Composite Beam Bending Experiment – Part 2: Testing and Data Analysis
For this portion of the laboratory, you must test your beam using the MTS machine and analyze the data to determine
the stiffness of your beam in bending, the maximum force carried by your beam, and both of these values normalized by
the mass of your beam.
Consider the four point beam bending test shown at right. The deflection is given by
the set of equations
The maximum deflection, w, found at the center of the beam, is given by the equation
. The figures and solution are taken from a table of solutions that can be found at
http://www.efunda.com/formulae/solid_mechanics/beams/theory.cfm
and elsewhere. The solution is valid for small deflections of long, slender beams. These equations may be rewritten in
the for P =  * w where is the bending stiffness of the beam. Given this form, the stiffness , , may be determined from
a load vs. deflection curve. HOWEVER, in our experiments, we know only the defection at x=a (and at x=L-a).
Calculations
1.
2.
3.
4.
5.
Plot the force versus deflection curve for your beam (determine the correct units).
Estimate the curve’s initial slope by placing a trend line on the graph (determine the correct units).
Derive an expression for  and calculate its value.
Estimate the maximum load carried by your beam.
Normalize the results in (2) and (3) by the mass of your beam.
Questions
1. Discuss, using text and figures, how you intended for your beam to resist transverse and longitudinal shear as well
as the bending moment.
2. Discuss how your beam performed with respect to your expectations using direct observations, and data. If it
failed, discuss why. If it performed well, discussed why.
Deliverables
Complete 3 page report, single-spaced, including text and figures in which you provide results of al calculations, the
result of the derivation in calculation (3) and in which you answer the two questions. The Introduction section should be a
short paragraph giving dimensions and measurements of the test setup and your beam. Be sure to point out the highlights
of your data in the Results section beyond including just graphs( USE UNITS). The bulk of your writing should go
toward answering the questions in your conclusions section. YOU MAY WORK IN PAIRS. Due April 22th.