ADAPTING GLASS REINFORCED HASTICS TO A
RIGID FRAME DESIGN

by
R o b ert Adams A ld rio h .

AN ABSTRACT

S u b m itted t o t h e s c h o o l fo r Advanced G raduate S t u d ie s o f
M ich igan S t a t e U n iv e r s it y o f A g r ic u lt u r e and
A p p lie d S c ie n c e i n p a r t i a l f u l f i l l m e n t o f
t h e r e q u ir e m e n ts f o r th e d e g r ee o f
DOCTOR OF PHILOSOPHY

D epartm ent o f A g r ic u lt u r a l E n g in e e r in g
1958

ii
The prim ary o b j e c t i v e o f t h i s i n v e s t i g a t i o n was t o d e te r m in e th e
f e a s i b i l i t y o f u s in g f ib r o u s g la s s r e in f o r c e d p l a s t i c s a s a s t r u c t u r a l
m a t e r ia l i n farm b u ild in g d e s i g n .
A r e v ie w o f l i t e r a t u r e in d ic a t e d v e r y few i n s t a n c e s where g la s s
r e in f o r c e d p l a s t i c s h a v e b een u sed t o p r o v id e b o th s t r u c t u r a l member and
c o v e r in g la y e r fo r c o m p lete s t r u c t u r e s .
A r i g i d fram e was c h o sen a s t h e s t r u c t u r a l form t o be u sed i n
th e in v e s t ig a t io n .

A

m o d ifie d T c r o s s s e c t i o n was a d o p ted t o p r o v id e

d e p th o f s e c t i o n t o r e s i s t b en d in g moments and p r o v id e r i g i d i t y .

A tw o

f o o t w id th o f s e c t i o n w ould a llo w c o n v e n ie n t b u ild in g c o n s t r u c t i o n .
B ased on a s u r v e y o f c o m m e r c ia lly a v a i l a b l e p l a s t i c r e s i n s and
f ib r o u s g l a s s r e in fo r c e m e n t, a m o d ifie d epoxy and a p o l y e s t e r r e s i n
w ere u sed w it h 10 ounce p la i n w eave g l a s s c l o t h a s r e i n f o r c i n g in t h e
c o n s t r u c t io n o f t h e t e s t s t r u c t u r a l e le m e n t s .

A s tr u c tu r a l a n a ly s is

was c o m p le te d t o e s t im a t e s t r e s s e s and d e f l e c t i o n s i n t h e fr a m e .
A m odel a n a l y s i s o f th e frame was made t o f a c i l i t a t e t h e i n v e s ­
tig a tio n .

D is t o r t e d m odels were u se d and p r e d i c t i o n f a c t o r s f o r s t r e s s

and d e f l e c t i o n e s t a b l i s h e d t o t e s t t h e h y p o t h e s e s .

Two m od els w ere

b u i l t o f each r e s i n ; one e s s e n t i a l l y a d i s t o r t e d m odel o f t h e o t h e r .
The la y o u t s c a l e b etw een t h e m odels and t h e f u l l s c a l e fram e was f o u r ,
t h a t i s , t h e m odels w ere o n e -f o u r th t h e s i z e o f th e f u l l s c a l e fram e in
la y o u t.

W ith a g iv e n r e s i n , one m odel frame was b u i l t f u l l s c a l e i n

c r o s s s e c t i o n , t h e o th e r o n e - h a lf s c a l e .
The tw o m odel fram es o f ea ch r e s i n w ere t e s t e d by a p p ly in g s h o r t
term s t a t i c lo a d s p e r p e n d ic u la r t o th e span th r o u g h a sy ste m o f h y d r a u lic
c y lin d e r s and lo a d in g s h o e s .

Loads w ere a p p lie d in in c r em en ts t o e s t a b ­

l i s h d e f i n i t e l o a d - d e f l e c t i o n and l o a d - s t r e s s r e l a t i o n s h i p s fo r each
fr a m e .

The s p e c i a l t e s t f lo o r p e r m itte d t e s t i n g th e m odels i n a h o r i -

R ob ert Adams A ld r ic h

iii
z o n t a l p la n e .

S t r a i n i n t h e o u te r f i b e r a t m idspan was m easured by

SR -4 s t r a i n g a g e s and d e f l e c t i o n m easured by d i a l i n d i c a t o r s .
M oduli o f e l a s t i c i t y and maximum s t r e n g t h s i n t e n s io n and bend­
in g w ere e s t a b l i s h e d f o r each r e s i n - g l a s s c l o t h la m in a te from sa m p les
c u t from t h e f la n g e s e c t i o n s o f t h e m odel fr a m e s .

The m o d u li o f e l a s ­

t i c i t y i n t e n s i o n w ere u se d w ith th e SR -4 s t r a i n gage s t r a i n r e a d in g s
t o r e l a t e s t r e s s t o lo a d on t h e fr a m e .

The m od u li o f e l a s t i c i t y i n

b en d in g w ere u sed t o e s t im a t e t h e d e f l e c t i o n o f t h e fr a m e s .
M easured s t r e s s e s and d e f l e c t i o n s w ere compared w ith e s tim a te d
v a lu e s f o r t h e phenomena f o r t h e fo u r m odel fram es t o ch eck t h e a n a l y s i s
o f th e s tr u c tu r e .

The p r e d ic t i o n f a c t o r s fo r s t r e s s and d e f l e c t i o n f o r

t h e d i s t o r t e d m odels w ere compared t o ch eck t h e v a l i d i t y o f t h e model
a n a ly s is .

R ea so n a b le agreem ent e x i s t e d i n a l l c o m p a r iso n s.

Prom t h e r e s u l t s o f t h e i n v e s t i g a t i o n t h e f o ll o w i n g c o n c lu s io n s
w ere made*
(1 )

Epoxy and p o ly e s t e r r e s in s r e in f o r c e d w ith g la s s c l o t h

produce a la m in a te w ith e x c e l l e n t m ec h a n ic a l p r o p e r t i e s .
(2 )

The u se o f s t r u c t u r a l m odels p erm its i n v e s t i g a t i o n o f

h y p o th e s e s c o n c e r n in g m e c h a n ic a l phenomena i n s t r u c t u r e s .

D is t o r t e d

m od els c a u s e no in c r e a s e i n d i f f i c u l t y over tr u e m odels i n t h e u se o f
m odel a n a l y s i s .
(3 )

F ib ro u s g l a s s r e in f o r c e d p l a s t i c r e s i n s can be u se d w ith

c o n fid e n c e i n farm b u ild in g d e s ig n and c o n s t r u c t io n .
(4 )

The s t r u c t u r a l t e s t f lo o r w ith t h e h y d r a u lic lo a d in g s y s ­

tem p r o v id e s a c o n v e n ie n t and a c c u r a te means fo r a p p ly in g s t a t i c lo a d s
t o s t r u c t u r a l e le m e n ts su ch a s th e m odel fr a m e s.
R o b ert Adams A ld r ic h

ADAPTING GLASS REINFORCED PLASTICS TO A
RIGID FRAME DESIGN

by
R ob ert Adams A ld r ic h

A THESIS
S u b m itted t o th e s c h o o l fo r Advanced G raduate S t u d ie s o f
M ich igan S t a t e U n iv e r s it y o f A g r ic u lt u r e and
A p p lie d S c ie n c e in p a r t i a l f u l f i l l m e n t o f
t h e r e q u ir e m e n ts fo r th e d eg ree o f

DOCTOR OF PHILOSOPHY

D epartm ent o f A g r i c u l t u r a l E n g in e e r in g
1958

ProQuest Number: 10008605

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ACKNOlfifllEDGEMENTS

W ith out t h e c o n s ta n t su p p o rt and encouragem ent from my w i f e ,
R o b e r ta , and my fo u r d a u g h te r s , t h i s work c o u ld n ev er have b een accom p­
lis h e d .
I w ould l i k e t o th an k D r . J . S . Boyd f o r h i s su p p o rt and coun­
s e l th r o u g h o u t t h e c o u r se o f t h e p r o j e c t .
Thanks a r e g iv e n t o D r . A . W. F a r r a ll f o r p r o v id in g fu nds fo r
th e a s s i s t a n t s h i p , m a t e r ia ls and equipm ent w h ich made p o s s i b l e th e
c o m p le tio n o f t h i s w ork .
I w is h t o th a n k Mr. James Cawood and h i s cow orkers i n t h e A g r i ­
c u l t u r a l E n g in e e r in g r e s e a r c h la b o r a to r y f o r t h e i r a s s i s t a n c e i n co n ­
s tr u c tio n of th e t e s t in g f a c i l i t i e s .
A p p r e c ia t io n i s e x p r e s s e d f o r t h e i n t e r e s t and s u g g e s t io n s co n ­
c e r n in g t h e program from t h e members o f th e g u id a n c e com m ittee;
D r s . M. L . Esmay, W. A . B r a d le y , C . L . Shermer and W. P . R e id .
Thanks a r e g iv e n t h e Dow C hem ical Company o f M idland, M ich ig a n ,
f o r t h e i r i n t e r e s t i n t h e problem and t h e i r g i f t o f expanded p o ly s ty r e n e
f o r u se i n t h e

c o n s t r u c t io n o f th e m odel fr a m e s.

VITA
F in a l e x a m in a tio n s

D is s e r ta tio n s

29 A p r il 1 9 5 8 , 3*00 P .M ., Room 218 A g r ic u lt u r a l
E n g in e e r in g B u ild in g

A d a p tin g G la ss R e in fo r c e d P l a s t i c s t o a R ig id Frame
D e s ig n

O u tlin e o f s t u d ie s *
Major s u b j e c t s A g r ic u lt u r a l E n g in e e r in g
Minor s u b j e c t s * A p p lie d M ech a n ics, C i v i l E n g in e e r in g
P e r s o n a l data*
D ate o f b ir th *
25 A p r il 1924
P la c e o f b ir th * H o r se h e a d s, New York

E ducation*
H ig h so h o o l*
C o lle g e
*

B em id ji H ig h s c h o o l, B e m id ji, M in n esota
B em id ji S t a t e T each ers C o lle g e , B e m id ji, M in n e so ta , 1946
Grays Harbor C o lle g e , A b erd een , W ash in gton , 1 9 4 6 -4 8
W ashington S t a t e C o ll e g e , P u llm a n , W a sh in g to n ,
1 9 4 8 -5 0 . BS i n AE
W ashington S t a t e C o lle g e , P u llm a n , W ash in gton ,
1 9 5 0 -5 2 . MS i n AE
M ich igan S t a t e U n i v e r s i t y , E . L a n s in g , M ich ig a n ,
1 9 5 6 -5 8 .

P r o f e s s i o n a l e x p e r ie n c e *
G raduate t e a c h in g a s s i s t a n t , W ashington S t a t e C o lle g e , 1950
I n s t r u c t o r and J u n io r E n g in e e r , W ashington S t a t e C o lle g e , 1 9 5 1 -5 4
A s s i s t a n t P r o f e s s o r and A s s i s t a n t E n g in e e r , W ashington S t a t e
C o lle g e , 1 9 5 4 -5 6
R e se a r c h g ra d u a te a s s i s t a n t , M ich ig a n S t a t e U n iv e r s i t y , 1 9 5 6 -5 8
P r o f e s s io n a l and h on orary s o c i e t i e s *
A m erican S o c i e t y o f A g r i c u lt u r a l E n g in e e r s 1954
S o c i e t y o f A m erican M il it a r y E n g in e e r s
1956
Tau B eta P i , Sigma T au, P h i Kappa P h i, A lph a Z eta
M ilit a r y s e r v ic e *
45 months US Army Corps o f E n g in e e r s

1 9 4 2 -4 6

TABLE OP CONTENTS
Page
INTRODUCTION.........................................................................................................................

1

LITERATURE R E V IE W ...........................................................................................* . .

2

P l a s t i c R e s in s

.

• • • • ...........................................

2

Epoxy R e s in s » • • • • • • • * • • • • • • . • • •
P o l y e s t e r R e s in
. • • . • • • • • • • • • • . •
F ib ro u s G la ss R e in fo r c em e n t

*

G la ss R e in fo r c e d P l a s t i c R e sin s

2
3

• • • • • • • •

3

............................ • .

5

R e in f o r c in g Methods • • • ......................... • • • . •
•
M ech an ical P r o p e r t i e s ............................................. . . .
F a tig u e C h a r a c t e r is t i c s
• • • • ....................... • • .
P r e s e n t Use o f R e in fo r c e d P l a s t i c s • • • • • • •
Frame

A n a ly s is

Model A n a ly s is

. • • • • ...........................................
....................................................••

•

•

*

10

The P r e d ic t io n E q u a t i o n ............................. . • . . •
S t r u c t u r a l M odels
• • • • • • • . • • • • • • •
TEE

INVESTIGATION.......................................................................................................
P r e lim in a r y C o n s id e r a tio n
Frame A n a ly s is

5
6
7
9

10
12
15

• • • •

. . . . . .

15

. • • • • • • • • .

. . . . . .

17

Model A n a l y s i s .........................................................

21

P r e d ic t io n E q u a tio n f o r S t r e s s .......................................
P r e d i c t i o n E q u a tio n f o r D e f l e c t i o n ............................
• • • • ....................
Frame A n a ly s is fo r The M odels
E x p e rim en ta l I n v e s t i g a t i o n

...................................................

T e s t F a c i l i t i e s .................................
Model C o n s tr u c tio n
« • • • •
I n s tr u m e n ta tio n
............................
D e te r m in in g M a te r ia l C o n sta n ts . . . • • • • • •
Model T e s t in g
....................................... . . . . . . . .
L on g-term S t a t i c L oad in g
iv

....................

21
23
25
28
28
28
36
38
43
44

•. 10

TABLE OP CONTENTS (C on t*)
Page
RESULTS AM) DISCUSSION.................................................................................................

56

Use o f The C o n s tr u c tio n M a t e r i a l s ................................................

56

M ech an ical P r o p e r t ie s o f The M a t e r i a l s .......................................

59

T e n sio n
F le x u r e

, • .............................................................. • • • • •
•

59
61

E v a lu a t io n o f The Model A n a l y s i s .................................

63

L on g-term L o a d s ..................................................................

67

CONCLUSIONS........................................................................................................................

68

SUMMARY.................................................................................

70

SUGGESTIONS FOR FURTHER S T U D Y .............................................................................

72

BIBLIOGRAPHY........................................................................................................................

73

v

LIST OF FIG-URES
F ig u r e
L ayout and c r o s s s e c t i o n o f e x p e r im e n ta l r i g i d fram e o f
g l a s s c l o t h r e in f o r c e d p l a s t i c r e s i n la m in a te s and
expanded p o ly s t y r e n e •

16

D e f i n i t i o n s k e t c h fo r fram e a n a l y s i s .

18

3.

Load and moment diagram s f o r s o l u t i o n o f t h e r i g i d fram e*

19

4.

C ro sa s e c t i o n d im en sio n s fo r t h e fo u r m odel fram es u sed
i n t h e stu d y *

27

S c h e m a tic diagram o f h y d r a u lic s y ste m u sed in t h e lo a d
t e s t s o f t h e m odel fram es*

29

6•

M a te r ia ls u sed i n la m in a tin g w ith epoxy r e s i n .

31

7.

Model E 025050 under s h o r t-te r m s t a t i c t e s t i n t h e s t r u c t u r e s
t e s t la b o r a t o r y .

31

M a te r ia ls and proced u re u sed i n c o n s t r u c t io n o f m odel
P025050.

33

L o a d - s t r e s s c u r v es i n b en d in g as d eterm in ed by f o r c e
tr a n s d u c e r and SR-4 s t r a i n gage mounted on b en d in g
sp e c im e n .

37

A v era g e s t r e s s - s t r a i m c u r v e s i n t e n s i o n p a r a l l e l t o th e
warp f o r ep o x y r e s i n - g l a s s c l o t h la m in a t e .

39

A verage s t r e s s - s t r a i n c u r v e s i n t e n s i o n f o r p o ly e s t e r
r e s i n - g l a s s c l o t h la m in a t e .

40

A verage s t r e s s - s t r a i n c u r v e s i n t e n s io n f o r p o ly e s t e r
r e s i n - g l a s s c l o t h la m in a t e .

41

F le x u r e t e s t i n g m achine and o s c il lo g r a p h r e c o r d s from
tw o t e s t s on p l a s t i c la m in a te s a m p le s .

42

L o a d - s t r e s s c u r v e s i n b en d in g fo r model E025050 (ep o x y
r e s i n - g l a s s c l o t h la m i n a t e ) .

45

D e f l e c t i o n o f m odel E 025050 a t t h e crow n due t o a u n i­
fo r m ly d i s t r i b u t e d l o a d .

46

1.

2

.

5.

8.
9*

10*

11

12

.
.

13.
14.

15.

vi

LIST OF FIGURES (C o n t .)
Page

F ig u r e
16.

17.

18.
19.
20.
21.
22.
23.
24.

L o a d - s t r e s s c u r v e s i n b en d in g f o r m odel E 025100 (ep o x y
r e s i n - g l a s s c l o t h la m i n a t e ) .

47

D e f l e c t i o n o f m odel E 025100 a t t h e crown due t o a u n i­
fo rm ly d i s t r i b u t e d lo a d .

48

L o a d - s t r e s s c u r v e s i n b en d in g fo r m odel P025050 (p o ly ­
e s t e r r e s i n - g l a s s c l o t h la m in a t e ) .

49

D e f l e c t i o n o f m odel P025050 a t th e crown due t o a u n i­
fo r m ly d i s t r i b u t e d lo a d .

50

L o a d - s t r e s s c u r v e s i n b en d in g fo r m odel P025100 ( p o ly ­
e s t e r r e s i n - g l a s s c l o t h la m in a t e ) .

51

D e f l e c t i o n o f m odel P025100 a t t h e crow n due t o a u n i­
fo r m ly d i s t r i b u t e d lo a d .

52

D e f l e c t i o n o f m odel E 025100 a t t h e crown w ith a co n ­
s t a n t u n ifo r m lo a d o f SOj^/ft o f beam a p p l i e d .

53

D e f l e c t i o n o f m odel P025050 a t th e crown w ith a c o n s ta n t
u n ifo r m lo a d o f 4 2 . 5 ^ / f t o f beam a p p li e d .

55

Two ep o x y r e s i n - g l a s s c l o t h la m in a te s show ing th e e f f e c t
o f r e s i n s t a r v in g on g l a s s d i s t r i b u t i o n and s u r fa c e
app earance.

58

v ii

LIST OF TABLES
Page

T ab le
1.

M ech a n ica l p r o p e r t ie s o f tw o p l a s t i c r e s i n - g l a s s c l o t h
la m in a te s •

6

L ayout and c r o s s s e c t i o n d im en sio n s o f t h e frame and
m od els •

21

3.

M o d e l-p r o to ty p e r e l a t i o n s h i p s fo r t h e d i s t o r t e d m o d e ls .

26

4.

M ech an ical p r o p e r t ie s o f tw o p l a s t i c r e s i n - g l a s s c l o t h
la m in a te s as d eterm in ed from sam p les ta k e n from t h e f la n g e
la m i n a t e s •

43

E stim a te d and m easured v a lu e s o f d e f l e c t i o n (d ) and low er
f i b e r s t r e s s ( s ) a t t h e crow n o f th e fo u r m odel fr a m e s.

65

R a tio s o f e s tim a te d and m easured v a lu e s o f d e f l e c t i o n and
s t r e s s f o r th e m odel and p r o to ty p e fo r th e tw o p l a s t i c
r e s i n - g l a s s c l o t h la m in a t e s .

65

2.

5*

6•

v iii

INTRODUCTION

Farm b u ild in g s h ave t r a d i t i o n a l l y b e e n c o n s tr u c te d o f wood,
m e t a l, m ason ry, c o n c r e t e , or c o m b in a tio n s o f t h e s e m a t e r i a l s .

T h is

d o es n o t n e c e s s a r i l y im p ly t h a t th e u se o f one or more o f t h e s e m ater­
i a l s w i l l a lw a y s produce t h e b e s t farm b u ild in g t o f i t a s p e c i f i c need*
For many farm b u ild in g s a s u b s ta n c e w h ich com bines some o f t h e more
f a v o r a b le c h a r a c t e r i s t i c s o f t h e t r a d i t i o n a l m a t e r ia ls w ould h e lp t h e
farm er i n h i s s e a r c h fo r b e t t e r b u ild in g s *

For ex a m p le, a m a t e r ia l

w h ic h com bines t h e im p e r m e a b ility o f m e t a l, t h e l i g h t w e ig h t o f wood,
and t h e d eca y r e s i s t a n c e o f c o n c r e te i n a d d it io n t o a d eq u a te m e c h a n ic a l
s t r e n g t h and h e a t c o n t r o l , w ould be an e x c e l l e n t c h o ic e fo r m ilk h o u se
c o n s t r u c t io n *

JL b u ild in g composed o f r e in f o r c e d p l a s t i c s

fo r s t r e n g t h

and c o v e r in g w it h a foamed p l a s t i c fo r te m p e r a tu r e c o n t r o l w ould d i s ­
p la y t h e above c h a r a c t e r i s t i c s t o a marked d e g r e e .
T h is i n v e s t i g a t i o n d e a ls w ith t h e u se o f g l a s s r e in f o r c e d p l a s ­
t i c s t o form s t r u c t u r a l u n it s f o r farm b u ild in g s *

The stu d y may be

d iv id e d i n t o t h e f o llo w in g o b j e c t iv e s *
1*

t o exam ine p l a s t i c r e s i n s c o m m e rc ia lly a v a i l a b l e t o d e t e r ­

m ine t h o s e s u i t a b l e f o r u se i n s t r u c t u r a l la m in a te s ;
2*

t o e s t a b l i s h a b u ild in g form w hich w ould b e a c c e p t a b le from

a management v ie w p o in t and w h ich would be s t r u c t u r a l l y sound;
3*
u tility

t o d e te r m in e a method o f a n a l y s i s and t e s t i n g t o p ro v e th e

o f t h e m a t e r ia l;
4*

t o make a m odel a n a l y s i s and from such a n a l y s i s p r e d ic t t h e

b e h a v io r o f t h e p r o t o t y p e .
1

LITERATURE REVIEW'

P l a s t i c R e s in s
P l a s t i c s a r e d e f in e d a s ”a la r g e and v a r ie d group o f m a ter­
i a l s w hich c o n s i s t s o f , or c o n t a in s a s a n e s s e n t i a l i n g r e d i e n t , an
o r g a n ic s u b s ta n c e o f la r g e m o le c u la r w e ig h t w h ic h , w h ile s o l i d i n t h e
f i n i s h e d s t a t e , a t some s t a g e i n i t s m an u factu re i s made l i q u i d and
th u s c a p a b le o f b e in g form ed i n t o v a r io u s s h a p e s , m ost u s u a ll y th ro u g h
t h e a p p l i c a t i o n , e i t h e r s i n g l y or t o g e t h e r , o f h e a t and p r e s s u r e ” ( 2 2 ) •
P l a s t i c s a r e s u b d iv id e d i n t o two g e n e r a l c a t e g o r i e s , th e r m o p la s t ic and
t h e r m o s e t t in g *

L am inates and r e in f o r c e d p l a s t i c s a r e th o s e m a t e r ia ls i n

w h ich t h e p l a s t i c , u s u a ll y i n a l i q u i d form , i s used a s a b in d e r and
s u r f a c in g m a t e r ia l i n c o n ju n c tio n w ith r e in f o r c in g m a t e r ia ls su ch a s
g l a s s m at, g l a s s c l o t h , p a p e r , e t c .
From a r e v ie w o f t h e th e r m o s e t t in g r e s i n s a v a i l a b l e tw o w ere
c h o s e n t o be u se d i n t h e s t u d y .

Epoxy r e s i n w hich i s b a sed g e n e r a ll y

upon e p ic h lo r o h y d r in and b is p h e n o l-A , and p o ly e s t e r r e s i n .

No a ttem p t

i s made t o p r e s e n t t h e c h e m ic a l fo r m u la tio n s a s t h e y a r e c o n s id e r e d t o
be o u t s id e t h e sco p e o f t h e i n v e s t i g a t i o n .

E poxy R e s in
C om m ercial r e s i n s a r e a m ix tu re o f p o ly m e r s.

They c o n t a in b o th

e p o x id e and h y d r o x y l groups c a p a b le o f f u r t h e r r e a c t i o n .
p e r t i e s su ch a s p o t l i f e ,

H a n d lin g pro­

s t r e n g t h , c h e m ic a l r e s i s t a n c e , h ig h -te m p e r a -

t u r e s t r e n g t h r e t e n t i o n , and e l e c t r i c a l p r o p e r t ie s o f t h e cu red r e s i n s
a r e d i r e c t l y d ep en d en t on t h e c u r in g a g e n ts ( 2 9 ) .
2

P r e s e n t a p p li c a t io n s

o f ep o x y r e s i n s in v o lv e u s e o f p o ly a m in e s, a s w e l l a s p o ly a m id e r e s i n s ,
a c id a n h y d r id e s , and o th e r r e s i n ty p e s *

They a r e g e n e r a ll y 100 p e r c e n t

r e a c t i v e , i * e * , no gas or l i q u i d i s e v o lv e d d u r in g t h e c u r in g p r o c e s s *
Compared w it h o th e r r e s i n s , ep o x y r e s i n la m in a te s p r e s e n t t h e optimum
m e c h a n ic a l s t r e n g t h p r o p e r t i e s , e x c e l l e n t th e r m a l in s u l a t i n g c h a r a c t e r ­
i s t i c s , s h a t t e r and fu n gu s r e s i s t a n c e *

They c a n he fo r m u la te d t o any

v i s c o s i t y and b le n d ed w it h a v a r i e t y o f r e i n f o r c in g .a g e n ts and f i l l e r s *
They have e x c e l l e n t a d h e s io n q u a l i t i e s

(2 8 )*

P o l y e s t e r R e s in
A p o ly e s t e r r e f e r s t o an u n sa tu r a te d p o ly e a te r b a se r e s i n d i s ­
s o lv e d i n a p o ly m e r iz a b le monomer*

P o ly e s t e r r e s i n s f o r r e in f o r c e d

p l a s t i c s come g e n e r a ll y from t h e p o ly f u n c t io n a l u n sa tu r a te d e s t e r s su ch
a s d i a l l y l ph tha l a t e *

They a r e p o ly m erized or c o p o ly m e r iz e d th ro u g h

t h e u se o f p e r o x id e s *

The b a se r e s i n component ca n be p rep ared from

in n u m erab le c h e m ic a l

c o m b in a tio n s ( 2 6 , 2 7 )*

B a sic a d v a n ta g e o f t h e s e

m a t e r ia ls i s t h a t t h e y s t a r t a s m o b ile l i q u i d s and
q u ic k ly t o s o l i d s *

can be c o n v e r te d

They a r e a l s o 1 0 0 p e r c e n t r e a c t iv e *
F ib r o u s G la ss R e in fo r c em e n t

G la s s f i b e r s make e x c e l l e n t p l a s t i c s r e in fo r c e m e n t b e c a u s e t
1.

t h e y have s t r e n g t h s g r e a t e r th a n s t e e l ,

2*

t h e y have f la m e , h e a t , and c h e m ic a l r e s i s t a n c e o f c e r a m ic s ,

3*

t h e r e i s no m o is tu r e a b s o r p t io n ,

4*

th e y are

5*

t h e y d d v e lo p h ig h i n t e r f a c e sh ear s t r e n g t h s w it h many o f t h e

a v a i l a b l e i n a lm o st u n lim it e d q u a n t it y ,

p l a s t i c r e s in s *
F ib r o u s g l a s s r e in fo r c e m e n t i s a v a i l a b l e i n mat form , a s g l a s s

3

c l o t h i n s e v e r a l d i f f e r e n t w eave p a t te r n s * and a s r o v in g s *

G la s s mat

c o n s i s t s o f random le n g t h s o f f i b e r s w ith no p a r t ic u l a r o r ie n t a t io n *
G la s s c l o t h h as th r e a d s i n tw o d i r e c t i o n s i n t h e w eave#

T hreads run­

n in g p a r a l l e l t o t h e le n g t h o f th e c l o t h a r e known a s "warp” th r e a d s *
T hose ru n n in g a c r o s s t h e c l o t h and p e r p e n d ic u la r t o th e warp a r e r e f e r ­
red t o a s " p ic k ” t h r e a d s •
a lte r n a te ly *

I n p l a i n w eave th e warps and th e p ic k s c r o s s

R o v in g s a r e produced e s s e n t i a l l y by w in d in g a number o f

ends o f s l i v e r o n to a c o r e *

They a r e n o t t w is t e d or p l i e d , b u t some­

tim e s a b in d e r i s u se d t o h o ld them t o g e t h e r

(1 0 )*

S p e c ia l f i n i s h e s a r e a p p lie d t o g l a s s t o im prove i t s w e t t a b i l i t y
w it h t h e r e s i n s •

One su ch f i n i s h i s known a s t^114 i n w h ich m e th a c r y la te

chrom ic c h lo r id e i s a p p lie d t o h e a t c le a n e d f a b r ic from an aqueous s o l u ­
t io n *

V o la n A. i s an im proved ^ 1 1 4 where t h e c h lo r in e i s h y d r o ly z e d o f f *
A c c o r d in g t o B r o s s y , e t a l ( 8 ) , i n d iv id u a l g l a s s f i b e r s have in ­

t r i n s i c s t r e n g t h s i n e x o e s s o f 5 0 0 ,0 0 0 p s i f o r c o n tin u o u s lo a d s and
s t r e n g t h s h a l f a g a in a s h ig h fo r lo a d s o f s h o r t d u r a tio n *

R oughly o n e -

h a l f o f t h i s s t r e n g t h i s l o s t by s p in n in g and w ea v in g t h e f ib e r s *

Ad­

d i t i o n a l s t r e n g t h i s l o s t i n u se i n g la s s r e in f o r c e d p l a s t i c s b e c a u se
t h e t w i s t e d f i b e r s ca n n o t e q u a lly sh a r e a p p lie d lo a d s *

The maximum

s t r e n g t h o f a l l t h e f i b e r s i s n o t r e a l i z e d s im u lt a n e o u s ly r e s u l t i n g in
p r e fe r e n tia l fa ilu r e *

T h is a c c o u n ts fo r th e c u r v ed s t r e s s - s t r a i n

f o r c o m p o s ite r e s i n - f i b e r m a t e r ia ls *

ourve

The c h a r a c t e r o f t h e g la s s s u r f a c e

i s im p o rta n t i n d e v e lo p in g bond w it h p l a s t i c r e s i n s s i n c e a l l t h e lo a d
must be t r a n s f e r r e d th r o u g h t h i s bond by i n t e r f a c e sh ear •
I n t h e work r e p o r te d by B r o s s y , e t a l ( 8 ) , b o th epoxy and p o ly ­
e s t e r r e s i n s w ere u sed w ith p a r a l l e l g l a s s f i b e r s *

I n d iv id u a l g l a s s

f il a m e n t s w ere spun o n to a r o t a t i n g drum and sp ra y ed w ith a b in d in g

4

r e s i n t o p r e s e r v e t h e i r r e l a t i v e p o s i t io n *

F le x u r a l t e s t s made w ith

sa m p les la m in a te d from t h e s e s h e e t s d e v e lo p e d d ry maximum u lt im a t e
s t r e n g t h s o f 2 1 1 ,0 0 0 p s i w it h s p e c i a l g la s s *

The im p o rta n ce o f i n t e r ­

f a c i a l b o n d s, g l a s s s u r f a c e n e u t r a l i t y and b in d e r r e s i n i s
w it h p a r a l l e l g l a s s f i b e r r e in f o r c e d la m in a te d *

e s ta b lis h e d

T h is i s su p p o r te d by

T r iv is o n n o and Lee ( 3 0 ) , who fou nd th e s t r e n g t h o f a d h e s iv e bond b e ­
tw e e n r e s i n and g l a s s c a n be g r e a t l y a l t e r e d r e s u l t i n g i n in c r e a s e d
f l e x u r a l s t r e n g t h o f p o ly e s t e r la m in a te s by th e u se o f g la s s f i n i s h i n g
a g e n ts•
G la ss R e in fo r c e d P l a s t i c R e s in s
R e in f o r c in g Methods
A lth o u g h t h e r e a r e a v a i l a b l e and i n u s e s e v e r a l d i f f e r e n t r e i n ­
f o r c in g m a t e r ia ls t h e d i s c u s s i o n h e r e w i l l be lim it e d t o g l a s s f ib e r s ;
s in c e t h e y w i l l produce a la m in a te w ith th e m ost d e s ir a b l e m ech a n ica l
and c h e m ic a l p r o p e r t ie s f o r farm b u ild in g s *

Used in t h e mat form , t h e r e

i s random o r i e n t a t i o n o f t h e f i b e r s Tnhich p rod u ces an a p p r o x im a te ly i s o ­
t r o p i c m a t e r ia l*

Many o f th e p r e s s u r e la m in a te d p r o d u cts u s e g l a s s mat

f o r s t r e n g t h and f i l l e r as i t i s t h e l e a s t e x p e n s iv e o f th e form s o f
g l a s s r e in f o r c in g *

H ow ever, i t r e q u ir e s abou t tw ic e as much g la s s mat

t o produ ce t h e same s t r e n g t h a s w it h g l a s s i n c l o t h form *

The r a t i o o f

g l a s s t o r e s i n v a r i e s from a p p r o x im a te ly 7(tf> glass-3Q !£ r e s i n t o BCffo
g la s s - 5 0 ^ r e s i n by volum e (31 ) •
One method o f la m in a tin g i s t o u se g l a s s c l o t h w h ich p ro d u ces
a n o r t h o t r o p ic m a t e r ia l*

L am inates ca n be produced w it h no p r e s s u r e

han d -w et la y u p or w it h th e a d d i t i o n , e i t h e r s i n g l y or t o g e t h e r , o f h e a t
and p r e s s u r e *

D i r e c t i o n a l r e in fo r c e m e n t ca n be o b ta in e d by la y in g

th r e a d s i n a p r e d e te rm in e d p a t t e r n such t h a t maximum s t r e n g t h can be

5

o b ta in e d i n th e d i r e c t i o n o f e x p e c te d maximum s t r e s s .
V e lle u

D o n a ld so n and

( 1 6 ) , d e v e lo p e d d i r e c t i o n a l l y r e in f o r c e d p l a s t i c s w ith t e n s i l e

s t r e n g t h s up t o 1 2 0 ,0 0 0 p s i a t t e n s i o n m o d u li up t o 5.9x10® p s i*

They

fou n d t h e e p o x ie s a r e n o t s e n s i t i v e t o e n v ir o n m e n ta l c o n d i t i o n s , a b ra ­
s i o n s , n o tc h e f f e c t s , e t c .

The e l a s t i c l i m i t s o f th e la m in a te s a r e

v e r y c l o s e t o u lt im a t e s t r e n g t h s .
M ech an ical P r o p e r t ie s
T e s ts have b e e n c o n d u cted w h ich have e s t a b l i s h e d a f a i r l y d e f i n ­
i t e ran ge o f v a lu e s f o r t h e m e c h a n ic a l p r o p e r t ie s o f g la s s c l o t h - r e i n ­
fo r c e d p l a s t i c s .

T y p ic a l v a lu e s f o r g l a s s c l o t h - r e i n f o r c e d epoxy and

p o ly e s t e r r e s i n la m in a te s a r e g iv e n i n T ab le 1 .
TABLE 1
MECHANICAL PROPERTIES OF TWO PLASTIC RESINS
REINFORCED TOTH CLASS CLOTHl

M ech an ical P r o p e r ty

Maximum
Maximum
Maximum
Modulus
Modulus

R e s in s

s t r e n g t h i n b en d in g ( p s i x 10~^ )
str e n g th in te n s io n (p s i x 1 0 -3 )
s t r e n g t h i n c o m p r e ssio n ( p s i x 1 0 - 3 )
o f e l a s t i c i t y i n b en d in g ( p s i x 10“ 6 )
o f e l a s t i c i t y i n t e n s i o n ( p s i x 10-® )

Epoxy

P o ly e s te r

4 5 -8 0
3 5 -5 0
5 0 -9 0
2 .0 - 3 .6
2 .5 - 3 .5

50—63
4 0 -5 0
3 0 -6 0
2 . 0 —3 .0
1 .0 -2 .8

^ d ata from Modern P l a s t i c s E n c y c lo p e d ia I s s u e

XXX111 ( 1 9 5 5 ) .

I n v e s t i g a t i o n s have shown t h a t g la s s r e in f o r c e d epoxy and p o ly ­
e s t e r la m in a te s s e r v e e x c e p t i o n a l l y Trail over a w id e range o f te m p er a tu r e
and h u m id ity .
s ta tio

Lower te m p e r a tu r e s g e n e r a lly r e s u l t i n s l i g h t l y h ig h e r

str e n g th p r o p e r tie s .

6

The F o r e s t P r o d u c ts L a b o r a to r y , TJSDA, M adison, W is c o n s in , has
c a r r ie d on an e x t e n s iv e program o f t e s t i n g and e v a lu a t i o n o f p l a s t i c
la m in a te s #

W erren ( 3 1 , 3 2 , 3 3 , 3 4 ) , p r e s e n t s t h e r e s u l t s o f a number

o f t h e s e t e s t s on p o l y e s t e r , ep oxy and p h e n o lic r e s i n la m in a te s #
V a lu e s o b ta in e d f o r th e m e c h a n ic a l p r o p e r t ie s s u b s t a n t ia t e t h o s e g iv e n
i n T a b le 1 ,
D e lla R occa ( 1 2 ) , r e p o r t s t h a t f i b e r g l a s s r e in f o r c e d p o l y e s t e r
r e s i n la m in a te s e x h i b i t v e r y l i t t l e

c r e e p a t room te m p e r a tu r e s#

In r e ­

l a t i n g t h ic k n e s s o f la m in a te t o s t r e n g t h i t a p p ea rs t h a t o n e -e ig h t h
in c h t h ic k n e s s g iv e s t h e optimum s t r e n g t h p r o p e r t ie s #

He c o n s id e r s

r e in fo r c e m e n t and m old in g method t o be o f prim ary im p o rta n ce t o la m in ­
a t e p r o p e r t ie s and v a r i a t i o n s due t o r e s i n fo r m u la tio n , h u m id ity , e t c # ,
a s b e in g sec o n d a ry s i n c e t h e i r e f f e c t , w h ile im p o r ta n t, ca n be m in im ized
w it h proper q u a lit y c o n t r o l#
F a tig u e C h a r a c t e r is t ic s
A lth o u g h c y c l i c lo a d in g I s g e n e r a ll y n o t c o n s id e r e d i n farm
b u ild in g d e s ig n , i t i s n e c e s s a r y t o have some know ledge o f f a t i g u e
c h a r a c t e r i s t i c s o f a new m a t e r ia l b e fo r e co m p lete a c c e p ta n c e f o r d e s ig n
and c o n s t r u c t io n p u rp oses*
U sin g 5x 106 c y c l e s a s c r i t e r i o n f o r f a t i g u e s t r e n g t h i n f l e x u r e ,
F r ie d ( 1 7 ) , fou nd t h a t t h e r a t i o o f f a t i g u e s t r e n g t h t o u lt im a t e s t a t i c
s t r e n g t h ran ged from 0#20 t o 0*30 f o r p o ly e s t e r r e s i n w it h la m in a te s
u s in g a c o m b in a tio n o f g la s s c l o t h and mat#

No endurance l i m i t was

r e a c h e d up t o 1 0 7 c y c l e s a lth o u g h th e d a ta ap p eared t o be a p p ro a ch in g
a n asy m p to te*
For f a t i g u e t e s t s , Mara ( 2 1 ) , u sed r e c ta n g u la r c r o s s s e c t i o n
c a n t i l e v e r beams o f both epoxy and p o ly e s t e r r e s i n r e in f o r c e d w it h
7

l o n g i t u d i n a l f i b e r s c o n tin u o u s over t h e le n g t h o f t h e beam .

F a ilu r e

was i n sh e a r i n t h e form o f d e la m in a tio n b e g in n in g a t t h e n e u t r a l a x i s •
He p l o t t e d sh e a r s t r e s s v e r s u s t h e lo g a r ith m o f th e c y c l e s and n o te d
t h a t t h e *knee * o f t h e S -N cu rve ap p eared b etw een 10^ t o 10^ c y c l e s .
U sin g th e kn ee a s a f a t i g u e s t r e n g t h v a l u e , t h e r a t i o o f f a t i g u e
s t r e n g t h t o u lt im a t e s t a t i c s t r e n g t h i s a p p r o x im a te ly 20 p e r c e n t f o r
p o ly e s t e r r e s i n la m in a te s and 32 p e r c e n t f o r ep oxy la m in a te s #
B o ile r

( 7 ) d eterm in ed f a t i g u e s t r e n g t h b a se d on a x i a l lo a d i n g .

A t a f a t i g u e s t r e n g t h f o r t e n m i l l i o n c y c l e s th e r a t i o o f f a t i g u e
s t r e n g t h t o u lt im a t e s t a t i c s t r e n g t h ra n g ed from 20 t o 25 p e r c e n t fo r
p o l y e s t e r la m in a te s t o 4 0 p e r c e n t f o r ep oxy la m in a t e s .
te m p er a tu r e c u r in g r e s i n s *

He found t h a t m o is tu r e e f f e c t s t h e f a t i g u e

s t r e n g t h o f sta n d a rd p o ly e s t e r r e s i n s o n ly s l i g h t l y
t e n s i l e str e n g th a t te n m illio n c y c le s ) ;
change i s i n s i g n i f i c a n t .

Both w ere room

(2 p e r c e n t o f s t a t i c

f o r epoxy r e s i n la m in a te s th e

Both m a t e r ia ls show a d e c r e a s e i n s t a t i c and

f a t i g u e s t r e n g t h s a t in c r e a s e d te m p e r a tu r e .
I n f l e x u r a l f a t i g u e t e s t s o f 32 d i f f e r e n t p o l y e s t e r , e p o x y , and
p h e n o lic r e s i n s la m in a te d w ith e i t h e r g la s s c lo t h or g l a s s m a t, F u sey
( 2 4 ) , found t h a t th e p o ly e s t e r s o f f e r t h e w e a k e st f a t ig u e s t r e n g t h s .
The c h o ic e o f r e s i n i s s i g n i f i c a n t w it h in t h e e p o x y group bu t c h o ic e o f
h ard en er w it h in t h e same group has no s i g n i f i c a n t e f f e c t .

He a l s o n o te d

t h a t g l a s s c l o t h p rod u ces s tr o n g e r la m in a te s th a n g la s s mat and t h a t
c lo th f in is h e f f e c t s fa tig u e s tr e n g th .

U sin g t h e f a t i g u e s t r e n g t h a t

t e n m i l l i o n c y c l e s , t h e r a t i o o f f a t i g u e s t r e n g t h o f a l l la m in a te s t o
s ta tic

f l e x u r a l s t r e n g t h i s 24 p e r c e n t .

8

P r e s e n t Use o f R e in fo r c e d P l a s t i c s
One o f t h e many a p p l i c a t i o n s o f r e in f o r c e d p l a s t i c s i s

in sa n d ­

w ic h c o n s t r u c t io n w h ich c o n s i s t s g e n e r a ll y o f a lo w d e n s it y c o r e w ith
g l a s s r e in f o r c e d p l a s t i c s u r f a c e s •

P a n e ls b u i l t i n t h i s manner a r e

u se d p r im a r ily a s non lo a d b e a r in g w a lls in s t r u c t u r e s , a s r e f r i g e r a t o r
w a l l s and o th e r i n s t a l l a t i o n s w here t h e i r e x c e l l e n t i n s u l a t i n g q u a l i t i e s
a r e i n demand and a s p a n e ls in a i r c r a f t , tr u c k t r a i l e r and b o a t h u l l
d e s ig n ( l l , 1 2 )*
T here has b een e x t e n s i v e u se o f r e in f o r c e d p l a s t i c p a n e ls f o r
l i g h t i n g and d e c o r a t iv e p u rp o ses in home and com m ercial c o n s t r u c t io n *
R e ce n t u s e s o f t h e s e p a n e ls or fo r s im i la r la m in a te s in c lu d e s

p a n e ls

f o r g e o d e s ic dome c o n s t r u c t i o n , s m a ll b o a t d e s ig n , and radome c o n s tr u c ­
tio n *

Epoxy r e s i n la m in a te s a r e b e in g u sed i n K e lle r m odel c o n s t r u c t io n

f o r th e a u to m o tiv e t o o l and d ie in d u s t r y (1 9 )*
A 'new* hou se c o -s p o n s o r e d by MIT and M onsanto C hem ical Company
h as b een b u i l t i n w h ich t h e f l o o r s e c t i o n s a r e h o llo w g ir d e r s c o n s i s t i n g
o f an o u te r m olded p o r t io n and an in n e r f l a t s e c t i o n *

Woven r o v in g

r e in f o r c e d p o ly e s t e r r e s i n la m in a te i s u sed fo r t h e s u r fa c e s k in s *
D ietar, e t a l ( 1 4 ) , i n r e p o r t in g t h e p r o j e c t , in d i c a t e a w orking s t r e n g t h
o f 50 p e r c e n t o f u lt im a t e s t a t i c s t r e n g t h was u sed i n d e s ig n o f th e
h o u se c o m p o n en ts.

S in c e t h e d e s ig n was f a i r l y c a m p le s, f u l l s c a l e

p r o to t y p e s o f p o r t io n s o f th e hou se w ere b u i l t and t e s t e d *

F u l l d e s ig n

lo a d h e ld on t h e f l o o r f o r s i x weeks produced no a p p r e c ia b le c reep *
The s t r u c t u r e r e a c te d a s d e s ig n c a l c u l a t i o n s had p r e d ic te d *
G la ss r e in f o r c e d epoxy r e s i n p a r a b o lic r e f l e c t o r s show no c r e e p
or d i s t o r t i o n a f t e r t h r e e y e a r s s e r v i c e

(2 0 )*

S u c c e ssfu l f u l l s c a le

t e s t s on g l a s s r e in f o r c e d p o ly e s t e r r e s i n s p h e r ic a l radomes o f 2 1 , 3 1 ,

9

and 55 f e e t e q u a t o r ia l d ia m e te r h a v e b een co n d u cted and th e radomes a r e
now i n s e r v i c e under a r c t i c c o n d it io n s *

The 21 f o o t radome i s m olded,

t h e 31 f o o t and 55 f o o t radomes a r e b u i l t o f s t i f f e n e d t r ia n g u l a r p a n e ls *
The s t r u c t u r e s r e a c t e d w it h in th e a c c e p ta n c e l i m i t s e s t a b l i s h e d from
s t r u c t u r a l a n a l y s i s and p r e lim in a r y t e s t s

(ll)*

Frame A n a ly s is
Most t e x t s : on in d e te r m in a te s t r u c t u r e s p r e s e n t one or more
methods

f o r a n a ly z in g r i g i d fram es*

I n a l l c a s e s u se i s made o f t h e

d is p la c e m e n t c h a r a c t e r i s t i c s o f t h e s t r u c t u r e t o p ro v id e t h e e q u a tio n s
n e c e s s a r y f o r s o lu t io n *

The most b a s ic method i s t h a t known a s V ir t u a l

Work or E l a s t i c E nergy*

I n fram e a n a l y s i s , when th e d e fo r m a tio n i s

p r im a r ily f l e x u r a l , t h e e n e r g y due t o sh ea r and a x i a l s t r e s s e s i s
g e n e r a ll y ig n o r e d a s i t s c o n t r ib u t io n i s a v e r y sm a ll p e r c e n ta g e o f t h e
t o t a l e l a s t i c en e rg y o f th e s t r u c t u r e ( 4 , 5 )*
Model A n a ly s is
A m odel i s a d e v ic e w h ich i s s o r e l a t e d t o a p h y s ic a l sy stem
t h a t o b s e r v a t io n s on t h e m odel may be u sed t o p r e d ic t th e fu tu r e p er­
form ance o f th e p h y s ic a l sy ste m i n a g iv e n r e s p e c t (2 )*

In many eng­

in e e r in g problem s i t becom es a d v a n ta g e o u s , e v en n e c e s s a r y a t t im e s , t o
u se m odels t o p r e d ic t perform ance o f a p h y s ic a l s y s te m .

A c c u r a te p r e ­

d i c t i o n s can be made i f th e p r i n c i p l e s o f m odel th e o r y and s i m i l i t u d e
a r e em ployed c o r r e c t l y .

The P r e d ic t io n E q u a tio n
A d e p e n d a b le p r e d i c t i o n e q u a t i o n c a n b e s t
th e

u se o f d im e n sio n a l a n a ly s is *

be o b ta in e d th ro u g h

The d evelopm ent o f th e id e a o f dim en-

s i o h a l a n a l y s i s has b e e n a t t r ib u t e d g e n e r a ll y t o Buckingham and
10

Bridgem an*

The th eo rem i s d e v e lo p e d from a c o n s i d e r a t io n o f th e dim en­

s io n s i n w h ich ea ch o f t h e p e r t in e n t q u a n t i t i e s i n a phenomena e x i s t *
I n g e n e r a l, g iv e n a s e t o f p h y s ic a l q u a n t i t i e s w h ich d e s c r ib e
a phenom ena, a s e t o f d im e n s io n le s s and in d ep en d en t term s c a n be
e s t a b l i s h e d b y a c o m b in a tio n o f d im e n s io n a l a n a l y s i s and t h e Buckingham
P i th eorem *

The Buckingham P i th eorem s t a t e s t h a t th e number o f dim en-

s i o n l e s s and in d ep en d e n t q u a n t i t i e s r e q u ir e d t o e x p r e s s a r e l a t i o n s h i p
among th e v a r i a b l e s i n any phenomena i s e q u a l t o th e number o f quan­
titie s

in v o lv e d m inus t h e number o f fu ndam en tal d im en sio n s i n w h ich

t h e s e q u a n t i t i e s may be e x p r e s s e d *

In e q u a t io n form s r = n - a , where

r i s t h e number o f P i te r m s , n i s th e number o f q u a n t i t i e s and a i s
t h e number o f fu n d am en tal d im en sio n s in v o lv e d *

A problem i s g e n e r a ll y

s e t up su ch t h a t one P i term i s e x p r e s s e d as a f u n c t io n o f th e rem ain­
in g te r m s , i . e . ,

TTj

= F(TT2 , TT^ ,***TT ) •

The o n ly

r e s t r i c t i o n s p la c e d on t h e P i term s are t h a t th e y be d im e n s io n le s s
and in d ep en d en t*

A g e n e r a l p r e d i c t io n e q u a tio n in v o lv e s d e te r m in in g

t h e r e l a t i o n s h i p b e tw e en t h e P i term s a s e x p r e s s e d a b o v e .
A g e n e r a l th e o r y o f m od els c a n be d e v e lo p e d b y e x t e n s i o n o f th e
e q u a t io n g iv e n a b o v e .

The e q u a t io n fo r th e p r o to ty p e i s
IT,

= F(Tr2 ,T T g , • • • Trr )

C l)

S in c e t h i s e q u a t io n i s p e r f e c t l y g e n e r a l i t c a n be a p p lie d t o
any o th e r s im ila r p h y s ic a l system *
m odel o f th e p r o t o t y p e .

Hence i t a p p lie s i n p a r t ic u l a r t o a

Thus
(2 )

An e q u a t io n f o r p r e d ic t in g TTj

tr<m i r |in c a n be m ost s im p ly

o b ta in e d b y d iv i d in g e q u a t io n ( l ) by e q u a t io n (2 )*

11

TT|
^Im

FCTTg ,T T 3 , • • • TTr )
F(lT2irt>1T3m ' ' ‘ ‘ ^ rm *

Now, i f t h e m odel i s d e s ig n e d su ch t h a t

"^2 8 "^2m’

*^3 “ ^ 3 m 1

(3 )

5 ^ rm

th e n
U)
T h e re fo r e

E q u a tio n ( 5 ) becom es t h e p r e d ic t io n e q u a tio n fo r th e sy ste m and
must be v a l i d i f e q u a tio n s ( 3 ) (known a s th e d e s ig n and o p e r a tin g c o n d i­
t i o n s ) a re s a t i s f i e d .
I f a l l t h e d e s ig n c o n d it io n s are s a t i s f i e d , th e m odel i s s a id
t o be

a ‘t r u e 1 m o d e l.

If a ll

th e d e s ig n c o n d it io n s a r e n o t s a t i s f i e d ,

th e b e h a v io r o f th e m odel may be d i s t o r t e d w ith r e f e r e n c e t o th e f a c t o r s
in c lu d e d i n t h e c o r r e sp o n d in g P i term s and th e p r e d ic t io n e q u a t io n may
be a f f e c t e d m a t e r i a l l y .
In g e n e r a l, t h e d e s ig n c o n d it io n s w i l l in v o lv e d is t a n c e s i n d i c ­
a t i v e o f th e s i z e o f m odel and p r o t o t y p e .

The r a t i o o f a g iv e n d is t a n c e

on th e p r o to ty p e t o th e c o r r e sp o n d in g d is t a n c e on t h e m odel i s known a s
th e le n g t h s c a l e and i s d e s ig n a te d a s n .

L =

S t r u c t u r a l m od els
S t r u c t u r a l m odels a r e g e n e r a ll y c o n s tr u c te d fo r th e purpose o f
s tu d y in g b e h a v io r under l o a d .
o f r e s is ta n c e t o f a i l u r e .

The b e h a v io r i s th e n e v a lu a te d i n term s

T h e r e fo r e , t h e problem i s one o f e v a lu a t in g

d e f l e c t i o n and s t r e s s .
12

D e f l e c t i o n s and s t r e s s e s a r e f u n c t io n s o f ( l ) g e o m e try , ( 2 ) lo a d s
and r e s t r a i n t s , and ( 3 ) p r o p e r t ie s o f th e m a t e r ia l*

The e f f e c t o f two

r e s u l t a n t f o r c e s on a s h o r t le n g t h o f a s t r u c t u r a l member i s

one or more

o f th e f o llo w in g *
1*

a x i a l t e n s i o n or c o m p r e ss io n ,

2*

cross sh ea r,

3*

to r s io n ,

4•

b en d in g •

The r e sp o n se o f t h e member t o th e a c t i o n o f t h e s e f o r c e s i s a
f u n c t io n o f t h e geom etry and p r o p e r t ie s o f t h e m a t e r ia l*

For exam p le,

i f a member i s s u b je o te d t o b e n d in g , t h e p r in c ip a l moments o f i n e r t i a
and d is t a n c e s from th e n e u t r a l a x is are t h e im p o rta n t g e o m e tr ic c h a r a c ­
t e r i s t i c s , w h ile t h e m o d u li o f e l a s t i c i t y and some m easure o f f l e x u r a l
s t r e n g t h are t h e r e q u ir e d p r o p e r t ie s o f m a t e r ia l*
A tr u e s t r u c t u r a l m odel i s e x p e c te d t o g iv e a c c u r a te in fo r m a tio n
ab ou t s t r e s s and d e fo r m a tio n *
F r e q u e n tly i t i s n ot p o s s ib l e t o s a t i s f y a l l t h e d e s ig n c o n d i­
t i o n s f o r a tr u e m odel*

A m odel so d e s ig n e d t h a t one or more o f th e

d e s ig n or o p e r a tin g c o n d it io n s i s n o t s a t i s f i e d i s known a s a d i s t o r t e d
m odel*

D i s t o r t i o n may e x i s t i n any one or a c o m b in a tio n o f t h e t h r e e

p r in c ip a l f a c t o r s in v o lv e d i n s t r u c t u r a l a n a l y s i s , v i s * , s t a t i c s , geom©"fcry, and p r o p e r t ie s o f t h e m a t e r ia l*

The p r e d ic t io n e q u a tio n f o r a

d i s t o r t e d m odel may be e s t a b l i s h e d by d e te r m in in g a p r e d ic t io n f a c t o r

S

su c h t h a t

1 Ii * & l r lm
Murphy ( 2 ) g iv e s p r e d ic t io n f a c t o r s fo r s t r e s s and d e f l e c t i o n
b a se d on t h e fo u r b a s ic t y p e s o f lo a d in g *

13

The p r e d i c t i o n f a c t o r ,

S

,

i s g iv e n i n term s o f a d i s t o r t i o n f a c t o r

•

V a lu e s o f

8

a r e g iv e n

f o r e x a c t , p a r t i a l , and no s i m i l a r i t y o f c r o s s s e c t i o n b e tw e en m odel
and p r o t o t y p e .

14

THE INVEST IG&TION

P r e lim in a r y C o n s id e r a tio n
The r e v ie w o f l i t e r a t u r e i n d i c a t e s u se o f r e in f o r c e d p l a s t i c s
i n many a r e a s w it h a g r e a t d e a l o f s u c c e s s *

H ow ever, w ith a few e x c e p ­

t i o n s , t h e i r u s e i n b u ild in g c o n s t r u c t io n has b e e n l i m it e d t o c o r r u g a te d
or f l a t s h e e t s a s w a l l s and r o o f p a n e ls fo r l i g h t a n d /o r a r c h i t e c t u r a l
e f f e c t , or a s s k in s i n san d w ich c o n s tr u c tio n *
A s a g u id e t o a f i n a l c h o ic e o f s t r u c t u r a l shape and c r o s s s e c t i o n , th e f o ll o w i n g p o in t s were c o n s id e r e d ;

The form sh o u ld

1*

p r o v id e c l e a r sp a n fo r optimum f l o o r and sp a ce u t i l i z a t i o n ,

2*

p erm it pre f a b r ic a t i o n ,

3*

p r o v id e s k in and frame as an i n t e g r a l u n i t , and

4*

a llo w c o n v e n ie n t b u ild in g ex p a n sio n *

U sin g t h e g u id e p o in ts l i s t e d , a r i g i d frame v/as d e s ig n e d a s
shown i n F ig u r e 1*
farm b u ild in g s *

The f o r t y f o o t span was c h o s e n as b e in g maximum fo r

T en f o o t s id e w a lls sh o u ld be ample f o r m ost a p p l i c a t i o n s ,

A lo n g r a d iu s was u se d t o h o ld head room t o a minimum and s t i l l a llo w
w a te r t o move o f f th e s u r fa c e *

The frame c a n be e r e c t e d on c o n c r e te pad

f o o t i n g s w it h sim p le anchor s t r a p s and b a c k f i l l p r o v id in g a d eq u a te fou n ­
d a t io n su p p o rt*
The m o d ifie d T c r o s s - s e c t i o n p e r m its th e c o n s t r u c t io n o f th e
s k i n and fram e a s an i n t e g r a l u n it *

The a d h e s iv e q u a l i t i e s o f th e r e s i n s

p r o v id e a s tr o n g w eld b e tw e en stem and f l a n g e , p e r m ittin g th e s e c t i o n
t o a c t a s a u n it *

Expanded p o ly s ty r e n e a c t s i n th e d u a l r o l e o f s t i f -

fe n e r and i n s u l a t o r •

The 24 in c h w id th o f s e c t i o n w i l l a llo w b u ild in g
15

r

LAYOUT

jixpanded p o l y s t y r e n e
Glass c l o t h r e in fo r c e d
p l a s t i c r e s in lam inate

r i p ar e 1.

L a y o u t a no c r o ' s s - s e c t i o n o f e x p e r i m e n t a l r i ^ i a f r a me o f p^lass
c l o t h r e i n f o r c e a p l a s t i c r e s i n l a m i n a t e s snu expanded p o l y s t y r e n
Gee T a o l e 2 f o r d i m e n s i o n s of p r o t o t y p e and r r o a e l s .

16

e r e c t i o n i n in c r e m e n ts .

A d ja c e n t u n i t s c a n be f a s t e n e d t o g e t h e r e i t h e r

b y u s e o f a r e s i n and g l a s s c l o t h b a t t e n on t h e j o i n t or by u s in g m a s tic
i n th e j o i n t and f a s t e n e r s ( b o l t s , r i v e t s , e t c . ) a t i n t e r v a l s a lo n g t h e
common e d g e .

The r e s i n - c l o t h b a t t e n w ould p r o v id e a perm anent w a te r ­

tig h t jo in t.

Frame A n a ly s is
The fram e a n a l y s i s was made u s in g t h e method o f V i r t u a l Work.
F ig u r e 2 i s a d e f i n i t i o n s k e tc h fo r e s t a b l i s h i n g g e o m e tr ic r e l a t i o n s h i p s
u sed in th e a n a ly s is .
The fram e i s in d e te r m in a te t o t h e f i r s t d e g r ee s o t h e h o r iz o n t a l
r e a c t i o n com ponent a t A i s c h o se n a s t h e r e d u n d a n t.

The problem becom es

one o f d e te r m in in g X^ su c h t h a t t h e h o r iz o n t a l d is p la c e m e n t a t A i s e q u a l
to zero.
W ith a v i r t u a l u n it lo a d a c t in g h o r i z o n t a l l y a t A i n th e d i r e o t i o n o f X^, F ig u r e 3 o , th e d is p la c e m e n t due t o t h e u n ifo rm lo a d 1w*
p lu s th e d is p la c e m e n t due t o th e u n it lo a d , i s made e q u a l t o z e r o .
J fm ^ /fe ljd s

+ X^

m ^ds/tel

(1)

i n w h ich t h e i n t e g r a l s a r e e v a lu a te d o v er t h e e n t i r e fra m e.
R e fe r r in g t o F ig u r e s 3c and 3 d , th e f o llo w in g moment e q u a tio n s
ap p ly*
For t h e colum ns i n th e red u ced s t r u c t u r e ;
\

*

0,

m -= y .

For th e beam , from t h e end t o th e c e n t e r ;
My; = -w L x/2 + w x 2 /2 ,
T h e r e fo r e , t h e i n t e g r a l s above becom e;

17

m = h + y.

(x s 0

to

x = L /2 ) ;

w #/f+

x = d i s t a n c e fr^m the o u t s i d e o f
trie l e g to-ward the c e n t e r o f
the span.
x = l/ 2 - r sine*; cos© + r c o s ^ s in ©
y — distance
c o l urn.

.A
rrrrj

from trie top o f the

y = r co3s(cose + r sin«(sin£ +• D
r = r a d i u s of c u r v a t u r e o f the
beam.
D = y0 “ r

y ^ ~ t o t a l r i s e of the r o o f .
h = h e i g h t o f the column.
°< - o n e - h a l f the c e n t r a l a n g l e .

9 = variable angle.
610 = increment in ©.
ds * r d© , arc l e n g t h a l o n g the
be am•
w = i n t e n s i t y o f the u n if o r m ly
d i s t r i b u t e d lo a d on the aeam
in # / f t o f beam, l e n g t h .
L/2 = o n e - h a l f th e span.
( A l l l e n g t h s are in f e e t , a n g l e s
in ra di ans )

Figure 2.

D e f i n i t i o n s k e t c h f o r the frame a n a l y s i s .

18

w # /ft

w #/ft
L _L

c

Xa

O riginal structure
(a )

Reduced s t r u c t u r e
(*}

a J c -^
im

jLr

Moment d i s t r i b u t i o n on the r ed uc ed s t r u c t u r e due to a u n i t lo a d a p p l i e d
at A.
(c)
w # /ft
L

Moment d i s t r i b u t i o n on the red uced s t r u c t u r e due to a u n i f o r m l y d i s t r i ­
buted load.
(*)

F i n a l moment d i s t r i b u t i o n on the frame.
(e )
Figure 3 .

Load and moment diagrams f o r s o l u t i o n o f the r i g i d frame.

19

2 rw /E I

r*

J
(-L h x /2 -V h x 2 /2 - Lyx/2 ■¥ x 2 y /2 )d© +
°
<*
♦ 2Xj1>r / t e l J
(h 2 + 2hy + y 2 )d0 = 0
o

2 ^ /f e I

>

I
S

y2dy
(2 )

S u b s t i t u t i n g t h e proper e x p r e s s io n s f o r x , y , h , and r ( g iv e n
i n F ig u r e 2 and T ab le 2 ) i n t o e q u a tio n ( 2 ) and p erfo rm in g th e i n t e g r a t i o n ,

% =

1 1 .2 ti#

(3 )

The moment a t th e j u n c t i o n o f beam and colum n i s th u s 1 1 2 i # - f t ,
and a t t h e crow n , -65.6w jj£-ft •

The maximum s t r e s s w i l l be a t t h e j o i n t ;

t h e r e f o r e , w it h a d e s ig n lo a d o f 6 < # / f t o f beam and u s in g th e c r o s s s e c t i o n shown i n F ig u r e 1 , (d im e n sio n s from T ab le 2 ) , t h e s t r e s s i n th e
o u te r f i b e r s o f th e stem w i l l be 1 2 ,5 0 0 p s i .
s t r e n g t h v a lu e s l i s t e d
tic s .

T h is i s w e l l b elo w th e

i n T ab le 1 a s t y p i c a l f o r g l a s s r e in f o r c e d p l a s ­

A ssum ing maximum c o m p r e ssiv e s t r e n g t h o f 3 0 ,0 0 0 p s i , t h i s w ould

p r o v id e a s t r e s s f a c t o r o f s a f e t y o f 2 . 5 .
fo r t h e frame i s

shown i n F ig u r e 3 e .

The f i n a l moment d i s t r i b u t i o n

I n a frame su ch a s t h i s o n e , th e

e n e r g y due t o sh e a r and a x i a l lo a d in g i s v e r y s m a ll compared t o b en d in g
e n e r g y ; t h e r e f o r e , t h e i r e f f e c t s w ere ig n o r e d i n th e a n a l y s i s .
From th e p r e lim in a r y a n a ly s is i t became a p p a ren t t h a t th e con ­
s t r u c t i o n o f 4 0 f o o t sp an fram es w ould r e q u ir e c o n s id e r a b le amounts o f
m a t e r ia ls and r e p r e s e n te d a la r g e in v e stm e n t i n fu n d s f o r m a t e r ia ls and
c o n s t r u c t io n l a b o r .

T h e r e fo r e , t o red u ce th e c o s t fo r t e s t fr a m e s, a

m odel a n a l y s i s was c o m p le te d w h ich a llo w e d t e s t i n g th e h y p o th e s is a t
l e s s ex p e n se e v e n th o u g h tw o m odels w ere r e q u ir e d t o v a l i d a t e th e a n a l y s i s .

20

TABLE 2
IAYOUT AND CROSS-SECTION DIMENSIONS OF
THE FRAME AND THE MODELS
.m .Lii

I . 111 J -1 .............. ■ • i . "f". I

«-*

D im en sio n
S tru ctu re

L
(ft)

g
(ft)

h
(ft)

r
(ft)

b
(in )

d
e
c
(in ) (in ) (in )

Frame

40

2

10

100

24

1 .5

Model
E 025050

10

0 .5

2 .5

25

12

0 .7 5 4 .3 8

E 025100

10

0 .5

2 .5

25

24

1 .5

P 025050

10

0 .5

2 .5

25

12

F 025100

10

0 .5

2 .5

25

24

1 .5

8

t
(in )

(in 4 ) (in )
6 .2

4

0 • 125

40

2

(1 )

3 .0 3

3 .3 8

3 5 .9 0

5 .5 5

0 .7 5 3 .7 5 2 .1 3

4 .1 3

2 .8 2

7 .7 0 4 .1 9

4 4 .2 9

5 .6 6

8

4

(-l-)See F ig u r e 4 fo r la m in a te t h ic k n e s s o f th e m odels#
Model A n a ly s is
The m odel a n a l y s i s in v o lv e s c h o ic e o f la y o u t and c r o s s - s e c t i o n
s c a l e s , m a t e r ia l t o be u s e d , and d e v e lo p in g p r e d ic t io n e q u a tio n s fo r th e
d e s i r e d phenomenon*
The f i r s t s t e p i s t o d e v e lo p p r e d i c t i o n e q u a tio n s fo r s t r e s s
and d e f l e c t i o n o f t h e m o d e ls , t h e tw o f a c t o r s w hich b e s t d e s c r ib e th e
a c t i o n o f a s t r u c t u r a l member under lo a d *

T h is i s done u s in g t h e d e v e l­

opment p r e s e n te d i n th e l i t e r a t u r e r e v ie w .

P r e d i c t i o n E q u a tio n fo r S t r e s s
The v a r ia b le s and t h e i r r e s p e c t i v e d im en sio n s t o be c o n s id e r e d
are I

21

V a r ia b le s
s

x str ess

L

= le n g t h o f sp an

D im en sio n s
F-L”2
L

A * any le n g t h ( l a y o u t )

L

= an y le n g t h ( c r o s s - s e c t i o n )
w

* l o a d / f o o t o f beam

E

s m odulus o f e l a s t i c i t y

From t h i s

L
F-L“l

in te n s io n

s x f(L ,

w,

F-L~2
E)

There a re s i x v a r i a b l e s and tw o fu ndam en tal q u a n t i t i e s ; t h e r e ­
f o r e , t h e r e w i l l be
TT1 =

6 -2

sL /w ,

= 4

TT2

P i term s*

=

V l,

TT3

=

rJ/L,

TT4

= w/EL

or

“" i

s

tt2

,

tt3

,

tt4

)

The same term s a p p ly t o th e m odel*
*^lm

“

s m'^‘W /win*

"^lm

“

^2m '

*^*2m

“

^m /^m *

"^*3m ”

and
"^3ma

The d e s ig n c o n d it io n s becom e;
V .

*W

VL

a

V * *

The o p e r a tin g c o n d it io n s a r e ;
■w/fcL = l y ^ , ^
And th e p r e d ic t io n e q u a tio n fo r s t r e s s i s
sL /w

= s mLn/w m

22

*^*4m= wra/^

P r e d i c t i o n E q u a tio n f o r D e f l e c t i o n
V a r ia b le s

D im en sio n s

d

= d e fle c tio n

L

L

= le n g t h o f sp an

L

X = any le n g t h ( la y o u t )

L

= any le n g t h ( c r o s s - s e c t i o n )
w

= l o a d / f o o t o f beam

B

s m odulus o f e l a s t i c i t y

From t h i s

d a f(L ,

L
F-L“ ^

i n b en d in g

X,

w,

F-L"^

E)

A g a in t h e r e a r e s i x v a r i a b le s and tw o fu n d am en tal q u a n t i t i e s ;
th e r e fo r e * t h e r e a r e
TTj

“

6 - 2 = 4
TT2

P i term s •

fyh,

=

TTg

=

TT4 = w A L

and fo r th e m o d e l,
^ lm ~

*^2m

s

*^3m "

^*4m “ ^W^m^m

The d e s ig n c o n d it io n s are*
h /L

=

X „ A i.

\A >

* ^nA a

The o p e r a tin g c o n d it io n s a r e ;
W/& L s " j A A a
And t h e p r e d i c t i o n e q u a t io n fo r d e f l e c t i o n i s
d /li

-

The d e s ig n c o n d it io n s in d i c a t e t h a t th e m odel and p r o to ty p e
s h o u ld be g e o m e t r i c a lly s im ila r and th e o p e r a tin g c o n d it io n s g iv e th e
lo a d r e l a t i o n s h i p .
A le n g t h s c a l e o f fo u r was u s e d , or L * 4 1 ^ .

T h is s c a l e was

s a t i s f a c t o r y f o r la y o u t b u t i f used f o r th e c r o s s - s e c t i o n w ould r e s u l t
i n a v e r y t h i n s k in w h ich would o a u se d i f f i c u l t y , b o th i n c o n s t r u c t io n
and i n b e h a v io r under lo a d .

T h e r e fo r e , d i s t o r t e d m od els were u s e d ,
23

t h a t i s , t h e c r o s s - s e c t i o n s c a l e d i f f e r e d from th e la y o u t s c a le *
When a d i s t o r t e d m odel i s
e s s e n t i a l l y one a d i s t o r t e d m odel
ord er t o

*prove* th e m odel*

u s e d , t h e r e h a v e t o be tw o m o d els;
o f t h e o th er *

T h is i s n e c e s s a r y i n

I f t h e p r e d ic t i o n e q u a tio n s f o r th e d i s ­

t o r t e d m o d els are p ro v en c o r r e c t , t h e n th e in fo r m a tio n s e c u r e d from th e
t e s t s c a n be a p p lie d w it h c o n fid e n c e t o th e f u l l s c a l e s t r u c t u r e *
For t h e d i s t o r t e d m o d el, th e d e s ig n c o n d it io n s a r e ;

?\/L -

Ajq/Ljjj,

■where £ i s t h e d i s t o r t i o n f a c t o r *
From Murphy ( 2 ) , t h e p r e d ic t io n f a c t o r s fo r s t r e s s and d e f l e c t i o n
c o n s id e r in g b en d in g ty p e lo a d s , a r e ; fo r d is p la c e m e n t,
o(3 *

i s d e f in e d

=

o(4 , fo r s t r e s s ,

o(4 I / n4 , n i s th e le n g t h s c a l e ,

I i s th e

momento f i n e r t i a o f th e c r o s s - s e c t i o n *
T h e r e fo r e , t h e p r e d ic t i o n e q u a tio n s become
(sL/W ) / (sjjjLjjj/Wj^)

=

*3.

(a /L y U n / L n )

=

c<4 .

R e f e r r in g t o t h e o p e r a tin g c o n d i t i o n s ,
w/tSL =
i f t h e same m a t e r ia l i s u se d i n m odel and p r o to t y p e , t h e n
w/ wm = E^ / Em^im ~ ^V^*m = n *
From th e p r e d i c t i o n e q u a t io n fo r s t r e s s
(s/s^CL/Ljn) (wjq/ w )

=

o(3,

s

„

oC3s m.

From t h e p r e d i c t i o n e q u a tio n fo r d e f l e c t i o n
^ /U d n A )

=

<*4 .

d ■ 11 < A i .

The r e l a t i o n s h i p b etw een m odel E 0 2 5 0 5 o (l) and th e f u l l s c a l e
frame

(•^The m odel frame d e s i g n a t i o n . E in d ic a t e s ep o x y r e s i n , th e
f i r s t 3 d i g i t s in d i c a t e la y o u t s c a l e , ( e . g . , 050 s o n e - h a lf s c a l e ) , th e
l a s t 3 d i g i t s i n d i c a t e c r o s s - s e c t i o n s c a l e , ( e . g . , 050 = o n e - h a lf s c a l e ) .
24

n = L/Lj, = 4 ,

O f4 = ( 4 ) 4 d

^ =2 Hm
)4

=

16

<X = 2

Thus*
s as 8Sjjj5

d — 64dj^

The r e l a t i o n s h i p b etw een m odel E 025100 and t h e f u l l s c a le

frame
n - 4,
o<4 = ( 4 ) 4 ( l ) 4 - 256
oC * 4

Thus I
s s 6 4 s m,

d

1024dm

Frame A n a ly s is fo r The Models
The g e n e r a l e q u a tio n s d e v e lo p e d fo r t h e a n a ly s is o f t h e f u l l
s c a l e frame a l s o a p p ly t o t h e m odels*

T h e r e fo r e , th e e x p r e s s io n s f o r

L , h , x , y , and r fo r th e m odel a s in d ic a t e d i n F ig u re 2 and T ab le 2 ,
w ere s u b s t i t u t e d i n e q u a t io n ( 2 ) g iv in g
= 2 .7 w #
Thus th e moment a t m idspan f o r th e m odel i s
XA (h + g ) - wL2 /8

=

-4 .4 w # - f t

The s t r e s s a t m idspan i s
s

= Mj/ I

*

~ 5 2 * 8 w c /l

The d e f l e c t i o n a t th e crow n (m idspan) was e s t im a te d by th e
m ethod

o f V ir t u a l Work. A u n it lo a d was assum ed t o a c t a t th e

t h e d i r e c t i o n o f th e e x p e c te d d is p la c e m e n t*

The

crow n i n

frame i s in d e te r m in a n t

t o th e f i r s t d e g r ee s o a g a in th e h o r iz o n t a l r e a c t i o n a t A was assum ed as
th e red u n d an t t o ta k e ad van tage o f th e p r e v io u s a n a l y s i s .

25

The v a lu e o f

d e te r m in e d due t o

a.

The e q u a t io n

u n i t v e r t i c a l lo a d a c t i n g a t th e

crow n i s 0.445j^*

f o r d e f l e c t i o n a t th e crow n i s

rh
6C -

J*

2 J (m M ^/felJds +

o
From 0 t o h ,

o

= 2 .7 y ,

From 0 t o L /2 ,

2 I (m B ty fc ^ d s

m = 0 .4 4 5 y ,

= 2.7w h + 2.7 w y m

d s^ d y.

(w L /2 )x + (w /2 )x ^ ,

= 0*445h ■+• 0 .4 4 5 y - 0 « 5 x ,

ds = rd©.
C a r ry in g out th e in d ic a t e d o p e r a t io n s , s u b s t i t u t i n g e x p r e s s io n s
f o r x , y and ds a s in d ic a t e d i n F ig u re 2 and g iv e n i n T able 2 , th e
d e f l e c t i o n a t th e crow n i s
dc

=

( 0 . 12x 106

The r e l a t i o n s h i p b etw een th e m odels b u i l t w ith a g iv e n r e s i n ,
u s in g th e c r o s s s e c t i o n d im en sio n s f o r th e fo u r m odels g iv e n i n T a b le 2 ,
and F ig u r e 4 , i s g iv e n i n T able 3*

In th e f o llo w in g d i s c u s s i o n , th e

fram e w ith th e la r g e r c r o s s - s e c t i o n d im en sio n s i s c o n s id e r e d th e m od el,
th e o th e r i s th e p r o t o t y p e .
TABLE 3
MODEL KBIATIOMSKIPS FOR THE DISTORTED MODELS

P o ly e s te r r e s in

E poxy r e s i n
n
o(
s
d

n
«
s
d

« 1
= 1.86
— 6 •4 7 s1Il
= 11.83dm

26

= 1
* 1 .8 1
— 5*968^
= 1 0 ,8dm

to

for

study.

o

cvi

O

00
00

o

*V5

00.

H

8
o
r-l
-UO.

09
'CJ

o

27
LO

o
o

cO

rH

<D
-n
o

o
o

o

o>

C\2
O

LO

3
o
£4

O

lO

o

CO

o
o

r—
I
LO
-a
o
J-V|

o
F-j|

useti in the

<T>

four model*frames

CO

the

See

in

Cross-section dimensions
for layout d i n s n s i o n s .

- -

4.

* +*
CQ

Figure

Table

LO

6\|

E x p erim en tal I n v e s t ig a t io n
T e st F a c i l i t i e s
The f i r s t s t a g e o f th e e x p e r im e n ta l work in v o lv e d t h e c o n s t r u c ­
t i o n o f th e t e s t f a c i l i t i e s *

To f a c i l i t a t e t e s t i n g * a s p e c i a l f l o o r

was c o n s t r u c t e d s o t h a t t h e fram es c o u ld be lo a d e d i n a h o r iz o n t a l p la n e
th r o u g h a s y ste m o f h y d r a u lic c y lin d e r s and lo a d in g sh o e s*

The f l o o r

a s c o n s t r u c t e d i s b a sed on p la n s fo r a s im ila r f l o o r i n u se a t Purdue
U n iv e r s it y *

Minor ch a n g es w ere made t o f i t th e a v a i l a b i l i t y o f sp a ce

and m a t e r ia ls #

F ig u r e 5 i s a sch em a tic diagram o f th e h y d r a u lic s y ste m

u s e d t o a p p ly th e lo a d s *

I fe ils b u i l t up from I beams a r e imbedded i n

t h e f l o o r t o p r o v id e r e a c t i o n s u p p o r t s •

S t e e l c o n c r e te i n s e r t s a re s e t

i n a g r id p a t t e r n i n th e f l o o r t o p r o v id e anchors f o r th e h y d r a u lic
c y lin d e r s *

F ig u r e 7 shows m odel E 025050 under t e s t *

The r e a c t i o n

b r a c e s a r e t i e d t o g e t h e r , i n a d d it io n t o b e in g b o lt e d t o t h e r e a c t i o n
r a i l s , t o r e s i s t th e h o r iz o n t a l t h r u s t o f th e frame*

The w h i f f l e t r e e

arran gem en t o f t h e lo a d in g sh o e s a llo w s lo a d in g i n a p la n e p e r p e n d ic ­
u la r t o th e span*

The in d iv id u a l lo a d in g sh o e s a re 6 in c h e s on c e n t e r ;

e q u iv a le n t t o 2 f o o t on c e n te r lo a d in g on th e f u l l s c a l e frame*

T h is

i s an a c c e p t a b le a p p r o x im a tio n t o a u n ifo r m ly d i s t r i b u t e d l o a d .

The

r e a c t i o n b r a c e s a r e b u i l t h ea v y enough t h a t t h e r e w i l l be no d i s p l a c e ­
ment o th e r th a n t h e d e f l e c t i o n o f th e frame under t e s t .

Model C o n s tr u c tio n
The m odel fram es w ere c o n s t r u c t e d u s in g a h a n d -w e t-la y u p p r o c e s s .
Wood fe m a le m olds w ere b u i l t fo r th e f la n g e c o n s t r u c t i o n .

A fte r con­

s t r u c t i o n o f th e m olds fo r t h e ep o x y r e s i n la m in a t e , t h e y w ere f i r s t
g iv e n a c o a t o f J o h n so n ’ s p a s te w a x .

Then a la y e r o f form r e l e a s e

a g e n t (a p r o p r ie t a r y m ix ) was a p p lie d , a llo w e d t o d r y , and a seco n d
28

Cylinder

P r e s s u r e gaga

P r e s s u r e gage
Giate v a l v e
date

4 -way v a l v e

val/e

Gi©1 i e f va 1 ve

Pump

Figure

5*

S c h e m a t i c diagram o f h y d r a u l i c
o f the model f r a m e s .

29

s y st e m us ed

in l o a d t e s t s

c o a t o f J o h n so n ’ s p a s te wax a p p lie d t o c o m p lete th e mold p r e p a r a tio n *
The m o d ifie d ep o x y r e s i n c o n s is t e d o f a la m in a tin g m ix and
h a r d e n e r w h ich w ere m ixed and a p p lie d w it h a s m a ll p a in t ‘brush*
th e pot l i f e

S in c e

a f t e r m ix in g was o n ly 30 m in u tes a t 7 0 °F , th e r e s i n was

m ixed i n on© p in t b a tc h e s and a p p lie d *

F ig u r e 6 shows t h e m olds and

m a t e r ia ls u s e d t o b u ild t h e f la n g e s e c t i o n s o f m odel E 025050*
The la m in a tin g p r o c e s s c o n s i s t s o f t h e f o llo w in g s t e p s *

(l)

a p p ly a c o a t o f r e s i n t o t h e m old , ( 2 ) p la c e a la y e r o f g l a s s c l o t h
i n t h e m old and work out a l l t h e a i r b u b b les w ith a f l a t p a d d le , ( t h i s
a l s o a s s u r e s a d eq u a te w e t t i n g ) , ( 3 ) a p p ly a n o th er la y e r o f r e s i n ,
p la c e a n o th e r la y e r o f g l a s s c l o t h ,

( 5 ) a p p ly a la y e r o f r e s in *

(4 )
Con­

t in u e th e p r o c e s s u n t i l th e d e s ir e d number o f la m in a tio n s i s o b ta in e d *
As recommended by th e m an u fa ctu rer o f th e r e s i n , a n a ttem p t was made
t o produce a la m in a te a p p r o x im a te ly 50^ r e s i n - 5 ( $ c l o t h by volum e*
The r e s i n r e a c h e s i t s peak exotherm a few m in u tes b e fo r e b e g in n in g t o
g e l*

A t t h i s tim e i t h as t h e c o n s is t e n c y o f w a te r so th e r e i s danger

o f r e s i n s t a r v in g i f t h e la m in a tin g p r o c e s s i s c a r r ie d on t o o r a p i d l y .
T h is o c cu rr e d i n b o th o f t h e ep oxy r e s i n m odels •
t h e f i r s t t o be b u i l t ,

s u f f e r e d th e m o s t.

Model E 0 2 5 0 5 0 , b e in g

The r e s i n c u r e s t o a hard

m ass i n a p p r o x im a te ly 3 ^ h ou rs a t 70<2F and r e a c h e s f u l l s t r e n g t h i n
ab o u t 12 h o u r s .

P r e c a u tio n s must be o b serv ed i n h a n d lin g ep o x y r e s i n

a s r e s i n c o n t a c t w it h th e s k in c a u s e s i r r i t a t i o n and m ild d e r m a t i t i s .
I n c o n s t r u c t io n o f th e m o d e ls, a s so o n as t h e fla n g e was b u i l t
up t o t h e d e s ir e d number la m in a t io n s , th e expanded p o ly s ty r e n e c o r e fo r
th e stem was s e t i n p o s i t i o n and t h e s k in la m in a te d i n p la c e on i t .
E poxy and p o ly s ty r e n e a r e non r e a c t i v e s o t h i s c o u ld be done w ith e a se *
In f a c t , ep o x y r e s i n i s a n a t u r a l a d h e s iv e and p rod u ces a s tr o n g bond
w it h p o l y s t y r e n e .

The stem la m in a te was bonded d i r e c t l y t o th e fla n g e
30

F i g u r e 6*

M a t e r i a l s u s e d i n l a m i n a t i n g w i t h epoxy r e s i n *
( l ) f e m a l e m o ld ,
( 2 ) g l a s s c l o t h , ( 3 ) m o d i f i e d epoxy r e s i n , ( 4 ) r e s i n h a r d e n e r *

Figure 7.

Model E025050 u n d e r s h o r t - t e r m s t a t i c t e s t i n t h e s t r u c t u r e s
t e s t laboratory*

31

la m in a te so th e p o ly s ty r e n e se r v e s o n ly as a s t i f f e n e r and form in th e
core.

The p o ly e sty r e n e board was s e t i n p la ce in th e fla n g e w h ile

th e

r e s i n was s t i l l liq u id t o a llo w a bond t o be produced t o h o ld i t
s e c u r e ly i n p o s i t i o n .
The beam and columns were l a id up s e p a r a te ly , w ith an e x tr a two
f o o t s e c t i o n o f th e column fla n g e produced from which sam ples were cu t
t o p ro v id e d ata fo r e s t a b lis h in g m a te r ia l c o n s t a n t s .
A f te r th e beam and columns were cu r e d , m iter c u ts were made on
th e ends o f th e beam and th e upper end o f th e columns and th e two p a rts
jo in e d by a p p ly in g a r e s i n - c l o t h scab t o th e j o in t alon g th e stem and
over th e o u ts id e o f th e f la n g e .

A g u s s e t p la te was s e t in th e j o in t t o

a llo w th e e n t ir e w id th o f th e fla n g e t o ca rry load around th e corn er
from th e beam in t o th e colum n.
The c o n s t r u c t io n o f th e p o ly e s t e r m od els was e s s e n t i a l l y th e
same a s f o r t h e e p o x y r e s i n e x c e p t fo r th e r e s i n m ix t u r e .

F ig u re 8

shows th e v a r io u s s t a g e s i n th e c o n s t r u c t io n o f m odel P 0 2 5 0 5 0 .

The

p o l y e s t e r r e s i n p r e p a r a tio n in v o lv e s more m a t e r ia ls and t h u s , from t h a t
p o i n t , i s n o t a s c o n v e n ie n t t o use as th e ep oxy; h o w ev er, i t i s non
t o x i c t o th e s k i n .

A n oth er a d van tage t o th e p a r t ic u la r fo r m u la tio n o f

p o l y e s t e r w h ich was u se d i s i t s t r a n s lu c e n c y w h ich allo w s one t o s e e a i r
b u b b les i n t h e la m in a te and t h e r e f o r e work them o u t .

In w e ld in g th e

tw o p ie c e s o f c u r e d la m in a te i t i s n e c e s s a r y t o rou gh en t h e s u r f a c e s
s l i g h t l y w it h f in e sand paper or emery c l o t h and c le a n them th o r o u g h ly
w it h a lc o h o l i n order t o in s u r e developm ent o f ad eq u ate b o n d .

P o ly e s te r

r e s i n w i l l d i s s o l v e th e expanded p o ly s ty r e n e ; t h e r e f o r e , i t was n e c ­
e s s a r y t o a p p ly a la y e r o f epoxy r e s i n on th e stem c o r e s b e fo r e c o v e r ­
in g them w ith th e p o ly e s t e r r e s i n - g l a s s c l o t h la m in a te .
In a l l la m in a tin g w ork, c a r e must be e x e r c is e d t o m a in ta in c l e a n
32

33

F ig u r e 8*

M a te r ia ls and p roced u res u sed in c o n s t r u c t io n o f m odel
P025050.

a*

M a t e r ia ls u se d i n la m in a t in g w it h p o l y e s t e r r e s i n .
( l ) fe m a le m o ld , ( 2 ) g l a s s c l o t h , ( 3 ) s u r f a c e r e s i n ,
(4 ) in t e r io r r e s i n , (b ) th ix o t r o p ic a g e n t, (6 ) c o b a lt
n a p th a n a te a c c e l e r a t o r , ( 7 ) M3K p e r o x id e c a t a l y s t .

b.

F in is h e d f la n g e s b e f o r e rem o v in g from t h e m o ld .

c.

C om p leted beam and cojum n s e c t i o n s rem oved from t h e m o ld .
The c o r e o f t h e ste m i s exp an d ed p o l y s t y r e n e .

d.

Frame s e c t i o n s w it h m it e r c u t s f i t t e d and h e ld i n p o s i t i o n
f o r w e ld in g *

e.

C om p leted m odel P 0 2 5 0 5 0 under lo n g - t e r m lo a d t e s t .

F i g u r e 8#

M a t e r i a l s and p ro c e d u re s used in c o n s t r c t i o n
34

of n o d e l P 0 2 5 0 5 0 .

g,\

(d)

urn
f f i i| j

(e)

Figure 8.

M aterials

an d p r o c e d u r e s u s e d i n c o n s t r u c t i o n

35

o f model P 0 2 5 0 5 0

m old s w ith, a good c o v e r in g o f wax b e fo r e a p p ly in g any r e s i n * W ith t h e s e
p r e c a u t io n s , th e cu r ed la m in a te ca n be s t r ip p e d from th e mold w ith e a s e *
In s trum e n t a t i on
To c h e c k a d eq u acy o f a s t r u c t u r a l d e s ig n some m easurem ent o f
e i t h e r s t r e s s or d is p la c e m e n t or b o th sh o u ld be made*

As d e v e lo p e d i n

t h e m odel a n a l y s i s , m easurem ents o f b o th phenomena i s r e q u ir e d t o ch eck
th e a n a l y s i s *

D e f l e c t i o n s a r e c o n v e n ie n t ly and a c c u r a t e ly m easured

u s in g d i a l in d ic a t o r s *

S t r e s s can n ot be m easured d i r e c t l y but must be

o b ta in e d by m ea su rin g s t r a i n and r e l a t i n g s t r a i n t o s t r e s s th ro u g h known
s t r e s s - s t r & i n r e l a t i o n s h i p s fo r th e m a t e r ia l*

E le c t r ic r e s is ta n c e s t r a in

g a g e s , s e n s i t i v e t o s m a ll changes i n s t r a i n , a r e e a s i l y m ounted, and
f o r s t a t i c s t r a i n s , r e q u ir e o n ly sim p le in d ic a t i n g in str u m e n ts*

A d ia l

in d i c a t o r was u se d i n th e t e s t s t o m easure d e f l e c t i o n a t th e crow n,
w it h a n in d ic a t o r on th e o u t s id e o f each colum n t o in d ic a t e any l a t e r a l
movement o f t h e fram e •
Type A - l , SR-4 e l e c t r i c

r e s i s t a n c e s t r a i n g a g es w ere mounted on

th e o u te r s u r fa c e o f t h e f la n g e

and stem a t th e crow n and on one colum n

t o p r o v id e s t r a i n m easurem ent a t tw o p o s it io n s on th e frame*

A Young

s t r a i n in d i c a t o r was u sed t o in d ic a t e th e s t r a i n s se n se d by th e g a g es*
Two f le x u r e sam ples (one from e a c h r e s i n la m in a te ) were p re­
pared f o r la b o r a t o r y t e s t i n g w ith Type A - l , SR-4 ga g es mounted on them
t o ch eck t h e r e s p o n s e o f SR-4 g a g es on t h e la m in a te s*

The tw o sp ecim en s

w ere lo a d e d i n th e same manner a s th e sam ples u se d t o d eterm in e th e
e l a s t i c m o d u li.

A ch eck o f s t r e s s v e r s u s lo a d in d ic a t e d maximum

d i f f e r e n c e o f 2% b etw een s t r e s s e s in d ic a t e d by SR-4 g a g es
tr a n sd u c e r .

The r e s u l t s o f t h e

i n t h e fo r c e

t e s t s a r e shown i n F ig u re 9*

36

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D e te r m in in g M a te r ia l C o n sta n ts
V a lu e s fo r th e d i f f e r e n t m od u li o f e l a s t i c i t y and maximum
s t r e n g t h s f o r t h e la m in a te s l i s t e d i n T able 1 w ere u se d i n t h e o r i g i n a l
d e s ig n c a l c u l a t i o n s f o r t h e fra m e.

To ch e ck b o th th e q u a l i t y o f lam­

in a t e produced and th e d e s ig n p r e d i c t i o n s , i t was n e c e s s a r y t o d eterm in e
t h e m a t e r ia l c o n s t a n t s fo r ea ch r e s i n la m in a te u se d i n th e p r o j e c t *
T h e r e f o r e , sam p les f o r d e te r m in in g b en d in g and t e n s i o n m o d u li and
s t r e n g t h s w ere c u t from t h e e x c e s s fla n g e la m in a te o f ea ch m a t e r i a l .
The t e s t sam ples w ere p rep ared and t e s t e d a c c o r d in g t o ASTM d e s ig n a ­
tio n s

(l),

ASTM d e s ig n a t io n D63 8 - 52T was u sed f o r th e t e n s i o n s p e c ­

im ens and ASTM d e s ig n a t io n D790-49T was u sed f o r th e b en d in g sp ecim en s*
The t e n s i o n t e s t s w ere c a r r ie d out u s in g a Baldwin-Em ery S R -4,
Model FGT, u n i v e r s a l t e s t i n g machine fo r a p p ly in g th e lo a d s and a
T in iu s - O ls e n s u b s iz e s t r a i n gage (one in c h gage l e n g t h ) t o m easure
s tr a in *

A t o t a l o f tw e n ty sam ples were t e s t e d from ea ch r e s i n lam -

i n a t e - 1 0 from ea ch m o d el, w ith 5 p a r a l l e l t o th e warp and 5 p e r p e n d ic ­
u la r t o th e w a rp .
12

R e s u lt s o f th e t e s t s a r e shown i n F ig u r es 1 0 , 11 and

.
The f l e x u r a l t e s t s w ere made u s in g an in stru m en t d e v e lo p e d fo r

d e te r m in in g p h y s ic a l p r o p e r t ie s o f g r a in s ( 3 6 ) ,
t e s t i n p r o g r e s s on an ep oxy r e s i n sp e cim en .

F igure 13a shows a

F ig u r e 13b shows sam ple

d a ta s h e e t s from t h e Brush O s c illo g r a p h u sed t o r e c o r d th e in fo r m a tio n
from th e t e s t s .

The graphs p ro v id e a r e c o r d o f b o th lo a d and d e f l e c ­

t i o n from w h ich modulus and maximum s t r e n g t h v a lu e s c a n be r e a d i l y
com p u ted .

T able 4 l i s t s th e v a lu e s o f E and

p o ly e s t e r r e s i n la m i n a t e s .

38

f o r th e ep o x y and

Figure

10*

Average s t r e s s - s t r a in
laminate.

curves

in tension

parallel

to

the warp

for

epoxy

resin- glas s

cloth

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40

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41
curves

CO

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cloth

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o

in tension

to
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Average~s*&Tess-strain

o

Figure IE*

o

lO

(a)

(b)
( a ) F l e x u r e s amp e fr o m m o d e l E0 25 050 u n d e r t e s t u s i n g t h e
( b ) T y p c i a l o s c i l l o g r a p h c h a r t r e c o r d from
fo rce tran sd u cer
th e fle x u re te s t s *
42

TABI£ 4
MECHANICAL PROPERTIES OP TWO PLASTIC RESIN-GLASS CLOTH
LAMINATES AS DETERMINED PROM SAMPLES TAKEN PROM
THE FIANCE LAMINATES OP THE MODEL FRAMES

R e s in s

Maximum
Maximum
Modulus
Modulus

s t r e n g t h i n b en d in g ( p s i
str e n g th in te n s io n (p si
o f e l a s t i c i t y i n b en d in g
o f e l a s t i c i t y in te n s io n

(^ M o d e l P025100*

x 10”3 )
x 10~3 )
(p s i x 1 0 -6 )
( p s i x 10*“3 )

Epoxy

P o ly e s t e r

2 0 .8
2 1 .9
2 .4
1 .5

23*3
1 7 .3
2 .3
1 . 5( 1 )
1 . 7 (2)

^ M o d e l P025050.

M odel T e s t in g
M odel E 025050 was th e f i r s t frame t o be c o n s tr u c te d and t e s t e d *
No s e r io u s d i f f i c u l t i e s w ere e x p e r ie n c e d i n th e u se o f th e t e s t e q u ip ­
ment and a r o u t in e was e s t a b lis h e d w hich p e r m itte d lo a d in g i n in c r em en ts
up t o t h e d e s ir e d l e v e l *

Model E 025050 was lo a d e d t o f a i l u r e d u rin g

t h e secon d lo a d in g c y c le *

The beam broke i n t h e stem o f t h e beam i n a

c o m b in a tio n o f c o m p r e ssio n and b u c k lin g f a i l u r e a p p r o x im a te ly e ig h t
in c h e s i n from th e end*
to its

The lo a d was r e le a s e d and th e frame r e tu r n e d

o r i g i n a l p o s it io n *

A one in c h s e c t i o n o f s k in e n c lo s in g th e

f r a c t u r e was exit from t h e beam and new g la s s and r e s i n l a i d i n th e s e c ­
t i o n and

a llo w e d t o c u r e .

i n s t r e n g t h i n th e fr a m e .

The t e s t s were resumed w ith no a p p a ren t l o s s
The frame f a i l e d a seco n d tim e i n one colum n

a t a p o in t a p p r o x im a te ly 24 in c h e s from th e b a se*

The seco n d f a i l u r e

was s im ila r i n n a tu r e t o th e f i r s t , i . e . , a c o m b in a tio n o f b u c k lin g and
c o m p r e s s io n .

Both f a i l u r e s o ccu rred a t th e same s t a t i c l o a d .

A g a in a

one in c h s e c t i o n was c u t from t h e la m in a te d s k in and new r e s i n and c lo i h
43

0 -p p lied and a llo w e d t o c u r e .

The t e s t s were resum ed w ith no ap p aren t

ch an ge i n p h y s ic a l p r o p e r t i e s .

The v a lu e f o r th e modulus o f e l a s t i c i t y

m t e n s i o n a s d e te r m in e d b y sam ple t e s t i n g was u sed i n com puting th e
s t r e s s from in d ic a t e d v a lu e s o f s t r a i n a t th e o u te r f i b e r o f th e stem a t
t h e cro w n .

R e s u l t s o f t h e t e s t s are shown i n F ig u r e s 14 and 1 5 .

M odel E 025100 was th e seco n d frame b u i l t and t e s t e d .

Loads

w ere a p p lie d i n in c r e m e n ts and th e s t r a i n and d e f l e c t i o n a t th e crown
r e c o r d e d f o r e a ch l o a d .

A t th e upper l i m i t o f th e l o a d s , th e r e was

some c r u s h in g o f th e colum n fla n g e due t o t h e h o r iz o n t a l t h r u s t d e v e l­
oped i n th e fl'am e.

The r e s u l t s o f t h e t e s t s a r e shown i n F ig u r e s 16

and 1 7 .
L oading t e s t s

o f th e fram es o f p o ly e s t e r r e s i n - g l a s s c l o t h

la m in a te s w ere co n d u cted i n th e same manner a s th o s e f o r t h e ep oxy
r e s i n fr a m e s .

The r e s u l t s o f th e t e s t s a r e shown i n F ig u r e s 1 8 , 1 9 , 20

and 2 1 .
L on g-term S t a t i c L o a d in g . - The s h o r t-te r m s t a t i c lo a d t e s t s as
d e s c r ib e d p r e v io u s ly do n o t p ro v id e in fo r m a tio n on b e h a v io r o f t h e
fram es and m a t e r ia l i f lo a d s o f c o n s id e r a b le m agnitude a r e im p ressed
on th e s t r u c t u r e over a p e r io d o f t i m e .

To d e te r m in e th e p o s s ib l e

p r e s e n c e o f c r e e p i n th e m a t e r i a l , m odel E 025050 was s u b j e c te d t o a
u n ifo r m ly d i s t r i b u t e d c o n s ta n t lo a d o f 50 # /ffc o f beam, (a p p r o x im a te ly
40^ o f th e s t a t i c f a i l u r e lo a d )
and r ec o r d e d from t h e crow n .

D e f l e c t i o n m easurem ents w ere o b serv ed

The lo a d was l e f t i n p la c e u n t i l an e q u i­

lib r iu m p o s i t i o n was d e f i n i t e l y e s t a b l i s h e d .

The lo a d was th e n removed

and t h e fram e ch eck ed t o d eterm in e i f i t would r e c o v e r t o i t s o r i g i n a l
u n lo a d e d p o s i t i o n .

The r e s u l t s o f th e t e s t are shown i n F ig u re 2 2 .

Model P025050 was s u b je c te d t o a lo n g -te r m lo a d t e s t s im ila r t o
th e t e s t o f E 025050.

A u n ifo r m ly d i s t r i b u t e d lo a d o f 4 2 . 5 # / f t o f beam
44

(■;i<3pq j o

avcrr
45

(uiBpq j o %j / &)

46

Figure

a'fcn ;TCO£iHn

15*

Deflection

of model

d025050

-fit the

crown

due

to a uniformly

uistri outed

load.

500

O

o

o

Load-stress

curves

for

o —
O CM
o c
CM -r

cm

en

~1o

irH

o

cO

o

CM

(cuEsq j o %j / # )

47

o
1o
—
4

avoT ;r:c^ii:n

o
o

model £325100

{epox;/ resin -g la ss

cloth

O

in bending

laminate)

rQ

16.

o
o

Figure

LO

cO

(ureeq j o %j/$)

48

500-

Figure 17*

GVCTL ;$?0£IKn

Deflection

of model

ai025100

at

tne crown

aua to a uniformly

distributed

load.

o
to

o

to

'M
*

o

(cueeq j o « / * )

49

o

XEOJIJSin
o
o

Los d-s tress

'O

o

18«

o
cur/es

CM

P025050

o

o

o

o
o

o

for aoael

~ o
o

uenaing

(polyester

O
o

in

resin -g la ss

i CO

Figure

cloth

larrina

A>

CM

load
distributed

8d

©

rd
+3

d

©

to
©
©
fc

+j

<+H

O
O

*
J
>

o

:o m

©

Vi

:o

Vi

o

\ \

c

\

-*->
d
0
>1
to

.

\ \\ \ *

\A\ \

1O
C
*4
-u
'd
<rt
b>:
*fH

o

GO

o
3
r-M
Crl
PI
CJ
io

Ho

o

uD

o

(taepo j o * u /# )

o
c\j

C?07 LIKMTNX1

50

o

at the

oq
p
o

<*■»
cs
©
t:

of rrodel P025350

•e*

1 9 # Deflection

m
rrl

Figure

o

crown aue

to a unidorrr.ly

LO
■d
©
■cvti>
t?.
•)—t

( (Zitreq JO

u / Jf)

IV 0 1

51

figure

.'rH O JI:in

20«

Losd-stress

curves

in bending

for rrodel

F025100

(polyester

resin-glass

cloth

lsrrinatej

21o
Deflection

tfir
of measurement

F
o-*
n
r-t,
r-ri
n

(meeq j o a j / £ )

crvcn: rcjojitm

52
at

JS
*>
-*->
m
PQ25100

the crcwn

a?
o

of model

Point

<5

igure

4001-

due to a uniformly

m
n>
a
a

r-t,

distrioutad

load

0. 8

of Fodel 3025050

at

CQ
o

O
O

o
o
(serjouf) &
A10H
0

53

CM

OO

o

o

HOtiLOSrUSQ.

the

crown

with

o
o

Deflection
a p p lie d .

a constant

uniform

load

of 50 #/ft

o

22.

of

o

Figure

beam

o
CO

o

w as p la c e d on t h e fram e and o b s e r v a tio n s o f th e d e f l e c t i o n a t th e crown
w ere made a t i n t e r v a l s u n t i l t h e frame had rea ch ed an e q u ilib r iu m p o s i­
tio n *

The lo a d was t h e n rem oved and o b s e r v a tio n s c o n tin u e d u n t i l th e

fram e had a g a in r e a c h e d e q u ilib r iu m *

The lo a d o f 42.5jSf/ffc o f beam on

t h e m od el i s e q u iv a le n t t o a lo a d o f 17Q$/ffc o f beam on t h e f u l l s c a le
fram e*

The r e s u l t s o f t h e t e s t a re shown i n F ig u re 23*

54

0.8

DilFkiCTlOfc

(in ch es)

0.6

'0 .4

0.2

Load removed
Load a p p l i e d
0

100

0
200

TIILS
FijRrure 23.

300
(h r s )

___ 1400

500

D e f l e c t i o n o f model P025050 at th e crown w ith £ c o n s ta n t
un iform load o f 4 2 ,5 fi-/ft o f beam a p p l i e d .

55

RESULTS AND DISCUSSION

Use o f The C o n s tr u c tio n J & t e r ia ls
S u c c e s s f u l u se o f t h e p l a s t i c r e s i n s fo r hand-w et la y u p m old ing
d ep en d s on r e s i n fo r m u la tio n , c a t a l y s t , h a r d e n e r , m old p r e p a r a tio n , and
o p e r a to r e x p e r ie n c e #

Some o f t h e s e f a c t o r s a r e d eterm in ed by th e

m a t e r ia l m an u factu rer and some a re c o n t r o lle d by t h e f a b r ic a t o r #

The

tw o r e s i n s em ployed i n t h i s p r o je c t a r e r e l a t i v e l y e a s y t o work
a lth o u g h son© e x p e r ie n c e i s h e l p f u l , i f n o t n e c e s s a r y , t o in s u r e a u n i­
form p r o d u c t•
P a r t ic u l a r ca re must be ta k e n t o p r o te c t a g a in s t a i r in c lu s io n #
E v e n w it h t h e t r a n s lu c e n t p o ly e s t e r r e s i n b u b b les a re d i f f i c u l t t o s e e
u n l e s s t h e background and l i g h t i n g a r e r ig h t #

A l i g h t c o lo r e d back­

ground w it h d i r e c t l i g h t i n g a id s i n d e t e c t i o n o f t h e a i r p o o k ets#
common e r r o r
c lo t h #

A

(e x p e r ie n c e d by th e a u th o r ) i s t o r e s i n s ta r v e a r e a s o f

T h is i s g e n e r a ll y due t o ig n o r in g , or n o t b e in g aware o f , th e

change i n v i s c o s i t y o f th e r e s i n a t peak exotherm - th e h e a t g e n e r a te d
c h e m ic a lly d u rin g t h e c u r in g p r o c e s s #

For a v e r y sh o r t p e r io d o f t im e ,

a s t h e r e s i n ap p roach es peak ex o th erm , th e v i s c o s i t y r ed u c es m ark ed ly,
r e s u l t i n g i n a runou t o f r e s in #

I f la m in a te t h i c k n e s s , and th u s r e s i n ,

i s b u i l t up t o o q u ic k ly , th e runout a t peak exoth erm w i l l r e s u l t i n th e
upper c l o t h f i b e r s b e in g w ith o u t s u f f i c i e n t r e s i n t o produce t h e i r max­
imum s t r e n g t h s «

T h is ca n be p r e v en te d by la m in a tin g such th a t th e

r e s i n h as begu n t o g e l b e fo r e th e s u c c e e d in g la y e r i s a p p lie d #

F igu re

24 i l l u s t r a t e s an a d eq u ate r e s i n —c l o t h r a t i o and a r e s i n s ta r v e d la m in a te#
Too r a p id r e s i n b u ild u p w i l l a l s o r e s u l t i n th e c l o t h *f l o a t i n g 1,
r e s u l t i n g i n u n even d i s t r i b u t i o n o f c l o t h a c r o s s th e s e c t io n #
56

It is

n e c e s s a r y t o u se a t h ix o t r o p ic a g e n t i f th e la m in a te i s t o

b e c o n s t r u c t e d on a s t e e p l y s lo p in g or v e r t i c a l s u r fa c e *

The t h i x o -

t r o p i c a g e n t p r e v e n ts s a g g in g w ith o u t a p p r e c ia b ly a l t e r i n g t h e m e c h a n ic a l
p r o p e r t ie s o f t h e f i n a l p rod u ct*
R e p a ir s t o t h e la m in a te s made w ith e i t h e r r e s i n ca n be made v e r y
sim p ly b y rem oving th e f r a c tu r e d p o r tio n and la y in g i n new m a t e r ia l w ith
no a p p a re n t l o s s i n s tr e n g th *

T h is i s a s m a ll b u t im p o rta n t p o in t i n

m a in te n a n c e o f b u ild in g s *
The p l a i n w eave g l a s s c l o t h u se d i n th e la m in a te s i s v e r y e a sy
t o h a n d le a lth o u g h i t i s n o t p o s s ib le t o bend i t i n t o abrupt 90 d eg ree
corn ers*

T h is c h a r a c t e r i s t i c i s n o t im p o rta n t i n t h e f a b r ic a t io n o f

r e l a t i v e l y sim p le frame c r o s s s e c t io n s *
Type A - l , SR-4 s t r a i n g a g es a r e e a s i l y mounted on e i t h e r r e s i n
la m in a t e .

The a d ju stm en t n e c e s s a r y t o a cco u n t fo r d if f e r e n c e s i n

m odulus o f e l a s t i c i t y b etw een la m in a te and gage m a t e r ia l i s l e s s th a n
one per c e n t*

T h is c o r r e c t i o n was c o n s id e r e d n e g l i g i b l e i n th e p r e s e n t

w ork.
F ig u r e 24 i l l u s t r a t e s t h e d if f e r e n c e b etw een a s a t i s f a c t o r y
la m in a te and one t h a t has b een r e s i n s ta r v e d due t o runou t*
from la m in a te s o f fo u r la y e r s o f g la s s c l o t h .

Both a re

F ig u re 24a i s an edge

v ie w o f t h e tw o sam p les w ith th e g la s s th r e a d s b la c k e n e d fo r c o n t r a s t
w it h th e r e s i n .

N o tic e how th e one la y e r o f g l a s s i n sam ple A i s a t

t h e edge o f th e la m in a te w ith v e r y l i t t l e

r e s i n c o v e r in g , ev en th o u g h

t h e o th e r g l a s s la y e r s appear t o be f a i r l y e v e n ly d i s t r i b u t e d th r o u g h
th e sa m p le .

Sample B shows v e r y c l e a r l y th e u n ifo rm d i s t r i b u t i o n o f

g l a s s a c r o s s th e la m in a te w ith ample r e s i n c o v e r in g on b o th s i d e s *
F ig u r e 24b i s a

p la n v ie w o f th e same sam ples a g a in show ing th e c o n ­

t r a s t b etw een th e tw o la m in a t e s .

The weave p a t te r n o f t h e c l o t h i s
57

(a )

24

*

( a ) P d g e v i e w o f two eoo:xy r e s i n - g l a s s c l o t h l a m i n a t e s s h o w i n g
g la ss d i s t r i b u t i o n through th e cro ss s e c t i o n .
(b) P la n view
o f the laminates s h o w i n g the s u r f a c e a p p e a r a n c e .
58

c l e a r l y shown i n sam ple A i n d i c a t i n g th e la c k o f r e s i n c o v er *

Sample B

show s how a la m in a te s u r fa c e sh o u ld appear i f proper r e s i n - g l a s s d i s t r i ­
b u t io n i s m a in ta in e d *

M ech a n ica l P r o p e r t ie s o f The M a te r ia ls
T e n s io n
The s t r e s s —s t r a i n c u r v es fo r b o th r e s i n la m in a te s are q u ite
s im i l a r I *1 t h a t t h e y e x h i b i t th e g e n e r a l c h a r a c t e r i s t i c s o f a t y p i c a l
b r i t t l e m a t e r ia l*

T h is i s a d e m o n str a tio n o f what B r o s s y , e t a l ,

c a l l p r e f e r e n t ia l1 fa ilu r e *

( 8 )*

T his was a u d ib ly app arent d u rin g th e t e s t s

as th e i n d iv id u a l f i b e r s and s tr a n d s would b rea k w ith a pronounced snap
as t h e lo a d in c r e a s e d up t o th e p o in t where t h e t o t a l rem a in in g s tr a n d s
w ould f a i l su d d en ly and d r a m a tic a lly *

There was no n o t ic e a b l e *n e c k in g

down* o f t h e sp ecim en b e fo r e f a i l u r e *
One s e t o f c u r v e s i s shown fo r th e epoxy r e s i n la m in a te s - th o s e
fo r lo a d a p p lie d p a r a l l e l t o th e warp (F ig u r e 1 0 ) •

T h is i s done b eca u se

t h e r e i s no a p p a ren t d if f e r e n c e i n th e b e h a v io r o f th e la m in a te lo a d e d
p e r p e n d ic u la r t o th e warp u n t i l th e s t r e s s - s t r a i n r e l a t i o n s h i p has pro­
g r e s s e d beyond th e l in e a r p o r t io n o f t h e curve*

S in c e th e s t r a i g h t l i n e

segm en t i s th e im p ortan t p a r t i n d e te r m in in g modulus o f e l a s t i c i t y and
t h e m odulus p a r a l l e l t o th e warp i s th e one t h a t a p p lie s t o t h e problem ,
t h e o th e r c u r v e s a r e n o t p r e se n ted *

The tw o epoxy la m in a te s a r e u n i­

form i n s t r e n g t h p r o p e r t ie s a s th e c u r v es c o in c id e on th e s t r a i g h t l i n e
p o r tio n *

The ap p aren t w eakness o f th e t h in n e r la m in a te can be a t t r i b ­

u t e d t o t h e f a c t t h a t th e r e a r e few er g la s s f ila m e n ts and a l s o th e
t h in n e r la m in a te was r e s i n s ta r v e d t o a g r e a t e r d eg ree th a n th e h e a v ie r
one*

The modulus o f e l a s t i c i t y and maximum s tr e n g th i n t e n s i o n d e t e r ­

m ined fo r th e epoxy r e s i n la m in a te s from th e sam ples a r e low compared t o
59

t h e v a lu e s g iv e n i n T ab le 1 .

The d i f f e r e n c e s a r e most l i k e l y due t o

lo w er q u a l i t y la m in a te p lu s t h e f a c t t h a t th e r e s i n u sed i s a m o d ifie d
e p o x y w it h t h e m an u factu rerC 1 ) in d ic a t in g p o s s ib l e s t r e n g t h s s l i g h t l y
lo w e r th a n t h o s e g iv e n i n T able 1 *
T here i s a d if f e r e n c e i n th e s t r e s s - s t r a i n c u r v e s f o r th e p o ly ­
e s t e r r e s i n la m in a te s (F ig u r e s 11 and 1 2 ) , b o th a c c o r d in g t o t h e m odel
from w h ich t h e sam p les w ere ta k e n and a c c o r d in g t o d i r e c t i o n o f th e
sam ple w it h r e s p e c t t o th e warp o f th e c l o t h .

Sam ples from m odel

P 025050 show t h e h ig h e s t modulus o f e l a s t i c i t y i n t e n s i o n ev en though
t h e y r e p r e s e n t t h e th in n e r la m in a te th ic k n e s s *

The d if f e r e n c e h ere

m igh t be due a g a in t o b e t t e r q u a lit y workmanship as m odel F025050 was
c o n s t r u c t e d a f t e r c o m p le tio n o f P 0 2 5 1 0 0 .

A noth er f a c t o r w hich c o u ld

c o n t r ib u t e t o t h e d i f f e r e n c e s i s th e am bient tem p era tu re d u rin g th e
c u r in g p e r io d .

The am bient tem p era tu re was a p p ro x im a te ly 50°F th ro u g h ­

out t h e c u r in g tim e fo r P025100 w h ile i t was a p p ro x im a te ly 75°F
th r o u g h o u t t h e c u r in g p e r io d fo r P 0 2 5 0 5 0 .
I t i s n a tu r a l t o e x p e c t a low er modulus p e r p e n d ic u la r t o th e
w arp as th e c r o s s t h r e a d s , or p ic k , a r e fo r c e d t o bend around th e warp
d u r in g w e a v in g , th u s when a p u r e - t e n s io n lo a d i s p la c e d on th e la m in a te
i n th e d i r e c t i o n o f th e p ic k th e g la s s fila m e n ts must be p u lle d s t r a i g h t
b e fo r e t h e y c a n d e v e lo p maximum lo a d c a r r y in g c a p a c it y .

Fewer fila m e n ts

a r e e q u a ll y lo a d ed a t any one tim e d u rin g th e t e s t s .
The v a lu e s f o r E i n t e n s i o n l i e w it h in t h e range g iv e n i n
T ab le 1 a s t y p i c a l fo r p o ly e s t e r r e s i n la m in a t e s .

The maximum s t r e n g t h

i n t e n s i o n i s lo w , b u t th e com p arison can n ot be made t o o s t r i c t l y s in c e
^ V h e m a n u factu rer o f th e ep oxy r e s i n g iv e s th e f o llo w in g
v a lu e s as r e p r e s e n t a t iv e f o r th e la m in a tin g m ix u sed in th e m odels*
maximum s t r e n g t h i n t e n s i o n - 2 7 ,4 0 0 p s i, i n b en d in g - 2 8 ,0 0 0 p s i .
60

t h e t a b l e v a lu e s a p p ly t o lo w p r e ssu r e la m in a t e s .

Mb v a lu e s a r e a v a i l ­

a b le f o r no p r e s s u r e hand la y u p la m in a t e s .
The m o d u li o f e l a s t i c i t y d eterm in ed w ere u sed t o r e l a t e th e
s t r a i n s e n s e d b y t h e SR—4 s t r a i n ga g es t o th e s t r e s s i n t h e o u ter f i b e r s
o f th e fram e c r o s s s e c t i o n a llo w in g a r e l a t i o n s h i p t o be e s t a b l is h e d
b e tw e e n s t r e s s i n th e frame and th e a p p lie d l o a d .
F le x u r e
B ecau se o f th e s m a ll s i z e o f th e b en d in g sp ecim en s (one in c h by
fo u r in c h e s b y th e t h ic k n e s s o f th e la m in a te ) i t i s d i f f i c u l t t o d e v e lo p
eq u ip m en t w h ich w i l l a c c u r a t e ly a p p ly th e lo a d and measure th e d i s p l a c e ­
m e n t.

A fo r c e tr a n s d u c e r d e v e lo p e d by G, C. Zoerb (3 6 ) u sed i n d e t e r ­

m in in g th e m e c h a n ic a l p r o p e r t ie s o f g r a in p ro v id ed t h e b e s t means fo r
a c c u r a t e l y and c o n v e n ie n t ly c o n d u c tin g th e b end ing t e s t s .

The t e s t

m achine p rod u ces a c o n s ta n t r a t e o f d e fo r m a tio n i n th e t e s t sp ecim en as
s p e c i f i e d by ASTM d e s i g n a t i o n s .

Through th e use o f SR -4 gages w ith a

B rush o s c il lo g r a p h and a m p l i f i e r s , a permanent r ec o r d o f c o n tin u o u s
l o a d - d e f l e c t io n r e l a t i o n s h i p i s o b ta in e d from w hich th e maximum s t r e n g t h
and m odulus o f e l a s t i c i t y ca n be com puted.

F ig u re 13a shows one o f th e

ep o x y r e s i n la m in a te sp ecim en s b e in g t e s t e d .
F ig u r e 13b shows t y p i c a l d a ta from th e tw o r e s i n la m in a t e s .

The

upper c h a r t i s from th e t e s t o f sample P -A i5 ( p o ly e s t e r r e s i n , model
P 0 2 5 1 0 0 , p a r a l l e l t o th e w arp, f i f t h sam ple o f th e l o t ) .
chart is

The low er

fo r sam ple E-A1 2 * A s im ila r d e s c r ip t i o n a p p lie s t o t h i s

sam ple •
It is
la m i n a t e s .

o f i n t e r e s t t o compare th e f a il u r e p a t te r n o f t h e two

The lo a d on th e p o ly e s t e r la m in a te in o r e a s e d a t n e a r ly c o n ­

s t a n t r a t e t o th e maximum and th e n t h e sp ecim en f a i l e d a b r u p tly w ith
61

n e a r ly c o m p le te r e l e a s e o f lo a d *

The epoxy la m in a te d id n o t b rea k com­

p l e t e l y a t t h e maximum lo a d bu t f a i l e d i n c l e a r l y d e fin e d s t e p s i n d i ­
c a t i n g d i s c r e t e c l o t h f i b e r f a i l u r e as t h e d e f l e c t i o n was in c r e a s e d *
The maximum s t r e s s was c a lc u la t e d as th e s t r e s s a t maximum lo a d
b e fo r e fa ilu r e *

W ith sam ple

P « A « L (o * 1 3 2 ) » I 6 5 pounds*

th e maximum lo a d i n pounds,
A i s th e a tt e n u a to r s e t t i n g and L i s th e

maximum number o f l i n e s o f pen d e f le c t io n *

The c o n s t a n t , 0 * 1 3 2 , i s

tr u e fo r a p a r t ic u l a r c a l i b r a t i o n o f t h e o s c illo g r a p h *

S in c e th e moment

a t t h e c e n t e r o f a s im p ly su p p o rted beam w ith a c o n c e n tr a te d lo a d a t
m id sp an i s P L /4 , th e maximum s t r e s s i s 3P L /2bh^#
2 in c h e s ; t h e r e f o r e , s m s 3P /bh2 *

L f o r t h e sam ple i s

For sam ple £ ^ 1 5 * s m = 2 2 ,5 0 0 p s i*

The m odulus o f e l a s t i c i t y i n b en d in g i s d eterm in ed from th e
r e l a t i o n s h i p f o r m id sp an d e f l e c t i o n o f th e sim p le beam, i * e . ,
d = F L ^ /4 8 E I.

Thus E « EL^/48Id = (2/b h ^ ) ( P / d ) , where P /d i s t h e lo a d

p er in c h o f d e f l e c t i o n *

The l o a d - d e f l e c t io n r e l a t i o n s h i p i s d eterm in ed

from t h e i n i t i a l lin e a r 1 p o r tio n o f th e c u r v e s*

E f o r ^"^15 i s ,

2 .6 1 x 1 0 s p s i .
The v a lu e fo r maximum s t r e s s i n b en d in g a s g iv e n i n T able 4 fo r
t h e ep o x y r e s i n la m in a te s i s low a s compared t o th e f ig u r e s g iv e n by
t h e r e s i n m a n u fa ctu rers*

No v a lu e was in d ic a t e d fo r E b u t th e f ig u r e

2 *4x 106p s i a s d eterm in ed from th e t e s t s l i e s w it h in th e range g iv e n i n
T a b le 1*

The v a lu e o f E f o r th e p o ly e s t e r r e s i n ( 2 .3 x l 0 ^ p s i ) a l s o l i e s

w i t h i n t h e ran ge o f v a lu e s g iv e n i n T ab le 1 .

H owever, t h e maximum

s t r e n g t h i n b en d in g f o r t h e p o ly e s t e r r e s i n la m in a te i s lo w compared t o
th e in d ic a t e d normal r a n g e .

The d i f f e r e n c e s b etw een n o rm a lly e x p e c te d

v a lu e s and th o s e com puted u s in g sam ples from t h i s work a r e p ro b a b ly due
t o th e same in f lu e n c e s a s g iv e n f o r t h e t e n s i l e t e s t r e s u l t s *
A maximum s t r e s s o f a p p r o x im a te ly 3 0 ,0 0 0 p s i i n t e n s i o n ,
62

c o m p r e ss io n and b e n d in g was assumed i n th e o r i g i n a l d e s ig n a s g iv in g a
s t r e s s s a f e t y f a c t o r o f 2*5 (page 20 )*
i n a t e s p rod u ced v a r i e s from
t h e assum ed d e s ig n v a lu e *
from 2*5 t o a b ou t 1 #4#

The maximum s t r e s s f o r t h e lam­

1 7 ,3 0 0 t o 2 3 ,3 0 0 p s i j a p p r o x im a te ly 2 /3 o f
T hus, th e s t r e s s f a c t o r o f s a f e t y i s red u ced

T h is would s t i l l be a c c e p ta b le f o r farm b u ild ­

in g c o n s t r u c t io n i f a s su r a n c e c o u ld be had t h a t th e m a t e r ia l w ould be
u n ifo r m i n q u a lit y #

A com m ercial p r o d u c tio n o f t h e la m in a te s would

in s u r e b e t t e r q u a l i t y c o n t r o l so t h a t s t r e s s f a c t o r s o f s a f e t y c o u ld be
red u c ed a llo w in g f o r more eco n o m ica l u se o f t h e m a t e r ia l.

W ith co m p lete

kn ow led ge o f t h e r e s i n b e in g u s e d , i t s s t r e n g t h c h a r a c t e r i s t i c s , e t c # ,
d e s ig n s c o u ld be d e v e lo p e d w hich w ould a llo w t h e fa n n er t o ta k e f u l l
a d v a n ta g e o f t h e in h e r e n t s tr e n g th o f th e m a t e r ia l.
E v a lu a tio n o f The Model A n a ly s is
For th e p rop osed s o l u t i o n o f th e frame t o be v a l i d , th e t e s t
r e s u l t s on th e m odels sh o u ld show r e a so n a b le agreem ent b o th from a
m o d e l-p r o to ty p e com p arison and from a com p arison o f t e s t r e s u l t s w ith
t h e e s t im a te d v a lu e s f o r th e phenomena b e in g measured#

A d e c is io n as to

w hat c o n s t i t u t e s r e a s o n a b le agreem ent i s c o n d itio n e d by p e r so n a l o p in io n
b a se d on e x p e r ie n c e w i t h , and know ledge o f , a g iv e n s i t u a t i o n .

The

l i m i t s fo r agreem ent v e r s u s d isa g r ee m e n t cannot be s e t r i g i d l y b u t s h i f t
t o f i t t h e s i t u a t i o n w ith r e a so n c o n t r o l l i n g th e f i n a l c h o i c e .
E x a m in a tio n o f F ig u r es 14 th ro u g h 21 w i l l p ro v id e a c le a r p ic tu r e
o f t h e co m p a riso n o f t e s t r e s u l t s w ith e s tim a te d v a lu e s fo r s t r e s s and
d e f l e c t i o n a t t h e crow n .

There i s q u ite a la r g e sp rea d i n v a lu e s fo r

s t r e s s and d e f l e c t i o n i n th e p r o to ty p e s (E025050 and P 025050) a t any
g iv e n lo a d #
fic u ltie s .

T h is i s due p a r t ly t o o b s e r v a tio n and in s tr u m e n ta tio n d i f ­
I t was d i f f i c u l t t o h o ld th e lo a d c o n s ta n t a t any g iv e n p o in t
63

i n th e lo w range i n w h ich th e t e s t s were run and th e bourdon ty p e p r e s ­
su r e g a g e s w ere som etim es s lu g g is h in r e sp o n se a t t h e s e p r e s s u r e s •
H ow ever, enough r e p l i c a t e s were run t o e s t a b l i s h d e f i n i t e r e l a t i o n s h i p s
b e tw e en t h e v a r ia b le s con cern ed *
T h is d i f f i c u l t y was n o t p r e se n t i n t e s t i n g m odels E 025100 and
P 0 2 5 1 0 0 , p r im a r ily b e c a u se o f th e m agnitude o f th e a p p lie d lo a d s w hich
r e s u l t e d i n b e t t e r p r e ss u r e c o n t r o l and b e t t e r gage r e s p o n s e , b u t a l s o
b e c a u s e o f th e in c r e a s e d r i g i d i t y o f th e la r g e r s e c t io n s w hich te n d ed t o
s t a b i l i z e t h e fram e a c t io n *
The b e s t s t r a i g h t l i n e was drawn th ro u g h th e p lo t t e d p o in ts an d ,
i f n e c e s s a r y , c o r r e c t e d t o pass th ro u g h th e o r ig in *

S in c e a lin e a r

s t r e s s - s t r a i n r e l a t i o n s h i p was assu m ed , th e e stim a te d v a lu e s fo r s t r e s s
and d e f l e c t i o n w ere d eterm in ed as fu n c tio n s o f lo a d per f o o t o f beam
and p l o t t e d on th e cu rv e s h e e t s w it h th e m easured v a lu e s *
e x c e p t o n e , th e m easured v a lu e s a r e l e s s th a n e stim a te d *

In a l l c a s e s
The one

e x c e p t io n i s F025050 i n w hich th e measured s t r e s s i s a p p ro x im a te ly 9
per c e n t above th e e s t im a te d v a lu e *

T hese r e s u l t s a re shown i n T able 5*

The g r e a t e s t d if f e r e n c e i n s t r e s s o ccu rred w ith E 025100, 16*4 per c e n t ,
and th e l e a s t d if f e r e n c e w ith P 025100, 1*5 per c e n t*

The g r e a t e s t

d i f f e r e n c e i n d e f l e c t i o n occu rred w ith P 025050, 17*5 per c e n t , and th e
l e a s t d if f e r e n c e w it h E 025100, 9 .3 per c e n t*
th e g r e a t e s t d iffe r e n c e s in d e fle c tio n *

The p r o to ty p e s e x h ib it e d

A lth o u g h th e d if f e r e n c e s i n

some in s t a n c e s appear t o be r a th e r h ig h i t i s f e l t t h a t t h i s does n o t
d e t r a c t from th e v a l i d i t y o f th e a n a l y s i s .

I n a c c u r a c ie s i n frame con ­

s t r u c t i o n and frame m easurem ents p lu s any e r r o r s i n th e t e s t i n g f a c i l ­
i t i e s c o u ld e a s i l y com bine t o produce th e d if f e r e n c e s shown b etw een
e s t im a t e d and o b se rv e d v a l u e s .

E f f o r t s w ere made t o produce a uniform

la m in a te on t h e fram es and m a in ta in u n iform d im en sio n s i n la y o u t and
64

c r o s s s e c t i o n b u t i t i s d i f f i c u l t t o c o n t r o l t h e s e item s w ith o u t u s in g
l a r g e , p r e c i s i o n made molds w ith s k i l l e d t e c h n ic ia n s d o in g th e la m in a t­
in g *

A s m a ll e r r o r i n m easu rin g s k in t h ic k n e s s fo r d e te r m in in g th e mom­

e n t o f i n e r t i a f o r th e frame c r o s s s e c t i o n s w ould ca u se a r e l a t i v e l y
la r g e d i f f e r e n c e i n t h e f i n a l e s t im a te o f s t r e s s and d e f l e c t i o n .
TABLE 5
ESTIMATED AMD MEASURED VALUES OF DEFLECTION (d ) AMD LOWER FIBER
STRESS ( s ) AT TEE CROWN OF THE FOUR MODEL FRAMES.

R e sin

Epoxy

Model

E025100
d
( in )

E stim a ted .00139w
Measured •00126w
% d iff.
9 .3

P o ly e s te r
E0250S0

PQ25050

P025100

(# /in 2 )

( in )

(# /in 2 )

( in )

( # /i n 2 )

( in )

(# /in 2 )

8 .08w
6 .75w
16 .4

• 0165w
• 0139w
1 5 .8

59 .Ow
5 1 .8w
12 .2

•00118w
•00105w
1 1 .0

6.75w
6.65w
1 .5

•0126w
• 0104w
1 7 .5

3 6 .lw
3 9 .4w
9 .1

TABLE 6
ESTIMATED A I'D MEASURED VALUES OF DEFLECTION AMD STRESS FOR THE
MODEL AMD PROTOTYPE'1 ) FOR TWO RESIN-GLASS CLOTH LAMINATES.

P o ly e s t e r

Epoxy

R e s in
R a t io

d/^m

s/ sm

d/^m

s/ s m

E stim a te d
M easured
% d iff.

1 1 .8 3
1 1 .0 3
6 .8

7 .3
7 .6 3
5 .1

1 0 .8
9 .9
8 .3

5 .3 5
5 .8 4
9 .1

( ^ P r o t o t y p e s are E 025050, P025050; m odels are E 025100, F 0 2 5 1 0 0 .
E x a m in a tio n o f T able 6 w i l l p ro v id e in fo r m a tio n o f th e v a l i d i t y
o f th e m odel a n a l y s i s .

The agreem ent b etw een e stim a te d and m easured
65

v a lu e s o f t h e r a d io s f o r s t r e s s and d e f l e c t i o n b etw een m odel and p r o to ­
ty p e i n d i c a t e w h eth er or n o t th e a n a ly s is can be a c c e p te d and th e
r e s u l t s o f t h e t e s t s p r o j e c t e d t o a f u l l s c a l e frame •
c o n s i s t e n t f o r b o th r e s i n s *

The r a t i o s are

The m easured r a t i o s a r e b elo w e s tim a te d

r a t i o s f o r d e f l e c t i o n , above fo r s t r e s s *

H owever, th e d if f e r e n c e s

b e tw e en m easured and e s t im a te d v a lu e s a re a l l b elo w 10 per c e n t*

A g ree­

ment w i t h i n t h i s range su p p o rts th e d e c i s i o n t h a t th e a n a ly s i s ca n be
a c c e p t e d and th e r e s u l t s u se d i n th e d e s ig n o f a f u l l s c a le s tr u c tu r e *
I t i s n e c e s s a r y t o exam ine th e c u r v e s t o g e t an e s tim a te o f t h e
m agn itu d e o f s t r e s s and d e f l e c t i o n w hich m ight be e x p e c te d i n a f u l l
s c a l e frame b a sed on th e r e s u l t s o f th e model a n a l y s i s .

R e fe r r in g t o

t h e o r i g i n a l m odel a n a l y s i s , th e p r e d ic t io n e q u a tio n s f o r s t r e s s and
d e f l e c t i o n a r e ; f o r m odel P 025 1 0 0 , s ® 6 4 sm,
and c r o s s s e c t i o n s c a l e s are u se d a s g iv e n *

^ * 3*024dm, i f th e le n g t h
T h e r e fo r e , i f we want t o

u se m easured s t r e s s and d e f l e c t i o n v a lu e s t o p r e d ic t frame b e h a v io r , we
f i n d , f o r a d e s ig n lo a d o f 6 0 # / f t o f beam, t h a t th e s t r e s s i n low er
f i b e r s a t t h e crown w i l l be 6 4 (1 0 1 * 2 5 ) » 6 4 8 0 p s i, and th e d e f l e c t i o n a t
t h e crow n w i l l be 1 0 2 4 (0 * 0 1 5 7 5 ) » 16*1 in c h e s .

I t sh o u ld be remembered

t h a t i n making th e p r o j e c t io n a 1 5 # / f t lo a d on th e model i s e q u iv a le n t
t o a 6 0 # / f t lo a d on th e fram e, i . e . , w = 4wm*

I t i s im m ed ia tely

a p p a ren t t h a t th e o r i g i n a l frame d e s ig n i s e x tr e m e ly f l e x i b l e and b e ­
c a u se o f t h i s w ould p ro b a b ly n o t be a c c e p t a b le , ev en th ough t h e s t r e s s
is

q u ite lo w .

T h is d o e s n o t p r e s e n t any problem , h ow ever, as the d e s ig n

i s e a s i l y m o d ifie d t o c o r r e c t t h i s d e f e c t *

The p o in t t o be em phasized

i s t h a t t h e m odel a n a l y s i s i s v a l i d and in fo r m a tio n from th e problem ca n
be u sed t o su p p o rt fu b u re d e s ig n e s t im a te s *

66

L ong-term Loads
A s tu d y o f F ig u r e s 22 and 23 su p p o r ts t h e sta te m e n t o f D i e t z ,
e t a l ( l 4 ) , t h a t t h e m a t e r ia ls do n o t e x h i b i t any c r e e p under lo n g -te r m
lo a d s *

The c u r v e s are r e p r e s e n t a t iv e o f th e e l a s t i c a f t e r e f f e c t as

shown by t h e in c r e a s e i n s t r a i n w ith tim e a f t e r lo a d a p p l i c a t i o n and th e
c o r r e s p o n d in g tim e d ep en d en t r e le a s e o f s t r a i n a f t e r u n lo a d in g *

The

e f f e c t o f te m p er a tu r e on m a t e r ia l b e h a v io r i s d em on strated by t h e c y c l i c
n a tu r e o f t h e v a lu e s f o r d e f l e c t i o n o f F025050 a f t e r th e r a te o f s t r a i n ­
in g had red u ced t o a lm o st zero *

The o b s e r v a tio n s were made a t 0800 and

a t 1 7 0 0 d a i l y w it h th e tem p era tu re d if f e r e n c e b etw een th e two tim e s
ab ou t 20°F *

T h is e f f e c t , th ough n o t i c e a b l e , i s n o t o f s u f f i c i e n t mag­

n it u d e t o be o f any co n seq u en ce i n th e d e s ig n o f farm b u ild in g s •

67

C(INCLUSIONS
1*

Epoxy and p o ly e s t e r r e s in s r e in f o r c e d w ith g la s s f i b e r s pro­

duce a la m in a te u n iform i n m ech a n ica l p r o p e r tie s s u i t a b l e fo r u se a s a
s t r u c t u r a l m a t e r ia l#

Hand w et la y u p o f th e la m in a te i s p o s s ib le a l ­

th o u g h i t i s d i f f i c u l t t o m a in ta in good q u a l it y c o n t r o l u n le s s th e
la m in a to r h as had c o n s id e r a b le e x p e r ie n c e and th e molds a r e c a r e f u l l y
c o n s tr u c te d *

In a d d it io n t o t h e i r a d v a n ta g es such a s , r o t r e s i s t a n c e ,

w a te r p r o o f n e s s , s t r e n g t h , e t c . , th e r e in f o r c e d p l a s t i c s ca n be molded
i n t o a n i n f i n i t e number o f shapes w ith e a se *
SR -4 e l e c t r i c r e s i s t a n c e ty p e s t r a i n gages a r e v e r y e a s i l y
mounted on t h e la m in a te s p r o v id in g a v e r y c o n v e n ie n t means fo r m easur­
in g s t r a i n , and th u s s t r e s s , i n a s tr u c tu r e b u i l t o f th e g la s s r e i n ­
fo r c e d p l a s t i c s .
2*

The u se o f s t r u c t u r a l m odels p erm its i n v e s t i g a t i o n o f hypo­

t h e s e s c o n c e r n in g m ech a n ica l phenomena i n s t r u c t u r e s w ith o u t th e ex p en se
and d i f f i c u l t i e s

en co u n tered w ith a f u l l s c a le u n i t •

D is t o r t e d m odels

c a u s e no in c r e a s e i n d i f f i c u l t y over tr u e m odels when c o n s id e r in g t h e
u s e o f m odel a n a l y s i s .
3*

A greem ent b etw een model and p r o to ty p e i s w it h in a c c e p ta b le

d i f f e r e n c e s b etw een m easured and e s tim a te d v a lu e s fo r th e phenomena
ob served .

The r e s u l t s o f th e model s tu d y in d ic a t e fib r o u s g l a s s r e i n ­

fo r c e d p l a s t i c r e s i n s can be used w ith c o n fid e n c e i n farm b u ild in g
d e s ig n and c o n s t r u c t io n *
4*

The s t r u c t u r a l t e s t f lo o r w ith th e h y d r a u lic lo a d in g sy ste m

p e r m its c o n v e n ie n c e , a c c u r a te c o n t r o l and r a p id v a r i a t i o n i n lo a d
68

a p p l i c a t i o n t o any s t r u c t u r e t h a t i s r e l a t i v e l y narrow i n d im en sio n p e r ­
p e n d ic u la r t o t h e f l o o r and th e d i r e c t i o n o f th e a p p lie d lo a d s #

W ith

t h e w h i f f l e - t r e e ty p e lo a d in g s h o e s , no d i f f i c u l t y was e x p e r ie n c e d i n
t e s t i n g a s e c t i o n o f tw o f o o t depth#

69

SUMMARY

The o v e r a l l o b je c b iv e o f bhe in v e s b ig a b io n v/as bo deberm ine bhe
f e a s i b i l i b y o f u s in g fib r o u s g la s s r e in f o r c e d p la s b ic r e s i n s i n farm
b u ild in g c o n s b r u c b io n .
A lib e r a b u r e r e v ie w was conducbed bo deberm ine bhe s u i b a b il ib y
bhe c o m m e r c ia lly a v a ila b le p la s b ic r e s i n s fo r su ch u s e s*

Two r e s i n s

w ere c h o s e n f o r u se i n bhe p r o j e c t — a m o d ifie d epoxy and p o ly e s b e r
r e s in *

P l a i n w eave g l a s s c lo b h was u sed as r ein fo r ce m e n t •
A r i g i d frame wibh a m o d ifie d T c r o s s s e c b io n was d e v e lo p e d as

a b u ild in g form w h ich w ould p ro v id e c le a r span and a llo w u se o f bhe
r e in f o r c e d p la s b i c s a s bobh s k in and frame*

The bwo foob depbh o f bhe

u n ib w ould a llo w c o n v e n ie n t b u ild in g e x p a n s io n w ibh a d ja c e n t u n ib s
e a s i l y w eld ed bogebh er w ibh r e s i n and g la s s c lo b h .
A m odel a n a ly s is was made and d isb o r b e d sb ru cb u ra l m odels were
u s e d bo ch e ck bhe o r i g i n a l d e s ig n .

Two m odels o f d i f f e r e n t c r o s s s e c ­

b io n s c a l e w ere b u ilb o f each r e s i n , bhus p r o v id in g a mebhod o f 'p ro v in g *
bhe m o d e l.

The m odels were b esb ed by a p p ly in g shorb berm u n ifo r m ly

d is b r ib u b e d sb a b ic lo a d s bhrough a sysbem o f h y d r a u lic c y lin d e r s and
s p e c i a l lo a d in g s h o e s , w ibh d e f l e c b i o n and s b r a in m easured ab bhe crow n .
M a b erial consbanb s w ere deberm ined from sam ples cub from bhe
f la n g e lam in ab e o f e a ch model fram e*

E v a lu e s i n b en d in g deberm ined

from b h ese sam ples w ere u se d bo esbim abe d e f le c b io n s i n bhe fr a m e s.
S b r a in s w ere s e n s e d by SR.—4: s b r a in ga g es mounted on bhe o u ter s u r f a c e s
o f bhe sbem and f l a n g e .

S b r e s s e s were deberm ined by m u lb ip ly in g bhe

s b r a in bhus m easured by bhe v a lu e o f E deberm ined from bhe s a m p le s.
70

E stim a te d and m easured v a lu e s o f s t r e s s and d e f l e c t i o n fo r th e
fo u r m odels a r e shown i n T ab le 5 .

S a t i s f a c t o r y agreem ent was o b ta in e d

b e tw e e n m easured and e s t im a te d v a lu e s o f b o th phenomena*

R eason ab le

agreem en t was o b ta in e d b e tw e en e s tim a te d and m easured p r e d ic t io n f a c t o r s
f o r t h e m odel a n a l y s i s ; t h u s , th e r e s u l t s o f t h e t e s t s on t h e model
fram es c a n be e x t r a p o la t e d w it h c o n fid e n c e •

71

SUGGEST10 IS FOR FURTHER STUDY

1*

I n v e s t i g a t e th e u se o f g l a s s r e in f o r c e d p l a s t i c s fo r p a r t i ­

c u la r farm "bu ilding a p p lic a t i o n s such as tow er s i l o s .
2.

I n v e s t i g a t e b u ild in g elem en t c r o s s s e c t i o n and la y o u t t o

d e te r m in e t h e most e co n o m ic a l u n it o f r e in fo r c e d p l a s t i c s s u i t a b l e fo r
c l e a r sp an c o n s t r u c t io n f o r farm b u ild in g s *
3.

I n v e s t i g a t e th e u se o f g la s s r e in fo r c e d p l a s t i c s i n t h i n

s h e l l c o n s t r u c t io n *
4*

I n v e s t i g a t e th e p o s s i b i l i t i e s o f d e v e lo p in g sta n d a rd s i z e

p r e f a b r ic a t e d b u ild in g e le m e n ts o f r e in f o r c e d p l a s t i c s w hich w ould p er­
m it f l e x i b l e b u ild in g arrangem ent*
5.

I n v e s t i g a t e th e u se o f d i f f e r e n t forms o f fib r o u s g la s s as

p l a s t i c r e s i n r e in f o r c in g m a te r ia ls *

72

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75