xt7mw669631f https://exploreuk.uky.edu/dips/xt7mw669631f/data/mets.xml  United States. Federal Highway Administration United States. Bureau of Public Roads United States. Federal Highway Administration. Offices of Research, Development, and Technology United States. Federal Highway Administration. Offices of Research and Development 1939 v.: ill., ports.; 30 cm. UK holds archival copy for ASERL Collaborative Federal Depository Program libraries. Call Number FW 2.7: 20/6 journals English Washington: U.S. Federal Highway Administration etc. Contact the Special Collections Research Center for information regarding rights and use of this collection. Works Progress Administration Transportation Publications Roads -- United States -- Periodicals Highway research -- United States -- Periodicals Public roads: a Journal of Highway Research August 1939 text Public roads: a Journal of Highway Research August 1939 1939 2019 true xt7mw669631f section xt7mw669631f . .' .~. »., __ . 7—»: 05:37» .~N- -. ..;»-: - A. ' .2..- .3" 1;..::.. 1‘ , , 7v w...»— 7
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. A SECTION OF STATE ROUTE 37 IN CALIFORNIA ' “II
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I For sale by the Superlntandent of Documents, Washington. D. C. - - - - - - - ~ - - I I,”
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l P U BLIC ROADS I I I A journal 0f
. I ' Highway Research 1‘
Issued by the
li
j PUBLIC ROADS ADMINISTRATION
‘ ‘ D. M. BEACH, Editor
Volume 20, No. 6 August I939
________________——__———————-———
, se
1 , The reports of research published in this magazine are necessarily qualified by the conditions of the tests from which the data are obtained, ::
I > I Whenever it is deemed possible to do so, generalizations are drawn from the results of the tests; and, unless this is done, the conclusion: fl)
1‘ formulated must he considered as specifically pertinent only to described conditions. hi,
*1 _ bL'
j s0
‘. _ In This Issue 01"
. Page
. . . ess
g; .- Application of the Results of Research to the Structural DeSIgn of Concrete Pavements— C:
l Concluded. . . . . . . . . . . . . . . . . . . . . . . . l07 861
i; L , Disposition of State Motor-Fuel Tax Receipts, I938 . . . . . . . . . . . . l27 :12
j, Disposition of State Motor-Vehicle Receipts, I938 . . . . . . . . . . . . . 128 33
Ii“ . . . . . 1i
‘1; DispOSItion of State Motor—Carrier Tax Receipts, I938 . . . . . . . . . . . 129 inc
If Disposition of Receipts from State Imposts on Highway Users, 1938 . . . . . . . I30 3&1;
; 9 firs
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:I . In
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1 1 REGIONAL HEADQUARTERS - - - - - - - - ~ - - - Federal Building, CIVIC Center, San FranCIsco, Calif. l
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(36)
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CERTIFICATE: By direction of the Commissioner of Public Roads. the matter contained herein is published as administrative information Issue.
, . and is required for the proper transaction of the public business. . . . ,

 111; 1
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11‘
id] of . 11 ;=
I PPLICATION OF THE RESULTS OF RE- 1'
earch1 A ' 11.1
1 SEARCH TO THE STRUCTURAL DESIGN «1
l a 1 1

1 OF CONCRETE PAVEMENTS
.1 11
1 Reported by E. F. KELLEY, Chief, Division of Tests, Public Roads Administration II1III 1

lgust 1939 1 Shape of cross- scct’ion of slab.——Two types of cross viously in Maricopa County, and in the final report I1
—-—> section of the pavement slab are in general use; the (37), issued January 1, 1923, this section was given the :1?
. ‘ cross section of uniform thickness, and the cross highest rating of any of the sections included in the 1;“;

I6 “blamed‘ section in which the edges of the slab are thicker than investigation. 1,1
:onclusiom ;e the central portion. An appreciable number of State The sections of the Bates Road (:21) that were built 111
:i highway departments use slabs of uniform thickness in 1920 and 1921 did not include any thickened-edge 11:5,
{I but the majority use the thickened-edge design. design. However, sections of this design were built in 1111]
: I Since the thickened-edge pavement design is used the fall of 1922 and were subjected to traffic tests dur— 1311
, so extensively at the present time, the history of its ing 1923. The results corroborated the earlier findings 11‘:1

I development is of interest. - of the Pittsburg tests that thickening the edges of a 111.1

‘ So far as is known, the thickened—edge section in relatively thin pavement slab greatly increases its re- 1‘ 1:

Pa“ , essentially its present form was first utilized by the sistance to concentrations of heavy wheel loads. 11‘ 1
L California Highway Commission, as an alternate to a In general, two types of thickened-edge cross sections 1: 1

07 I section of uniform thickness, in the construction of are used. In one, the upper and lower boundaries of :11 I

' concrete bases. In this design the edge depth of the the section are parabolic curves so arranged that the '1

127 slab was 2 inches greater than the interior depth, the thickness gradually increases from a minimum at the . 1' 1
128 " slab thickness being reduced from the edge depth to center to a maximum at the edge, the edge thickness ‘ 1
‘ the interior depth at a uniform rate in the outer 18 being from 2 to 3 inches greater than the center thick— } 1

129 ' inches of pavement width. This alternate design is ness. The second type, which is used by a majority of 1
130 3; shown in the May 1, 1913, issue of the California the State highway departments, is the same as that : 11
:3 Highway Bulletin and it is shown subsequently in the used originally by the California Highway Commission. 1 1 1

3; first and second biennial reports of the California High- The central portion of the slab is of uniform thickness 1

way Connnission (Dec. 31, 1918, and Dec. 31, 1920). and the edge thickness exceeds this by 2 to 3 inches. 11

In the biennial report for 1921—22 (Nov. 1, 1922) the The edge section is a trapezoid, the edge thickening 1 11

ton, D, C; thickened-edge cross section appears as a standard taking place at a uniform rate over the outer 2 to 4 feet I #111
‘. , rather than an alternate design. of slab width. In the Arlington tests (1'7) it has been : 11.1
USCG. C3111" According to T. E. Stanton 4.tlie alternate thickened- found that with this type of cross section the greatest 1 HI
:._ edge section was oflicially adopted in November 1912, uniformity of load stresses throughout the section may 11-1

1, for base construction and was used for this purpose be obtained. 111:,

from time to time until 1921 after which it was made Another type of thickened-edge section that is used ,111

standard for all concrete pavement construction. to a considerable extent is the lip-curb design. In this "1':

:lTennessee. ‘1 In 1920 Maricopa County, Ariz., undertook a very designalow curb of approximatelywedge shapeis formed 111
Vlontgomcry.Ala.I extens1ve paving program and on November 12 of that along the edge of the slab._ The base of the curb 1s 1 111
. j; year construction was started on a contract involving generally about 12 inches Wide and the height is about ‘ 111
amPShI’Cvagg 141 miles of concrete pavement, all with thickened 3 inches. When such a curb is superimposed 011 a slab 1 31
THAT: N 1,1 edges (35).b The design provided for a uniform interior of uniform thickness the stress diagram for loads is very ; , 1
“I" “y' ' thickness of either 5 or 6 inches and an edge thickness similar to that for slabs of the conventional thickened— 1 .3
i, and District? 3 inches greater than the interior thickness. The edge edge type in which the edge thickening is on the under- 1.111
w ha: m D‘cfi thickness was reduced to the interior thickness at a side of the slab (17). However, the lip-curb design is 1111
“5 g ' i1 uniform rate in a distance of 2 feet. Thus the section not used primarily to strengthen the slab edge but I 1
.g, Juneau, A1351“: was identical with that which is used today by a number rather as a drainage measure to prevent erosion of the 1 |
.1 of States and was similar to that now used by a majority road shoulders by storm water. ’11

d1 8 Ogden W151 2f the States. The stated purpose of the design was to 111
n . . 1 strengthen the edge and at the same time permit EFFECT or LOAD srnnsses 0N SLAB DESIGN DISCUSSED 1:
“lat and W651; Simple construction 0f the subgrade” and 130 secure “a Use of stress analysis in design:.—In introducing the 1f 3‘
sparmbmsci P‘ng slab Wlth a more unlform res1sting strength” discussion of the application of stress analysis to the 11:}
‘21 (36)- 1 . design of pavement slabs it is well to emphasize that I1

1 The Piittsburg Test Road at PittSburgi Cfi'llf" was one of the basic assumptions of the Westergaard anal- 1I

:itution other; b1111t durmg the summer Of 1921- . Traffic tests were yses, both for load stresses and temperature warping _ 1‘11
' engineeringgl begun that year and were finally discOntinued 1n JUIY stresses, is that the thickness of the slab is uniform. 111
:ancies occur; 1922,- The 'test road contained 0116 thickened-edge The equations for edge stress and corner stress are not ' 1 1111
. 1e co yi section, 5111111511“ ’00 the 9—6-9-ln0h SGCthD used pre- directly applicable to slabs of thickened—edge des1gn. 111

r sing p I: ‘Materials and Research Engineer, Division of Highways, California Department With respect to interior stresses the Situation is some- 1 11
j; “31131191” Wm? . . . . what different. In the Arlington tests (I 7) it was found I; .1
—II—'"__‘ TheEfcéuislisglliiiefiigeiiiiiiiipiiii llilg'risssggd In IWOISSMSO‘PUBUC ROADS‘ that in slabs of uniform thickness the critical stress 5 ‘~
. I'- issIIuIeiwc figures I“ parenthes“ ”19”" the bibIIOWDhY’ 1" 102’ 0f the preceding under a load in the interior of the slab was practically 11

‘ , 4 . 1 168494—39—1 107 111

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 5 55 - ~
5‘ ‘
" 108 PUBLIC ROADS Vol.2o,N,_5
, 1
1 5 ”/W‘ :
1| the same from the center of the slab to a point about modified analysis of interior stresses, it will be Sutfi-
5. 5 2% feet from the edge. A similar condition was found ciently accurate to use interior thicknesses of 6 inches e
5 5’ to exist, over an evéi greater portion of the slab width, and 5.5 inches, respectively. 8
5 -* 5 ‘ in thickened—edge slabs in which the edge thickness was Multiplying these figures by 1.67 gives an edge I3
5 5 reduced to a uniform interior thickness in a short thickness of 10 inches for the first design and 9.2 inches
5 “‘5 distance and at a uniform rate. Therefore, it appears for the second. The data obtained in the Arlington F
55 ‘5 - appropriate to use the equation for interior load stress tests indicate that the load stresses in the edge and c
55 5 both for slabs Of uniform thickness and for those with interior of the 10—6—10-inch cross section will be ap. 5’
f5 55 thickened edges Since, in the latter case, the inaxnnum prox1mately. balanced and equal to about 350 pounds 3
5‘5 5 interior stresses are not affected appreCiably by the edge per square inch and that the edge and interior load
,5 thickening. Although test data are not available, stresses in the 9.2~5.5—9.2—inch cross section will be c
5‘5 55 considerations of similar character lead to the 0011— approximately balanced and equal to about 400 pounds d
55 :5 clusion that it will be approximately correct to con- per square inch.
55 5 sider interior warping stresses in a slab of uniform thick— Permissible unit stresses.~Bef0re discussing the de- 1'
555 ’ ness to be the same as in a thickened-edge slab in which sign of pavement slabs to resist the combined stresses 1]
55 5. the interior portion is of equal uniform thickness. due to load and temperature warping it is desirable to t
55 55 Tn applying stress analysis to the design of slabs of consider the factors that should influence the selection 0
55 5 uniform thickness, curves Similar to those of figure 9 of permissible maximum unit stresses. Most of these )5
55‘ 55 may be used to determine the thickness required to factors have been mentioned in the previous discussion,
55: 55 resist load stresses. For example, assume that it is As has been stated, consideration of the available 2
55 5 desired to determine the required thickness of a slab data concerning the fatigue limit of concrete has led
5‘5 5 havmg a modulus Of rupture of 700 pounds per square to the rather general practice of assuming about 50 5f:
‘5 55 inch for load A, an 8,00_O—po_und wheel equipped with percent of the ultimate flexural strength as a safe value
55 55 high—pressure pneumatic tires. If the conservative of the unit stress to be used in designing pavements to 55
5 55 working unit stress of 350 pounds per square inch is resist wheel loads. In general the probable strength
55 5;? used, figure9 shows that the requiredthicknesses for the of paving concrete at ages greater than 28 days is not n
555 5 Interior, corner and edge are approxunately 6.2 inches, definitely known and therefore the design stress has t
'5‘, 9 inches, and 8.6 inches, respectively. These figures usually been based on the 28-day strength. Since con- a
‘55 55 indicate that if the allowable unit stress is to be limited crete of the character used in pavements may be ex- (5
5 ‘55 to 350 pounds per square inch the slab should have a pected to have a flexural strength at 28 days of from t
555 5 uniform thickness of 9 inches. However, the load 600 to 700 pounds per square inch, the customary a
55 5'5 stresses Will not be equal in the several portions of the design stress has been of the order of 300 to 350 pounds e
55 5 55 slab. The indicated stresses at the interior, corner, and per square inch. a
555‘ 55 edge Of this 9-inch Slab- are approximately 190’ 350’ and FOR COMBINED STRESSES ALLOWABLE STRESS MAY EXCEED 455
555 330 pounds per square inch, respectively. On the other POUan PER SQUARE INCH 7)
55 E hand, if a less conservative unit stress _is used, say 400 . . _ _ d
'55 555 pounds per square inch, then the required thickness of As apphed to load stresses this practice is a con- . S
55‘. 55 slab, as determined by the corner stress, is approxi- servative one and the cons1derations that lead to this e
5. 3555 mately 8.3 inches. In this case the computed load concluSion are; .. _ h
55 5% stresses at the interior, corner, and edge of the slab are 1. The poss1bility_that the fatigue limit of concrete, a
55 5555 approximately 220, 400, and 370 pounds per square for the loading conditions that obtain in pavements, is j,
55 555 inch, respectively. greater than 50 percent of the ultimate strength.
5 5‘55 In the Arlington tests (17) it has been found that the 2. The possibility that the stresses in pavement f5
5: 5‘ 5 thickened-edge cro'ss section gives the nearest approach slabs caused by impact forces are less than those t
55 55 '5 to a design that is balanced for load stresses; that is, caused by static loads of the same magnitude. t
55 t, 5 - one in which the stresses in a cross section of the slab 3. The fact that concrete increases in strength with S
55 are approximately equal for all positions of the load. age and the probability that by the time the pavement 15
5 55 It has also been found that the section which most has been subjected to enough repetitions of stress due 15
j“! 55 nearly accomplishes this is of uniform thickness in the to maximum wheel loads to require consideration of i5
5‘ 55 interior and has an edge thickness about 1.67 times the fatigue limit, the concrete will have attained a 0
51 "5-5 the interior thickness, the edge thickness being reduced strength appreciably in excess of its strength at 28 t
5, 5:55 to the interior thickness at a uniform rate over a dis- days. e
5“ 55 tance of 2 to 2% feet. The numerous investigations that have been made F
5. 55 At present, the only means of applying stress analysis indicate that the rate at which concrete increases in 5
5f. 55 to the design of thickened-edge slabs is to determine strength after the age of 28 days is a variable that
515 :5 the interior thickness in the same manner as for slabs depends on several factors. The averages of the results '1
5‘5 ,5 of uniform depth and to determine the edge thickness obtained in a number of these investigations give _
1 by the empirical relation between edge and center -values of the moduli of rupture at the age of 1 year
55 5555 thickness that has been indicated by the Arlington that exceed the average moduli at the age of 28 days
55 55 5- tests. by amounts ranging from about 20 to 45 percent. I
55 ‘z 5 On the basis of the same assumptions that have been Since these are average figures it is apparent that
55 5 5 made for the slabs of uniform thickness, the interior under some conditions the 1-year strength will exceed
5; 5 thickness required to resist load A in a thickened—edge the 28—day strength by less than 20 percent. ‘
55 5 5 slab is indicated to be approximately 6.2 inches if the It must be recognized that, for a given concrete, the
5 5 5 allowable unit. stress is 350 pounds per. square inch 1—year strength cannot be predicted with any certainty 9.
‘1 .5 and 5.7 inches if the allowable u_nit stress is 400 pounds from test results Obtained at 28 days. However, 8'
5 5‘ per' square inch. Since these dimenSions are based on when all the factors are considered, it does not seem
j. 535 Westergaard's original analysis rather than on the unreasonable to believe that in general there may be ‘
5. 5 '
5‘5 js
35 g.
5,5 .5 . '

 . . :33
In
1353
Vol. 20. N... ”mm, P U B L 1 C R 0A D S 109 333
. 3‘3
111 be. suffi- expected a minimum increase in strength between the 6"NC23033L2823‘L2E3T'0N 3331'
Of 6 Inches ages Of 28 days and 1 year of the general order of 20 3~—L°NG|TUDI~AL JOINI m: snag—.3 333
a s A .31 .
ercent. . . . ' ’
38 an‘ edge p If the practice of limiting load stresses to about 50 "‘ 3‘33
:1 9‘2 inches percent Of the 28-day strength of the. concrete is a '0” 333
8 Ajhngmfl conservative one, then the same practice would cer- O 9 a 7 STRESS Po'sNTS 3 33
e 3e ge an tainl be unduly conservative if applied to the design 0 ' “ a l
W111 be ap. of slidbs proportioned to resist the combined stresses -----mm“m: 31i
350.1)0unds due to load and temperature warping. The additional 20., ----Lm .2}?!
iterlOI‘. load considerations that lead to this conclusion have been I-n-mmmmm- 33
ion W111 be discussed previously and. are: ' 3 m, I----W//A?//d74m’ll}}§l 3 33
400 pounds 4, The fact that vehicles hav1ng maXImum wheel -----m/WARPING sazss 1m. 3 3g.
. loads constitute a small percentage of the traffic on 5 -----W’mmm- .3 33
3mg the de- most roads. The occurrence of maximum stress due 5 6C’0. --""-"‘fi"-"iw. - y. 2!
ned. stresses to load is therefore relatively infrequent and the 9;“ ------- 3 i3
deSIrable.t° occurrence of maximum load stress in combination .9. 50° 333
,he 531803310“ with maximum warping stress is much less frequent. 5 9_6_9_3NCH sgcnoa 33
053i Of these This is particularly true in those localities where the : WOWOUND LOAD 3
a discussion. movement of heavy trucks is principally at night when 2 3 3
1e available the warping stresses that are of consequence are gen— 2 3 "44‘4“ ‘
fete has led erally such that the combined stresses are less than ‘ o ‘ ‘ ‘ . s 3 ,4
lg about 50 the load stresses. _ l----N\mmmml ' 3i
a safe value 5. The fact that the unknown stresses due to m01sture ; 200 -----mm- is
avementS tfi warping appear to reduce, rather than to increase, the .----;,»»www- ’ 33
ble strengt maXImum stresses due to temperature warping. m I----mmmmm- .5
days 153103 On the baSIS of present knowledge the fivle factors ----mrm- , ,3
n s ress ias ' . b d ' 1— - r ‘ ‘ '5!
8' co _ that have been mentioned cannot e efinite y eva u m ----mmm- :33
1nce n ated. However, when all of them are cons1dered, 1t .------—fim- .3
may be eX- does not appear unreasonabl? to conclude that, Wilen ------- ' 3-.3
lays 0f from the design is based on combined stresses due to load coo ---- 3h
3 0115“)“er and temperature, the safe allowable unit stress is in FIGURE 18.—MAXIMUM STRESS DIAGRAMS FOR COMBINED 33
)350 pounds excess of 400 pounds per square inch and may be LOAD AND WARPiNG STRESSES FOR Two TYPICAL CROSS 3,3?
1. h as 500 ounds er sc uare inch SECTIONS; SLAB LENGTH 20 FEET; BASED ON DATA FROM 3 [3
as 11g, ‘ . p .p l . ' THE ARLINGTON TESTS. DOUBLE HATCHED AREA SHOWS 33'
AY EXCEED 400 D3319” of cross 360mm for combined lofld and tem‘ THE SMALL REDUCTION APPLIED TO THE OBSERVED LOAD 3 '3
percture-warpmg stresses.~«A cons1derat10n of slab STRESS VALUES TO CORRECT FOR THE EFFECT OF WARPING. 3
_ design on the basis of combined load and warping . . ' . _ _ 3 '3
ce 15 a 0013' ’ stresses leads to the conclusion that there must be thickness is 9 inches and [62100; and that 1t 13 not 3
lead to thls either an increase in permissible unit stresses even until the Slab length is reduced to 10 feet that the ‘3
beyond the limits that have been suggested or an edge stresses are reduced to values equal to or less than 3
. 0f concrete, acknowledgment that current practice with respect to about 400 pounds per square inch. , , 3 '3
yavements, 15 joint spacing in nonreinforced concrete slabs is incorrect. Since, as has been stated, only the interior stresses if
ength. In the previous discussion it has been shown that, can be computed in a thickened-edge slab, It is neces- i ‘
.n pavement for the assumed conditions, a slab of 9-inch uniform sary. to depend on the data from the Arlington tests 3
than those thickness is required if the unit load stress is limited for information concerning balanced deSIgn 'of cross 3
lde- _ to 350 pounds per square inch and that the thickness SBCEIOD for slabs Wlth thickened edges. Figure 18 :3 .
itrength Wlth should be about 8.3 inches if the unit load stress is ShOWS SUCh data for a 6411011 uniform SGCtiOD and a 3
,he pavement limited to 400 pounds per square inch. The combined 9—6—9-inch section, the load stresses in both being the I.
of stress due interior and edge stresses (from figures 15 and 16) stresses observed under a load of 8,000 pounds and the j 3
sideration 03 in these same slabs are shown in table 14. It will be slab length being 20 feet. '3; 3
e attained a Observed that the edge stresses are always greater ASSUMPTIONS NECESSARY IN APPLYING WESTERGAARD ANALYSIS ‘
rength at 28 than the interior stresses; that in a 30—foot slab the TO THICKENED-EDGE SLABS 3 ‘
d edge stresses are equal to or greater than 600 pounds In the 6-inch uniform-thickness slab» the observed :32
e_been mai: per square inch; that 1113a 15—foot slab they exceed load stresses of figure 18 are somewhat less than the '3
:zsifiizdglfe’ihat 500 pounds per square inch except when the slab corgputed stresses shown1 in figures 15 {1111(l 16. This is
Of the results TABLE 14,—Combmed edge and interior shesses in slabs 10 feet to 9 expected 511106 the (Pads are n0t t 16 same. 0W' 3 3 :‘
icrations ive wide and of um‘formzhz‘cknessl ever, the Observed warping stresses Of figure 18 are ,3?
‘b of 1 gear w greater than the computed warping stresses of figures
:ieof 28 days Lengthnrslb 15 and_ 16 even for a Slab length of 30 feet. The net ; g ,
,3 45 percent. Defithgfslab Posmon "—301;_~fl_1;;*_41@— result is that tfhe Observed combined stresses in the 33
rent that no es) _~ _______ 6—Inch slab, 20 eet'long, of figure 18 are of about the f .
tipaill exceed k_100 k_300 [Pm [Hm k_100 k_300 same order of magnitude as the average values, for k: 3 .
nltw ‘ ’ _.-_____ ____ _:___;_h‘_“ ‘ _ _:__ 100 and k=300, Of the computed combined stresses in 3 , ‘
‘ the 6-inch slab 30 feet long of figures 15 and 16. This 3
9 Lb. I Lb. Lb. LI). 7 Lb. Lb. . 7 . 1:! a .
:§;%r;tgi§tly 9.........._. {Interior.....,._. sq. 3571:; 30.537: sag; sq. :21: 512.32; sq. 221:) is merely a demimstration Of thef fact that 1observiald 3
rs However. ‘ affirm-~7- 650 600 490 530 330 370 stresses are 0 tie same order 0 magnitme 3.5 t e .3.
- ' 8%3 {Eu ”mm-w" 57.0 550 410 200 290 350 maXImum stresses obtained by theoretical analys1s. 3 ;
1063 not seem dilefi—nn...“ 600 600 510 L60 380 410 . . .
there may be \‘ The real importance Of figure 18-1188 1n the fact that, 3
- ‘ 1Fromfigg,15and m from the standpomt both of maxunum stress and of 3
' a,
l

 'l , . Mg-
l l ' ‘
l ' l ~ :
L . . . . .
l L uniformity of stress, there is no Significant difference in the 9—6—9—inch section. Also the ratio of the com. l
l l between the thickened—edge section and the section of puted edge stress in a 9-inch slab to that in a 6-inch
.l .. L uniform thickness. The maximum combined stresses slab is approximately the same as the ratio of the 0b-
-‘ : L are approximately the same for both slabs and the stress served stress in the edge of the 9-6—9—inch section to '
= l diagrams are of approx1mately the same shape. There- that in the edge of the 6-inch section. Therefore, it
1 fore, it may be concluded that for long slabs (20 feet or appears that it is a reasonable approximation to assume
ll l more) there is no particular advantage, from the stand- that in a thickened—edge slab the edge warping stress is
LL L point of combined stresses at the edge and interior, of of the same order of magnitude as in a uniform-thick. ‘
‘L ‘l‘ 2 thickening the slab edges. This conclusion does not ness slab having the same edg