y - &
J O U R N A L
of the
AMERICAN CONCRETE INSTITUTE
(ACI PROCEEDINGS Vol. 41)
V o l. 1 6 September 1 9 4 4 N o . 1
C O N T E N T S <
Papers and Reports... 1-52
Preparation of Technical Papers W . D. BIGLER 1
The Effectiveness of Various Treatments and Coatings for Concrete in Reduc
ing the Penetration of Kerosene...F. B. HORNIBROOK 13 Two-W ay Reinforced Concrete Slabs...PAUL ROGERS 21 Reactivity of Aggregate Constituents in A lk a lin e Solutions...
...LEONARD BEAN a n d J. J. TREGONING 37
Job Problems and Practice... 5 3 -6 0 M ix for Pre-stressed Concrete Tanks Using Coral and Porous Limestone.. . .
... J O H N G. DEMPSEY 53 Durability of Asbestos-Cement Siding...C. R. HUTCHCROFT 55 Frozen Concrete Cheaply Repaired...WALTER H. WHEELER 56 Color Variation in Concrete Products...J. W. KELLY 59
Current Reviews... 6 1 -7 2
News Letter... 1 -1 6 Report of 19 4 4 Nominating Committee • Who's W ho • Three New Standards
• 107 New Members • Honor Roll • Personnel • A IS I Research • A C I Construction-Practice Aw ard • Special A C I Publications • Advertisers in February J O U R N A L • Recent A C I Standards
to provide a com radeship in finding the b est ways to do concrete work of all kinds an d in spreading th at know ledge
A D D R E S S . 7 4 0 0 S E C O N D B O U L E V A R D , D E T R O I T 2 , M I C H .
t 7.50 bv the year $1.50 per copy
Exlra copies to members SI .0 0
Discussion closed on a ll Journal contents, Sept. 1 9 4 3 to June 1 9 4 4
— for publication N ovem ber 1 9 4 4 Supplement
Sept Jl *44 Preparation of Technical Papers—W. D. Bigler
The Effectiveness of Various Treatments and Coatings for Concrete in Reducing the Pene
tration of Kerosene—F. B. Hornibrook T w o-W ay Reinforced Concrete Slabs—Paul Rogers
Reactivity of A g greg ate Constituents in A lk a lin e Solutions—Leonard Bean and J. J.
Tregoning
V o l. 16— N o. 1 September 1944 (Proceedings V o l. 41)
O U R N A L
o f the
AM ERICAN C O N C R E T E INSTITUTE
P u b lish e d b y th e A m e ric a n C o n c r e te In s titu te . T he In s titu te w a s fo u n d e d 1 9 0 5 / in c o r p o ra te d in th e D is tric t o f C o lu m b ia in 1 9 0 6 as T he N a t io n a l A s s o c ia tio n o f C e m e n t U s e rs /th e nam e c h a n g e d 1 9 1 3 b y c h a r te r a m e n d m e n t. T h e J o u r n a l is issued six tim es y e a r ly in th e m onths o f J a n u a ry , F e b ru a ry , A p r i l , J u n e , S e p te m b e r a n d N o v e m b e r u n d e r th e a u th o r ity o f th e
BOARD OF DIRECTION, AMERICAN CONCRETE INSTITUTE
President ROY W. CRUM
V ice Presidents
DOUGLAS E. PARSONS, J O H N R. NICHOLS Secretary-Treasurer
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T H O M A S E. S TA N TO N Directors-at-Large
S T A N T O N WALKER Past Presidents
ROBERT F. BLANKS
FRANK E. RICHART RODERICK B. Y O U N G
BEN MOREELL RAYM O ND E. DAVIS M O R TO N O . WITHEY
Papers a n d o th e r c o n trib u tio n s p re p a re d w it h a v ie w to J o u r n a l p u b lic a tio n s h o u ld b e s u b m itte d in t r ip lic a t e , a d d re s s e d : S e c re ta ry , P u b lic a tio n s C o m m itte e , A m e r ic a n C o n c r e te In s titu te , 7 4 0 0 S e co n d B o u le v a rd , D e t r o it 2 , M ic h ig a n . P u b lic a tio n o f a c o n trib u tio n d o e s n o t im p ly th e a c q u ie s c e n c e o f c ritic s ( w h o s e a d v ic e is so u g h t b y th e C o m m itte e , p r io r to a c c e p ta n c e ) o r o f th e In s titu te in th e o p in io n s w h ic h it e xpresses n o r th e a p p r o v a l o f d a ta o r p r a c tic e w h ic h th e c o n tr i
b u tio n re c o rd s . In s titu te a u th o r ity a tta c h e s o n ly to S ta n d a rd s fo r m a lly a d o p te d as p ro v id e d in th e By- L a w s . A co m m itte e r e p o r t im p lie s m e re ly th e jo in t c o n tr ib u tio n o f a n a p p o in te d g ro u p .
Subscription price $ 7 .5 0 p e r y e a r p a y a b le in a d v a n c e . To mem bers, $ 7 .5 0 p e r y e a r , in c lu d e d in th e a n n u a l
d u e s . ( A s p e c ia l d ue s ra te o f $ 3 .0 0 p e r y e a r a p p lie s fo r “ a s tu d e n t in re s id e n c e a t a re c o g n iz e a te c h n ic a l o r e n g in e e rin g s c h o o l” a n d in c lu d e s J o u r n a l s u b s c rip tio n . Bound volumes 1 to 4 0 o f P R O C E E D IN G S O F T H E A M E R IC A N C O N C R E T E IN S T IT U T E (1 9 0 5 to 1 9 4 3 ) a re fo r sa le as fa r as a v a ila b le , a t p ric e s to b e h a d on in q u ir y o f th e S e c re ta ry -T re a s u re r. S p e c ia l p ric e s a p p ly fo r members o rd e rin g b o u n d volum es in a d d itio n to th e m o n th ly J o u r n a l.
P ublication address: 7 4 0 0 S eco n d B o u le v a r d , D e tro it 2 , M ic h ig a n . C o p y r ig h t, 1 9 4 4 , A m e ric a n C o n c r e te In s titu te , P rin te d in U . S. A . E n te re d a t th e Post O f fi c e a t D e tr o it, M ic h ig a n , as m ail o f th e se co n d class u n d e r p ro v is io n s o f th e A c t o f M a r c h 3 ,1 8 7 9 .
2 ' J O U R N A L 'OF THE A M E R IC A N CONCRETE INSTITUTE September 1944
have earned recognition by devoting their lives to the practical m echanics of their work; th ey have, as a rule, spent all their time in acquiring know ledge of m athem atics, m aterials, labor problems, and continuous changes in practice to the exclusion of the finer arts such as writing. As a resu lt m any of America’s best engineers are handicapped in th is essential work of com m unicating ideas.
I t would be far from true to say th a t there have been no technical men w ith ability for interesting and lucid presentation of observations.
E very stru ctu ra l designer of m ature age is acqu ainted w ith J. A. L.
W addell’s “ Bridge Engineering” of three decades ago, a set of two large volumes th a t reads like a novel in its m asterly presentation of the subject.
Instances of well-planned and clearly presented contributions to engin
eering literature in recent years are th e num erous exact and com pre
hensive studies on stru ctu ra l steel by the late Leon S. Moisseiff, noted stru ctu ra l engineer. M any present-day authors deserve com m endation.
B u t it is a m isfortune th a t so m any of A m erica’s scientific m en, who as a class enjoy unquestioned rank am ong the w orld’s best, should ap p ear mediocre in one branch of their activity.
B ritish engineering journals show th a t English engineers look to America, sometimes enviously, to stu d y sta n d a rd practice, working conditions, and salaries. We in tu rn m ight well look back across th e A tlantic to stu d y our neighbors’ superior use of words. A difference in literary tendencies betw een these two peoples w ith com m on speech is to be expected. The B ritish have cultivated th eir n ative English for centuries w ith the result th a t accum ulated refinem ents in expression have passed down from father to son. Likewise o th er E uropeans have a unified heritage of speech. We Americans, however, have no common language background. Our population is derived from all races of Europe and each race has brought its own vocabulary. In th e shift to English th e heterogeneous people have no t been able to assim ilate the new language as com pletely as th ey m ight absorb a nativ e tongue. We see a t tim es disappointing evidence in th e result such as the excessive slang and inten tional misuse of words th a t h in t a t disrespect for the adopted language.
In to our textbooks, reports, journals, and popular books on science goes a g reat deal of confused, half-thought-out wording. Am bitious salary workers who spend evenings in stu d y waste m uch tim e glaring a t pages and wondering w hat the w riter intended to say. I t should be axiom atic th a t if a w riter expects his words to be read he should accept th e responsibility of m aking them unquestionably clear a t a glance and n o t leave sentences th a t th e reader will have to puzzle over. The reader should n o t be expected to ponder over th e m eaning of words while he is
PREPARATION OF TE CHN IC AL PAPERS 3
thinking of the ideas them selves. As a rule engineering concepts, as such, are easily com prehended by an educated and experienced engineer.
G rasping of knowledge is no t difficult to a m ind th a t understands the facts upon which the knowledge is based. S tud y of the p rin ted page usually is necessary only to ferret ou t meanings of obscure passages.
T h a t thou g h ts can be conveyed concisely and efficiently to the reader is proved b y new spapers in which journalists present the m ost complex national and international problems so th a t even the partially educated masses read th e accounts w ith in terest and rapid ity of comprehension
;e and feel th a t th ey have knowledge of th e world a t their fingertips.
I t is no t the intention of this paper to discourage any engineers, a- in du strial leaders, or other technical men from w riting for publication.
B y all m eans a stru ctu ral designer who has worked out an im proved m ethod of stress analysis or a m anufacturer advocating a new use for concrete should give his findings and opinions to the world even though
,3
he has h ad no w riting experience a t all. In his verbal presentation the am ateur cannot be expected to show the exactness of John H enry Newm an or th e ability for detail of R obert Louis Stevenson, nor will he use th e interest-catching devices of the journalist, b u t he can a t least give his paper the th o u g h t necessary to arrange ideas in an orderly fashion and present words which m ost exactly fit the intended meaning.
tllP • • • •
L et us consider some details in the preparation of a technical paper.
T he w riter can fu rther clearness a t the s ta rt by explaining in the first paragraph why the subject discussed is w orthy of presentation. Such a statem en t when used as justification of a news account is known to journalists as the “feature” or “lead.” Two examples of possible open
ings of this typ e are:
This paper is the first description presented to th e public on the use of glued scrap-lum ber lam inated arches.
W hen N avy engineers tore down sections of a quay wall in salt w ater th ey found reinforcing bars completely rusted through. In the new concrete sea wall, described here, special coverings protect the steel.
F rom such an introduction the reader learns w hat the article contains and judges w hether it will be of interest to him.
If th e paper describes an engineering project, a sum m ary giving a com plete picture will prevent the necessity of th e reader struggling later to piece together the com ponent parts. This sum m ary corresponds to the plot plan of a set of architectural or stru ctu ral drawings. Such a iceept description m ight b e :
The project consists of 250 duplex dwellings; office building;
Imhoff tan k with sewage pum ps; water, gas, sewer, and power lines;
ieis
4 JO U R N A L OF THE A M E R IC A N CONCRETE INSTITUTE September 1944
3 acres of grading and sodding for lawn; 8000 sq. ft. of concrete sidewalk; and 2.5 miles of street grading and pavem ent.
As th e w riter later discusses each item in tu rn the reader expects it and understands w ithout undue th o u g h t its proper relation to th e whole.
W ording thro ughout th e article requires m ost conscientious care. Too often a w riter hastily accepts inaccurate wording th a t comes to his mind, assum ing th a t because it has for him an association w ith his idea, it will also have the same association for th e reader. In this respect w riting is a sort of self-delusion. The author-to-be creates the subject m a tte r in his m ind and after a period of reflection embellishes it w ith exact m ental details. The ideas are now all perfectly clear. H e will p u t them into words. H e composes a sentence th a t recalls to him the first m ental picture. He writes th e sentence. A second sentence recalls another m ental picture; he puts th a t down, and so on. A fter com pleting the article he reads it over. The words rem ind him of all th e ideas he intended to present, the ideas th a t were already clear and fixed in his mind. Good, he says, w riting th a t recalls such vivid pictures m ust be perfect.
The au th o r offers the paper to a friend to read. The friend looks a t it. His face registers perplexity. W h at does this sentence m ean, and this one? The au th o r feels annoyed by the stu p id ity of th e friend whom until then he considered intelligent. He explains w ith em phasis th a t it is all perfectly clear; th e words m ean th u s an d thus. Oh, yes, now the friend understands, afte r it is explained to him.
General and a b stra c t ideas are th e m ost difficult to describe. C oncrete objects and actions appealing to the senses, on th e o th er hand, can be pictured m ore effectually. L et us tak e this sentence as an exam ple:
A large white horse galloping down th e center of the 20-foot- wide asph alt pavem ent stum bled and fell in a heap.
H ere fam iliar objects and concrete actions which in real life would be directly perceivable by th e senses present a clear and forceful picture.
B u t it is difficult to im p art to others knowledge th a t cannot by its n atu re be reduced to sense perception and simple basic actions associated w ith our lives. In selecting words to use as th e m eans of expressing such general ideas, the w riter m ust tak e pains first to decide exactly w hat he w ants to say and then to say exactly th a t. In th e struggle to find th e elusive right word the thesaurus is a g reat help, and no w riter, even the m ost accomplished, can work satisfactorily w ith ou t this h an d book.
A stu d y of engineering publications and textbooks provides am ple evi
dence of fau lty expressions. A few tak en from th e prin ted pages of cu rrent
PREPARATION O F TECHN IC AL PAPERS 5
lite ratu re will illu strate the tendencies tow ard inexactness. The first is from a well-known publication dealing with concrete design:
F or each of th e four types (of haunch shapes in beams) th e shape of a m em ber is characterized b y two ratios, a representing the
min. I len gth and b the depth of th e haunch. The value of b — r max.
1
/ min. d
\ 3
is assumed to equal the ratio of I r I , the beam w idth being
\m a x . d /
considered constant and reinforcem ent disregarded.
The idea intended b y these two sentences is simple, b u t it is given only partially. E very engineer who has read th e publication has had to stop and stu d y th e inferences th a t follow this q uotation to learn w hat ratio a is. I t would have been as easy to present the first sentence as follows and allow the reader to grasp the thou gh t im m ediately:
Two ratios determ ine the characteristics of each of th e four types: a, the length of th e haunch divided by th e to ta l length of the beam ; and b, th e m om ent of inertia of the m axim um haunch divided by th e m om ent of in ertia of th e beam.
In the second sentence the words “ the ratio of” are unnecessary.
This ending of a paragraph is from a popular book on science:
As no ghost can talk to a biologist, so no biologist can talk to a spiritualist. Biology, sp irituality; m aterialism , m ysticism ; n atural, supernatural; faith in the present, fa ith in and hope for the future;
science, religion.
Here is th e case of a w riter erroneously assum ing th a t words which recall an idea to him will necessarily present th e idea to others. A ppar
ently the late noted anthropologist h ad a definite message on the con
tra s t between religion and science, perhaps a statem en t th a t the two modes of thought are irreconcilable; b u t exactly w hat he wished to convey we cannot ascertain from th e words.
In an interesting detailed report on th e repaving of a highway by laying a brick course over the existing concrete the project engineer included a contradictory statem en t:
As the new crown did n o t correspond to th e old (which was very irregular), the elevation used depended on the crown of the old slab a t any point.
F rom the controlling d a ta given, one would judge th a t th e w riter wished to say:
As th e new crown did no t correspond to the old, which was very irregular, the elevation used depended largely on the peaks of the old crown.
6 JO U R N A L OF THE A M E R IC A N CONCRETE INSTITUTE September 1944
The report continues:
The elevations were p lotted to a scale of 1 m m ., or .01 ft., and where th e existing crown was more th a n th e new, th e center eleva
tion was plotted. Otherwise th e highest edge was plotted.
The description of scale is not clear. “ M ore” probably refers to elevation.
T he elevations were p lotted to a scale of
1
m m. to .01 ft. W here the existing crown was higher th an th e new, the center elevation was shown; otherwise th e highest edge was plotted.This sentence is from an account of the m anufacture of plyw ood:
W artim e dem and for logs has decreased b y ab o u t 2 feet from th e o- to
6
-foot m inim um diam eter form erly accepted.The w riter sta rts wdth one sentence and ends w ith another. Though the m eaning is apparent, the words actually indicate th a t th e dem and for logs has decreased. D eletion of “fro m ” will correct th e defect.
W artim e dem and for logs has decreased b y ab o u t 2 feet th e 5- to
6
-foot m inim um diam eter form erly accepted.The m eaning of th e following sentence is doubtful:
Consider a sym m etrical beam w ith straig h t haunches, dim ensions and loads being as shown in Fig. 2.
A t first glance the reader assumes th a t “ straig h t haunches, dim ensions and loads” forms a series; then he decides th a t probably “ dim ensions and loads” sta rts a separate, second phrase. N o dou bt th e w riter m ean t:
Consider a sym m etrical beam w ith straig h t haunches, th e dim en
sions and loads being as shown in Fig. 2.
Long unbalanced sentences hinder free flow of th o u g h t. The q u o ta tion below is from a discussion of stre n g th of spaced wood colum ns in an au th o rita tiv e publication on tim ber design.
W hen blocks are placed and calculations for permissible loads are m ade as recom m ended, safe unit loads for spaced columns result (so far as stren g th or resistance to lateral buckling in a direction perpendicular to th e m utually contactin g surfaces of the blocks and individual m em bers is concerned) an d it is unnecessary to check the unstayed portions (from center of bolt in end blocks to center of spacer block) of th e individual m em bers.
T he first parentheses set aside an essential idea th a t should be prom i
nent. This example dem onstrates, b y th e “ are placed” an d “ are m ad e”
of th e first clause, anoth er practice general am ong technical m en, the free use of th e passive voice in verbs in p redom inating positions. Profes
sional au th ors, however, know th a t forceful w riting requires, when feas-
PREPARATION OF T E C H N IC A L PAPERS 7
ible, th e active voice in leading verbs. R earranging this obscure sentence will m ake it clear.
Calculations of permissible loads for spaced columns with blocks placed as recom m ended do not need correcting for possible buckling in a direction perpendicular to the contacting faces of th e spacers, and it is unnecessary to check th e unstay ed portions, from the center of bolt in end blocks to center of spacer block, of the indi
vidual m em bers.
An engineer who had observed flood dam age m ade valuable conclusions on th e causes and possible preventive m easures, b u t he stated a finding erroneously:
I th in k th a t m uch of the flood damage is due to the fact th a t our citizens really do not know how high their land is above m axim um flood level.
Knowledge of how high land is above m axim um flood level will n o t help in preventing dam age. Such land is safe.. I t is th e area below high w ater and dep th of possible inundation th a t is a measure of potential destruction.
I th in k th a t m uch of the flood dam age is due to the fact th a t m any of our citizens really do not know to w hat extent their land is below m axim um flood level.
An article on th e stren g th of concrete construction joints had defective syntax.
The fundam ental principle of the sand cure m ethod of joint clean
up was to place th e ty p e of concrete and in such a m anner th a t the surface which form ed one face of the joint would be equal in quality to the concrete mass and then protect and m aintain th a t surface in th e sam e condition as it was when placed until the next concrete lift was placed.
The conjunction “a n d ” joins the noun phrase “ the ty pe of concrete”
and the adverbial phrase “ in such a m anner th a t . . . ” leaving aw kward sentence stru ctu re and confused thought. R earranging will im prove the sentence.
T he basis of th e sand cure m ethod of joint cleanup is the placing of concrete of suitable quality in such a m anner th a t th e surface forming-one face of th e joint will be equal in q u ality to th e concrete mass, and then, u n til the next lift is poured, protecting and m ain
taining th a t surface in the same condition as it was when placed.
T his is from an engineering m agazine:
In let and outlet structures in the canal system of the Im perial Irrigation D istrict began to be m ade of precast concrete when war
8 JO U R N A L OF THE A M E R IC A N CONCRETE INSTITUTE September 1944
necessity brought ab o u t restrictions in the use of lum ber for such purposes.
I t is tru e th a t th e intended m eaning is obvious. I t is illogical, how
ever, to say th a t “ stru ctu res began to be m ade” because th e beginning was m ade b y the D istrict, no t the inanim ate objects.
The Im perial Irrigation D istrict changed th e construction of inlet and ou tlet structures in its canal system to precast concrete when war necessity brought abo u t restrictions in th e use of lum ber for such purposes.
W ords and phrases of transition are often necessary to explain relations betw een successive ideas.
Following retaining wall construction, repairs were m ade to th e road pavem ent. T he sm aller breaks were repaired as th e wall was
poured.
An added short explanation will elim inate th e a p p a ren t contradiction.
Following retaining wall construction, th e m ajor repairs were m ade to th e road pavem ent. The sm aller breaks, how ever, were repaired as the wall was poured.
W ebster’s D ictionary does n o t give a m eaning for th e word “ o rien t”
th a t would conform to this u s e :
To orient on the specific work th a t was carried out, T able 1 has been prepared.
A su b stitutio n will elim inate the defect.
As a guide to th e work th a t was carried out, T able 1 has been prepared.
In a description of th e higher cost of G unite work in N ew Y ork a w riter has offered th is statem en t:
W ork done in New York C ity requires th a t th e nozzlem an be a cem ent finisher and the gun be operated b y a concrete laborer.
In skeleton form the sentence is: “ W ork . . . requires th a t . . . ” A ctually it is no t the work th a t requires specially classified m e n ; it is th e labor union th a t m akes the requirem ent. T he work itself would dem and no greater skill in New York th a n in any o ther city.
On work done in New York C ity there is a requirem ent th a t the nozzleman be a cem ent finisher and th e gun be o p erated b y a concrete laborer.
T he following is from a discussion of analysis of bending m om ents in statically indeterm inate structures:
There are perhaps two additional features th a t en ter into s tru c tu ra l design and analysis. These are: a. The necessity of tak in g
PREPARATION OF TECHN IC AL PAPERS 9
into account th e often wide d epartu re from theo ry dependent on a different stress distribution from th a t on which th e theory is based.
T he last sentence can be revised to provide more logical sequence of th o u g h t.
These are: a. The necessity of tak in g into account th e fact th a t theoretical stress distribution upon which com puted stresses are based m ay often be greatly erroneous.
T his selection dealing w ith road alignm ent does n o t give enough inform ation to indicate the intended m eaning:
An a tte m p t was m ade to keep the grade breaking in a given direction for a m inim um of
100
feet, b u t during the la tte r p a rt of the project this was reduced.The word “ u n it” has become popular w ithin recent years as a sub
s titu te nam e for a great v ariety of objects. F or the sake of conciseness, however, a w riter should n o t allow this word to replace repeatedly th e exact term . Especially, two “u n its” w ith different m eanings w ithin one sentence will no t m ake for greatest clarity.
A pproxim ately 210,000 tem porary fam ily dwelling u nits with wall area aggregating ab o u t 180,000,000 sq. ft. and requiring more th an
200
,000,000
u nits have been or are being built of concrete m asonry.The first “ u n it” is unnecessary; “blocks” or “sections” would be more exact for the second.
A pproxim ately 210,000 tem p orary fam ily dwellings w ith wall area aggregating about 180,000,000 sq. ft. and requiring more th an
200
,000,000
blocks have been or are being built of concrete m asonry.I t is true th a t th e foregoing defects are extreme. Our technical litera
ture, nevertheless, shows too m uch of such obscurity. Vagueness m ay n o t be, as in the examples, confined to one or two sentences: it m ay run through paragraphs or the article as a whole.
As to the question of raising th e stan d ard s of American technical literature, it should be ap p a ren t th a t some steps need to be taken, such as stressing English in the curriculum of engineering colleges. The belief th a t English should play only a m inor p art, if any, in engineering courses is an u n fo rtu n ate corollary to th e present-day supposition th a t m ach
inery and in d u stry are th e highest forms of intellectual achievem ent.
I t should be obvious, in this connection, th a t although some forms of engineering exist w ithout higher m athem atics, no technical work of any kind would be possible w ithout language. Such instruction, however, should no t w ait for college; high school years are the m ost practical period for grounding the stu d en t thoroughly in English. In any case,
10 JO U R N A L OF THE A M E R IC A N CONCRETE INSTITUTE September 1944
our language stan d ard s will n o t im prove until there develops a general realization th a t English deserves m ore respect, m ore tim e, and m ore work th a n it receives now.
R E C O M M E N D E D B O O K S FOR STUDY A N D REFERENCE W riting th e Technical R eport, J. R . Nelson, M cGraw-Hill.
The P rep aratio n of R eports, R. P. B aker and A. C. Howell, R onald Press.
T he E ngineer’s M anual of English, W. O. Sypherd an d Sharon Brow n; Scott, Fores- m an & Co.
R eport W riting, C. G. Gaum , H . F. Graves, and L. S. S. H offm an; Prentice-H all.
W riter’s Guide and Index to English, P . G. P errin ; Scott, Foresm an & Co.
E nglish and Engineering, F ran k A ydelotte, M cGraw-Hill.
T he A rt of W riting, Sir A rth u r T. Quiller-Couch, Cam bridge U niversity Press.
Expressive English, J. C. F em ald, G rosset & D unlap.
W h at a W ord! A. P. H erb ert; D oubleday, D oran & Co.
College H andbook of Composition; E . C. Woolley, F. W. Scott, and E . T. B erdahl;
D. C. H e a th and Co.
A D ictionary of M odem E nglish Usage, H . W . Fow ler, G. P . P u tn a m ’s Sons.
R oget’s T hesaurus, G rosset & D unlap.
Discussion of this paper should reach the A C I Secretary in triplicate by March 1, 1945 for publication in the J O U R N A L for June 1945.
e
ies-
Ii
aU;
A part of PROCEEDINGS OF THE AM ERICAN CONCRETE INSTITUTE V o l. 41
A M E R I C A N
J O U R N A L
o f the
C O N C R E T E I N S T I T U T E
V o l. 16 N o. 1 7400 SECOND BOULEVARD, DETROIT 2, MICHIGAN September 1944
The Effectiveness of V a r i o u s T r e a t m e n t s a n d Coatings for Concrete in R e d u c i n g th e P e n e tr a ti o n of K e ro se ne *
By F. B. H O R N IBR O O Kt
M e m b e r A m e ric a n C o n c r e te In s titu te
S Y N O P S I S
M easurem ents were made of th e penetration of kerosene under a 12 foot pressure h ead into discs of concrete which had received various treatm en ts or coatings. The tests were classified into 7 groups as follows: (1) reference concrete, (2) integral admixtures, (3) sodium silicate and magnesium fluosilicate treatm ents, (4) plaster coats, plain and w ith adm ixtures, (5) magnesium oxychloride type coatings,
(6) linseed oil and spar varnish coatings, and (7) synthetic plastic and latex coatings. Comparisons of the relative rates of penetration of kerosene into th e specimens of each group are given, together w ith a discussion of various other properties of each group.
IN T R O D U C T IO N
From tests reported in this Jo u r n a l in 1921f it was concluded th a t oils having viscosities lower th a n abo ut
6
centipoises a t 21C m ight leak excessively from unlined concrete tanks. Oils having viscosities lower th a n th a t value include Diesel oils, light fuel oils, kerosene and, of course, gasoline. The increased w artim e use of concrete tanks for the storage of such oils prom pted a lim ited investigation a t th e N ational B ureau of S tandards of proposed m aterials for rendering th e concrete adequately im perm eable to light oils. Although there are m any lining m aterials, m ethods of application, and observations of long-time effects th a t could no t be included in a lim ited investigation, it is believed th a t some of th e results obtained m ay be of value in connection w ith the problem of liquid storage in concrete.♦R e ceiv e d b y th e I n s tit u te , M a rc h 29, 1944.
Î
N a tio n a l B u re a u of S ta n d a rd s , W a sh in g to n , D . C.“ F u r th e r T e s ts of C o n c re te T a n k s for Oil S to ra g e ,” b y G eo rg e A. S m ith . Proc. A m . C o n cre te I n s t., Vol. 17, p . 22, 1932.
(13)
14 JO U R N A L OF THE A M E R IC A N CONCRETE INSTITUTE September 1944
Fig. 1— Testing apparatus shown schematically
DESCRIPTION O F TESTS
The m ethod adopted in th e present tests consisted of tre a tin g or coat
ing concrete discs and subjecting one face of th e discs to a
12
-ft head of kerosene which had a viscosity a t 21-C of ab o u t 1.6 centipoises. The daily inflow of th e kerosene was m easured. T he ap p a ratu s, shown schem atically in Fig. 1, consisted essentially of a channel-iron base to which a 4-in. section of a 12-in. pipe was welded. An inflow pipe an d a bleeder valve were thread ed into the b o tto m of th e base as illu strated . Difficulties experienced w ith leaking pipe joints were overcom e w ith a quick-setting oil-resistant gasket cement. A grad u ated b u re tte was sealed into th e top of th e standpipe for m easurem ent of th e inflow. The ap p a ratu s was set up in a constant tem p eratu re room.T he gasket for sealing th e specimen in place consisted of tw o con
centric rings spaced about V/2 in. ap art, th e inner ring of No.
12
copper wire and th e outer ring solder wire; the space betw een th e rings was filled with a hot glycerine glue gel* which is fluid when h o t b u t tough an d ru b bery when cold. The specimen was p u t in place while th e gasket m aterial was hot, and th e clamps tightened over th e specimen.The concrete used in fabricating th e te s t specimens was a nom inal
6
-bag,6
jdj-gal. per bag concrete having a 2y 2 to 3-in. slum p. In tests where integral adm ixtures were used, th e mixing w ater was ad ju sted to obtain a slum p of 3 in. A fter th e molds were filled th e concrete was vibrated for10
seconds w ith an internal vib rato r, th e n th e surface was struck off and screeded. T he specimens were disc-shaped, approxim ately l l j ^ in. in diam eter and 4 in. deep. M ost specimens were cast on an oiled plywood surface, b u t a few com parative specimens were cast on a lac-*O ne p a r t b y w eig h t of a n im a l g lu e a n d 1 p a r t of w a te r a r e allo w ed t o s ta n d to g e th e r o v e r-n ig h t. O n e p a r t of g ly c erin e is th e n a d d e d a n d th e m ix tu re w a rm e d in a n o v en to a b o u t 150 F . A b o u t 1 p a r t b y w e ig h t of fine sa n d (m in u s N o . 50) is th e n ad d e d , a n d th e m ix tu re is r e a d y fo r u se. G a s k e ts c a n b e re -u s e d b y sim p ly rew arm in g .
C O A T IN G S TO REDUCE PENETRATION OF KEROSENE 15
quered plywood surface. T he cast face of th e specimen was used as th e te s t surface.
General practice was to cure th e specimens one day in th e mold,
6
days in th e dam p room, and 7 days in th e labo ratory air. Specimens th a t were to receive pain t-ty p e coatings were usually given a ‘"'sacking” w ith a 1:1 cement-fine sand (minus No. 50) grout, upon rem oval from th e molds, to fill small surface voids and then, after the 7-day drying period, were given th e first application of th e prescribed coating. Specimens th a t were to receive plaster-coats of m o rtar were, upon removal from th e forms, roughened w ith a steel brush, given a th in grout coat followed by the plaster coat and th en th e usual curing. The ages of the specimens a t th e tim e of testing are listed in T able 1.T he am ount of fluid inflow was determ ined daily. F or those specimens having an appreciable inflow, the am ount was usually large a t first and th en dim inished gradually un til an approxim ately constant inflow was reached in usually
8
to 12 days. W hen th e inflow became reasonably constant th e average daily am ount for 3 to 5 days was reported as th e inflow for th e specimen. All tests were m ade in duplicate, unless otherwise noted. F o r specimens having appreciable inflows (greater th a n 0.4 gal. per 1000 sq. ft. per 24 hrs.) th e average variation from th e m ean value for duplicate specimens was 14 per cent.
M any tests which are no t reported were m ade on m aterials subm itted by m anufacturers and others interested in th e developm ent of satisfactory linings for the storage of gasoline. For various reasons these m aterials were unsatisfactory, th e m ost frequent cause being th eir in stability to w ater, as m anifested b y visible softening or disintegration of th e coating after storage in th e fog room for two weeks. Tests of other m aterials are reported, however, even though these m aterials were found unsatisfactory because th ey represent commonly suggested approaches to th e solution of th e problem a t hand.
DISCUSSIO N O F RESULTS
The results obtained are presented in Table 1. Each value listed is the average of two specimens unless special notation is m ade. The retests listed in th e fourth column were, as a rule, m ade after th e specimens had dried in th e laboratory
6
to8
weeks after completion of th e initial tests.The tests have been divided into 7 groups, as follows: (1) reference con
crete; (2) integral adm ixtures; (3) sodium silicate and m agnesium fluo- silicate trea tm e n ts; (4) plaster coats, plain and w ith adm ixtures; (5) m agnesium oxychloride-type coatings; (
6
) linseed oil and spar varnish coatings; and (7) synthetic plastic and latex coatings.16 JO U R N A L OF THE AM E R IC A N CONCRETE INSTITUTE September 1944
TABLE 1— RATE O F P E N E T R A T IO N O F KEROSENE U ND ER A 12-FT H E A D IN T O P L A IN A N D S P E C IA L L Y TREATED CONCRETE SPECIM ENS
Approxi
mate Age a t
In tial T est D ays
Liquid gal. pr sq. ft. pe
Inflow
;r 1000 r 24 hours
Spec.
No.
D escription and T reat
m ent of Specimen
Initial T est
R etest After D rying
6 to 8
W eeks R em arks
G ro u p 1 — Reference Concrete
88 6 bag, 6.5 g al/b ag con
crete
14 1.7 11.3 C ast in lacquered
forms 89 6 bag, 6.5 g al/b ag con
crete
14 2.2 17.1 C ast in oiled forms
115a Field prepared G unite specimen
unknown 117 («) Specim en h ad prob- bably dried several weeks before test
G ro u p II— Inte gral A d m ix tu re s
94 Admix. A, inorganic, contained chloride, sulfate, soluble and insoluble silica.
Added in ratio of C ast in lacquered
33di lb /b a g of cement 14 1.0 9.1 forms
95 Admix. A, same as
above 14 2.6 11.0 C ast in oiled forms
96 Admix. B, contained sulfonated l i g n e n calcium chloride and a filler, added in ratio of 1 lb /b a g of c e m e n t , m i x i n g w ater reduced by 11% to keep slump
constant 14 1.3 7.6 Lacquered forms
97 Admix. C, contained a carbohydrate and a filler, added in ratio of 1 lb /b a g of ce
ment, mixing w ater
reduced 6 % 14 1.7 6.5 Lacquered forms
G ro u p I l l- -S ilic a te a nd Fluosilicate Treatments
113 Plain concrete—trow T est m ade on trow
eled face 14 1.9 eled face
98 High silica sodium sili
cate o n t r o w e l e d
face, 2 coats, 1:4 by T est m ade on trow
volume 21 2.1 6.1 eled face
101 Same as 98 b u t applied
on cast face 21 4.0 12.4 T ested on cast face
T ested on troweled 102 Mag. fluosilicate on
troweled face, 2 coats, first dil. 1 :16, second dil. 1:4 by*
weight 21 1.9 face
103 Same as 102 b u t
applied on cast face 21 2.8 T ested on cast face
C oating unstable in 43 C o m m e r c i a l sodium
silicate P a in t D con
taining iron oxide
pigm ent 21 0.2 w ater
C O A T IN G S TO REDUCE PENETRATION OF KEROSENE 17
T a b le 1 — lontinued
Approxi
m ate Age at
Intial T est D ays
Liquic gal. p sq. ft. pe
Inflow 3r 1000 r 24 hours
Spec.
No.
D escription and T reat
m ent of Specimen
Initial T est
R etest After Drying
6 to 8
Weeks Remarks
G ro u p I V — M o rta r Coats
104 JT in. troweled m ortar coat 1:2.5 m ortar
troweled hard 14 0.1 1.5
105 Same as 104 w ith 2 coats high silica sod
ium silicate diluted
1:4 applied 21 0.3 2.5
54 Powdered iron—type Admix. E in m ortar 15% admix, in l : 2 Y
m ortar 14 9.960
56 Powered iron—agent Admix. F in m ortar.
5 successive layers as directed by m anu
facturer 21 17.
42 Caustic liquid type Admix. G in m ortar
approx. 33% sol. Liquid flowed lateral
calc, as K2C O3 21 excessive ly through m ortar
G ro u p V — M a g n e s iu m O x y c h lo rid e T y p e Coatings
17 Magnesium oxychlor Fairly stable to
ide type paint H 21 1.6 moisture
19 Magnesium oxychlor
ide type Paste I; J4"
thick coat w ith cloth
mesh 14 3.6(«)
19a Magnesium oxychlor
ide type Paste I;
neat, Y " thick 14 .8W
111 Magnesium oxychlor R etest on new sample
ide type Paste I 14 10. Surface crazed
38 Magnesium oxychlor
ide type Paste J.
Coating about Ys"
thick 14 0.1 43.(0
52 Same as 38 b u t pre
ceded by a powdered
< .05 iron-cem ent grout 14
Coating developed 52a Same as 52 b u t dam p-
cured (fog room) 14 6.6 gel-like spots
G ro u p V I — Linseed O i l and V arnish
64 Linseed oil; 2 coats, t h i n n e d , d r i e d 6
weeks 50 2.4
51 One coat linseed oil plus one coat spar varnish, each dried 1
week 28 .2
57 Spar varnish; 3 coats, dried 2 weeks alto
gether 28 .2
T a b le 1 concluded next p a g e
18 JO U R N A L OF THE A M E R IC A N CONCRETE INSTITUTE September 1944
T a b le 1 co ncluded
Approxi
m ate Age a t
In tial T est D ays
Liquic gal. pi sq. ft. pe
Inflow 3r 1000 r 24 hours
Spec.
No.
Description and T re a t
m ent of SDeeimen
Initial T est
R etest A fter D rying
6 to 8
Weeks Rem arks
G io u p V I I — S ynthetic Plastics and L a te x
59 Polyvinyl Chloride Type P a in t K ; 3
coat application 21 .4 3 .0 «
73 Polyvinyl C h l o r i d e T ype P a in t L ; 3 coat
application 30 < .0 5
107 Emulsified polysulfide latex type P ain t M, 2 prim er coats, one
finish coat 14 < .05
115 P ain t M, job prepared specimens on G unite c o n c r e t e . Fabric
reinforcem ent < .0 5 « . . .
« V a lu e for 1 specimen only.
O Large difference between duplicates; 54a = 4.5 gal., 54b = 15.3 gal.
(e) R etest m ade approxim ately 1 year after initial test. Specimens were drying in laboratory during th a t time.
« R e t e s t a t 14 m onths. Specimen stored in laboratory.
The reference concretes had com paratively low p en e tratio n for th e initial te s t (concrete aged 14 days) b u t during th e retest, afte r th e con
crete h ad dried, th e p enetration was high. This large increase of pene
tra tio n as th e concrete dries illustrates one of th e probable advantages of placing concrete tan k s under ground where drying m ay n o t be severe.
T he use of th e integral adm ixtures of group 2 indicates little advan tage in th e initial tests. After drying, however, th e p en etratio n was some
w hat reduced w ith respect to th e dried reference concrete. A p en etratio n of 1 gal per 1000 sq ft per 24 hours is roughly equivalent to a one per
cent annual loss from a 50,000 or a 100,000 gal. tan k , assum ing uniform loss from th e sides and th e bottom . I t is indicated therefore th a t th e adm ixtures do no t sufficiently reduce th e pen etratio n to w a rran t th eir use for th e purpose of rendering concrete im perm eable to oils as light as kerosene.
Coupled with the tests of group
1
and group 2 is a com parison of concretes cast on oiled plywood and on plywood which h ad been coated with acetate ty p e commercial form lacquer. In b oth th e initial tests and in th e retests, th e specimens cast on th e lacquered surface h ad lower rates of penetration. T he reason for this reduction is n o t ap p aren t, unless th e lacquered forms act in a m inor w ay as absorptive forms.
C O A T IN G S TO REDUCE PENETRATION OF KEROSENE 19
The tests in group 3 indicate th a t sodium silicate and m agnesium fluosilicate, as applied, did n o t confer m uch benefit, tho ug h th e appli
cation to th e trow elled face was considered som ew hat more effective th a n application to th e cast face. The commercial pigm ented sodium silicate p ain t was very effective in reducing penetration, b u t this coating proved to be highly unstable in a satu ra te d atm osphere or in water.
The group 4 tests on m o rtar coat applications indicated some success with a
1
:23
^ m o rtar applied to % -m . thick when th e specimens were removed from th e mold a t ab out 24 hours. The m o rtar was trowelled h ard when it was 3 to 4 hours old. This te st is probably not representative of w hat m ight occur on a job, since a small specimen is a p t to receive more favorable troweling. F urtherm ore, shrinkage cracks probably did no t develop on th e small specimens as extensively as th ey m ight on large surfaces. The m ortars containing iron-type adm ixtures E and F were applied in accordance w ith m anufacturer’s directions for w ater
proofing concrete. T he m o rtar containing adm ixture G was placed according to directions for coating concrete tan k s “ for storing m ineral oils (crude oil, fuel oil)” . None of th e m o rtar coats containing adm ix
tures were effective in stopping the inflow of kerosene.
The magnesium oxychloride-type paste coatings tested in group 5 have been suggested as possible linings for gasoline storage. The cement (I, Table 1) had a tendency to craze and was relatively ineffective. This lining appeared to be unaffected by storage in w ater for 2 weeks. The cement (J) had a low rate of penetration on the initial test, except for the specimen kept in th e fog-room after application of coating. The a p plication, first, of a powdered iron grout coat on specimen No. 52 appeared to be beneficial, b u t fu rth e r testing would be required to determ ine if th e benefit is real or only accidental. After standing in the laboratory abo ut 1 year, specimens coated w ith cem ent (J) showed excessive crazing. A very small concrete ta n k lined w ith cement (J) was buried in the ground so th e top of th e ta n k was even w ith th e soil surface. No protection from th e w eather was provided. The tan k was filled with kerosene and a cover sealed on. The leakage from the tan k has been low, b u t not m easurable due to th e “ creeping” of th e kerosene over th e to p of th e tank.
After 16 m onths there is no appearance of crazing or of swelling of the lining.
M aterials of this type have th e advantage of low m aterials cost, low cost of application and sim plicity of application. The lim ited laboratory tests available indicate their use m ight be satisfactory for light fuel and diesel oil storage where drying conditions are n o t severe. Job applica
tions have been m ade and it is hoped th a t service reports will be made available.
20 JO U R N A L OF TFHE AM E R IC A N CONCRETE INSTITUTE September 1944
Considering th e length of drying given th e linseed oil applications of group
6
, it appears th a t a m oderate decrease in p en etratio n was effected with this m aterial. The principal question b oth w ith th e linseed oil and spar varnish applications, is th e lasting power of these m aterials under field exposure conditions.The m aterials in group 7 are representative of the ty p e of linings th a t have come into use for aviation gasoline storage since th e inception of this study. Their m aterials costs an d application costs are high, how
ever, leaving considerable room y et for th e developm ent of low-cost b u t satisfactory lining m aterials.
A C K N O W L E D G E M E N T
A cknowledgm ent is m ade to form er and to present m em bers of th e staff who assisted in m aking th e tests, including H. E. Newcomer, T. M. Kelly, H. Freiberger and R. Valore, Jr.
Discussion of this paper should reach the A C I Secretary in triplicate by March 1, 1945 for publication in the J O U R N A L for June 1945.
A part of PROCEEDINGS OF THE AM ERICAN CONCRETE INSTITUTE V ol. 41
J O U R N A L
o f th e
A M E R I C A N C O N C R E T E I N S T I T U T E
V o l. 1 6 N o . 1 7 4 0 0 S E C O N D B O U L E V A R D , D E TR O IT 2 , M I C H I G A N Seplember 1 9 4 4
Tw o -W a y Rei nfo rced Concrete S l a b s
'1
By PAUL ROGERSt
M e m b e r A m e ric a n C o n c r e te In s titu te
S Y N O P S I S
Design formulas for two-way reinforced concrete slabs are given in the ACI Building Regulations (318-41). No derivations, however, are included for these formulas. While outstanding scientific works are at hand dealing w ith this problem (Timoshenko, W estergaard, etc.), it is obvious th a t th ey are out of reach for the average office designer. The foregoing simplified method, developed by Dr. H enri Marcus, m ay clarify certain principles and help visualize th e effect of th e torsional moments.
As a first approach in analyzing th e bending m om ents in slabs sup
ported on four edges, a typical slab was divided in strips of u n it w idth in both directions, and the strips were trea ted as independent beams. At the intersection of the strips from two directions, both beams have equal deflections and m om ents of inertia, which led to a simple way of deter
mining the portions of load to be carried by these beams.
These assum ptions, however, did not take into account th e lateral restraining forces which act upon these im aginary strips, and which tend to decrease th e deflections. As a result, th e obtained bending m om ents
*R eceiv ed b y th e I n s tit u te M a rc h 8, 1944.
tA s s ’t P ro f. of S tr u c tu r a l E n g in e e rin g , C h ic ag o T e c h n ic a l C ollege, C h icag o , 111.
(2 1)
22 JO U R N A L OF THE A M E R IC A N CONCRETE INSTITUTE September 1944
did not correspond to th e actual ones. To overcome these difficulties and to provide for an economical design, certain codes (as th e “ Conseil général des ponts et chaussées” in F rance) perm itted th e use of some empirical coefficients, which decreased the bending m om ents b y 10 to 30 per cent. N atu rally , this m ethod was very crude because th e actual decrem ents do no t follow a straig h t line proportion, and are also depend
en t on th e re strain t and contin u ity along th e edges.
M eanwhile several E uropean and A m erican scientists developed and perfected th e “ exact” th eo ry of plates and slabs. B u t to u n d ersta n d and apply this theory in practice requires a very good knowledge of th e th eo ry of elasticity and of higher m athem atics, no t considering th e tim e to be spent in arriving a t a solution.
Thus there were th e two alternates : (1) T he “ exact” theory, know n and applied by the very few, an d (
2
) th e “ approxim ate” th eo ry which was sim ply incorrect. D r. H enri M arcus, in his rem arkable book “ Verein- fachte B erechnung biegsam er P la tte n ” has bridged the difficulties in a unique way. C om paring th e bending m om ents o btained by the “exact”theo ry w ith those obtained b y dividing th e slab in strips in tw o directions, he derived an easy form ula for th e practically precise bending m om ent
Ma = m A
(1
~(pA) = m AvA M B = mB (1 — <pB) = m BvB (1
) where M A indicates th e final M om ent in “ A ” directionMbindicates th e final M om ent in “ B ” direction.
mA indicates th e M om ent obtained b y loading th e strip in “A ” direction w ith wA.
m B indicates the M om ent obtained b y loading th e strip in “ B ” direction w ith wB.
(wA + wB = w = to ta l uniform ly d istribu ted load per u n it square area), while
_ 5 A 2 w mAmax . 5 _ B 2 . . m Bmax ...
<PA — — X — X ——— <PB = —X — X ... (2)
6 B 2 M oA 6 A 2 M oB
M oA and M oB indicating th e respective B ending M om ents of strips of u n it w idth, sim ply supported and loaded w ith th e fu ll load of w per linear ft.
The derivations for th e E qu ations (
2
) are beyond th e scope of this article and will not be given here. They, however, satisfy th e requirem ents for a correct coefficient to supply th e “exact” bending m om ents. I t could be proven th a t there is practically no discrepancy betw een m om ents obtained by E quations (1) and (2
), and those obtained by th eo ry of elasticity. I t should here be m entioned, however, th a t th e torsional m om ents, which produce th e decrem ent of th e bending m om ents, can not be com puted easily b y approxim ate m ethods. B u t there is very littleT W O -W A Y REINFORCED CONCRETE SLABS 23
need, if any, for these torsional m om ents, as far as stru c tu ra l design is concerned.
In this ra th e r popular article, th e subject of tw o-day slabs will be confined to th e derivations of bending m om ents for slabs of different edge conditions, and th e graphical illustration of th e torsional m om ents.
(The curved lines of th e torsional m om ents are replaced by straig h t lines for b e tte r illustration.)
Case a. Slab freely supported on all four edges, w = Load per square foot of slab (D .L .+ L .L .).
wA and w B = portions of w in directions A and B respectively (wA + wB = w).
A and B = Spans in directions A an d B respectively.
M axim um deflection of one foot wide m iddle-strip in A direction:
5^ wA X A
4
32 E X h
3
M axim um deflection of one foot wide m iddle-strip in B direction:
5_ ^ wB X B 4 32 E X h
3
The m axim um deflection occurs a t the middle-span, where bo th deflec
tions are equal, or
wA X A 4 = wB X B*, and thus w X B 4 , w X A 4
wA = --- and wB = ... (3)
A 4 + -B
4
A 4 + B 4w X A 2 B 4 w X A 2
m A m ax = ---; M
o4
- ■,8
A 4 + B 48
, t o 4 max B 4 w X B 2 A 4
and — --- = ; m B max =
M oA A 4 + B 4
8
A 4 + B 4w X B'2 , m B max A 4 Mob = — --- , and —
M o b A 4 + B*
5 A 2 X B 2 n , _
<pa = <pb = <p = ~ X [
4
+ — ; or (1 - tp) - va - ( 5 A 2 X g a\ and finaU\6
A 4 + B 4)+ B 4Ma max = ~ X wA X A 2 X va] and M B max = \ X wB X B 2 X va; (4)
8 8
I t is an easy task to set up tables for the values of wA, wB, va. F o r a square plate, th e value of va is equal to 0.583 which certainly is a sub
stan tial reduction of M oment-value.
24 JO U R N A L OF THE A M E R IC A N CONCRETE INSTITUTE September 1944
M axim um torsional m om ent T a = w X x A f i X B f (5) 6 A
4
+ B 4Case b. Slab fixed along all four edges.
1
^ ^ ^4 M axim um deflections in A and B d ire c tio n s :— X --- and32 E X h 3
1 v, wB X B 4 , . , • w X B 4 , w X A 4 X — —j which gives wA = ——:—— and wB =
32 E X 1
13
mu X A
2
„N „m ax = — ; m B max = — ; M oA = A 4 + B 4
wB X B 2
A 4 + L w X A 2
MoR —
24 w X B 2
24 5 N/ A
2
X B 2■ ” ' T
8
X -(1
- « ). (6)
Ma m ax= — wA X A 2 X vh]
24 Mb m ax = — wB X B 2 X vb. . . (7) 24
F or a square plate, th e value of vb = 0.861, which is a far sm aller reduction th a n th a t for th e sim ply supported slab. The 1/24 coefficient is theoretically correct, b u t it is unusual to apply more th a n 1/16 or 1 A
8
for practical purposes.
M axim um torsional m om ent w X A* X »
100 A
4
+ B4 . ( 8)M Bmin.
M.rnax.
Fig. 3
