# civil engineering w2

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```					   Materials
Characterization
Learning Objectives
• Identify compressive and tensile forces

• Identify brittle and ductile characteristics

• Calculate the moment of inertia

• Calculate the modulus of elasticity
Elasticity

• When a material returns to its original shape
after removing a stress

• Example: rubber bands
Elastic Material Properties

Unstressed Wire

Apply Small Stress

Remove Stress and
Material Returns to
Original Dimensions
Inelastic Material Properties

Bottle Undergoing
Compressive
Stress
Unstressed                       Inelastic
Bottle                         Response
Compression

• Applied stress that squeezes the material

• Example: compressive stresses can crush
an aluminum can
Compression Example

Unstressed Sponge   Sponge in Compression
Compressive Failure

• This paper tube was
crushed, leaving an
accordion-like
failure
Tension

• Applied stress that stretches a material

• Example: tensile stresses will cause a
rubber band to stretch
Tension Example

• Steel cables
supporting I-Beams
are in tension.
Tensile Failure

• Frayed rope
failed
• Prior to catastrophic
fail
Tensile Failure

• This magnesium test bar is tensile strained
until fracture
• Machine characterizes the elastic response
• Data verifies manufacturing process control
Force Directions

• AXIAL: an applied force along the length
or axis of a material

• TRANSVERSE: an applied force that
causes bending or deflection
Force Direction Examples

Transverse Stress on the
Horizontal Aluminum Rod
Axial Stress on the
Vertical Post
Graphical Representation
• Force vs. Deflection in the elastic region
25

20

15

10

5                             Steel Beam Data

Linear Regression
0
0    5           10             15           20

Deflection, y (in x 0.01)
Yield Stress

• The stress point where a member cannot
large amounts of deformation.
Ductile Response

• Beyond the yield stress point, the material
responds in a non-linear fashion with lots of
deformation with little applied force

• Example: metal beams
Ductile Example

Unstressed Coat Hangar

After Applied Transverse
Stress Beyond the Yield
Stress Point
Brittle Response

• Just beyond the yield stress point, the
material immediately fails

• Example: plastics and wood
Brittle Example

Unstressed Stick

Brittle Failure After
Applied Stress Beyond
the Yield Stress Point
Brittle and Ductile
Response Graphs
25

20

15

Ductile Response
10
Brittle Response

5
Failure

0

0   15           30         45              60

Deflection, y
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
Moment of Inertia for
Common Cross Sections
• Rectangle with height


‘h’ and length ‘b’                h


bh3
• I = ____ (in4 or mm4)     b 
12
 2r 
π r4
• I = ____ (in4 or mm4)
4
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
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)
Calculating the
Modulus of Elasticity
• Slope =    48EI
_______
L3
25

• Measure L           20

• Calculate I         15
Slope is 1.342 lb/in

• Solve for E         10

5                                    Steel Beam Data
Linear Regression
0
0          5               10      15          20

Deflection, y (in x 0.01)
Acknowledgements
• Many terms and the laboratory are based a
paper titled A Simple Beam Test:
Motivating High School Teachers to
Develop Pre-Engineering Curricula, by
Eric E. Matsumoto, John R. Johnson,
Edward E. Dammel, and S.K. Ramesh of
California State University, Sacramento.

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