civil engineering w2

Document Sample
civil engineering w2 Powered By Docstoc
					   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
    • Most strands already
      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
  take any more loading without failure or
  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
• Circle with radius ‘r’
                            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.

				
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
views:0
posted:10/1/2012
language:Unknown
pages:27