Mechanics of Materials I
Overview
School of Aerospace and Mechanical Engineering
Lecturer: Seongpil Cho
Introduction
❖ General Information
Course Number
AM3201, AA3203
Course Title
Mechanics of Materials I
Credit Hours
3
Instructor
Prof. Seongpil Cho
Office
R308, Mechanical Engineering Building
Office Hours
Mon – Thu, 10 am to 3 pm
E-mail
spcho@kau.ac.kr
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Introduction
❖ Textbook
❖ Mechanics of Materials 9th Edition by Barry J. Goodno and James M. Gere
3
Introduction
❖ Assessment
▪ The course will be assessed in the following manner:
➢ Mid-term exam
40%
➢ Final exam
40%
➢ Others
20% (*)
(*) Date due Assignments and Class Attendance.
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Introduction of Mechanics of Materials
❖ Engineering Mechanics
Engineering mechanics
Fluid mechanics
Solid mechanics
Mechanics of
deformable bodies
Mechanics of
rigid bodies
Statics
Dynamics
Kinematics
1. Mechanics of materials
2. Theory of elasticity
3. Theory of plasticity
1. Ideal fluid
2. Viscous/inviscid fluid
3. Comp./incompressible fluid
Kinetics
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Introduction of Mechanics of Materials
❖ Mechanics of Materials
▪ A branch of applied mechanics that deals with the behaviour of solid bodies subjected to various
types of loading
▪ Principal objective:
a. To determine the stresses, strains, and displacements in structures due to the loads acting on them
b. The safe design of all types of structures, whether airplanes and antennas, buildings and bridges,
machines and motors, or ships and spacecraft.
(a) Airplane
(b) Bridge
Deformable structures
6
Statics Review
❖ Equilibrium Equations
▪ Vector Form
• Resultant Force R
→
Resultant Moment M
→
→
R = F = 0
→
→
M =  M =  (r  F ) = 0
▪ Scalar Form
F = 0 F = 0 F = 0
x
y
z
M = 0 M = 0 M = 0
x
y
z
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Statics Review
❖ Applied Forces
▪ Concentrated Forces/Moments – applied to a single point.
▪ Distributed Forces – applied along a portion of the
member’s length.
▪ Free-Body Diagram – includes all applied forces and
moments, reaction forces and moments, and connection
forces between individual components.
▪ Static Sign Convention
▪ Forces acting in the positive direction of the coordinate
axes are positive.
▪ The right-hand-rule is used to determine the signs of
moment vectors.
Plane frame structure.
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Statics Review
❖ Reactive Forces and Support Conditions
▪ Forces at structural supports which result from the action of applied forces to the overall structure.
▪ Reaction Force – shown as a single arrow with a slash drawn through it.
▪ Reaction Moment – shown as a double-headed arrow or curve with a slash.
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Loads
❖ Loads: Forces and moments
Tension
Torsion
Shear
Bending
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1.2 Normal Stress and Strain
❖ Forces and moments
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Normal Stress and Strain
❖ Stress, strain, and displacement (deformation)
▪ Difference between stress and strain
Definition
Formula
Unit
Stress
Strain
The restoring or resistive force
per unit cross-sectional area
when equal opposing forces act
on a body.
𝜎 = 𝑃ൗ𝐴
𝑁Τ
𝑚2 or Pa
The change in the shape of a
body per original shape due to
an applied stress.
Relationship of each parameter
𝜖 = ∆𝐿ൗ𝐿
None
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Normal Stress and Strain
❖ Normal stress and strain
▪ An elementary form by considering a prismatic bar subjected to axial forces.
▪ Prismatic bar: a straight structural member having the same cross section throughout its length
▪ Axial force: a load directed along the axis of the member (tension or compression).
▪ Other examples: the members of a bridge truss, connecting rods in automobile engines, spokes of
bicycle wheels, columns in buildings, and wing struts in small airplanes.
Structural members subjected to axial loads
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Normal Stress and Strain
❖ Normal stress
▪ Normal stress 𝝈: the normal restoring or deforming force
per unit cross-sectional area
𝐟𝐨𝐫𝐜𝐞
𝑷
=
𝐜𝐫𝐨𝐬𝐬 − 𝐬𝐞𝐜𝐭𝐢𝐨𝐧𝐚𝐥 𝐚𝐫𝐞𝐚 𝑨
The normal stress acts in a direction perpendicular to the
(a) free-body diagram of a segment of the bar
𝜎=
•
(b) segment of the bar before loading
cut surface
✓ L: the original length of the bar
✓ 𝜹: the increase in length due to the loads
•
Sign: Tension (tensile stress, +),
(c) segment of the bar after loading
compression (compressive stress, -)
•
Unit
- SI: Pa = 𝑁/𝑚2 or MPa = 106 𝑁/𝑚2
(d) normal stresses in the bar
- USCS: psi = lbf/in2 or ksi = 103 psi
FIG. 1-2 Prismatic bar in tension
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Normal Stress and Strain
❖ Normal strain
▪ Normal strain 𝝐: the elongation per unit length
𝝐=
•
𝐞𝐥𝐨𝐧𝐠𝐚𝐭𝐢𝐨𝐧
∆𝑳 𝜹
=
=
𝐭𝐨𝐭𝐚𝐥 𝐥𝐞𝐧𝐠𝐭𝐡
𝑳
𝑳
The normal stains are associated with normal stresses.
✓ L: the original length of the bar
✓ 𝜹: the total elongation due to the loads
•
Sign: Tension (tensile strain, +), compression (compressive strain, -)
•
Unit
- Dimensionless quantity (independent of any system of units)
- Forms: mm/m, m/m, and in./in, percent
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Course overview
❖ Course overview
Axially Loaded Members
Torsion
Shear forces and
bending moments
Stress in Beams
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