civil engineering disciples session 02 and 03 subject: s0012 / introduction to civil engineering...
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CIVIL ENGINEERING DISCIPLESSession 02 and 03
Subject : S0012 / Introduction to Civil EngineeringYear : 2007
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Elasticity
Unstressed Wire
Apply Small Stress
Remove Stress and Material Returns to Original Dimensions
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UnstressedBottle
Inelastic Material Properties
Bottle UndergoingCompressive
Stress
InelasticResponse
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Compression
Unstressed Sponge Sponge in Compression
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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 I-Beams 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
cross-sectional 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
Axial Stress on the Vertical Post
Transverse Stress on the Horizontal Aluminum Rod
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Ductile Example
Unstressed Coat Hangar
After Applied TransverseStress 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• 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
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Moment of Inertia forCommon Cross Sections
• Rectangle with height ‘h’ and length ‘b’
• I = (in4 or mm4)
• Circle with radius ‘r’
• I = (in4 or mm4) 2r
b
12
bh3____
4____π r4
h
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Modulus of Elasticity
• 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
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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 =
• Most codes require minimum Factor of Safety > 1.6
Failure LevelActual Level
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Cross-Sections and Cross-Sectional Area
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Lever Concept
Lever Relationship: F1 * L1 = F2 * L2
L1 L2
F1 F2
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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 = c2a
b
c
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Sine (sin) of an Angle
• The angles are related to the lengths of the sides by the equations:
sinθ1 = =
Opposite aHypotenuse c
sinθ2 = =Opposite b
Hypotenuse c
a
b
c
θ1
θ2
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Cosine (cos) of an Angle
• The angles are related to the lengths of the sides by the equations:
cosθ1 = =Adjacent bHypoten use c
cosθ2 = =Adjacent a
Hypotenuse c
a
b
c
θ1
θ2
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This Truss Bridge is Built from Right Triangles
a
b
c
θ1
θ2
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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 y-direction.
• 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.