CIVIL ENGINEERING DISCIPLES Session 02 and 03 Subject: S0012 / Introduction to Civil Engineering Year: 2007.

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.