PASCO ME-9891 User Manual
®
Flexible I-beam
ME-9891
Included Equipment Part Number
Flexible I-beam ME-9891
Instruction Manual
012-09977A
Recommended Equipment
Force Sensor
Motion Sensor
2
2
1
PS-2104
PS-2103
or
Rotary Motion Sensor
Large Table Clamp ME-9472
Base and Support Rod ME-9355
45 cm Rod ME-8736
Multi Clamp SE-9442
String (about 1 m) SE-8050
Small hanging mass (about 50 g) SE-8759
(2) Pencils
Adhesive tape (about 20 cm)
1
Equipment recommended for experiment on page 6.
2
Simultaneous use of two PASPORT sensors requires a multi-port PASPORT interface such as Xplorer
GLX (PS-2002) or PowerLink (PS-2001); or two single-por t interfaces such as USB Link (PS-2100).
2
PS-2120
Introduction
The model ME-9891 Flexible I-beam illustrates beam stiffness and deflection. Because it flexes more than a
metal or wooden beam, students can easily observe that its vertical stiffness is greater than its horizontal stiffness. Use the Flexible I-beam to demonstrate how a beam bends under various load and support configurations.
Add sensors to quantitatively explore the concepts of internal moment, second moment of area, and flexural
rigidity.
800-772-8700 www.pasco.com
Flexible I -beam Demonstrations
Demonstrations
Ease of Bending
Hold the I-beam in your hands and bend it in the “upright” and “side” directions as
illustrated. In which direction is it easier to bend? For the same effort, in which direction does it bend more?
Elastic Curves
Set up the beam (either upright or on its side) in the support-and-load configurations
diagramed in Figure 3.
The diagrams show two types of support: roller support, which restricts vertical displacement but not rotation; and fixed support, which restricts both displacement and
rotation. Use a pencil for a roller support and a large table clamp (PASCO part
ME-9472) for a fixed support (see Figure 2).
(a) Roller support (b) Fixed support
Figure 2
Figure 1: Exaggerated
illustration of I-beam
bent in upright and side
directions
To apply the load, press down on the beam with your hand or place a mass (about 1
kg) on the beam.
For each configuration, make an exaggerated sketch of the elastic curve showing
where the curvature of the beam is positive (concave upward), negative (concave
downward), and zero (a straight section or an inflection point). Hold a straight edge
against the beam to help determine the direction of curvature. Also mark the point (or
points) of maximum deflection.
Figure 3: Support-and-load configurations for elastic curve demonstration
2
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Model No. ME-9891 Theory
Theory
The deflection of a beam depends on how it is supported, the location and magnitude
of the load, the beam’s elastic modulus (E), and its second moment of area (I).
The vertical deflection of a beam (y) can be found using the formula
(eq. 1)
d2y
--------
dx
M
------=
2
EI
where M is the internal bending moment at horizontal position x. The product EI is
the beam’s flexural rigidity.
Second Moment of Area
b(y)
y
Figure 4
The second moment of area for a beam of constant cross section is
(eq. 2)
Iy2by()yd
=
∫
neutral axis
where b(y) is the width of the section at a distance y from the neutral axis (Figure 4).
For the upright I-beam in Figure 5a, the second moment of area is
3
(eq. 3)
WH
I
----------------------------= upright
12
3
wh
–
For the same I-beam turned on its side (Figure 5b), the second moment of area is
(eq. 4)
3
hW w–()
Hh–()W
----------------------------------------------------------=side
I
+
12
3
Note that these formulas for I are for calculating vertical deflection.
H
w/2
H
h
W
w/2
W
(a) upright
Figure 5
h
(b) sideways
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3
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