Introductory Material (ref Ch 1) MCH T 111 Mechanics for Technologists: Statics

Consultant: Instructor: Elastomer NVH design Structural Analysis FEA Perfect Compliment!! Consultant: Instructor: Elastomer NVH design Structural Analysis FEA Vibration Analysis Robert J. Michael, PhD, PE Office: Burke 230 Phone: (814) 898-6192 Email: rxm61@psu.edu

Today… Introduction Website: http://engr.bd.psu.edu/rxm61/ Syllabus Homework Guidelines Course Objectives Math/Trig Review Print out Handouts from Website!

SEE Syllabus – Key Points: 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

Homework Course Page Title 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 Box or underline answers Engineering Calculation Paper Homework

See HO 1,2

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

Branches of Mechanics Statics (MCH T 111) Strength of Materials (MCH T 213) Industrial Hydraulics (MET 432) Dynamics (M ET 206) ALSO, MCHT 214, Advanced SoM (320) and FEA courses

Why is Statics Important??

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

Structures: scaffolding burj khalifa

Middlebury College Library

Mechanical Assemblies S-92 Rotor Head Mechanical Assemblies GMT 900 Truck Ft Suspension

Small contact area; treat as a point “Types of Forces” Small contact area; treat as a point Applied Moment, M FR is resultant of w(s) = area under curve, acts at centroid One body acting on another M What’s a body? One body acting on another w/o contact Acting on narrow area

What’s Covered in MCH T 111? Fundamental Quantities & Units (ch1) Forces (2D and 3D)(ch2) 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) Draw simple Example!!

See HO

Table 1-1 in the textbook summarizes these unit systems. Statics:The Next Generation (2nd Ed.) Mehta, Danielson, & Berg Lecture Notes for Sections 1.1-1.6

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? Statics:The Next Generation (2nd Ed.) Mehta, Danielson, & Berg Lecture Notes for Sections 1.1-1.6

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 Statics:The Next Generation (2nd Ed.) Mehta, Danielson, & Berg Lecture Notes for Sections 1.1-1.6

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.

SI Unit Prefixes Prefix Symbol Value giga G 109 1 000 000 000 mega M 106 1 000 000 kilo k 103 1 000 BASE 100 1 milli m 10-3 0.001 micro 10-6 0.000 001 Down-RIGHT Up-LEFT 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. 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. Statics:The Next Generation (2nd Ed.) Mehta, Danielson, & Berg Lecture Notes for Sections 1.1-1.6

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. 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

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

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 of Gravitational 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).

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

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

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

Pounds-mass, lbm 1 slug = 32.2 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.

We will work with two unit systems in statics: 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) Statics:The Next Generation (2nd Ed.) Mehta, Danielson, & Berg Lecture Notes for Sections 1.1-1.6

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 Do examples on board.

Density & Specific Weight Density is a measure of mass per unit volume of a material. Specific Weight is a measure of weight per unit volume of a material.

Activity The block shown weighs .75 pounds. What is its specific weight? 1.25 in 2.1 in 1.00 in

Trig Review: Do example! Note, most of the math in this course is trig with a little algebra (solving simultaneous equations) and vectors.

Do example!

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!