Learning Objective
Learn how to determine the weight of one of your classmates using nothing more than a standard 2x4 and a measuring device.
Understand more about Moment of Inertia and how it can be used to determine the strength of beams.
Project Description
Moment of inertia changes from shape to shape. Engineers must be able to determine the moment of inertia in order to lower costs and make objects more lighter. In this project, we formed groups of 3 and used nothing but a 2x4 beam and a ruler to determine a classmate's weight. Several factors went into determining this, such as the moment of inertia, beam deflection, modulus of elasticity, and length. In the end, we compared the calculated weight with the classmate's actual weight.
Project Procedure
Position the beam on 2 stacks of notebooks, then measure the span between the supports and measure the distance between the floor and the bottom of the beam.
Position a volunteer to stand carefully on the middle of the beam and have a person on either side of the beam to help support the volunteer. Measure the distance between the floor and the bottom of the beam.
Calculate the beam's Modulus of Elasticity.
Place a second volunteer on the beam.
Calculate the volunteer's weight.
Tables
Moment of Inertia
Ixx = bh3/12
B - width of the beam (in.)
h - height of the beam (in.)
I - Moment of Inertia (in.4
Vertical Orientation
I = (1.5)(3.5)3/12
= 5.359375
Horizontal Orientation
I = (3.5)(1.5)3/12
= 0.984375
Modulus of Elasticity
Rearrange the equation
E = FL3/48IΔMAX
E = 135(81.5)3/[(48)(0.984375)(2.375)]
E = 651240.1504 psi
ΔMAX = FL3/48EI
to solve in terms of E
Substitute known values
Simplify
Weight of volunteer 2
What I Learned
I learned how to utilize the Modulus of Elasticity to determine how much a certain load would weigh. I also used the moment of inertia to find the Modulus of Elasticity. I predicted properties of the material by looking at the moment of inertia. I could predict how strong the beam was by looking at the Modulus of Elasticity. The strength depends on its material as well as it's dimensions.