PASCO ME-9891 Flexible I-beam - Manual (Page 3)

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M o d e l N o . M E - 9 8 9 1 T h e o r y
3
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)
where M is the internal bending moment at horizontal position x. The product EI is
the beam’s flexural rigidity.
Second Moment of Area
Figure 4
The second moment of area for a beam of constant cross section is
(eq. 2)
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
(eq. 3)
For the same I-beam turned on its side (Figure 5b), the second moment of area is
(eq. 4)
Note that these formulas for I are for calculating vertical deflection.
Figure 5
d
2
y
dx
2
--------
M
EI
------ =
y
neutral axis
b(y)
I y 2 b y
( ) y
d
∫
=
I
WH 3 wh 3 –
12
---------------------------- = upright
I
H h –
( )W 3 h W w –
( ) 3 +
12
---------------------------------------------------------- = side
H
W
h
w/2
(a) upright
H
W
h
w/2
(b) sideways