Purposes of Beam Testing

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Purposes of Beam Testing

• Structural Beam Testing and
• Material Beam Testing
• Determine the Modulus of
• Elasticity of the material by
• material Beam Testing
• comparing with tension
• compressions tests

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More Purposes of Elastic Bending Testing

• Familiarize with the essential features of
  bending tests
• Review the fundamental concepts associated with
  beam bending
• Review and calculate the bending and shear
  stresses at ultimate load
• Understand the factor of safety

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Loading for Pure Bending
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Bending in Beams

• Stress varies both across the cross section (y)
  and along the length of the member (x).

y
P
P
x
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Plane Assumption - for Pure Bending
Fundamental Assumption
Results for Linear Material
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Elastic Plastic Bending Action
Linear
Non-Linear

• (a) Stresses vary linearly across the
• section until the maximum stress
  (a)
• reaches yield.
• (b) As more moment is applied, the
• material starts yielding from the
• outer fiber inward until the entire (b)
• section is yielded.
  
• (c) Once the section is fully yielded, it
• will support no more moment and
• hence becomes a plastic hinge.
• The moment required to fully yield (c)
• the cross section is referred to as the
• plastic moment capacity of the section.

Me
MY
MYltMltMP
MP
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Stress above the Proportional Limit
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Modulus of Rupture

• Large moments cause increasingly large strains
  until the beam either breaks (if the material is
  brittle) or forms a plastic hinge (if the
  material is ductile).
• A fictitious equivalent linear stress
  distribution can be calculated based on
• The maximum value of the fictitious
  straight-line fiber stresses is called the
  Modulus of Rupture

?max
?max
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Deformation of Beams
Method of Successive Integrations
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Equations for Slope and Deflection
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Material Beam Testing Setup
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Specimens of Beam Testing

• 6063-T5 Aluminum Alloy Beam
• P1000 Channel
• Steel Beam
• P1000 Channel
• 3. Wood Beam

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• Beam Data
• (P1000 Channel)
• Cross Section
• Dimension
• Allowable Moment

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Data from a Bending Test

• Initial data
• Dimensions of the beam
• For each loading step
• A load value
• The maximum deflections at the center of
  the beam

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• Beam Data
• (P1000 Channel)
• Area of Section
• Moment of Inertia
• Section Modulus

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• Beam Data
• (P1000 Channel)
• Thickness
• Area of Section
• Moment of Inertia
• Section Modulus

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• References for Uniform loading
• Allowable Uniform Load
• Deflections for Different Spans

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Assumptions in Material Beam Testing

• Assumptions in Mechanics of Materials
• Linear
• Elastic material
• Small deformation.
• It is important in data reduction that follow the
  assumptions to select test data.

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Procedure of Material Beam Testing

• Measure and record beam span and cross sectional
  dimensions of a specimen.
• Apply load.
• Deflection data are to be acquired.
• Deflect the specimen at a constant rate until the
  beam fractures.
• Unload the specimen.

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Required Test Results

• Calculation of moment, shear, normal stress and
  shear stress in a beam.
• Modulus of Elasticity. (?)
• Effects of orientation and
• cross sectional dimensions.
• Experimental errors.

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Data Reduction

• Plot the Load vs. Deflection diagrams.
• Calculate the shear and moment at ultimate
  load.
• Comparing the allowable moment for the
  steel and
• aluminum beams and discuss the factor of
  safety.
• Calculate the modulus of elasticity by
  selecting
• suitable data.
• Calculate modulus of rupture.
• Draw the load, shear, and bending moment
  diagrams
• for the ultimate load.
• Compute the normal and shear stresses
  associated
• with the ultimate load. Discuss the
  results.

b.
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Beam Bending Testing
Have fun!