Introduction to Mechanics of Materials

MECH 260, Section 102
Introduction to
Mechanics of
Materials
Presentation Part 1
Clarence W. de Silva, Ph.D., P.Eng.
Professor of Mechanical Engineering
The University of British Columbia
e-mail: [email protected]
https:// www.sites.mech.ubc.ca/~ial
C.W.
de Silva
Announcements
Tutorial Sessions
Objectives of Tutorial Sessions:
1. Assist the students in problem solution and homework assignments.
2. Conduct some of the quizzes
Note 1: Tutorial sessions will start on September 14th. Homework
assignments are due at the tutorial sessions.
Note 2: Assignments 1 & 2 have been posted on the web site.
Please see the following web site for further details:
https://sites.www.mech.ubc.ca/~ial  Courses  MECH 260
Tutorial Schedule and Location:
Wednesdays 10:00 to 11:00 a.m.
Room: IBLC 182
Teaching Assistants: Mr. Tony Teng Li ([email protected]; ICICS 065—
Robotics Lab, Tel: 604-822-4850) and Mr. Hani Balkhair
([email protected]; ICICS 079, Tel: 604-822-6907)
Office Hours of Instructor and TAs: Please see the course outline.
MECH 260, Section 102, Introduction to Mechanics of Materials
3 Credits, 1st Semester 2016/17
(Tuesdays and Thursdays, 8:00-9:30 a.m.); Room: DMP 110
Course Web Site: www.sites.mech.ubc.ca/~ial
The course material including the lecture presentations, homework assignments, and
the solutions to homework problems and exams will be posted at this web site.
Instructor: Dr. Clarence de Silva, Professor
Office: CEME 2071; Tel: 604-822-6291; e-mail: [email protected]
Course Objectives
This course deals with the internal effects (primarily stresses and strains) in a deformable solid
boy due to external loads acting on it. The subject is also known as “Strength of Materials” or
“Solid Mechanics.” It is useful in a variety of engineering areas including mechanical, civil, and
mining engineering and biomechanics. It provides theory and formulas that are directly
applicable in the modeling, analysis, design, testing, and operation of engineering devices and
structures such as automobiles, airplanes, robots, machine tools, engines, bridges, elevated
guideways, and buildings. Stresses in an object are governed by the “internal loading,” which
are determined from “equilibrium equations” with external loading. Stresses are a determining
factor of the “strength” of the object. Strains caused by loading are directly related to the
“deflection” or “deformation” or “compatibility” of the object. The stress-strain relations (or
“constitutive relations”) determine the “stiffness” of an object are governed by the physics of
the object. In addition to strength, deformation, and stiffness, the subject of Mechanics of
Materials also concerns “stability” which studies the possibility of deformations that can grow
suddenly without limit (in theory). The course consists of lectures, tutorials, homework
assignments, quizzes, an intermediate examination, and a final examination.
Textbook
No specific textbook is assigned for this course. However,
one of the following books should be used for the reading
material:
• Beer, F. and Johnston, E.R., Mechanics of Materials,
McGraw Hill, New York, NY, 2009 (or later).
• de Silva, C.W., Mechanics of Materials, CRC
Press/Taylor&Francis, Boca Raton, FL, 2014.
• Hibbeler, R.C., Mechanics of Materials, Pearson, New
York, NY, 2011 (or later).
• Philpot, T.A., Mechanics of Materials, Wiley, Hoboken,
NJ, 2013.
MECH 260—102 COURSE LAYOUT
Week
1
2
3
4
Starts
Sept 06
Sept 13
Sept 20
Sept 27
Read Chapter on:
Statics
Stress
Strain
this topic
Nov 15
Nov 22
Topic
Introduction, Statics
Stress
Strain
Mechanical Properties of
Materials
Design Considerations
Axial Load and Deformation
Torsion
Bending
Bending
Intermediate Exam (In Class)
Shear Stress in Bending of
Beams
Deflection of Beams
Statically Indeterminate Beams
5
6
7
8
9
10
Oct 04
Oct 11
Oct 18
Oct 25
Nov 01
Tuesday, Nov 01:
Nov 08
11
12
13
Nov 29
Stress/Strain Transformations
these topics
Axial Load
Torsion
Bending
Bending
Transverse Shear
this topic
this topic
Note: The student must pass the final examination in order to pass the course.
Grade Composition
Homework Assignments
10%
Main Quizzes (during tutorial sessions)
10%
Pop Quizzes (during class)
10%
Intermediate Examination
20%
Final Examination
50%_
Total
100%
MECH 260 Roadmap
Design Considerations
Examples
Course Objectives
Importance
Plan
Review of Statics
Stress
Strain
Design Considerations
Applications
Revision
Mechanical
Properties of
Materials
Axial Loading
Torsion
Mohr’s Circle:
Stress Transformation
Strain Transformation
Examples
Bending
Beam Bending:
Shear Stress
Deflection
Statically Indeterminate Beams
Examples
Applications
Importance of
Mechanics of Materials
What is Mechanics of Materials?
Study of “internal” effects (stresses and strains) caused by
external loads (forces and moments) acting on a
deformable body/structure
Also known as: Strength of Materials or Mechanics of Solids
or Mechanics of Deformable Bodies
Determines:
1. Strength (determined by stress at failure)
2. Deformation (determined by strain)
3. Stiffness (ability to resist deformation; load needed to
cause a specific deformation; determined by the stressstrain “constitutive” relationship)
4. Stability (ability to avoid rapidly growing deformations
caused by an initial disturbance; e.g., buckling)
An Example (Aircraft)
External Loading
on the Aircraft
Dynamic Loads
Engine Thrust
Aerodynamic
Forces
Gravity
Wing Joint
(Attachment)
τ
Small Internal
Element
of the Joint
(Stresses and
Strains)
σ
Control Surface
Forces
An Example (Aircraft Disaster)
Aloha Airlines Boeing 737
Flight 243 on April 28, 1988 with 95 passengers and crew
Mid-air structural damage and component loss, with one
fatality (a crew member was sucked out)
The aircraft landed at Maui airport, Hawaii, without further loss
of human life (8 serious injuries)
Subject Definition
Statics
External Forces/
Moments
·
·
·
·
·
·
Geometry
Reactions, Internal
Forces/Moments
Constitutive
Relations
Modeling
Analysis
Computer Simulation
Design
Testing/Diagnosis
Operation
Engineering
Deflections
Deformations
(Rectilinear, Angular)
Application
Stresses
(Normal, Shear)
Constitutive
(Physical)
Relations
Strains
(Normal, Shear)
(Includes thermal effects)
Mechanics of
Materials
Application of the Subject
Useful in modeling, analysis, simulation, design, testing, and operation of
engineering systems (e.g., automobiles, airplanes, robots, machine tools,
engines, bridges, elevated guideways, and buildings)
Modeling: Determine “equations” governing stress-strain (or, loaddeflection) behavior of an object
Analysis: Determine stresses, strains (internal loads and deformations)
due to external loading
Simulation: Program a model of the system (using both analytical and
experimental equations and parameter values. Run the program under
specified loading conditions. Determine stresses, strains (internal loads,
deformations).
Design: Select materials, dimensions, and structure of a device to meet a
set of performance specifications (related to strength, size, cost, safety,
etc.)
Testing: Apply a specified regime of loading (single or repetitive) and
measure resulting deformations or determine loading that causes
failure
Operation: Make sure that the performance specifications are satisfied
during operation of the system
Importance of the Subject

Optimized (Light) Structures: Material optimization,
energy efficiency, and compact (light-weight) modern
designs of machinery and structures  Thin members;
high flexibility; complex geometry Large deformations
can mean poor vehicle ride quality (over guideways,
bridges, etc.), undesirable contact between components
causing wear, noise, sparks, hazard, etc.

More Powerful Machinery: Increased power levels and
longer and varied operating conditions of modern
machinery  larger loading; need for higher strengths

Regulatory Requirements: More stringent regulatory
requirements on safety, architecture, and esthetics 
complex and more rigorous analysis, design, and testing
Applicable Engineering Fields
Aeronautical and Aerospace Engineering: Design and
development of aircraft and spacecraft
Civil Engineering: Design and evaluation of bridges and
buildings
Electrical Engineering: Electronic hardware structural design,
“product qualification” testing for specialized
applications (e.g., nuclear power plants)
Manufacturing Engineering: machine component failure, tool
wear and breakage  reduced productivity and product
quality, increased costs of operation and maintenance
Proper design of machine tools and components
Mechanical Engineering: Design and testing of engines,
energy systems, vehicles, aircraft, robots, ships, etc.
Mining and Mineral Engineering: Design, development, and
testing of mining machinery that operate under severe
and hazardous conditions; emergency evacuations
Some Useful Terms
Force: A rectilinear load; has a magnitude and a direction (i.e., vector); Units: newton
(N), 1 kN = 1000 N
Normal Force: Force normal (perpendicular) to a considered area; tends to push/pull
(tension/compression) the body
Shear Force: Force along the plane of a considered area; causes a shearing (sliding
deformation along the plane; twisting)
Torque: A rotational load; torsional moment (or couple); tends to “twist” the object to
which it is applied; has a magnitude and a direction (i.e., a vector); Units: newtonmeter (N.m)
Bending Moment: A bending load; tends to “bend” the object to which it is applied; has
a magnitude and a direction (i.e., a vector); Units: newton-meter (N.m)
Stress: Force per unit area; not a vector but a 2-D tensor (because same force will cause
different stresses at a point depending on the area element that is considered); Units:
N/m2 (= pascal or Pa), 1 N/mm2 = 1 MPa; normal stress is caused by a normal force
component, shear stress is caused by a shear force component
Strain: Deflection per unit length (normal strain) or angle of deformation (shear strain);
dimensionless
Free-Body Diagram: “Virtually” separate the part of interest from the rest of the object
and mark the loads at the interface (and also external loads)
Homogeneous: Properties are uniform (do not change from point to point in the body)
Isotropic: Properties are non-directional (do not vary with the direction)
How many Pa in 1 MPa? in 1 kPa?
History
History of Mechanics of Materials
Archimedes (287-212 B.C.): Statics, equilibrium of a lever
da Vinci (1452-1519): Concept of moments
Galileo (1564-1642): Effects of loads on beams and rods, virtual
displacement
Newton (1642-1727): Foundation of mechanics
Bernoulli (1667-1748): Virtual displacement/work, beam bending
Hooke (1635-1703): Hooke’s law of stress-strain, Hooke’s joint
Euler (1707-1793): Moment of inertia, beam bending, instability, column
buckling, rigid body dynamics
d’Alembert (1717-1783): Inertia force (converts dynamics to statics)
Lagrange (1736-1813): Mechanics, energy methods
Coulomb (1736-1806): Friction (static and dynamic)
Laplace (1749-1827): Mechanics, etc.
Poisson (1781-1840): Lateral strain, Poisson’s ratio
Saint-Venant (1797-1886): Strain distribution at abrupt changes in
section/shape, strain tensor, torsion
Castigliano (1847-1884): Structural loads and deflections by energy
method
Galerkin (1871-1945): Elastic plates, stresses in dams and retaining walls
Timoshenko (1878-1972): Theory of thick beams
Disclosure by Galileo (1564-1642)
Roman engineers (perhaps around 1400, because
the Roman empire collapsed in 1453) first used two
logs (rollers) to support a stone column, for
transporting it to a temple. The column broke at one
of the supports.
Next they used three logs. Then the column broke at
the middle log!
Can you explain why?
I will l ask this question again toward the end of the
course.
Applications
Trump Tower, Toronto
(Closed due to Unstable Antenna)
High-Speed Ground Transit
(Vehicle/Guideway Design, Material Optimization, Cost, etc.)
The Sky Train
Vancouver, Canada—
A Modern Automated
Transit System
Torsional Guideway
Transit System (TGT)
Guideway
Car
Pier
Seismic Design
(Safety, etc.)
Earthquake in Kobe, Japan (Magnitude 7.2) on January 17, 1995
(Collapse of a Bank Building)
Building Design
(Design of Members, Joints, Configuration, etc.
for Structural Integrity, Safety, etc.)
Joints/Connectors of Machinery
(Under Dynamic Loading Conditions)
Booms, Cranes, etc.
(A window cleaner carriage)
Cable-stayed Bridges
(Incheon, South Korea)
Structural Tensioning Rods and Joints
(International Airport, Vancouver, Canada)
Exercising Equipment
(Fatigue Failure)
MEMS Devices (e.g., Accelerometer)
Approach: Acceleration  Inertia force of proof mass 
Capacitor plate (comb) movement  Measure capacitance
 Acceleration
Basic Problem Scenarios
• Axial Loading: Loads are forces (tensile or compressive)
applied along main axis of member  Deformations (primarily
extensions or compressions); occur along loading axis (Note:
Deformations (strains) can occur perpendicular to this axis
(Poisson effect).
• Shear Loading: Two equal and opposite parallel forces on
two equal parallel areas of member  Deformation: sliding
(shearing) of one area wrt other along the direction of loading.
• Torsional Loading: External loads are “torques”  tend to
twist the member.
• Bending Loading: External loads (forces and moments) 
bending deformations (i.e., flexure) of member. In practical
problems two or more of these basic scenarios may exist in
combination.
Studied Loading Scenarios
Original Member:
F
Deck Held by a
Pin-jointed
Light Rod:
(Axial Loading)
Bolted Lap Joint:
(Shear Loading)
Motorized
Belt Drive:
(Torsional
Loading)
Diving Board:
(Bending
Loading)
F
F
F
P
P
P
Shear-loaded
segment
P
Motor
P
P
Belt Drive
Shaft
T
T
T
T
M
F
F
M
M
Problem Solution
Involves three basic considerations:
• Statics (equations of equilibrium)  reactions at
supports and internal loads  stresses
• Nature of deformation (nature of strains)
• Stress-strain relations (i.e., constitutive
relations or physical relations)  strains
(deformations) once stresses are known (from
the knowledge of internal loads)
Note: Alternatively, we can determine stressstrain relation from known stresses and
corresponding strains.
Problem Solution Steps
1. Understand the problem: What has to be
determined; what information is given; what are the
assumptions and constraints; etc.
2. Plan the solution: Based on understanding of
problem (Step 1) and available approaches to solve
the problem, decide the most appropriate approach
(Note: Required approach is hinted in the problem)
3. Carry out the solution
4. Check the solution: E.g., for compatibility of units
and dimensions; proper sign of the results;
reasonability of magnitudes; and against results
from another approach
I-clicker Problem 1
FC = 2 kN
FB
45º
FA
A.
B.
C.
D.
E.
FA = 2; FB = 2
FA = 2/1.414; FB = 2
FA = 2x1.414; FB = -2
FA = -2x1.414; FB = 2
FA = 2; FB = -2/1.414
I-clicker Problem 2
10 kN
3L/4
L
R
A.
B.
C.
D.
E.
F
F = 10/4; R = 30/4
F = -10/4; R = 30/4
F = 30/4; R = 10/4
F = 30/4; R = -10/4
F = -30/4; R = -10/4