ENGR-45_Lab_08_Composite_Beams_Part-1 - Chabot College

frontdotardUrban and Civil

Nov 15, 2013 (3 years and 7 months ago)

81 views

© 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
Composite-Beam_VMY-0407.xls
PARAMETERS
• Vmax = F
BENDING-MOMENT
-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
Composite-Beam_VMY-0407.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
Composite-Beam_VMY-0407.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
=
=

=
=
va牤
p瑩捫⁒t汥l
=

=
=
qape=mea獵牥
=
=

=
=
me牭anen琠ma牫rng⁰en猠⡡⹫.a.
=
“Sharpie” marker)
=

=
=
q楧h琠ppo琠ea捫獡w
=
=

=
=
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 Cantilever-Beam 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 = Composite-Beam_VMY-0407.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