Freshman Engineering Clinic
Section 2
Lab 5: Galileo’s Flexure Theory
March 10, 2009
Galileo Galilei’s last book Dialogues Concerning Two New Sciences was published in 1638. This is often
credited as the beginning of the elastic theory of bending although notebooks of Da Vinci discovered in
1997 show he was working on bending theory 100 years earlier. Following Da Vinci and Galileo, Euler,
Bernoulli, and Parent made important contributions.
In his book Galileo developed a theory for the failure of beams. Many of his ideas were correct although
a fundamental assumption was flawed and resulted in a theory that over-predicted strength of a brittle
material in bending. There is no evidence that Galileo actually conducted any experimental testing of
his theories of bending.
Galileo predicted that the failure load of a cantilevered beam is
W
failure

1h
 
2  L  F AB
Where
Wfailure is the load applied to the beam
h is the depth of the beam
L is the distance from the load to the support point
FAB is the load required to fail the beam in tension
For the concrete used in this lab it is estimated that the failure tensile stress is approximately 400 psi
and the failure tensile load can then be determined from the stress and cross-section and the equation
can be rewritten as
W
failure

1h
hw
 
2  L  AB
where w is the width of the cross section.
Some of the implications of the above equation are that Galileo believed that




the failure load in bending is proportional to the tensile strength of the material
the failure load in bending is proportional to the height squared of the cross-section
the failure load in bending is proportional to the width of the cross section.
the failure load is inversely proportional to the distance from the load to the support point.
Figure 1. Galileo’s illustration of a beam subjected to bending.
Procedure:
Each team is provided with 5 small concrete beams that will be tested as cantilevers. The beam
dimensions are (w x h): 2 x 1, 2 x 2, 2 x 3, 3 x 2, 1 x 2 with the dimensions in inches (exact dimensions
should be measured during the lab). Half of the groups will test their beams with the load applied 12”
from the support and half with the load at 18” from the support. The load is applied by slowly adding
sand or other weights to a bucket suspended from the beam. All of the test data will be combined at
the end of the laboratory period.
Deliverable:
Each group is to prepare a properly prepared laboratory report including all of the standard report
sections. As a minimum, the discussion should address the validity of Galileo’s theory based upon the
results of the experiment including the relationships between failure load and the beam dimensions and
load application location as well as the constant at the front of the equation. Your report should also
include appropriate sketches of the experimental set-up and tables or graphs of the results.
Due Date: This laboratory report will be combined with that for Lab #6 and will be due March 31st.