Motion, you MUST divide pounds-mass by
32.2 to convert to slugs.
• This quantity isn’t generally used in statics.
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In Summary:
• Force, mass, time and acceleration are related by Newton’s
2nd law. Three of these are assigned units (called base units)
and the fourth unit is derived. Which is derived varies by
the system of units.
• We will work with two unit systems in statics:
• International System (SI)
• U.S. Customary (USCS)
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Calculating Volumes
• Volume of a rectangular Prism
V = Length * Width * Height
• Volume of a Triangular Prism
V = ½ Length * Width * Height
• Volume of a Pyramid
V = 1/3 Length * Width * Height
• Volume of a Cylinder
V = πr2L or 1/4πd2L
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Do examples
on board.
Density & Specific Weight
• Density is a measure of mass per unit
volume of a material.
mass
Density,  
v olume
• Specific Weight is a measure of weight per
unit volume of a material.
weight
Specif ic Weight,  
v olume
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Activity
• The block shown weighs .75 pounds.
What is its specific weight?
W

V
1.25 in
2.1 in
.75 lb

(2.1" )(1.25" )(1.0" )
1.00 in
  .286 lb / in3
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Trig Review:
Do example!
Note, most of the math in this course is trig with a
little algebra (solving simultaneous equations) and
vectors.
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Do example!
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See trig
handouts
Solution Process for Equilibrium
Problems
• Record all given data and define what you are
solving for
• Sketch a neat free-body diagram labeling all
known and unknown forces
• Write out the equations of Equilibrium
• Neatly and logically solve the Equilibrium
Equations
– Include units in each line of the solution along with
magnitudes
• When solution is complete draw a box around
each item in the Find list – Be sure to include
proper units
Let the
fun begin!
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