© Bruce
Mayer, PE • Chabot College •
frontdotard_310621f9

fd8e

4a13

904d

619c089dea32.doc
• Page
1
Engineering

45
Composite
(Sandwich)
Beams
–
Part

1
Lab

0
8
Lab Data Sheet
–
ENGR

45 Lab

0
8
Lab Logistics
Experimenter:
Recorder:
Date:
Equipment Used (maker, model, and serial no. if available)
NOT REQUIRED FOR THIS EXE
RCISE
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: Car
tesian (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 •
frontdotard_310621f9

fd8e

4a13

904d

619c089dea32.doc
• Page
2
Introduction
In this lab we will examine the deflection of pure

material and
sandwich

composite
i
material
SubScale structural beams. In
particular, we will test an end

load
ed
, 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
ENGR3
6
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.
F
R
F
R
Forces
0
0
0
0
Equation
1
L
F
M
L
F
M
Moments
x
about
0
0
0
0
0
Equation
2
i
Ref. W. D. Callister,
Materials Science and Engineering: An Introduction, Sixth Edition
, John Wiley & Sons, ISBN
2
00
6, pg 610
b
h
x
y
L
F
Figure
1

End Loaded Cantilever Beam
© Bruce
Mayer, PE • Chabot College •
frontdotard_310621f9

fd8e

4a13

904d

619c089dea32.doc
• Page
3
Figure
2

Static Vector

Mechanics Load

Analysis FreeBody Diagram
. Note the po
sitive
assumptions for M
0
and R
0
.
F
y
x
R
M
0
0
With reference to the V&M sign conventions
i
,
ii
as indicated in
Figure
3
, calculate the sh
ear and
bending

moment as a function of x:
const.
a
;
0
max
F
R
V
x
V
Equation
3
x
L
F
x
M
)
(
Equation
4
Using Mechanics

of

Materials Techniques
for a LINEAR

ELASTIC material, the
elastic
D
EFLECTION
for the beam
, y(x)
,
is found to be
:
L
x
x
EI
F
L
x
EI
Fx
y
2
3
2
3
6
3
6
Equation
5
Where
E
Material Elastic Modulus (Pa or
psi)
I
Area Moment of Inertia for the beam cross

section (m
4
or in
4
)
Using ENGR36 methods calculat
e the moment of inertia for a rectangular cross

section beam
with base

width, b, and thickness/height, h, about a centroidal horizontal axis as:
12
3
bh
I
rect
Equation
6
With the Boundary Condition, y(0) =0, find th
e maximum deflection at x
=
L:
© Bruce
Mayer, PE • Chabot College •
frontdotard_310621f9

fd8e

4a13

904d

619c089dea32.doc
• Page
4
EI
FL
EI
FL
y
3
3
1
6
3
3
max
Equation
7
To plot V, M, and y, normalize the variables such that the plotted values run 0
→
1. Use these
normalizing transformations
EI
FL
x
y
y
y
y
FL
x
M
M
M
M
F
x
V
V
V
V
L
x
x
3
3
max
max
max
Equation
8
Use
Equation
8
to transform
Equation
3
,
Equation
4
, and
Equation
5
:
1
max
F
F
V
x
V
Equation
9
1
)
(
max
L
x
L
L
x
FL
L
x
F
M
x
M
Equation
10
3
2
1
3
2
1
2
3
3
3
6
2
2
3
max
3
2
3
3
2
3
max
L
x
L
x
L
x
L
x
y
x
y
L
L
x
x
EI
FL
L
x
x
EI
F
y
x
y
Equation
11
© Bruce
Mayer, PE • Chabot College •
frontdotard_310621f9

fd8e

4a13

904d

619c089dea32.doc
• Page
5
Figure
4
contains
the normalized
shear, bending

moment, and deflection
plots for the
cantilever be
am
shown in
Figure
1
. For this case, note that by ENGR35 and Mechanics

of

Materials
ii
conventions:
The shear is POSITIVE
and
CONSTANT until clos
ing
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 effecti
ve 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
Figure
3
–
Positive Shear (V) and Bending

Moment (M) conventions for Beam Deflection/Stress
analy
sis
y
R
M
V
M
0
x
0
© Bruce
Mayer, PE • Chabot College •
frontdotard_310621f9

fd8e

4a13

904d

619c089dea32.doc
• Page
6
F
m
F
EI
L
EI
FL
y
3
3
3
3
max
Equation
12
Where “m” is the constant SLOPE of a plot of y
m
ax
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 calculation
s,
introduce the end

deflection
, δ,
as:
F
m
F
EI
L
EI
FL
y
3
3
3
3
max
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. Findi
ng the SLOPE,
m, of this line permits calculation of the elastic modulus for the material:
chk
UNITS
3
2
4
3
3
in
lb
lb
in
in
in
m
I
L
E
Equation
14
© Bruce
Mayer, PE • Chabot College •
frontdotard_310621f9

fd8e

4a13

904d

619c089dea32.doc
• Page
7
SHEAR
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
x/L
V/V
max
CompositeBeam_VMY0407.xls
PARAMETERS
• Vmax = F
BENDINGMOMENT
1.2
1.0
0.8
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
x/L
M/M
max
CompositeBeam_VMY0407.xls
PARAMETERS
• Mmax = FL
DEFLECTION
1.2
1.0
0.8
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
x/L
y/y
max
CompositeBeam_VMY0407.xls
PARAMETERS
• y
max
= FL
3
/3EI
Figure
4

Shear, Bending

Moment, and Deflection (VMY) plots for the Cantilever Be
am.
© Bruce
Mayer, PE • Chabot College •
frontdotard_310621f9

fd8e

4a13

904d

619c089dea32.doc
• Page
8
Exercise Outline
This exercise consists of two parts that cover two lab
oratory periods. A lab report will be
required for EACH
part of this
exercise
, with Due

Date
s
as indicated in the course schedule
PART

1:
Major activities for
each lab

team
Construct at total of SIX Test

Beam Specimens
o
Construct T
HREE
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
t
o 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 beam
s
o
Al reinforcement on the BOTTOM
,
beam

4
o
Al reinforcement on the TOP
,
b
eam

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 ReInfor
ced
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 elastici
t
y, E
e
, for the 2

sid
ed
composite beam
© Bruce
Mayer, PE • Chabot College •
frontdotard_310621f9

fd8e

4a13

904d

619c089dea32.doc
• Page
9
`
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 Tes
t
6.
09
Two

Sided Beam Deflection test
Directions
–
Part

1
Instruments & Supplies
1.
Cantilever Beam Test Fixture
2.
Vertical MeterStick Deflection Ruler
3.
Foamed Polystrene Sheet, 1” Thick
=
=
㐮
=
=
va牤
p瑩捫⁒t汥l
=
㔮
=
=
qape=mea獵牥
=
=
㘮
=
=
me牭anen琠ma牫rng⁰en猠⡡.a.
=
“Sharpie” marker)
=
㜮
=
=
q楧h琠ppo琠ea捫獡w
=
=
㠮
=
=
M⸰4

M⸰
U
=
?p瑥e氠t楲e
iii
9.
Diagonal WireCutting Pliers
10.
NeedleNose Pliers
11.
Bench Vise (on Back Table)
12.
Wood Glue Adhesive
iv
13.
HeavyDuty Aluminum Foil
14.
Box Cutter, razor blade type
15.
Cutting Pad/Board
16.
3” putty k
nife
=
ㄷN
=
=
Carpenter’s Square, 8”x12”
=
=
ㄸN
=
=
b汥捴物挠䡥a琠䝵nⰠapp牯r⸠N44Mt
=
ㄹN
=
=
Ma獳捡汥l=Ng
=⸰MO=汢l⤠F爠
be瑴e爠re獯汵l楯n
=
=
㈰O
=
=
1/4” Steel Fender

tasher
v
Force
Weight; nominal weight = 1
01
mN
21.
5/8” Steel Std

ta獨er
vi
Force
Weight; nominal weight = 291 mN
22.
Microm
eter 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 sp
lit.
iii
A jumbo PaperClip is an adequate substitute
iv
“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
© Bruce
Mayer, PE • Chabot College •
frontdotard_310621f9

fd8e

4a13

904d

619c089dea32.doc
• Page
10
Construct Beam
s
Construct
SIX
polystyrene beams per
design drawing
45

0
507
1
1

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” f
oil 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 to

size with the dull

side UP.
Figure
10
.
Protect the laminating

bench work
sur
face from glue

drips by covering it
with scrap

paper or scrap

foil.
On the 1” side of beams 4

6 use the Sharpie to apply an identifying label to the beam. Team

member 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 th
in 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

4 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 be
am should have an appearance similar to
that shown in
Figure
13
.
HANGER
FORCE LOAD
Figure
5

Hanger and weights installed for
measuring beam

deflection against the vertical rule.
VERTICAL DISPLACEMENT RULE
© Bruce
Mayer, PE • Chabot College •
frontdotard_310621f9

fd8e

4a13

904d

619c089dea32.doc
• Page
11
Figure
6

Proper form of weight

hanger.
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
.
Careful
ly apply the DULL side of the 2.0x25
Al lamination to the glue

covered surface of
beam

6. 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.
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 beam

6. 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 a
ny 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 beam
s
to the instructor for secure
storage until the next lab period when part

2 of this e
xercise will be completed.
Construct
Force

Load Hanger
Construct a washer

load hanger per design drawing
45

04071
5

01
;
Figure
8
. Use these tools
& instruments
Diagonal Cutter pliers; i.e., the wire

cutters
Tape

measu
re or ruler
Sharpie Marker
NeedleNose pliers
Bench Vise (lo
c
ated on ga
lvan
ized

steel

topped work table)
When properly fabricated the hanger should hav
e
a form similar to the prototype hangers
shown in
Figure
6
.
© Bruce
Mayer, PE • Chabot College •
frontdotard_310621f9

fd8e

4a13

904d

619c089dea32.doc
• Page
12
The h
anger 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 th
at does not
exceed 2.5g. Enter the hanger mass in the data

slot below:
Hanger Mass/Weight
F
hanger
=
Finally, measure the Aluminum Foil THICKNESS using either the Micrometer or the Dial

Calipers
Al Foil Thickness
t
Al
=
Also note the beam mate
rial DENSITY. Circle the appropriate density for your group’s material
below.
PolyStrene Material Density
HIGH
LOW
© Bruce
Mayer, PE • Chabot College •
frontdotard_310621f9

fd8e

4a13

904d

619c089dea32.doc
• Page
13
Figure
7

Fabrication Drawing for PolyStyrene Beam

Specimen. Fabricate
SIX
bea
ms
.
© Bruce
Mayer, PE • Chabot College •
frontdotard_310621f9

fd8e

4a13

904d

619c089dea32.doc
• Page
14
Figure
8

Fabrication Drawing for
washer

load hanger. Fabricate ONE hanger.
Bruce Mayer, PE • Chabot College •
frontdotard_310621f9

fd8e

4a13

904d

619c089dea32.doc
• Page
15
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 sto
ckpile 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)
1
0
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

1
0
, 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
washer
s
.
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 de
tails
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
. T
he overhang length should be more than 21”.
Bruce Mayer, PE • Chabot College •
frontdotard_310621f9

fd8e

4a13

904d

619c089dea32.doc
• Page
16
Next install the load

hanger in the beam as shown in
Figure
9
and
Figure
5
. Some details
To minimize beam

deflection during hanger inse
rtion, 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
Tabl
e
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 me
asure 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 cree
p

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
I
FLh
I
h
x
M
I
h
M
2
2
)
0
(
2
max
max
Equation
15
Using the proof load for F in
Equation
15
provides and estimate for σ
y
. Perform this calculation,
and enter the value in the data

reduction answer slot.
Bruce Mayer, PE • Chabot College •
frontdotard_310621f9

fd8e

4a13

904d

619c089dea32.doc
• Page
17
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 si
gnificantly
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 ove
rhang 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
Tabl
e
IX
.
Next add nine fender

washers, one at time,
to the load

hanger. After addition of each fender

washer, measure the vertical distance against the vertical

rule.
See
Figure
5
.
Record the
washer

weights (c.f.
Table
III
) and dist
ance

measurements in
Tabl
e
IX
.
After completion of the distance

measurements, these quantities should be
easily
CALCULATED
using sums & differences,
and
then
entered in
Tabl
e
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 •
frontdotard_310621f9

fd8e

4a13

904d

619c089dea32.doc
• Page
18
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 •
frontdotard_310621f9

fd8e

4a13

904d

619c089dea32.doc
• Page
19
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
. N
ote the
cut

to

size
Aluminum foil sheet
between the beam and glue bottle.
Bruce Mayer, PE • Chabot College •
frontdotard_310621f9

fd8e

4a13

904d

619c089dea32.doc
• Page
20
Figure
12

Beads of adhesive evenly
applied to the laminating surface of beam

2
with the putty knife.
Bruce Mayer, PE • Chabot College •
frontdotard_310621f9

fd8e

4a13

904d

619c089dea32.doc
• Page
21
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 o
f
Styrofoam.
Complete all calculation entries
in the data tables
Hanger

Hole
Location Mark
Figure
13

Completed
1

sided
San
dw
ich

B
eam
.
Hanger mounting location noted on beam

side.
Bruce Mayer, PE • Chabot College •
frontdotard_310621f9

fd8e

4a13

904d

619c089dea32.doc
• Page
22
Pure Material Property Estimates from Data
CALCULATED
Modulus of Elasticity for Pure Polystyrene
E
PS
=
o
Ref:
Equation
6
Equation
14
Use slope, m, from X

Y Plot of δ vs. F
CALCULATED
Y
i
eld Strength for Pure Polystyrene
σ
y,PS
=
o
Ref:
Equation
6
and
Equation
15
Bruce Mayer, PE • Chabot College •
frontdotard_310621f9

fd8e

4a13

904d

619c089dea32.doc
• Page
23
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

Washer
er Weights
Table
III

Fender Washer Weights
Washer
Mass
/Weight
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Table
IV

Standard
Washer Weights
Washer
Mass
/Weight
1.
2.
3.
4.
5.
Table
V
–
Small
Load
Washer Weights
Table
VI

0.
735
OD
Wa
sher Weights
Mass for
20
Washers
Average
Mass
Table
VII

0.
888
OD
Washer Weights
Mass for
20
Washers
Average
Mass
Bruce Mayer, PE • Chabot College •
frontdotard_310621f9

fd8e

4a13

904d

619c089dea32.doc
• Page
24
Table
VIII
–
Proof Load for 6mm Permanent Set
Test
UNLoaded
Vertical
Distance
Load
,
F
Loaded
Vertical
Distance
Removed

Load
Vertical
Distance
Unloaded
Permanent
Set
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 •
frontdotard_310621f9

fd8e

4a13

904d

619c089dea32.doc
• Page
25
Tabl
e
IX
–
Beam

2
Pure

Material Beam
Deflection Test
NOTE: Enter b, h, and L in
Table
I
Washer
Washer
Type
Washer
Weight
Vertical
Distance
Total
Load, F
Beam
Deflect, δ
Notes
0
n/a
n/a
0
0
Hanger i
s Dead Load
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
Bruce Mayer, PE • Chabot College •
frontdotard_310621f9

fd8e

4a13

904d

619c089dea32.doc
• Page
26
Table
X
–
Beam

3
Pure

Material Beam
Creep
Test
Creep

Load Mass/Weight (~80% of Permanent

Set Load)
F
creep
=
NOTE: Enter b, h, and L in
Table
I
Time
(min)
Vertical
Distance
Beam
Deflection, δ
Notes
0

Dead Load
0
+
Just After Load Applied
2
4
6
9
12
15
18
21
24

24
+
Just After Load Removed
26
28
30
33
36
39
42
45
4
8
Bruce Mayer, PE • Chabot College •
frontdotard_310621f9

fd8e

4a13

904d

619c089dea32.doc
• Page
27
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 distance

measurements in
Tabl
e
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 a
s
QUICKLY A
S POSSIBLE to give the next lab

team
acces
s 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
Tabl
e
IX
The total, or cumulative load, F
The beam end

deflection, δ
Print Date/Time =
16

Nov

13
/
08:09
Bruce Mayer, PE • Chabot College •
frontdotard_310621f9

fd8e

4a13

904d

619c089dea32.doc
• Page
28
Table
XI
–
Beam

1
Pure

Material Beam
PROOF

Load Deflection Test
Use this Table ONLY if required by the Ins
t
ructor
NOTE:
Enter b, h, and L in
Table
I
Washer
Washer
Weight
Vertical
Distance
Cumulative
Load, F
Beam
Deflection, δ
Notes
0
0
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 •
frontdotard_310621f9

fd8e

4a13

904d

619c089dea32.doc
• Page
29
PolyStyrene CantileverBeam Creep Behavior
0
25
50
75
100
125
0
5
10
15
20
25
30
35
40
45
50
55
Load Application time,t (min)
Vertical Deflection,
(mm)
No Reinforcement (mm)
file = CompositeBeam_VMY0407.xls
PARAMETERS
• Load = 1164 mN
• Load Removed at 24 minutes
• Beam Geometey, h x w x L = 1" x 1.5" x 21.43"
Figure
14

Typcial d

vs

t creep plot.
This data suggests a permanent set of 5mm after
unloading
Bruce Mayer, PE • Chabot College •
frontdotard_310621f9

fd8e

4a13

904d

619c089dea32.doc
• Page
30
i
F. P. Beer, E. R. Johnston,
Vector Mechanics for Engineer
s
–
Statics
, McGraw

Hill, 2004, pg 363
ii
A. S, Duetscheman, W. J. Michels, C. E. Wilson,
Machine Design
–
Theory and Practice
, MacMillan Publishing, 1975, pg 255
Enter the password to open this PDF file:
File name:

File size:

Title:

Author:

Subject:

Keywords:

Creation Date:

Modification Date:

Creator:

PDF Producer:

PDF Version:

Page Count:

Preparing document for printing…
0%
Comments 0
Log in to post a comment