Jeffrey Katz
ENGRD 202
Shaina Khan
Lab Report #3: Deformation and Failure of Beams
1. The calculations for the ratios are given on the table. To calculate stiffness, one must
divide the load that a beam is subjected to by its corresponding deflection (in essence,
find the slope of the line on the graph). For instance, if a beam were loaded with 20
pounds and it was deflected by .025 inches its stiffness would be (20 lb / .025 in), or 800
lb/in.
2. It should be noted that in the end, the numbers found in the stiffness ratio are rough
approximations. It would take multiple tests to determine a true stiffness of a beam.
Width: (compare beams 1 and 4) – It would seem that when one doubles the width, the
stiffness is roughly doubled as well, as the ratio is roughly 1.83.
Height: (compare beams 1 and 2) – It would seem that if the height is doubled, the
stiffness of the beam is increased by about seven times (rounding up a factor of 6.89). A
7 to 1 ratio is close to an 8 to 1 ratio, which would be the increase in the height cubed, so
doubling the height could lead to an increase in stiffness of 8 times, although jumping
from a 7 to 1 ratio to an 8 to 1 ratio is admittedly a large step.
.
Modulus: (compare beams 2 and 5) – Beam 5 has a modulus of elasticity of 10 x 10
6
psi,
which is 3 times less than that of the steel Beam 2. Beam 5’s stiffness is in turn about a
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 Fall '06
 ZEHNDER
 elastic modulus, Jeffrey Katz Shaina Khan

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