The flexural behavior of fibrous plaster sheets

CEMENT and CONCRETERESEARCH. Vol. 5, pp. 347-362, 1975. Pergamon Press, Inc Printed in the United States.

THE FLEXURAL BEHAVIOROF FIBROUS PLASTER SHEETS D.A. St John and J.M. Kelly Department of Scientific and Industrial Research, Lower Hutt, New Zealand and University of California, Berkeley, California, U.S.A. (Refereed) (Received March 3, 1975 and in final

form April 28, 1975)

ABSTRACT Tests on fibrous plaster sheet, reinforced with sisal and glass fibres in the bulk density range 56 to 72.5 I b / f t 3 (W/P : 0.9 to 0 . 6 ) , show that sisal f i b r e decreases the strength of the gypsum composite by approximately 30 to 50% and glass f i b r e by approximately 0 to 30%. The e f f e c t on compressive strength shown by the two fibres can be largely explained on the basis of d i f f e r i n g volumes and s t i f f n e s s . Variation of the f i b r e content in the plaster sheet increases the t e n s i l e strength with increasing f i b r e content much as would be expected. A theory based on a non-linear s t r e s s - s t r a i n curve is proposed and the predictions of this theory are found to be in reasonable agreement with the t e s t r e s u l t s . However, i t is concluded that variations in the ultimate flexural strength, where sisal is used as the reinforcing f i b r e , are of such magnitude that i t is impossible to predict flexural strengths with any degree of accuracy. Until the source of this v a r i a b i l i t y can be found i t is not possible to make any design improvements to the strength of the fibrous plaster sheet. The outlook is more hopeful for the use of glass f i b r e as a r e i n forcing material but further work is required to confirm this. Les essais sur les feuilles de pl~tre fibreux, renforc~es au sisal et avec de la fibre de verre, dont la densit~ volumique s'~tend de 56 a 72.5 I b / f t 3 (W/P = 0.9 ~ 0.6), montrent que la r~sistance du compos~ gy~seux est diminu~e d'environ 30% a 50% par la fibre de sisal et de 0 a 30% par la fibre de verre - L~ffet sur la r~sistance a la compression du aces deux fibres peut 8tre en grande partie expliqu~ par les differences de volume et de r i g i d i t ~ - L'augmentation du contenu fibreux dans la femille de pl~tre augmente la r~sistance a la tension comme i l ~tait pr~vu. Une th~orie bas~e sur une courbe nonlineaire de contrainte-d~formation est propos~e, et les previsions de cette thc~orie sont en accord satisfaisant avec les r~sultats des essais - De toute manie~es, on arrive ~ la conclusion que les variations de la conclusion que les variations de la r~sistance ultime de flexion guand le sisal est u t i l i s ~ comme fibre de renforcement ont une amplitude t e l l e q u ' i l est impossible de pr~voir de facon precise la r~sistance a la flexion. Tant que la cause de cette variation n'a pas ~t~ d~couverte i l n'est pas possible de pr~coniser des ameliorations pratiques pour augmenter la resistance de la f e u i l l e en pl~tre fibreux. Les perspectives sont plus optimistes quanta l ' u t i l i s a t i o n de la fibre de verre Commemat~riau de reinforcement mais cela doit ~tre confirm~ par des ~tudes plus pouss~es. 347

348

Vol. 5, No. 4 D. A. St. John, J. M. Kelly Introduction Fibrous plaster sheet is smooth-faced, cast gypsum board reinforced with

random fibres which is used extensively f o r the internal lining of buildings throughout Australasia.

(As specified by NZS 4221:1972 and AS A44:1960.)

The material was developed l o c a l l y and now has been in use for over f i f t y years.

However u n t i l

acterize this product.

recently, l i t t l e

work had been carried out to char-

Brotchie and Urbach (I) have formulated a theory to

account for the flexural behaviour of fibrous plaster sheet, and other workers (2-8) have investigated other properties of i n t e r e s t .

Ali and Grimer (I0)

have investigated the properties of cast gypsum reinforced with glass f i b r e , but the very low water/plaster ratios used in t h e i r investigations are not applicable to fibrous plaster as made in Australasia at present. The present s i t u a t i o n is that the fibrous plaster industry of Australasia is converting from the use of sisal f i b r e (agave sisalana) to that of preformed glass f i b r e mats in the hope that this w i l l

not only improve the product but

also to guard against a possible scarcity of sisal in the future.

Due to a

lack of information the industry is attempting the conversion on a t r i a l e r r o r basis.

and

This is unsatisfactory as the price of the glass mat is up to

three times that of sisal and i t s economic use w i l l call f o r economy in design. In addition to this problem, investigation of the existing commercial product reinforced with sisal has given confusing and highly variable results that could not be i d e n t i f i e d with any one cause (9).

An attempt to apply the

theory of Brotchie and Urbach ( I ) to these results was unsuccessful and indicated that the theory may be in gross error. Thus the purpose of this paper is to investigate the effect of sisal f i b r e and glass mat on cast gypsum and to propose a theory to explain the results obtained.

S p e c i f i c a l l y , an attempt is made to predict the ultimate

flexural strength of fibrous plaster sheet as at present made in Australasia. Materials The gypsum plaster used was casting plaster obtained l o c a l l y to comply with AS A43:1963.

Local plaster is made from Australian gypsum and should

have s i m i l a r properties to Australian plasters. the plasters used are given in Table I.

Details and properties of

The sisal f i b r e used was No. 1

grade originating from East Africa and was typical of the f i b r e as at present

Vol. 5, No. 4

349 FLEXURAL STRENGTH, FIBER REINFORCEMENT, PLASTER

Table l Properties of Gypsum Casting Plaster A

C

D

E

Setting timex (min)

33

31

21

21

Std. consistencyx (ml/lOOg)

0.61

0.60

0.61

0.60

W/P Compressive Strength

pfsi

V%

pf~i

V%

0 . 6 0 2210 7.5 0.65 1775 I ] . l 0.70 1510 4.1 0.75 1285 3.8

2340 1610 1335

5.0

2.8

0.80

1060

2.7

1220

0.85

925

4.1

-

0.90

735

6.0

780

2.5 6.4

6.8

pfsi

V% pfsi

1930

3.1

1385

3.9

950

2.1

If60

V%

6.2

x Tests as specified in AS A43:1963 used in the f i b r o u s p l a s t e r industry.

The f i b r e glass mat used originated

from the Asahi Fibre Glass Co. of Japan.

I t is a continuous preformed matt,

e s p e c i a l l y adapted f o r use in f i b r o u s p l a s t e r sheet and is known as F mat. i

Details of the f i b r e s used are given in Table 2 together with some p e r t i n e n t properties obtained from the l i t e r a t u r e . Experimental All samples of the sheet were made by pouring the wet s l u r r y of gypsum p l a s t e r on to the casting t a b l e without f i r s t

laying a face gauge and the

r e i n f o r c i n g f i b r e was then r o l l e d i n t o the s l u r r y .

The sheets were f i n i s h e d

by the usual techniques o f screeding and t r o w e l l i n g the backs. the various sheets cast are given in Table 3. Table 2 Properties o f Sisal and Glass Fibres (a) Sisal Type Weight (oz/yd2) Weight (Ib/in 2) Tenacity (in -l ) Bulk Density Average length of fibre

Teased 12 or as stated 6.1 x lO"4 1.55 x lO6 l . l l (b) 18"

(a) Properties mainly from ref. I. (b) Dry weight/wet volume

Glass Preformed F Mat 9 4.58 x lO-4 2 x lO6 2.5 Infinite

Details of

350

Vol. 5, No. 4 D. A. St. John, J. M. K e l l y

Tabl e 3 Fibrous P l a s t e r Sheets Cast Plaster C

W/P = 0.75 Sisal fibre (oz/yd 2)

Thick (in)

P/W = 0.90

V B.D. % ( I b / f t 3)

6x

Dl5 0.405 3.0

9

Cl

12 15 18 21

C2 C3 C4

V %

62.8

1.8

0.410 3.8

64.1

0.2

0.385 4.4 0.400 I0.4 0.415 4.8

64.3 61.2 63.8

1.9 0.7 0.5

Thick (in)

V B.Do % ( I b / f t 3)

V %

C5

0.470 7.1

56.0

0.5

C6 C7 C8

0.420 6.1 0.435 I0.6 0.440 7.2

57.7 58.0 57.6

0.7 0.6 0.9

x Cast with plaster D. Plaster D W/P

Sisal

(12oz/yd2)

Glass F Mat (9oz/yd2)

0.60 DI 0.65 0.70 D3

0.390 2.8 70.0 2.1 0.370 5.7 65.5 5.4

0.75 D4 0.80 D5

0.425 2.1 62.5 1.8 0.410 2.5 61.0 2.4

0.85 D6 0.90 D7

0.400 4.8 0.450 7.0

D8 D9 DlO Dll Dl2 Dl3

58.0 3.1 58.1 4.6

0.260 0.265 0.280 0.255 0.275 0.255

5.8 5.8 3.8 3.4 3.9 6.7

72.4 68.4 66.8 16.4 63.3 60.6

1.5 2.6 2.5 6.8 1.8 8.7

Dl4 0.265 4.9

61.2

1.2

Plaster E Sisal 0.75 0.75

El E2

(12oz/yd2)

0.415 0.390

3.8 3.3

61.5 62.4

3.2 3.1

lightly screeded off only heavily worked to finish back

The sheets were allowed to s e t , c u t i n t o 18" x 12" specimens and then d r i e d to constant w e i g h t at 45°C.

The s m a l l e r specimens r e q u i r e d f o r the

t e n s i l e and compression t e s t s were c u t a t t h i s stage.

All

then weighed and measured f o r dimension, and e q u i l i b r i a t e d 50% r . h .

f o r not less than 48 h r .

specimens were at 21°C. and

The a p p r o p r i a t e s i z e d specimens were then

t e s t e d i n f l e x u r e , t e n s i o n and compression.

D e t a i l s o f s i z e s and procedures

are given i n Table 4. Strength t e s t i n g o f u n r e i n f o r c e d c a s t gypsum was c a r r i e d o u t as f o l l o w s :

Vol. 5, No. 4

351 FLEXURAL STRENGTH, FIBER REINFORCEMENT, PLASTER Table 4 Details of Test Specimens & Testing Techniques Used

Fibre

Specimen Size

Test Span

None

4"x2" c y l s .

-

Compression

Sisal

3"xl"x3/8"

-

Glass

2-l/4"x3/4"xl/4"

-

Sisal

6"x3",6"xl"

2"

Glass

6"x3"

Sisal

18"x12",18"x6"

Glass

18"x6 .

2.

.

Test T y p e

.

.

.

Baldwin Universal

"

0.2cm/min

Instron Universal

"

O.2cm/min

"

2cm/min

"

.

.

.

Flexural .

Test Machine

lO00 Ib/min

Tensile

16"

L o a d Rate

.

.

.

.

2cm/min .

.

" .

.

The plaster was stirred at the selected water/plaster ratio for two minutes and then poured into 4" x 2" cylinder moulds.

End caps were then clamped

on to these moulds and the specimens allowed to set in the moulds which rested on their sides so that capping would not be necessary. When set, the cylinders were demoulded and dried at 45°C. for 24 hr and equilibriated at 21°C. and 50% r.h. before testing. Theory The notation of the following theory is essentially that used by Brotchie and Urbach (1).

For convenience a l i s t of the terms is appended. The theory

proposed assumes that when fibrous plaster sheet is tested in flexure, the stress-strain curve is non-linear and thus the ultimate stresses of the two components, fibre and cast gypsum, must be modified to give the ultimate stress in flexure. Following Brotchie and Urbach (1), i f all the fibres are oriented parallel to the direction of loading and there are n fibres per unit width, then F = nT

where z is the force per fibre and F is the effective force in tension. I t is more convenient to use the quantities p, the fibre stress per unit of linear density of fibre, and q, the weight of fibre per unit area of the sheet.

Thus F = nT = pq.

Since the fibres are randomly oriented and non-parallel, F w i l l be given by F=ypq

352

Vol. 5, No. 4 D. A. St. John, J. M. Kelly

where y is an orientation factor which is assumed to be 0.5 as derived in Ref. 1 To account for variable fibre length another modifying factor must be included. Ref. I .

This we w i l l denote by ~which is equivalent to that derived in That is L' = l - ~iZ = ML/M

where L' is the c r i t i c a l fibre length and L the actual f i b r e length. sisal ~ = 0.94 and for the glass F mat ~ = I.

For 18"

Thus the force per unit width

in tension is F = pq~y

I.

The assumed stress and strain d i s t r i b u t i o n in flexure are shown in the following diagram.

....

-

-

-

X' 5tr~

5ere

The depth of the compression zone is Klt and of the tension zone (l

-

Kl)t.

The strain d i s t r i b u t i o n is taken to be linear, the stress d i s t r i -

bution curved as shown and the computation based on square stress blocks. !

We denote the extreme fibre stress on the compression side by f c ' where f ' c is the ultimate compression strength of cast gypsum reinforced with fibre and K is the constant to allow for the stress curve. Similarly, the extreme c fibre stress on the tensile side is f~ = ccyp'q/t (where p' is the tenacity of the f i b r e used) and Kt allows for the curved stress d i s t r i b u t i o n .

The

tension force Ft and compression force Fc developed in the board w i l l be Ft = (I

Kl)Ktf~t = (I - Kl)Kt(~yp'q)

2.

and Fc = K1Kcf'c t Equilibrium requires that Fc = Ft; thus (I - Kl)Ktcq'p'q = KItKcf l c

3.

Vol. 5, No. 4

353

FLEXURAL STRENGTH, FIBER REINFORCEMENT, PLASTER and l Kl =

.

K f't l +

C C

Kt(~yP'q)

Since the lever arm between the resultant forces is t/2 l M = I/2

K f't l+

5.

x Kcf~t2

CC

Kt(~YP'q)

Equation 5 corresponds to equation 8 in ref. l but i t must be noted that the modifying factors appear in a t o t a l l y different context.

I t is assumed that

at flexural failure the sheet w i l l behave in a manner whereby the neutral axis w i l l adjust to compensate for lack of equilibrium.

I t should be noted

that unless one of the constants Kc or Kt can be evaluated this equation is essentially indeterminate. Results and Discussion The results of compression tests on reinforced cast gypsum are given in Table I.

They are similar and quite typical of results reported for Austral-

ian gypsum casting plasters (2,4,7).

The results of the compressive tests on

specimens are shown in Figs. 2 and 3, and of tensile tests in Figs. 4 and 5. The results of the flexural tests are shown in Figs. 5 and 6.

For reference

purposes the relationship between bulk density and water/plaster ratio (W/P ratio) is shown in Fig. I. The most striking effect observed from the results is that of random fibre reinforcement on the compressive strength of cast gypsum. For sisal fibre there is a 30% (approx) reduction in strength and the increase in strength with decreasing W/P ratio is much less than would be expected (Fig. 2) The effect of the glass F mat is similar.

However at the higher W/P ratios

the F mat has a small stiffening effect which may lead to some modest increase in compressive strength (Fig. 2).

These results show that the ultimate

compressive strength (f~) of fibre reinforced cast gypsum must be measured directly and the use of results, such as reported in Table l , can lead to serious error.

Also from the above results (see Fig. 2) i t would be expected

that varying the quantity of fibre reinforcement w i l l affect the compressive strength of cast gypsum. The results shown in Fig. 3 for sisal fibre only, indicate a small decrease in strength with increasing sisal content.

The

354

Vol. 5, No. 4 D. A. St. John, J. M. Kelly

Data from Russell 8, Btakey (1956) ==l[=11J= Ridge (1966)

0-----'(3

American Gypsum Co.

80

~'-----"~

Sheet reinforced with 9OZ F-~nat 12oz sisal

X

X

0

0

sisal (misc.) O

75

FIG. 1

<

Bulk Density of Gypsum Plaster Compared with Bulk Density of Fibre Reinforced Sheet.

X "~

\,,

\

-_"70 O

rn

65

B 60

SS | 50

I

I

I

I

I

t

I

.65

.60

-65

.70 W/P

-75 Ratio

.80

.65

I ~'-. .90

I .95

correlation of these last results is f a i r only, but as s i m i l a r results have been reported for glass f i b r e ( I 0 ) , i t is f e l t that the trends shown are real. The results derived from the d i r e c t t e n s i l e tests are also highly variable There appears to be systematic and unexplained differences between the results given by I" and 3" wide specimens.

The results of t e n s i l e tests on specimens

at W/P : 0.90 and 0.75, for varying quantities of sisal only and using I" wide specimens, are shown in Fig. 4.a and b.

Correlation is only f a i r .

However,

the trend shows that tensile strength increases with increasing sisal content much as would be expected.

Where the W/P r a t i o is varied from 0.90 to 0.60

and the sisal content held constant, the tensile strengths obtained are v a r i able and no correlation is possible.

The linear regression analysis indicates

that W/P r a t i o appears to have l i t t l e

effect on t e n s i l e strength in the range

studied and that other unidentified factors are causing large variations to

Vol.

5, No. 4

355

FLEXURAL STRENGTH, FIBER REINFORCEMENT, PLASTER

Z3 ZZ Zl

},~ FIG. 2 Compressive Strength of Specimens Cut from Fibre Reinforced Sheet Compared with Plain Gypsum Plaster.

IZ 11

r . O ~6

10

T

ll~,dll

~

FIG. 3 Compressive Strength (fc') of Specimens cut from Sisal Reinforced Sheet.

/

w / P , O 9 ry=" -" X)'gIIz'W'S30.82

,ooo

£ 900,

,

I

I

!

800

T

r'---~,

9

Z3

311

6 6

5"6

12

iS

18

i

i

Sisal

4a

Tensile Load Sustained by l" Wide Specimen of Sisal Reinforced Sheet.

( o l / $q.y4)

P

(%)

~- 500 600 =w

300

l~J"~"~

J.

, . , o=+-

100, ~ 3 "

$id Oev,at,on & (oz/sqyd)

S,sal

Tensile Load Sustained by I" Wide Specimen of Sisal Reinforced Sheet.

&~5 ~

= SO0 ? I 700 c ~. 600

~" 200

FIG. 4b

"'

6oo

x o 500 E U 600

FIG.

i ,o ;.; 2':i

l

W P

. ,ooL :

041n$ity ( I b $ / ¢ lI )

,c c

"~. soo

T

600 o

300

'~ c ~"

ZOO

/ / ~ -J , ,

,,ze ,=-Zl~ ,

100

°,T~',~ ~,~" l"& 3" Specimen

r - 0 9"; "r Std Owviition I

I

I

'~ 5,.I

i

IS le (oz/sq y~)

I

21

356

Vol. 5, No. 4 D. A. St. John, J. M. Kelly

7?

I

c

y=1

66~*?0

r =017 = Std OivltttlOn

50(

FIG. 5a Tensile Load Sustained by 3" Wide Specimens of Sisal Reinforced Sheet. (12 oz/sq.yd.)

~'~'~400 v 300 1"

"J ZOO

t ''r"

100 I 3

I Z

I 1

I 70

I 9

I 8

I I I I I I ? 6 65 t, 3 Z Bulk D e n s i t y ( I b s / / ¢ f )

I 1

I 60

I 9

I 8

I 7

I 6

55

FIG. 5b 600

Tensile Load Sustained by 3" Wide Specimens of Glass Reinforced Sheet. (9 oz/sq.yd.)

y = 4 59x÷&883 r=O 78

J= ¢ 50(;

J~

= Std OevLat,on

,o 30C

- i - - t t-

"J ZOG 4,

10C , 3

, z

, ,

i ~

occur (Fig. 5.a).

J 9

, a

i i t i i I 7 6 6s , 3 z Bulk D e n s i t y ( I b i / c f )

i t

i ~

, 9

i 8

~

~ ~5

Better correlation is observed for the glass F mat (Fig. 5.b)

indicating that the preformed mat does ensure better placement of the reinforcing fibre. When we consider the above results we would i n t u i t i v e l y expect that the flexural strength of specimens corrected for thickness w i l l be highly variable.

We would also expect that increasing the amount of sisal fibre rein-

forcement used would give small increases in flexural strength, while varying the W/P ratio of the cast gypsum w i l l result in highly variable results with l i t t l e change being apparent.

The results of the flexural tests shown in

Fig. 6 generally confirm these trends. The anistropy of the specimens tested in flexure should be noted.

In

many of the specimens i t is considerable and suggests that the fibre reinforcement is being incorrectly positioned when rolled into the wet plaster slurry.

This suggests that the techniques currently used are not satisfactory

in this respect as anistropy of sheet appears to be common throughout the fibrous plaster industry (9). Unfortunately due to lack of material, only limited tests were possible using the glass F mat. The results of flexural tests, with face in tension only, are shown in Fig. 6.

Due to possible anistropy of the specimens i t is

not possible to draw any firm conclusions from these results for glass reinforced sheets.

Vol. 5, No. 4

357 FLEXURAL STRENGTH, FIBER REINFORCEMENT, PLASTER 4~ X

(F4ce in tension only)

300

~" ZOO y • 15-3 :r.-?zg. 6

x -~-

r -o'gz

X : FaCe in t e n . o n 0 • Back in t e n s i o n

100

Bulk Oens=ty (IbJc f ) (b) S i s a l - k i P ~,~-o 200

0 go

y • &'&Ix+57- 6 r - O- 591 X

x

l

~-

0

~100

FIG. 6 Moments of Flexural Resistance corrected for thickness of Specimens Tested.

T~" ZOO

I.~100

y = 6 " 5 8 " +61"5 r : 0 69 X

Sisal (OZ//Sq. yd ) (c)

/

X

0

/

((:1) Sisal (12oz/soryd)W/P.O.6

to

O9

X

0 X

--X-100

75

(oz//sq yd)

Sisal

~

-W//P-O

0

y : Z / , S z - 26.16 r : 0 29

I¢_ . zoo

Sisal

0

Bulk

0 -

0

-

~

Density (Ib//c.f.)

Correlation of Theory with Results Taking into consideration the results reported in this paper i t is evident that the Brotchie theory is in error.

I f we consider equation 8 of this

theory, we see that for Kl = 0.18 as calculated in his paper (page 91) ' f 'c must be of the order of 2500 pfsi to give the test results reported. Even i f we increase Kl to 0.3 as used in his appendix l , f~ must s t i l l

be 1500 pfsi,

which is considerably higher than any of the compressive strengths at comparable W/P ratios found in this investigation.

I f we use the more r e a l i s t i c

value of 850 pfsi there are then problems of making the equations derived by Brotchie satisfy the basic concept that the force in tension must equal the force in compression.

In addition all the flexural tests carried out by

Brotchie were performed with the cast face in tension.

The seemingly inevi-

table anistropy of fibrous plaster sheet means that all these results w i l l be

358

Vol. 5, No. 4 D. A. St. John, J. M. Kelly

d i s t o r t e d in one d i r e c t i o n in a variable manner that cannot be estimated. In a d d i t i o n , the assumption t h a t the neutral axis can be determined on the basis of e l a s t i c response of the components is i n c o n s i s t e n t .

The neutral

axis (K I) is calculated by excluding some of the modifying f a c t o r s .

The

extreme f i b r e stresses are then taken to be the ultimate strengths of the components but modified to account f o r the f a c t that the s t r e s s - s t r a i n curves are non-linear.

This is a c o n t r a d i c t i o n and causes large errors in the

neutral axis calculated.

The lowest value of K1 calculated by the theory

given in t h i s paper is 0.3, the average is about 0.5, while the highest, which occurs f o r large amounts of s i s a l , is of the order of 0.8.

This is

v a s t l y d i f f e r e n t from the proposed maximum of 0.3. To correlate the present theory w i t h r e s u l t s , we take equation 5 and s u b s t i t u t e the following values Kc = 0.8

constant f o r compression zone

~9o ! (a) W / P = 0 . 7 5

180 170 160

==- +sO 140 ,t30 IZO 110 IO0

/

9O

I

9

I

12

I

I

I

15 18 Sisal (oz/sq.yck)

21

I

24

FIG. 7 (b) W/P., O" 90

170

Comparison of Theoretical Moment w i t h Test Moments f o r Various Values of Kt . Sisal Reinforced Sheet.

Theoretical K t ' O 8

160 150 ":c 140

..,.....- ""

-0_"~3o

'9% ,'oI3

I

I

9

12

I

I

I

I

15

18

21

24

Sisal (Oz/sq.yd.)

Vol. 5, No. 4

359

FLEXURAL STRENGTH, FIBER REINFORCEMENT, PLASTER

= 0.94 correction for sisal y

= 0.5

(av. 18" length)

correction for random orientation of fibre

f

= values obtained by best f i t lines shown in Figs. 2 and 3 c f t = ~YP'q where p' = 1.55 x lO6 in -l for sisal fibre p' = 2.0

x lO6 in °l for glass fibre

The theoretical moments for differing values of Kt can now be compared with the f i t t e d values of M/t 2 for the flexural test results.

The results are

shown in Figs. 7 and 8 and considering that coefficients of variation for many of the test results are of the order of 20%, the plots are surprisingly good.

For sisal, the best f i t

is given by Kt = 0.5 with some suggestion

that the values of ~y used may be a l i t t l e high.

I t w i l l also be seen from

Fig. 7.b that when the results are extrapolated to 24 oz/yd 2 of sisal there is a clearly indicated practical limitation on the amount of sisal that can be used. The elastic response of the sisal, i . e . Kt = 0.5, though surprising,

310 ~ p ~ , g e ~ / j . ~

36O

(8) 5holt rtinfor(:¢d with

~'-mat (9oz/so.Vd)

grass

3/.O 320 30(3

'°N

'~ 280 260

22C

180 160

FIG. 8 Comparison of Theoretical Moments with Test Moments for Various Values of Kt.

ZlC

(b) 5h4,tt ~inforct.d with sis~,l ( 12oz/sO, yd )

~.

200 190

~.

180

~ ~ ~..~he~t~41

170 'c 160

9 150 ~'~t40 130 tZO 110

tO0

&

i

,

,

3

Z

I

,

,

110 9

,

8

j

j

,

i

i

|

? 5 65 A 3 Z Sulk Ocn$1ty ( | b / e l . )

,

1

i

~1

¢

s

,

9

8

?

,

G ~S

360

Vol. 5, No. 4 D. A. St. John, J. M. Kelly

is quite reasonable considering the 30 to 45% void volume of the cast gypsum used. Also i t has been reported by Majumdar et. al. ( l l ) that the bond between fibre and cast gypsum matrix is discontinuous and consists of gypsum lying randomly against the fibre.

Scanning electron micrographs taken for the

authors of some of the test specimens confirm the work of Majumdar et. al. Thus, taking these two factors into account, i t is presumed that the fibres are acting as i f they are lacking local bond restraint at points of high stress, and co~ined with the very large deformations in flexure the fibres respond in an elastic manner. I t is also of interest to considerthe reasons for the difference between the compressive strength f ' of the glass F mat and the sisal. The 9 oz. c glass F mat is equivalent to approx, the volume of 4 oz/yd 2 of sisal and this smaller volume plus the extra stiffness is sufficient to explain the differences.

I t can be concluded that similar decreases in compressive

strength would occur i f heavier weights of the glass F mat were used as has occurred for sisal. Conclusions Tests on cast gypsum reinforced with sisal and glass fibres in the bulk density range 56 to 72.5 I b / f t 3 (W/P = 0.9 to 0.6) show that the sisal decreases the compressive strength of cast gypsum by about 30% to 50% and glass fibres from approx. 0-30%. The differences in strength between sisal and glass fibres can be largely explained by the differences of volume and stiffness between the two fibres.

The effect of increasing the amount of

sisal incorporated in the cast gypsum is to give the expected increase in tensile strengths of the composite. All the above results can be taken as only indicative as the coefficient of variation was often of the order of 20%. A theory based on a non-linear stress-strain curve is proposed in an attempt to predict the ultimate flexural strength of fibrous plaster sheet. When the predictions of this theory are compared with the moments resulting from flexure, a reasonable f i t

is found at a value of Kt = 0.5.

This indi-

cates that, in fibrous plaster sheet, sisal fibre acts essentially in an elast i c manner. The results indicate that the theory of flexural behaviour of fibrous plaster sheet proposed by Brotchie and Urbach is in error. The general conclusion is that attempts to try and predict the ultimate flexural strength of fibrous plaster sheet using the properties of the individ-

Vol. 5, No. 4

361 FLEXURAL STRENGTH, FIBER REINFORCEMENT, PLASTER

ual components, fibre and cast gypsum, are not possible at this stage with any accuracy, as the variations occurring from unknown causes are larger than the effects of varying the components. The situation is further complicated by the fact that, due to the method of fabrication used, considerable anistropy in the physical properties of sheet is occurring. The large effect of sisal, and to a lesser extent of glass fibre, on the compressive strength of cast gypsum limits i t s effectiveness as random reinforcement as there is a l i m i t on the maximum amount of fibre that can be used without decreasing the ultimate flexural strength.

Variability in the

ultimate strength of fibrous plaster sheet is such that, using randomly distributed sisal fibre, no design improvements are possible until the source of this v a r i a b i l i t y can be found and reduced to a reasonable level. The outlook is more hopeful for the use of the preformed glass F mat or other glass fibres but further work is required to confirm this last conclusion.

Acknowledgements

The sheets of fibrous plaster used for this investigation were cast by J. O'Sullivan of the Central Institute of Technology. Most of the mechanical tests were carried out by B. Woodhouse and J. Killalea.

The authors wish to

acknowledge this assistance given in this project• References

I

•

Brotchie, J.F., Urbach, G. 1962 Aust. J. Appl. Sci., 14 (I) 69-93. The Flexural behaviour of fibrous plaster sheets.

2.

Russell, J . J . , Blakey, F.A. 1955 Aust. J. Appl. Sci., 7 (2) 176-90. Physical and mechanical properties of one cast gypsum plaster: plaster AB/2

3.

Waters, E.H. 1956 C.S.I.R.O. Aust. Div. of Build. Res., Report G5.1-3. Tests on commercial fibrous plaster sheets with a criticism of Aust. Standard Specification A44:1950.

.

Blakey, F.A. 1959 C.S.I.R.O. Aust. Div. of Build. Res., Report Z.7. Cast gypsum as structural material.

5.

Waters, E.H. 1961 Mater. Res. Stand. l p. 374. Compression testing of gypsum plaster~

6.

Russell, J . J . , Bright, J.E. 1962 Zem. Kalk Gip. 15 (2) 52. Effect of moisture content on compressive strengt-}~of small gypsum cubes after long periods of storage.

.

Adami, A., Ridge, M.J. 1966 C.S.I.R.O. Aust. Div. of Build. Res. Report Fl-12. Application of high density cast gypsum in the fibrous plaster industry.

.

Adami, A., Ridge, M.J. 1968 Fibrous Plaster Bulletin. July and August pp. 14, 17, 18 & 2, 13, 14, 17, 18. Some physical properties of fibrous plaster sheeting manufactured in the Melbourne d i s t r i c t .

362

Vol. 5, No. 4 D. A. St. John, J. M. Kelly

9.

St. John, D.A. 1972 DSIR N.Z. Chemistry Division Report No. Some physical properties of fibrous plaster sheet manufactured in New Zealand.

lO.

A l i , M.A., Grimer, J.A. 1969 J. Mater. Sci. 4 (5) 389-95. Mechanical properties of glass reinforced gypsum.

II.

Majumdar, A.J., Ryder, J.F., Rayment, D.L. 1968 J. Mater. Sci. 3 561-3. Fracture studied in glass-reinforced gypsum plaster using the s~anning electron microscope. Appendix

Ft

=

Effective force in tension

Fc

=

Effective force in compression

T

= Tensile Force in a single fibre

n

= Number of fibres crossing a unit width

p'

= The tenacity of the f i b r e ; ultimate tensile stress per unit of linear density

q

= The weight of fibre per unit of sheet

L'

= The c r i t i c a l length of f i b r e

L

= Actual average length of fibre = Modifying factor to account for fibre length L

y

= Modifying factor to account for random d i s t r i b u t i o n of f i b r e

Kt

=

Constant.

Tensile zone

K c

=

Constant.

Compressive zone

f~

= Tensile stress; equivalent to p'q

f' c

=

t

= Thickness of sheet

Kit

:

Thickness of compression zone

M

:

Moment of resistance in flexure.

Compressive stress; test value for composite