Engineering-45
Composite (Sandwich) Beams – Part-1
Lab-08
Lab Data Sheet – ENGR-45 Lab-08
Lab Logistics
Experimenter:
Recorder:
Date:
Equipment Used (maker, model, and serial no. if available)
NOT REQUIRED FOR THIS EXERCISE
Executive Summary – Student Lab-Report Work-Product




Construct Six Beam Specimens
o 3 each, Pure Material; either HIGH-density or LOW-density
o 2 each, One-Sided Al-skin reinforced
o 1 each, Two-Sides Al-skin reinforced
Completed Data Tables: Table I thru Table X
X-Y Plots using MATLAB or MS Excel
o Beam-1 Proof Test - Load Beam Until it “fails”: Plot of δ vs. F
o Beam-2 Elastic-Loading test: Plot of δ vs. F
o Beam-3 creep test: Cartesian (X-Y) Plot of δ vs. t
Calculate
o Yield Strength for Pure Polystyrene
o Modulus of Elasticity for Pure Polystyrene
© Bruce Mayer, PE • Chabot College • 282217455 • Page 1
Introduction
In this lab we will examine the deflection of pure-material and sandwich-compositei material
SubScale structural beams. In particular, we will test an end-loaded, rectangular cross-section
cantilever beam to estimate the Modulus of Elasticity for the material of construction.
Consider a cantilever beam with the geometry and loading as shown in Figure 1. Recall from
ENGR36 Shear-Force (V) and Bending-Moment (M) analysis. Using the free body diagram as
depicted in Figure 2, write the Reaction (R), and V&M equations as a function of x, L, and F.
 Forces  0  R
0
 F  0  R0  F
 Moments  0  M
about x 0
0
 F  L  0  M0  F  L
Equation 1
Equation 2
y
F
b
h
x
L
Figure 1 - End Loaded Cantilever Beam
i
Ref. W. D. Callister, Materials Science and Engineering: An Introduction, Sixth Edition, John Wiley & Sons, ISBN
2006, pg 610
© Bruce Mayer, PE • Chabot College • 282217455 • Page 2
y
F
x
M0
R0
Figure 2 - Static Vector-Mechanics Load-Analysis FreeBody Diagram. Note the positive
assumptions for M0 and R0.
With reference to the V&M sign conventionsi,ii as indicated in Figure 3, calculate the shear and
bending-moment as a function of x:
V x   Vmax  R0  F ; a const.
Equation 3
M ( x)  F  L  x
Equation 4
Using Mechanics-of-Materials Techniques for a LINEAR-ELASTIC material, the elastic
DEFLECTION for the beam, y(x), is found to be:

Fx 2
 x  3L   F x 3  3 x 2 L
y
6 EI
6 EI

Equation 5
Where
 E  Material Elastic Modulus (Pa or psi)
 I  Area Moment of Inertia for the beam cross-section (m4 or in4)
Using ENGR36 methods calculate the moment of inertia for a rectangular cross-section beam
with base-width, b, and thickness/height, h, about a centroidal horizontal axis as:
I rect  bh 3 12
Equation 6
With the Boundary Condition, y(0) =0, find the maximum deflection at x = L:
© Bruce Mayer, PE • Chabot College • 282217455 • Page 3
ymax
FL3
FL3
1  3  

6 EI
3EI
Equation 7
To plot V, M, and y, normalize the variables such that the plotted values run 0→1. Use these
normalizing transformations
x x L
V  V Vmax  V  x  F
M  M M max  M  x  FL 

y  y ymax  y  x  FL3 3EI
Equation 8

Use Equation 8 to transform Equation 3, Equation 4, and Equation 5:
V x  F
 1
Vmax
F
Equation 9
M ( x) F  x  L  x  L x


 1
M max
FL
L
L

 
 
Equation 10
y x  F 6 EI  x 3  3x 2 L
x 3  3x 2 L


ymax
FL3 3EI
2 L3
y x  1  x 
x
    3 
ymax 2  L 
L
3
2
 1 x 
  
 2  L 
2

 x  
 L   3
  
© Bruce Mayer, PE • Chabot College • 282217455 • Page 4
Equation 11
y
x
M
V
M0
R0
Figure 3 – Positive Shear (V) and Bending-Moment (M) conventions for Beam Deflection/Stress
analysis
Figure 4 contains the normalized shear, bending-moment, and deflection plots for the
cantilever beam shown in Figure 1. For this case, note that by ENGR35 and Mechanics-ofMaterialsii conventions:
 The shear is POSITIVE and CONSTANT until closing at x = L
 The moment entirely NEGATIVE, but trending POSITIVE with increased x
 The deflection is entirely NEGATIVE
In this, and in the next, exercise we will use Equation 7 to determine an effective value of the
Elastic modulus for a single-material, and binary-composite. Recall and recast Equation 7
ii
Studied in detail in a Third-Year course for engineering students in the Structural Disciplines such as Mechanical
and Civil Engineering
© Bruce Mayer, PE • Chabot College • 282217455 • Page 5
ymax

FL3  L3 
 F  m  F

  
3EI  3EI 
Equation 12
Where “m” is the constant SLOPE of a plot of ymax vs. F
o Note that for the this physical situation the INTERCEPT, b, is ZERO as there is
no deformation a zero load
To eliminate the annoying “minus” sign from the test-data and subsequent calculations,
introduce the end-deflection, δ, as:
   ymax
FL3  L3 
 F  m  F
 
 
3EI  3EI 
Equation 13
Thus for a linearly-elastic beam loaded below its yield-strength, a plot of the end-deflection, δ,
versus the load, F, should result in a LINE that passes through the origin. Finding the SLOPE,
m, of this line permits calculation of the elastic modulus for the material:
L3
in 3
lb
E
 UNITS  4
 2 chk
3I  m
in  in lb
in
© Bruce Mayer, PE • Chabot College • 282217455 • Page 6
Equation 14
1.2
SHEAR
V/Vmax
1.0
0.8
PARAMETERS
• Vmax = F
0.6
0.4
0.2
0.0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.7
0.8
0.9
1.0
x/L
x/L
Composite-Beam_VMY-0407.xls
0.0
M/M max
-0.2
0.0
0.1
0.2
0.3
0.4
0.5
0.6
PARAMETERS
• Mmax = FL
-0.4
BENDING-MOMENT
-0.6
-0.8
-1.0
-1.2
Composite-Beam_VMY-0407.xls
x/L
0.0
-0.2
y/ymax
-0.4
-0.6
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
PARAMETERS
• ymax = FL3/3EI
-0.8
-1.0
DEFLECTION
-1.2
Composite-Beam_VMY-0407.xls
Figure 4 - Shear, Bending-Moment, and Deflection (VMY) plots for the Cantilever Beam.
© Bruce Mayer, PE • Chabot College • 282217455 • Page 7
Exercise Outline
This exercise consists of two parts that cover two laboratory periods. A lab report will be
required for EACH part of this exercise, with Due-Dates as indicated in the course schedule
PART-1: Major activities for each lab-team
 Construct at total of SIX Test-Beam Specimens
o Construct THREE pure-material test specimens (rectangular beams)
o Construct TWO, ONE-Sided Al-ReInforced Specimens
o Construct ONE, TWO-Sided Al-ReInforced Specimens
 Conduct a δ-vs-F PROOF test on the beam-1
 Conduct a δ-vs-F DEFLECTION test on the beam-2
 Conduct a δ-vs-t CREEP test on beam-3 to determine the amount, if any, of
VISCOelastic behavior
o Due to the duration of this test, ONE beam-set will be tested, and data shared by
he entire class, UNLESS we have sufficient Beam-Test Fixtures to accommodate
every team.
 We extend thanks to previous ENGR45 classes
 Create, using MSExcel or MATLAB, plots for the δ-vs-F and δ-vs-t tests
 Calculate an experimental value for E for the pure material
PART-2: Major activities for each lab-team
 Conduct TWO δ-vs-F DEFLECTION tests on the one-sided beams
o Al reinforcement on the BOTTOM, beam-4
o Al reinforcement on the TOP, beam-5
 Conduct a final δ-vs-F DEFLECTION test on the TWO-sided beam-6
 Create, using MSExcel or MATLAB, plot on the SAME graph the δ-vs-F and δ-vs-t tests
results for the four beam specimens
1. Pure Material
2. BOTTOM ReInforced
3. TOP ReInforced
4. TOP & BOTTOM ReInforced
 Calculate the empirical values for E for the four cases. Use MSExcel or MATLAB to
create a BAR CHART (NOT a COLUMN chart) to compare E for the four beams tested.
 Calculate the theoretical value of the equivalent modulus of elasticity, Ee, for the 2-sided
composite beam
© Bruce Mayer, PE • Chabot College • 282217455 • Page 8
`Beam Use Summary
Beam
Lab
Use Description
1.
08
Proof Test to Failure
2.
08
Main Pure & Composite Deflection Test
3.
08
Creep Test to Failure
4.
09
One-Sided Beam, BOTTOM Deflection Test
5.
09
One-Sided Beam, TOP Deflection Test
6.
09
Two-Sided Beam Deflection test
Directions – Part-1
Instruments & Supplies
1.
3.
5.
Cantilever Beam Test Fixture
Foamed Polystrene Sheet, 1” Thick
Tape measure
2.
4.
6.
7.
Tight Spot Hacksaw
8.
Vertical MeterStick Deflection Ruler
YardStick Ruler
Permanent marking pens (a.k.a.
“Sharpie” marker)
0.04-0.08 Ø Steel Wireiii
9.
Diagonal WireCutting Pliers
10.
NeedleNose Pliers
11.
Bench Vise (on Back Table)
12.
Wood Glue Adhesiveiv
13.
HeavyDuty Aluminum Foil
14.
Box Cutter, razor blade type
15.
Cutting Pad/Board
16.
3” putty knife
17.
Carpenter’s Square, 8”x12”
18.
Electric Heat Gun, approx. 1440W
19.
Mass scale, 1g (0.002 lbm) or
better resolution
20.
1/4” Steel Fender-Washerv Force
Weight; nominal weight = 101 mN
21.
5/8” Steel Std-Washervi Force
Weight; nominal weight = 291 mN
22.
Micrometer to measure
ReInforcing-Foil thickness
23.
Dial Caliper for miscellaneous
measurements
24.
StopWatch or Clock
NOTE: There are two types of Beam PolyStrene; HI-density and LO-density. The
instructor will assign the material type with a approximate 50-50 split.
iii
A jumbo PaperClip is an adequate substitute
“Elmer’s” glue is an adequate substitute
v Approx dims =0.28” ID x 1.50 OD x 0.047” thick, OR 0.28” ID x 1.25 OD x 0.06” thick
vi Approx dims = 0.68” ID x 1.75 OD x 0.11” thick
iv
© Bruce Mayer, PE • Chabot College • 282217455 • Page 9
Construct SIX polystyrene beams per
design drawing 45-050711-01; Figure
7. Use these tools & instruments
 YardStick ruler
 Sharpie Marker
 Tight-Spot (keyhole) hacksaw
The tolerance on the length and
width cut-dimension is ±1/8” (3mm)
With reference to Figure 1, use the
tape-measure or ruler to measure the
beam cross-section values b & h and
enter the results in Table I. Using
Equation 6 to calculate the area
moment of inertia, I, for the beam,
and enter the result in Table I
Use the ruler, Sharpie, box cutter,
and cutting-pad to fabricate FOUR
2.0”x25” foil strips. The “dull” side of
the foil strip will receive adhesive and
should then be kept as clean as
possible. Thus, cut the foil sheet tosize with the dull-side UP. Figure 10.
Protect the laminating-bench work
surface from glue-drips by covering it
with scrap-paper or scrap-foil.
HANGER
VERTICAL DISPLACEMENT RULE
Construct Beams
FORCE LOAD
Figure 5 - Hanger and weights installed for
measuring beam-deflection against the vertical rule.
On the 1” side of beams 4-6 use the Sharpie to apply an identifying label to the beam. Teammember names or initials, or a team-nickname are typical identifiers.
Place beam-4 and beam-5 on the protected surface and apply one or two full-length beads of
the laminating adhesive (wood glue). Figure 11.
Use the putty-knife to spread the glue-bead over the surface of each beam. Take care to
produce a thin layer of glue with full and uniform coverage. Figure 12.
Carefully apply the DULL side of the 2.0x25 Al lamination to the glue-covered surface of beam4 and beam-5. Use your hand to apply gentle pressure against the foil to remove air-bubbles
and to generate maximum contact between the structural materials and the adhesive.
Use a paper towel or tissue to remove any residual glue from the 1” sides/ends of the beam.
Allow the adhesive to cure for 20-30 minutes. The beam should have an appearance similar to
that shown in Figure 13.
© Bruce Mayer, PE • Chabot College • 282217455 • Page 10
Place beam-6 on the protected work surface
and apply to the “top” polystyrene surface,
one or two full-length beads of the laminating
adhesive (wood glue). Figure 11.
Use the putty-knife to spread the glue-bead
over the surface of the beam. Take care to
produce a thin layer of glue with full and
uniform coverage. Figure 12.
Carefully apply the DULL side of the 2.0x25
Al lamination to the glue-covered surface of
beam-6. Use your hand to apply gentle
Figure 6 - Proper form of weight-hanger.
pressure against the foil to remove airbubbles and to generate maximum contact between the structural materials and the adhesive.
Turn over beam-6 on the protected work surface and apply to the “bottom” polystyrene
surface, one or two full-length beads of the laminating adhesive (wood glue).
Use the putty-knife to spread the glue-bead over the surface of the beam. Take care to
produce a thin layer of glue with full and uniform coverage. Figure 12.
Carefully apply the DULL side of the 2.0x25 Al lamination to the glue-covered surface of beam6. Use your hand to apply gentle pressure against the foil to remove air-bubbles and to
generate maximum contact between the structural materials and the adhesive.
 One team member must then take the putty-knife to the wet-sink and remove any glue
from the application surfaces
Use a paper towel or tissue to remove any residual glue from the 1” sides/ends of the beam.
Allow the adhesive to cure on the 2-sided beam for 20-30 minutes.
Give the cured, 1-sided and 2-sided composite beams to the instructor for secure
storage until the next lab period when part-2 of this exercise will be completed.
Construct Force-Load Hanger
Construct a washer-load hanger per design drawing 45-040715-01; Figure 8. Use these tools
& instruments
 Diagonal Cutter pliers; i.e., the wire-cutters
 Tape-measure or ruler
 Sharpie Marker
 NeedleNose pliers
 Bench Vise (located on galvanized-steel-topped work table)
When properly fabricated the hanger should have a form similar to the prototype hangers
shown in Figure 6.
© Bruce Mayer, PE • Chabot College • 282217455 • Page 11
The hanger becomes part of the “dead load” for the beam (along with the weight of the beam),
and thus should be as small as possible. In this lab the weight of the hanger should be less
than 40 mN (4.0 g). Use the weight scale to confirm that beam has a mass that does not
exceed 2.5g. Enter the hanger mass in the data-slot below:

Hanger Mass/Weight
Fhanger =
Finally, measure the Aluminum Foil THICKNESS using either the Micrometer or the DialCalipers

Al Foil Thickness
tAl =
Also note the beam material DENSITY. Circle the appropriate density for your group’s material
below.
PolyStrene Material Density
HIGH
LOW
© Bruce Mayer, PE • Chabot College • 282217455 • Page 12
Figure 7 - Fabrication Drawing for PolyStyrene Beam-Specimen. Fabricate SIX beams.
© Bruce Mayer, PE • Chabot College • 282217455 • Page 13
Figure 8 - Fabrication Drawing for washer-load hanger. Fabricate ONE hanger.
© Bruce Mayer, PE • Chabot College • 282217455 • Page 14
Measure the Force-Load Increments
This exercise uses nut/bolt washers as the “Live Load” for the beam deflection test. The
available washers:
Load-Washer Summary
Mass
Description
2.1 g
0.629 OD x 0.282 ID x 0.075 t
2.6 g
0.735 OD x 0.308 ID x 0.0765 t
6.1 g
0.888 OD x 0.377 ID x 0.10 t
10 g
1/4” Fender washers
40 g
5/8” Standard washers
From the supply stockpile select washers
 20 each 0.735 OD x 0.308 ID x 0.0765 t (2.6 g)
 20 each 0.888 OD x 0.377 ID x 0.10 t (6.1 g)
 10 each 1/4” Fender washers, (10 g)
 5 each, 5/8” Standard washers (40 g)
Use the Sharpie (permanent) marker to label the fender washers 1-10, and the standard
washers 1-5. Next go the weight scale and determine the mass/weight for each type of
washer.
 Use the Sharpie pen to note the mass directly on the Fender and 5/8” Standard
washers. Enter the weight measurements in Table III and Table IV.
 Weigh the smaller in washers in groups of 20 each. Then determine the average weight
of the smaller washer by completing Table VI and Table VII.
o The average weight of the smaller washer will be entered in the beam-loading
Data tables
Beam-1 Proof Test
Mount beam-1 in the test Fixture as indicated in Figure 9. Some details
 The end of the beam should be FLUSH with the back of the beam mounting-stage
 The beam axis should be aligned with the fixture-base axis; i.e., the beam should be
centered in the fixture
 Do NOT overtighten the clamping nuts. The polystyrene should NOT be significantly
compressed after installation
Use the tape-measure to determine the cantilever beam overhang length, L as shown in Figure
9. Enter the measured value in Table I. The overhang length should be more than 21”.
Bruce Mayer, PE • Chabot College • 282217455 • Page 15
Next install the load-hanger in the beam as shown in Figure 9 and Figure 5. Some details
 To minimize beam-deflection during hanger insertion, support the beam with your hand
as you punch thru the polystyrene
 The 2.5” down-leg of the hanger should be flush with the end of the beam as indicated
in Figure 5
The beam is now ready for the deflection test. Place the vertical rule fixture behind the
“indicator” leg of still UNloaded hanger. Measure the dead-load vertical distance. Enter this
distance on the “Washer-0” line of Table IX.
Apply a standard (large) washer as the load. Quickly measure the deflection and then remove
the load. Weigh the combined mass of the washers, allowing the beam some time to relax to
its Unloaded geometry. Next measure the No-Load vertical distance. If the elastic limit for the
beam has not been exceeded, then the Pre-Post Load deflection should be small; perhaps
less than about 3mm (1/8”).
Next apply the Standard washers (S-washer) and a Fender washer (F-washer). Again quickly
measure the deflection and then remove the load. Also again measure the Pre-Post Load
deflection.
Continue adding F-washers, and making the Pre-Post Load deflection measurements until the
beam takes a permanent set of more than 6mm (1/4”). The Load that results in 6mm
permanent set will be the “Proof” Load. The creep-test will be performed at a load of 80% of
the permanent-set load.
Use the permanent-set load to estimate the elastic limit (yield stress) for polystyrene. For an
end-loaded cantilever beam, the maximum stress occurs at x=0, and is given by
 max  M max h 2I  M ( x  0)  h 2I  FLh 2I
Equation 15
Using the proof load for F in Equation 15 provides and estimate for σy. Perform this calculation,
and enter the value in the data-reduction answer slot.
Bruce Mayer, PE • Chabot College • 282217455 • Page 16
Beam-2 Deflection test
Mount beam-2 in the test Fixture as indicated in Figure 9. Some details
 The end of the beam should be FLUSH with the back of the beam mounting-stage
 The beam axis should be aligned with the fixture-base axis; i.e., the beam should be
centered in the fixture
 Do NOT overtighten the clamping nuts. The polystyrene should NOT be significantly
compressed after installation
Use the tape-measure to determine the cantilever beam overhang length, L as shown in Figure
9. Enter the measured value in Table I. The overhang length should be more than 21”.
Next install the load-hanger in the beam as shown in Figure 9 and Figure 5. Some details
 To minimize beam-deflection during hanger insertion, support the beam with your hand
as you punch thru the polystyrene
 The 2.5” down-leg of the hanger should be flush with the end of the beam as indicated
in Figure 5
The beam is now ready for the deflection test. Place the vertical rule fixture behind the
“indicator” leg of still UNloaded hanger. Measure the dead-load vertical distance. Enter this
distance on the “Washer-0” line of Table IX.
Next add nine fender-washers, one at time, to the load-hanger. After addition of each fenderwasher, measure the vertical distance against the vertical-rule. See Figure 5. Record the
washer-weights (c.f. Table III) and distance-measurements in Table IX.
After completion of the distance-measurements, these quantities should be easily
CALCULATED using sums & differences, and then entered in Table IX
 The total, or cumulative load, F
 The beam end-deflection, δ
Beam-3 Creep Test
Use a combination of S-washers and F-washers to weigh out a creep-load that is
approximately 80% of the permanent-set load as determined previously on Beam-1.
Load a previously unused Beam-3 into the test fixture. Measure the dead-load vertical
distance. Note this value in Table X. Next apply the load, and immediately measure the time 0 +
vertical deflection. Enter this value in Table X.
Use the clock or stopwatch to record in Table X the vertical distance as function of time.
Calculate the beam deflection for each time entry.
Bruce Mayer, PE • Chabot College • 282217455 • Page 17
L
Figure 9- Beam Installed in Test Fixture. Use the tape measure to determine the beam
overhang length, L, as indicated. The Length, L, should be 21-21.5 inches.
Bruce Mayer, PE • Chabot College • 282217455 • Page 18
Figure 10 - Aluminum foil sheet ready for cutting. Beam-2 itself may be used as a
sizing-gage for the cut.
Figure 11 - Beads of adhesive applied to the laminating surface of beam-2. Note the
cut-to-size Aluminum foil sheet between the beam and glue bottle.
Bruce Mayer, PE • Chabot College • 282217455 • Page 19
Figure 12 - Beads of adhesive evenly applied to the laminating surface of beam-2
with the putty knife.
Bruce Mayer, PE • Chabot College • 282217455 • Page 20
Data Reduction – Part-1

Plots (Attach separate sheets
to Lab report)
 Beam-1 Proof-Loading test:
Cartesian (X-Y) Plot of δ vs. F
o The last point or two
should show a distinct
change in the slope of
the plotted line
 Beam-2 Elastic-Loading test:
Cartesian (X-Y) Plot of δ vs. F
o Use Linear regression
to
determine
the
SLOPE, m, for this plot
 The slope is
REQUIRED
to
calculate E for
the
beam
material
 Beam-3 creep test: Cartesian
(X-Y) Plot of δ vs. t
o Provides a qualitative
assessment
of
the
viscoelastic behavior of
Styrofoam.

Complete all calculation entries
in the data tables
Hanger-Hole
Location Mark
Figure 13 - Completed 1-sided Sandwich-Beam.
Hanger mounting location noted on beam-side.
Bruce Mayer, PE • Chabot College • 282217455 • Page 21
Pure Material Property Estimates from Data

CALCULATED Modulus of Elasticity for Pure Polystyrene
EPS =
o Ref:



Equation 6
Equation 14
 Use slope, m, from X-Y Plot of δ vs. F
CALCULATED Yield Strength for Pure Polystyrene
σy,PS =
o Ref: Equation 6 and Equation 15
Bruce Mayer, PE • Chabot College • 282217455 • Page 22
Data Tables – Part-1
Table I - Pure-Material Beam Geometry
Beam
Width,
b
Height
h
Moment of
Inertia, I
As Mounted
Cantilever Length, L
1.
2.
3.
Table II – Large Loaad-Washerer Weights
Table III - Fender Washer Weights
Washer
Mass/Weight
Table IV - Standard Washer Weights
Washer
1.
1.
2.
2.
3.
3.
4.
4.
5.
5.
Mass/Weight
6.
7.
8.
9.
10.
Table V –Small Load Washer Weights
Table VI - 0.735 OD Washer Weights
Mass for
20 Washers
Average
Mass
Table VII - 0.888 OD Washer Weights
Mass for
20 Washers
Bruce Mayer, PE • Chabot College • 282217455 • Page 23
Average
Mass
Table VIII – Proof Load for 6mm Permanent Set
Test
UNLoaded
Vertical
Distance
Load, F
Loaded
Vertical
Distance
Removed-Load
Vertical
Distance
1.
2.
SAME
3.
SAME
4.
SAME
5.
SAME
6.
SAME
7.
SAME
8.
SAME
9.
SAME
10.
SAME
11.
SAME
12.
SAME
13.
SAME
14.
SAME
15.
SAME
Bruce Mayer, PE • Chabot College • 282217455 • Page 24
Unloaded
Permanent
Set
Table IX – Beam-2 Pure-Material Beam Deflection Test
NOTE: Enter b, h, and L in Table I
Washer
Washer
Type
0
n/a
1
F
2
F
3
0.888 OD
4
0.888 OD
5
0.888 OD
6
0.888 OD
7
0.735 OD
8
0.735 OD
9
0.735 OD
10
0.735 OD
11
0.735 OD
12
TBD
13
TBD
14
TBD
15
TBD
16
TBD
17
TBD
18
TBD
19
TBD
20
TBD
Washer Vertical
Weight Distance
n/a
Total
Load, F
Beam
Deflect, δ
Notes
0
0
Hanger is Dead Load
Bruce Mayer, PE • Chabot College • 282217455 • Page 25
Table X –Beam-3 Pure-Material Beam Creep Test

Creep-Load Mass/Weight (~80% of Permanent-Set Load)
Fcreep =
NOTE: Enter b, h, and L in Table I
Time
(min)
Vertical Beam
Distance Deflection, δ
Notes
0-
Dead Load
0+
Just After Load Applied
2
4
6
9
12
15
18
21
2424+
Just After Load Removed
26
28
30
33
36
39
42
45
48
Bruce Mayer, PE • Chabot College • 282217455 • Page 26
Appendix A - Alternative Proof-Load Test
This is NOT part of the lab unless required by the instructor
Next add two (2) STANDARD-washers, and then up to twenty (20) FENDER-washers, one at
time, to the load-hanger. After the addition of each washer, measure the vertical distance
against the vertical-rule. See Figure 5. Record the washer-weights (c.f. Table III) and distancemeasurements in Table IX.
 After adding each washer inspect the beam for signs of “Distress” that would
indicated that the load has exceeded the ELASTIC LIMIT of the materials. Some
indications of distress include
o “Cracking” or “Crunching” sounds
o A sudden increase in the deflection distance
o The failure of the beam to “Spring Back” when the load is removed
If insufficient Test Fixtures, then Please complete the deflection
measurements as QUICKLY AS POSSIBLE to give the next lab-team
access to the lab fixture(s).
The minimum Load that causes permanent deformation to the beam is the permanent-set, or
“Proof”, Load. The maximum loads for other test will be about 80% of this load.
After completion of the Loading vs. distance-measurements, these quantities should be easily
CALCULATED using sums & differences, and then entered in Table IX
 The total, or cumulative load, F
 The beam end-deflection, δ
Print Date/Time = 29-May-16/04:00
Bruce Mayer, PE • Chabot College • 282217455 • Page 27
Table XI – Beam-1 Pure-Material Beam PROOF-Load Deflection Test
Use this Table ONLY if required by the Instructor
NOTE: Enter b, h, and L in Table I
Washer
0
Washer Vertical
Weight Distance
Cumulative
Load, F
0
Beam
Deflection, δ
Notes
Hanger is Dead Load
1
Large (Std) Washer
2
Large (Std) Washer
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
Bruce Mayer, PE • Chabot College • 282217455 • Page 28
PolyStyrene Cantilever-Beam Creep Behavior
125
PARAMETERS
• Load = 1164 mN
• Load Removed at 24 minutes
• Beam Geometey, h x w x L = 1" x 1.5" x 21.43"
Vertical Deflection,  (mm)
100
75
50
25
No Reinforcement (mm)
0
0
5
file = Composite-Beam_VMY-0407.xls
10
15
20
25
30
35
Load Application time,t (min)
Figure 14 - Typcial d-vs-t creep plot. This data suggests a permanent set of 5mm after unloading
Bruce Mayer, PE • Chabot College • 282217455 • Page 29
40
45
50
55
i
ii
F. P. Beer, E. R. Johnston, Vector Mechanics for Engineers – Statics, McGraw-Hill, 2004, pg 363
A. S, Duetscheman, W. J. Michels, C. E. Wilson, Machine Design – Theory and Practice, MacMillan Publishing, 1975, pg 255
Bruce Mayer, PE • Chabot College • 282217455 • Page 30