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M
EC

251
Strength of Materials
Deflection of Beams
The College of New Jersey
I. Introduction
The purpose of this experiment is to measure the deflec
tion of simply supported
and cantilever beams, as seen in Figures 1 and 2. The deflection will be recorded upon
application of several different loading conditions on beams with different material and
section. The experimental results are to be compared
with analytical results in order to
confirm the theories of beam deflection. This is accomplished by computation of the
percent difference (errors).
The main objective of the experiment is to conclude that deflection of beams is a
function of the follo
wing parameters:
1. Loading conditions
2. Type of structure (supports)
3. Material properties
4. Section properties (area moment of inertia)
5. Size (length)
Simply Supported Beam
w(x) = Deflection in Y Direction
浡m
=⁄ 晬fc瑩潮琠te湴e爠潦 Bea洠⡦潲y浭e瑲tc潡摩湧
Figure 1
Cantilever Beam
w(x) = Deflection in Y Direction
浡m
=⁄ 晬fc瑩潮琠t牥e⁅湤 ⁂ea洠m
Figure 2
II. Equipment and Supplies
It is impo
rtant that lab members familiarize themselves with the following
equipment prior to starting the experiment.

Test frame and simple supports for beam analysis

Extensometer/dial indicators

Aluminum beam, (0.25 x 1 x 36 in)

Steel beam #1 (thin), (0.1
875 x 1 x 36 in)

Steel beam #2 (thick), (0.25 x 1 x 36 in)

Laboratory loading apparatus (support system and cradles)
III. Procedure
NOTE
: In the interest of time, two groups will be working on this experiment
simultaneously. Your group might be st
arting with either part A, simply supported beam
analysis, or part B consisting of experimentation on the cantilever specimens. For both
parts of this experiment, it is important to follow the steps shown to minimize the time of
experimentation.
WARNIN
G
: For all deflection scenarios, an excessive load or lengthy experiment
duration may permanently deform the specimen.
Part A

Simply Supported Beam Analysis (Refer to Figure 3 below)
1)
Set up the thin steel beam in a 34” simply supported arrangement so
th
at one end rests on the roller support while the other end rests on the
knife edge. (Although the beam is 36" long, we save 1" on each side
of the supports as overhang.)
2)
Install a dial indicator 10" from the left support and another at the
center of the b
eam (17" from the left support).
3)
Record the initial readings of the dial indicators.
4)
Install one of the five simply supported load distribution fixtures
(displayed in Appendix A). This is accomplished by carefully placing
the cradles on the supports.
5)
Recor
d the new values displayed on the dial indicators.
6)
Repeat steps 1 through 5 for both the thick steel and aluminum beams.
7)
Repeat steps 1 through 6 until all of the simply supported load
distribution fixtures have been tested on all three specimens.
8)
Once all
data has been collected, calculate the theoretical deflection
values at the points where the dial indicators had been placed.
9)
Using the theoretical and experimental deflection values, compute the
percent errors.
10)
Fill in the tables found at the end of this
lab guide
Figure 3. Simple Support Setup
Part B

Cantilever Beam Analysis (Refer to Figure 4 on the following page)
1)
Measure and record the weight of the thick steel specimen.
2)
Rotate the left support so that both supports are oriented in the same
direction.
3)
Place a 1/4" spacer in the right support
4)
Set up the thick steel beam in the left support bracket so that it
produces a 27” cantilever, but allow its free end to rest on the right
support for the time being.
5)
Install two dial indicators, the fir
st at the center of the cantilever and
the second at 26".
6)
Record the initial readings of the dial indicators while the beam is
resting on the right support.
7)
Install one of the three cantilever load distribution fixtures (displayed
in Appendix B). This is
accomplished by carefully placing the cradles
on the supports.
8)
Slowly slide the right support over and out of the way so that the
specimen acts as a cantilever. Make sure not to displace the support to
the point where the cradle is no longer braced by it
.
9)
Record the deflection on both dial indicators.
10)
It is critical that the support, loading and measurement setup remain as
unaltered as possible in order to eliminate minor disturbances for
comparison purposes. In order to do so, leave the loading bracket
on
the supports, and rearrange the point loads in order to create the
second load distribution.
11)
Record deflection values.
12)
Repeat steps 10 and 11 for the third and final load distribution.
13)
Once all data has been collected, calculate the theoretical deflect
ion
values at the points where the dial indicators had been placed. It is
important to note that for these cantilever scenarios, the weight of the
beam is acting as a uniform load across its span. This must be
addressed in the deflection calculations
14)
Us
ing the theoretical and experimental deflection values, compute the
percent errors.
15)
Fill in the tables found at the end of this lab guide.
Figure 4. Cantilever Support Setup
IV. Results and Discussion
Using equations from the back of the strength o
f materials text, calculate the
deflection for the simply supported beams subjected to uniform load,
linearly varying
triangle load, and sinusoidal load. In addition, determine theoretical deflection for the
three cantilever load scenarios. For the unpro
vided cases, such as the cosin
e
load
ing
,
develop the equation of deflection using integration method. The equation for the
linearly varying reverse triangle load is provided at the end of this hand out. Remember
to use superposition to calculate total de
flection when necessary. Compare theoretical
deflection data to the actual deflection obtained in this experiment in order to calculate
percent error.
How did experimental deflections compare to calculated values? For a given
loading, were all of the
percent errors for the three specimens either positive or negative?
If not, where might the discrepancy lie? While both the thin steel and aluminum
specimens were analyzed as simply supported beams, why was only the thick steel beam
tested as a cantileve
r? Comment on any sources of error that might be present in the
experiment.
Appendix A
Simply Supported Beam
With Uniform Loading
Beam
Loading
Deflection at
Center (in.)
Deflection 10" from left
support (in.)
Steel (Thin)
E=30x10
6
Measured (in.)

0.280

0.211
Calculated (in.)

0.276

0.222
Percent Error

1.45%
+4.95%
Steel (Thick)
E=30x10
6
Measured (in.)

0.116

0.0940
Calculated (in.)

0.120

0.0982
Percent Error
+3.33%
+4.28%
Aluminum
E=10x10
6
Measured (in.)

0.329

0.264
Calculated
(in.)

0.334

0.268
Percent Error
+1.50%
+1.49%
Simply Supported Beam
with Linearly Varying Triangle Load
Beam
Loading
Deflection at
Center (in.)
Deflection 10" from left
support (in.)
Steel (Thin)
E=30x10
6
Measured (in.)

0.598

0.462
C
alculated (in.)

0.630

0.502
Percent Error
+5.08%
+7.97%
Steel (Thick)
E=30x10
6
Measured (in.)

0.256

0.214
Calculated (in.)

0.274

0.243
Percent Error
+6.57%
+11.93%
Aluminum
E=10x10
6
Measured (in.)

0.757

0.564
Calculated (in.)

0.762

0.
609
Percent Error
+0.66%
+7.39%
Simply Supported Beam
with Linearly Varying Reverse Triangle Load
Beam
Loading
Deflection at
center (in.)
Deflection 10" from left
support (in.)
Steel (Thin)
E=30x10
6
Measured (in.)

0.465

0.368
Calculated
(in.)

0.475

0.384
Percent Error
+2.11%
+4.17%
Steel (Thick)
E=30x10
6
Measured (in.)

0.197

0.154
Calculated (in.)

0.207

0.164
Percent Error
+4.83%
+6.10%
Aluminum
E=10x10
6
Measured (in.)

0.576

0.462
Calculated (in.)

0.575

0.464
Perce
nt Error

0.17%
+0.43%
Simply Supported Beam
with Sinusoidal Loading
Beam
Loading
Deflection at
center (in.)
Deflection 10" from left
support (in.)
Steel (Thin)
E=30x10
6
Measured (in.)

0.642

0.513
Calculated (in.)

0.712

0.569
Percent Err
or
+9.83%
+9.84%
Steel (Thick)
E=30x10
6
Measured (in.)

0.270

0.216
Calculated (in.)

0.287

0.230
Percent Error
+5.92%
+6.08%
Aluminum
E=10x10
6
Measured (in.)

0.783

0.631
Calculated (in.)

0.861

0.688
Percent Error
+9.06%
+8.28%
Simply Supported Beam
with Cosin
e
Loading
Beam
Loading
Deflection at
center (in.)
Deflection 10" from left
support (in.)
Steel (Thin)
E=30x10
6
Measured (in.)

0.453

0.363
Calculated (in.)

0.711

0.417
Percent Error
+36.3%
+12.9%
Steel (Thick)
E=30x10
6
Measured (in.)

0.188

0.152
Calculated (in.)

0.310

0.183
Percent Error
+39.4%
+16.9%
Aluminum
E=10x10
6
Measured (in.)

0.556

0.451
Calculated (in.)

0.861

0.502
Percent Error
+35.4%
+10.2%
Appendix B
Cantilever Beam
With
Uniform and End Loading
Beam
Loading
Deflection at
center (in.)
Deflection at
end (in.)
Steel (Thick)
E=30x10
6
Measured (in.)

0.198

0.581
Calculated (in.)

0.213

0.588
Percent Error
+7.04%
1.19%
Cantilever Beam
With Partial Uniform
Load and Two Point Loads (1)
Beam
Loading
Deflection at
center (in.)
Deflection at
end (in.)
Steel (Thick)
E=30x10
6
Measured (in.)
0.182

0.549
Calculated (in.)
0.190

0.556
Percent Error
+4.21%
+1.26%
Cantilever Beam
With Partial Un
iform Load and Two Point Loads (2)
Beam
Loading
Deflection at
center (in.)
Deflection at
end (in.)
Steel (Thick)
E=30x10
6
Measured (in.)

0.104

0.301
Calculated (in.)

0.113

0.317
Percent Error
+7.96%
+5.05%
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