Subject
Year
: S0012 / Introduction to Civil Engineering
: 2007
CIVIL ENGINEERING DISCIPLES
Session 02 and 03
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Elasticity
Unstressed Wire
Apply Small Stress
Remove Stress and
Material Returns to
Original Dimensions
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Inelastic Material Properties
Bottle Undergoing
Compressive
Stress
Unstressed
Bottle
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Inelastic
Response
Compression
Unstressed Sponge
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Sponge in Compression
Compressive Failure
• This paper tube was crushed,
leaving an accordion-like
failure
Characteristic :
• depends on the cross-sectional
area
• depends on the material
• depends on the length
• depends on the cross-sectional
shape
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Tension
• Steel cables supporting IBeams are in tension.
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Tensile Failure
• Frayed rope
• Most strands already failed
• Prior to catastrophic fail
Characteristics :
• depends on the cross-sectional
area
• depends on the material
• does not depend on the length
• does not depend on the crosssectional shape
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Tensile Failure
• This magnesium test bar is tensile strained until fracture
• Machine characterizes the elastic response
• Data verifies manufacturing process control
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Force Direction
Transverse Stress on the
Horizontal Aluminum Rod
Axial Stress on the
Vertical Post
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Ductile Example
Unstressed Coat Hangar
After Applied Transverse
Stress Beyond the Yield
Stress Point
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Brittle Example
Unstressed Stick
Brittle Failure After
Applied Stress Beyond
the Yield Stress Point
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Moment of Inertia
•
•
•
•
•
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Quantifies the resistance to bending or buckling
Function of the cross-sectional area
Formulas can be found in literature
Units are in length4 (in4 or mm4)
Symbol: I
Moment of Inertia for
Common Cross Sections
h
(in4 or mm4)
12
• Circle with radius ‘r’
4
____
π
r
• I=
(in4 or mm4)
4
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
• I=
3
bh
____

• Rectangle with height ‘h’ and
length ‘b’
 b 
 2r 
Modulus of Elasticity
•
•
•
•
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Quantifies a material’s resistance to deformation
Constant for a material, independent of the material’s shape.
Units are in force / area. (PSI or N/m2)
Symbol: E
Flexural Rigidity
• Quantifies the stiffness of a material
• Higher flexural rigidity = stiffer material
• Product of the Modulus of Elasticity times the Moment of Inertia
(E*I)
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Factor of Safety
• Designers make a bridge stronger than design target
• Factor of Safety =
Failure Level
Actual Level
• Most codes require minimum Factor of Safety > 1.6
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Cross-Sections and
Cross-Sectional Area
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Lever Concept
F1
F2
L1
Lever Relationship: F1 * L1 = F2 * L2
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L2
Structural Analysis
• Structural analysis is a mathematical examination of a complex
structure
• Analysis breaks a complex system down to individual component
parts
• Uses geometry, trigonometry, algebra, and basic physics
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How Much Weight Can This Truss Bridge Support?
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Pythagorean Theorem
• In a right triangle, the length of
the sides are related by the
equation:
a2 + b2 = c2
c
a
b
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Sine (sin) of an Angle
• The angles are related to the
lengths of the sides by the
equations:
sinθ1 =
Opposite
=
Hypotenuse
a
c
Opposite
b
sinθ2 =
=
Hypotenuse
c
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θ2
c
a
θ1
b
Cosine (cos) of an Angle
• The angles are related to the lengths
of the sides by the equations:
cosθ1 =
Adjacent
Hypoten use
=
θ2
b
c
c
a
θ1
Adjacent
a
cosθ2 =
=
Hypotenuse
c
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b
This Truss Bridge is
Built from Right Triangles
θ2
c
a
θ1
b
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Vector Components
• Every vector can be broken into two parts, one vector with
magnitude in the x-direction and one with magnitude in the ydirection.
• Determine these two components for structural analysis.
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Structural Analysis Problem
• Calculate the internal member forces
on this nutcracker truss if the finger is
pushing down with a force of eight
newtons.
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