Glycerine Loading of Liquid-storage-tank Photoelastic models

Technical note describes the planning of a tank-model experiment and the stress-freezing procedure adopted for a model loaded by glycerine

by Robert Mark

ABSTRACT---The advantages of small-scale photoelastic- model analysis of welded-steel pressure vessels are well known. The object of a current investigation is to show tha t similar advantages accrue in the analysis of com- plex reinforced-concrete liquid-storage tanks. This technical note describes the planning of a tank-model experiment and the stress-freezing procedure adopted for a modeI loaded by glycerine.

Introduction C o n c r e t e s t r u c t u r a l des ign is u s u a l l y b a s e d on force d i s t r i b u t i o n s wh ich a re p r e d i c t e d b y l inea r e l a s t i c ana lys i s of a s s u m e d h o m o g e n e o u s (and m o n o l i t h i c ) m a t h e m a t i c a l m o d e l s . T h e use of smal l - sca le p h y s i - ca l mode l s f o r m e d of p l a s t i c to o b t a i n t hese d i s t r i b u - t i ons was e s t a b l i s h e d b y Beggs 1 a n d o t h e r s a l m o s t a h a l f c e n t u r y ago. I n s t r ess - f rozen t h i n p l a t e a n d shel l models , force d i s t r i b u t i o n s m a y be r e a d i l y de- t e r m i n e d f rom p h o t o e l a s t i c o b s e r v a t i o n s o f sur- face s t resses .

Robert Mark is Research Engineer and Lecturer, Department of Civil and Geological Engineering, Princetgn Univers:ty, Princeton, N . J .

Fig. 1--Tank model with Teflon cover

Experimental Design T h e l o a d i n g to be a p p l i e d to a p h o t o e l a s t i c m o d e l

c a n be e s t i m a t e d b y cons ide r ing t h e m a x i m u m f iber s t r a i n s t h a t wil l be p r e s e n t in b o t h p r o t o t y p e a n d mode l . F o r a wel l p r o p o r t i o n e d conc re t e s t r u c t u r e , t h i s s t r a i n will be a b o u t 500 # in . / i n . , whi le t h e m a x i m u m s t r a i n in a s t r e s s - f rozen e p o x y m o d e l is of t h e o r d e r o f 10 ~ # i n . / i n . T h e r e l a t i o n s h i p b e t w e e n p r o t o t y p e a n d m o d e l l o a d i n g dens i t i e s for t a n k s y s t e m s h a v i n g c o m p l e t e s i m i l i t u d e * is d e r i v e d f rom d i m e n s i o n a l ana lys i s :

(1) ~p (Ee ) , \X,,,/

where

o = d e n s i t y o f f lu id l o a d i n g

E = Y o u n g ' s m o d u l u s

�9 = s t r a i n

), = c h a r a c t e r i s t i c l e n g t h

a n d t h e s u b s c r i p t s m a n d p refer to m o d e l a n d p r o t o - t y p e .

F o r t he one f o r t y - e i g h t h scale m o d e l i l l u s t r a t e d in F ig . 1, w i t h Em = 3500 psi , a n d w i t h E~ = 3.5 (10) 6 psi , eq (1) i n d i c a t e s a f l u i d - d e n s i t y r a t i o o f p,,~/ pp ' ~ 1.0.

G l y c e r i n e h a v i n g a specif ic g r a v i t y of 1.26, h a s b e c o m e u b i q u i t o u s in our l a b o r a t o r y . U . S . P . g rade g lyce r ine ( s to red a t r o o m t e m p e r a t u r e in c losed con t a ine r s ) is i n e r t w i t h r e s p e c t to e p o x y dur - ing t h e s t r e s s - f r eez ing cycle. A s i t s d e n s i t y is o n l y a b o u t 1 p e r c e n t g rea t e r t h a n e p o x y ' s , g lyce r ine flo- t a t i o n is f r e q u e n t l y e m p l o y e d for t h e e l i m i n a t i o n o f body - fo r ce effects onf lex ib le e p o x y m o d e l c o m p o n e n t s a n d assembl ies . 2 I t is also u sed in c o m b i n a t i o n w i t h w a t e r a n d ge l a t i n in v a r y i n g p r o p o r t i o n s to fo rm a n e x t r e m e l y sens i t i ve m o d e l m a t e r i a l for t h e a n a l y s i s o f b o d y - f o r c e s t r ess d i s t r i b u t i o n . 3 T h e a p p l i c a t i o n of g lyce r ine as a l o a d i n g f luid for t a n k

* The effect of any differences in Poisson's ratio is not cortsidered.

Experimental iV[echanics I 47

Fig, 2--Model moment along vertical sec- tion at midspan

hi (3

O~ -r I-- Z 0 )-- 0

0 3 0 J

l BASE

5.0 TEST LIQUID - - 4 . 8 2

LEVEL

/ /

/

-o.50 -o.3o -o.lo o o.lo MOMENT (IN-LBS)

~ \ THEORETICAL LIQUID LEVEL

4.0-

I ~ ~PREDICTED 3.0 . l I i ~ (PINNED ~ OBSERvEDBASE}

2.0 ~ PREDICTED

I (FIXED BASE

I 0.30

testing, therefore, seemed most appropriate. An open-top square- tank model was selected for

the first experiment. Model dimensions: 91/2 in. on a side • 5-in. high (internal measurements) • 0.250-in.-thick walls, were scaled from a prototype design based on a publication of the Port land Cement Association. 4 A base having 0.65-in. thickness was chosen to act as a fixed boundary. The model was fabricated from machine-finished Photolastic PL-4 cast plates joined by Photolastic PC-1C cement. The stress-fringe constant for the model material was found from diametral loading of a disk to be 2.19 lb/fringe-in. (normal stress).

Model Testing The model was supported on a flat, rigid alum-

inum plate in the stress-freezing oven. /,~ was filled to within 0.1 in. from the upper edge and the fluid level was carefully measured. A 1/32-in.-thick Tef- lon plate covered the tank during the test to reduce fluid loss.

To eliminate any problems arising from the rela- t ively large thermal inertia of the model and the glycerine, the rather fast rise time of the s tandard stress-freezing cycle (room temperature to 290 ~ F in 3/4 hr) was abandoned. A revised cycle called for a 4-hr rise t ime followed by a 2-hr "soak" at 290 ~ F, and cooling at 5 ~ F /hr .

The fluid level was measured following stress freezing and a loss of 0.05 in. noted. Plate de- formations were measured and a number of slices were taken from the model to indicate the force distributions throughout the tank. A typical slice is the vertical section showing integer order fringes in Fig. 2. Bending moments corresponding to portions of the slice indicating linear stress distribu- tions have been plotted according to

h 2

M = (~v - ~t) 12 (2)

where

M = bending momen t /un i t width

~0 and ~t = stresses on the outer and inner sur- faces of the slice (determined from light- and dark-field fringe photo- graphs)

h = plate thickness

Moment at the lower boundary has been extrap- olated as shown.

Predicted moment values for fixed- and pinned- base tanks as given in Ref. 4 are also plotted on Fig. 2. Considering the differences between the mathe- matical and the physical models (i.e., fluid level not exactly equal to wall height and different Poisson's ratios) the test results are reasonable and sub- stantiate the approach for application to complex tank configurations.

Acknowledgments

The reported work is supported by a grant from the Reinforced Concrete Research Council. The author wishes to express appreciation to the Coun- cil, and to A. Lazaro, graduate student in the De- par tment of Civil and Geological Engineering, and L. Barth, model maker, School of Architecture, for their valuable assistance.

References 1. Beggs, G., "Design of a Multiple-arch System," Trans. A S C E

88, 1208-1230 (1925). 2. Mark, R. , "Eliminating the Body-force Effect in Stress-frozen

Models," EXPERIMENTAL MECHANICS, 5, 7, 239--240 (1965). 3. Richards, R. , and Mark, R. , "Gelatin Models for Photoelastic

Analysis of Gravity Structures," Proc. 2nd. S E S A Int. Cong. on Exp. Mech., 112-122 (1966).

4. "'Rectangular Concrete Tanks," Portland Cement Assoc. Info. Bull. S T 63 (1951).

48 I January 1968