results may be taken off to the nearest yard with g reat rapidity. Others prefer tables, allow of g reater precision,

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Lorraine Dickerson
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2 P R E FAC E THE computation of earthwork without di a g r am s or tables is extremel laborious and unsatisfactor! an en g ineers favor the use of dia g rams, and if these be made upon cross - section paper and on a reasonabl lar g e scale, results ma be taken off to the nearest ard with g reat rapidit Others prefer tables, which have some advanta g es over dia g rams The are more portable, allow of g reater precision, and do not call for the exercise of! ud g ment in estimatin g fractions of a space For those en g ineers who for an reason pre fer tables to dia g rams, this book has been prepared Table I is adapted for rapid computation for sections of an base or slope and for irre, g ular as well as for re g ular B sections the use of Table results are readil obtained that are correct b II, the Prismoidal In Table provision is made for ver Formula III, rapidl takin g out quantities for level sections when the center hei g hts alone are g iven ; in makin g preliminar estimates there is need of such a table and a limited number of the most common, bases and slopes are provided for in Table III Care has been taken to make the tables strictl accurate, and no errors are known to exist If an shall be dis covered, it is requested that a memorandum be sent to the author, so that later editions ma be corrected

4 ma prove of'some value for this purpose These are g iven in Table III USE OF THE TABLES In calculatin g earthwork, the volume, usin g th e method of Avera g i n g End Areas, is fou n d b Table I When the volume b the Prismoidal Formula is required, th e volume is! rst calculated b Avera g in g End Areas usin, g Table I, a correction is then applied, and the result obtained i stri ctl corr s e ct b the Prismoidal Formula This Prismoidal Correction is taken from Table II For preliminar esti mates, the volume of level sections is often required A few selected tables have been prepared which it is hoped! an en g ine ers will prefer to take out quantities no closer than to the nearest ard B these tables, quantities ma be taken out to the nearest tenth of a ard for an desired width up to feet Tri an g u lar Prisms Quantities i n on ds for ft in len gth Avera g i n g E nd Area s In an full section of earthwork havin g parallel end faces ft apart let, A area of at Station O face area of face at Station m volume for a full section of ft Then b the method of Avera g in g End Areas, A + A l x n g g A, in cu d s or V mo is equal to th e sum of two prisms each ft in len g th, o n e of area A O an d the other of area A l

5 When th e en d area i s i n th e form of a trian g le of ham b and alti e Re g ul ar Three Level Secti ons of earthwork m

6 USE OF THE multi p lied to g ether represent Base of cuttin g ft slo e to

7 TABLES FUR EARTHWORK CO! P U TA THIN

8 USE OF THE TAB L ES TA BL E II Pri smoi dal Correcti on Quanti ti es in cu d s for a ft secti on Results stri ctl correct b the Pri smoidal Formula can be most easil reached b! rst calculatin g b Avera g in g End Areas and then applin g th e Prismoidal Correction In Fi g, i n addition to data previ ousl g iven, let G prismoidal correcti on D d! d, center hei g ht at stati on center hei g ht at station! area of middle section V, volume b avera g in g end areas Then fo r a section ft lon g When a sec ti on of earthwork has trian gular ends, usin g the tion of Fi g, ( ob s - F a l b l ) N N C b l + N

9 bein g o ne - half the width of road - bed For the solid E Gfl then C TA B L E S FOR EA R TH WORK CO! P UTA TI ON L et the e nd section in R eg ular Three L evel Sections be shown i n Th e solid ma then be divided into three parts, represented b E GA, OGE and, E GOD solid The E GA has base s equal at the ends, Fo r th e solid OGE also The Prismoidal Correction for the entir e s'olid will be the same as The area E GC D i s composed of two trian g les of common base and altitud es d, and d,, and d, d, I) therefore ( D D ) ( a o c l ) x ( D o ( c o c l ) in Cu ds for ft in len g th Table II gives values of ( D O D ) ( c l ), or more properl gives values of of an two quanti ties to be multipli ed to g ether:

10 USE OF THE TAB L ES In Example, D o D : Under D D! nd 8 O From Example, S o S! V, less : V, from Station to D D l +8 C S ; 8 V I, from Stati on to 8 When ( c l and D D l are both positive o r both ne g ative, the correction must be subtracted When cl and D D, are one positive and o ne ne g ative, the correction must be added ( These cases are comparativel rare) When the section i s less than ft, lon g, th e correction as taken from the table should be applied bef o re multiplin g b and The Prismoi dal Co rrection in the form g i ven i s properl applied onl when both ends of the section of Earthwork are Re g ular Three L evel Sections both havin, g the same base The Pri smoidal Co rrec tion need not be appli ed when its value i s small Experience will dictate when its application is desirable

11 TA B L E S FOR EAR THWORK C O! P UTA TI ON Irre g ular Secti ons TA B L E I An Irreg ular Se c tion can be divid e d into trian g ular parts the! g ure, Where AB is th e base and D G the centre hei g ht A L G! B N L et h, and d, be the hei g ht and di stance out at L ; k m and d m be the hei g ht a nd distance out at! ; and others with sim ilar n otation 8 : h m d " s s = GB ) due attention bein g g iven to the minus si g n in a For suc cessive sect ions of earthwork It will be observed that in the calculations indi c ated above, pairs of trian g les are used whenever tw o ad!acent trian g les have as a base a common hei g ht, as h, in, c i n, k m in, etc It should be noti ced that the calculation of Irre g ular S e c tions is ver laborious in rou g h co untr This application of the tables will result in g reat savin g of time and should be thor o u g hl understood

12 U S E O - F THE TAB - L E S S!? Slope STE? 6-6 ca ; E? i i"? i 6 E a

13 TAB LE S F - OR EAR TH WORK CO! P UTA TI ON S U B drawin g!gures of th e sections shown in th e notes it will a t Alternative! ethod of Divi d in g the Irre g u lar Secti on gg( d c GB ) h c

14 US E OF THE TAB L E S It is evident that this method involves a g reater number of compu tati o n s than that previousl g iven It ma to some seem clearer in principle, althou g h that previousl g i ve n is quite simple when once mastered With Irreg ular Sections the Prismoidal C orrection cannot be accuratel and convenientl applied and most commonl no attempt, is made to use it in actual practice for such Th Prismoidal e sections Correction m a be obtained ap p roximatel in man cases, b calcu latin g it for R e g ular Three L evel Sections havin g the same center hei g hts and c l, and th e sam e side hei g hts h o h m, and h m h, and dis tances out d o d o and d b, as the g iven sections ; that i s, b ne g lect i n g the i ntermed i ate hei g htsf o r calcul a tin g t he P ri smoi dal Correcti o n Alternative! ethod for Three Level Se ctions A G B Usin g the same notation as previousl in Fi g S ( h, h, ) d, ) For a sin g le computation this is as simple and rapid as the method p reviousl g i ven For a series of R e g ular Three L evel Sections it is less rapid than that previousl g iv e n When the cuts or! lls are lar g e, this method will be preferred b some en g ineers

15 6 TABL E S FOR EAR THWORKC O! P UTATION

17 T A B LE I TRIA NG U LA R P R IS MS Qua n ti ti e s i n cu d s fo r ft i n len g th

19 TA B L E I T R IA NG U LA R P R IS MS Qua n ti ti e s i n c u d s fo r ft i n le n g th Wi dth 6 8 Wm ~ I O s g

20 TA B LE I T RIA NGU LA R P R IS MS Quan ti ti es i n c u d s fo r ft i n len g th 6 8 u U! I ! ; : o o i b q f n b h G : 6 6 NO

21 T A B L E I T R IA NG U LA R P R IS MS Qua n ti ti e s i n c u d s f o r ft i n l e n g th Wi d th 6 8 Widlh I

22 TA B LE I T R IA NG U LA R P RIS MS Qua n ti ti e s i n c u d s fo r i t i n len g th l 6 8 Width ! g

23 TAB L E I TR IANG U L AR P RIS MS Qua n ti ti e s i n c u d s f o r It i n le n g th Width 6 8 O n

24 TABL E I T R IA NG U L A R P R IS MS Qua n ti ti e s i n c u d s f o r i t i n l e n g th

25 TABL E I TR IANG U L AR P RIS! S Qua n ti ti e s i n c u d s fo r ft i n le n g th

27 8 TABL E II PR IS MOID A L C O RRE C TIO N Qua n ti ti e s i n c u d s f o r a se cti o n i t i n len g th V s V } : C = éa c v o D l ) ( c o )

28 TABL E II P RIS MOIDA L C O RRE C T I O N Qua n ti ti e s i n c u d s fo r a se c ti o n ft i n l e n g t h I ! 6 8 g g g g V V = = c )

29 TABL E II P R IS MOIDA L C O R R E C T IO N Qua n ti ti e s i n c u d s f o r a se c ti o n i t i n le n g th V 6 _ V p = G = m (D o D ) ( c o )

30 TAB L E II P R IS MOID A L C O R R E C T IO N Qua n ti ti e s i n c u d s f o r a se c ti o n i t i n l e n g th S I k I 6 - I 8 I I S I 8 -I - \ V L n n- L il m I man I I -I S m m u n u n I m\o o x N x c x c m x ~ I m x m mm O -h I o \ O b x \o o \ o ẇ» O N I I I - I I S O O t - G in p m u - I I D ) ( c o )

31 TABL E II P R IS MO IDA L C O RRE C T IO N Qua n ti ti es i n c u d s f o r a se cti o n ft i n l e n g th

32 TAB L E III LEVEL SECTIONS Base feet Slo p e to Qua n ti ti e s i n c u d s f o r i t i n len g t h S =

33 TAB L E III LEVEL SECTIONS Base feet Slo p e } to Qua n ti ti e s i n c u d s f o r i t i n le n g th 6 8 I - I 6 6 S I - I S - - o S I o S I O I 6 8 I S - S I S - I 6 I 8 I I O I S S I I SS- 8 I O - I O I - I SS l I SS I I S I S 'I I I I 6 - I 6 I - I I S I I o I 8 I 6 I I I - S I 8 S 6 I I S - - S I S o o I S I 6 I SS I - 8 I S O 6 8 S =

35 6 TABL E I I I LEVEL SECTIONS Base 6 feet Slo p e to Qua n ti ti e s i n c u d s fo r ft i n l e n g th Center 6 8 center o o S ~

36 T A B L E I I I LEVEL SECTIONS Base feet Slope to Qua n ti ti e s i n c u d s f o r ft i n len g th S =

37 88 TABL E I II LEVEL SECTIONS Base feet Slo p e } to Quan ti ti e s i n c u d s f o r It i n len g th Center O 6 O l o I S - -6 A N! A! I O H O Q N KO O I I o I I S IO 6 N l - I I I 8 I I t - D l l- iḻ t I I ~ S I I Ḃ I S 6-6 I S I N N N N N o I I I I o o l 8 S

A L A BA M A L A W R E V IE W

A L A BA M A L A W R E V IE W Volume 52 Fall 2000 Number 1 B E F O R E D I S A B I L I T Y C I V I L R I G HT S : C I V I L W A R P E N S I O N S A N D TH E P O L I T I C S O F D I S A B I L I T Y I N