Calculation of pressure of concrete on forms

~ III

UIJe/1deJ Jom NorgeJ byggforJkllingJi/1Jtit/lttJ Særtrykk

"';t}Il6tJliJ

VOLUME 81 SEPARATE No. 680

r 1P1R{)Clclc IDIIN(JS

AMERICAN SOCIETY

OF

CIVIL ENGINEERS

MAY, 1955

AMERICAH SOCltTyor

C1Yll EHGIHEERS

roIIlID[O 1852

CALCULA TJON OF PRESSURE OF CONCRETE ON FORMS

by R. Schjodt, M. ASCE

STRUCTURAL DIVISION

(DisClIssi01J opelllllilil September l, 195.5)

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CALCULATION OF PRESSURE OF CONCRETE ON FORMS R. Schjiidt; M.ASCE

SYNOPSIS

A formula for the calculation of pressure of con er ete on forms is deveioped mathematlcally.

The setting time, consistency and weight of the concrete, the smoothness, permeability and cross-section of the [orms, the rate of fUling and the depth

~hich the working penelrates are the ractors considered.

YThe material constants needed for the calculation are discussed, and safe values indicated .

. The pressures obtained by using the formulas are compared with bunding practice and with test5.

INTRODUCTION

The correct design of formwork is a necessary part of the design of any concrete structure, both from the point of view of safety and economy.

For a rational design, the size of the concrete pressure is needed. But reliable formulas for this pressure, taking into account all important factors, are not available, as far as the author lmows.

Several investigators, such as Teller(l) and Rodin, (2) have made experimen- tal determinations of the pressure. But in order to apply the results, formu- las are needed.

Severa! empirical formulas have been proposed. They all have the usua!

weakness of 6uch formulas, however, thattheyfit the tests and conditions from which they have been bullt up and not others.

Various authors 5uch as HOffmann(3) and Ljungberg(4) have developed theo- retically formulas for the concrete pressure. Hoffmann's form ula can be faund

i~ the above mentioned paper by Rodin. But they have used the exponential

•

^~ mula for bin pressure as a starting point,as it was developed by Koenen {5}

AlldJanssen)6} wjthouttakinginto account that an essential condition for the development of this form ula is a constant friction angle, which is very far from being the case with setting concrete.

This paper will give a rational and simple formula for the pressure on formwark, taking into account what the author believes to be all important factors. The results are shown to check with the known tests, but dilrer fre- quently very much from the usuaUy assumed values.

I. Bases for the Calculation.

When concrete is placed in the forms, it is usually worked over, byspading, puddling, vibrating or other means, down to a certain depth. During this proc- ess the concrete is constantly moved and deformed, and must be considered

.. Junior Technician, Norges Byggforsknings-institute, Blindern, Oslo, Norway.

680-1

as a liquid. All experience supports this point of view, the pressure curve begins always as a tangent to the line of hydrostatie pressure.

As soon as the con er ete is left alone, it develops a certain cohesion and fricUon.

As to the first, the slump test gives a good idea of its importance in fresh con er ete. li the mixture can stand up with a vertlcal wall of say 8 in. cor- responding to a slump of 4 in., it has a cohesion (shear reststance) of T= 1/2 x 0.087 x 8 = 0.35 ps i, ff 0.087 is the weight of concrete in lb per eu. in.

Testa of the strength of fresh ~oncrete give values of the same order of magnitude, according to

Of

jord. (7) Four to five houra later, the cohesion will be about twice the above amount.

The cohesion is not taken ioto account in the following. This provides an additional factor of safety, but is usually of HUle importance. Very dry and weU vibrated concrete (w/c = 0,35), however, will stand with a vertical wall of 3 to 4 feet hetght, il the forms are taken away immediately after vibrating.

Vacuum treated concrete will stand in the same way with up to 15 feet h e i . In these cases, of course, the cohesion is important and the pressure wlll ..

less than calculated.

A solution taking into account the cohesion is of theoretical interest, and may in same cases be of practical importance. This case is therefore con- sidered in the appendix.

The angle of interior friction will have a relatlvely small value to begin with, but will increase during setting. It can be considered to have reached 90⁰ at the end of the setting time, when the horizontal pressure is equal lo zero. For very dry concrete and very rigid forms, the latter may be under a certain pressure even after the final set, because the contraction of the concrete is not sufficient to free the forms. The remaining pressure may be considered a or passive pressure, n a pressnre of the forms on the concrele, and is of no importanee for the following considerations.

The setting time, ts ' can be defined for aur purpose as the time from the concrete is left al rest in the forms untU it has taken the finalset, and changes from a friction mass into a solid body.

The pore water pressure, finally, is a part of the total pressure against the forms, see for instance Terzagh1. (8) As we know, at least approximately, the amount of water and the voids in the mix, we can calculate the theoretical pore water sland Bul from this must be subtracted the loss through the forms, which in many cases is difficult to estimate. However, in the two ex- treme cases of impermeable forms, and of thin walls with forms made with ordinary formboards, we know the pore water pressure with good approxi~

tion. Based on the se, it is not difficult to arrive at safe values in the other cases.

The concepts developed above will serve as bases for the calculation. The actual values of the physical constants, and the safe values to be used in cal- culations, will be diseussed later in this paper.

n.

Pressure Without Friction Between Concrete and Forms.

In tids case, the horizontal pressure below the reach of the working will be, using the earth pressure theories (Terzaghi Art. 24), and assuming rapid internal drainage

p = [y (hl + h) - yohwl Al + yohw

= [(y - YO,,) Al + yo"l (hl + h)

(l)

Here hw ⁼ K(hl + h) is the pore water pressure, and K is a coefficient giv ing the pore water pressure as a function of the height of concrele.

y is the unit wetght of the mix, YO of water and hl the depth to which the ef- feet of the working reaches down. h is the distanee from this level to the point where the pressure shall be calculated, see Fig. 1.

The coefIicient .\1 is a fWlction of the stiffness (internal frietion) of the concrete, and varies with time. For a common friction mass, we have

A = tan2 (45

_1.) .

2

Here, in order to take lnto account the setting, we write

2 t/J h h

A = tan (45 - - ) (1 - - ) = A (1 - - )

1 2 hs ^hs

(2)

_ :V/here hs is the height to which the concrete has risen when it has taken the Vinal set, counting from the depth hl. fl> is therefore the initial fricUon angle of the concrete, after it has been worked over and is left at rest.

Assuming slow internal drainage, it mtght be more correct to write in- stead ol (1):

When the concrete does not rise toa quickly in the formsJ the equation chosen will be the best, and it is the ane most in agreement with the tests.

When K <: 1, the alternative formula g-ives smaller pressures.

If the tonerete rises at the speed v in the forms, we can write

where ts is the setting time.

(l) tan now be wriUen:

p =

Fy -

^YOK) A (1 - h: ) + YOKJ (hl + h)

If we want to find how the pressure varies when h is constant, during pauses in the pouring or after it is completed, we can write:

(3)

(4)

p =

[(y -

^{YOK) A (1 -}

t: )

^{+ YOK J'hl + h) (S)}

The maximum value of the pressure can be fOWld by derivation of (4). We lind

r

^{YA hl YOK hl ] ~ hs hl K Yo ]}

Pm = - (1 + - ) + - (1 - A - A - ) Lhl + - (1 - - + - - - - ) (6)

2 hs 2 hs 2 hs ^{A Y} + Yo K

hs [ hl K YO]

at a distance from the surface = - (1 -

-l+ - --'-"-

2 hs A Y - YOK

IT we take hl = K = O and A

=

1, we find Pm = -1 y hs' a formula which has 4

been much uSf!d for calculation of the pressure.

The formulas (4) and (6) take lnto account the weight and consistency (through y and A), the rate of pauring, the pore water pressure and the

680-3

working of concrete. They can be used in many cases where the forms are smooth or the dimensions ample.

The formula (2) and the following are based on the assumption that the value of >'1 decreases followtng a straight line, and that the efiect of working the con er ete ceases abruptly at a certain depth, as shown in Fig. 2.

What happens, of course, is that the eifeet of the working disappears grad- uaUy, and that the value of >'1 approaches zero tangentially instead of at an angle, as shown with the dotted line in Fig. 1.

The effect of these approximations is not very important. The first has as aresult that a jump wi11 appear in the value of p at the point hl' whereas it usually will fellow a smooth curve, see Fig. 5. Where the working staps sud- denly, however. 5ueh a jump really appears in the pressure curves. Tellers Fig. 7 gives a typical example of this.

To evaluate the irnportance of the second approxlmation, we can write for instance

Å nh

Ål = - (1 + cos -h )

. 2 s

insteadof (2). This gives a smooth curve, with a very reasonable curvature. For the sake of simplicity, we consider here the case of hl = O. Now the calcula- tion for K. = O gives a maximum Pm = 0,26 YAhs at a depth of 0,42 hs as corn- pared to Pm = 0,25 YAhs at a depth of 0,50 hs for the straight line assumption.

Other reasonable curves also give only slightly different results, proving that the errOr of the approximation Is not great.

ill. Pressure with Exterior Frlct!on.

In narrow walls and in columns, especially when the forms have the rough surface of ordinary form boards, the friction of concrete against forms has a preponderant influence and cannot be left out.

In order to !ind an express ion for the pressure in this case, we consider the equilibrium of a horizontal section in the concrete below hl (Fig. 2), and

!ind

Pl is the horizontal pressure not counting the pore water pressure, Yl = Y -YOK., see equation (l), F is the concrete area in a horizontal section, and U Us circumference. Øl is the angle of friction between concrete and forms. We write-,.!.. = R, and !ind

U

(7) In the paper by Koenen referred to above, the relation between horizontal and verUcal pressure was given as:

h-=

^Å

Pv

As mentioned before, this is not a constant for setting· concrete. Instead of this expression, we write as befare:

and equation (7) becomes

with

~=Å(l_J.!....)

Pv ^hs

hs a=Uanl!\- R

(8)

(9)

We rind as a 501ution of (9L using Pv = 'Yl hl for h = O for determination of the constant :

el

_{Here is:}

h h

- a - ( l - - ) A = e hs 2hs

(10)

(11)

The numerical values of A can be fouod from the diagram in Fig. 3, and of K from Fig. 4.

The second part of formula (10), but with 'Y instead of 'Yl has already"been given 1n another paper by this author . (9)

A and K can evidently be calculated with the help of the tables of exponen- tial functions and the error integral. Unfortunately, as the expression for K is Iound by multiplying the great value of the exponential functien with the small value of the error integral, the usual tables do not have the necessary numher of decimals for most values oL~ a. ¹¹

l)

^K can alsa of course be evolved In series. But again, the convergenee is bad for most values of" a. "

Fortunately, therefore, tables for error integrals with the necessary num- ber of decimals have been calculated by v. Oppolzer. (lO) The diagram in Fig.

4 is drawn with the help of these tables.

The pressure against the forms is now found from (8) and (10), and adding the pore water pressure:

If Øl is small, or if the walI. is thick sa that R is great, .. a" will have a small value. In this case, we find A - l and K - h/hs , and (12) becomes identical with (4).

680-5

(12)

IV. Material Constants.

All factors of importance for the calculation of the concrete pressure seem to be included in the formula (l2). But in order to use it, it is neces- sary to have an idea of the safe values of the varJous material constants used.

These shall now be diseussed. The following is not meant to give the exact values of the constants, but to give an ide~ of the limits within which they will be found, and to indicate safe values based on tbis.

The setting time ts can ^~e foun?7from curves for the early strength of the concrete, see for instance Of jord. Weseethat it depends very much on the temperature of the concrete, the cement quality alsa is important, but the water-cement factor and the quality of the sand and stone make Httle dUfer- ence.

ts ^will be near ly constant and about 4 hours with cement of usual quality and temperatur es above 50⁰F. At 40⁰ we must expect a value of 6 hours, and at 350 F it is necessary to reckon with more than 10 hours.

Same cements are slower than indicated above, and ts can reach 5 and u p . to 6 hours for usual temperatures. Sand-rich mixtures also tend to have a ^I somewhat langer setting time.

n

may be of interest in this connection to mention that the ASTM specifi- cations require that cement shall have acquired Us final set, according to the Gillmore test, in not more titan ten hours.

H ane has no information about the cement, it is safe to reckon with a ts of 5 hours for normal temperatures.

The value of hl, the depth to which the working reaches down, can vary very much. If the surface is only tamp ed, as is frequently the case, hl is equal to zero. li the con er ete is spaded or puddled, hl is equal to the penetra- tion of the spade or bar lnto the concrete, usually ane to three feet. Under laboratory conditions, and occasionally elsewhere, puddling may reaeh deeper.

When vibr~tion is used, it is dUfieult to define hl' According to

L'Hermite,(l1) fresh concrete whieh is being vibrated with a 3000 rev. per min.

vibrator acts as a liquid until it is subjected to a pressure of 12 psi. In other words, it can be consldered as a liquid whlle vibrated il the vibration does not reach more than about 11 it. down.

With that pressure, the con er ete begins to develop an interior Iriction even during vibration. This constitutes the upper limit for hl, but generally of course the penetration of the vibration depends on the concrete section, the construetion ~f the forms, and the size of the vibrator.

For walls, it seems that areasonable figure is the penetration of the vi- • brator plus two feet.

The fricUon angle

ø

for ordinary qualities of cot:J.crete is 20⁰ to 300 , but may for dry concrete go up to 350 • For design purposes, 20⁰ is on the safe side. After vibration the angle can increase considerably, and reach 50^0, ac- cording to V Hermite.

The friction angle, Ø11 between concrete and forms, Is equal to rP for or- dinary rough formboards. For smooth, oiled boards placed vertically, or for steel forms, figur es for

ø

down to 50 can be calculated from the tests.

l· l

if1

^{= - ri> to Øl = - -}are safe Iigures in most cases.

2 3'"

K can be estimated from the 'Vater content of the mtx, the quality of the sand and the permeabiUty of the forms.

A good concrete will have a K of 0,70 - 0,90, supposing that the voids con- tent of the concrete when set and the shrinkage during setting are both small, and that no water is lost through the forms. The amount of water which must be considered to be already chemically bound to the concrete is uncertain.

Usually, however, water is lost through the forms, K will decrease cor- respondingly and is, strietly, a variable. In this case, the pore water pres- sure roay reach a high value locally, when a large batch of concrete has just been dumped, but will have decreased lang befare the height of concrete has reached the value giv ing maximurn pressure.

Fig. 6 will give an idea of the variations of the pore water pressure during filling, for a column with vertical form boards. For a thin wall with hori- zontal boards in the formwork, the pore water pressure can hardly be mare than corresponding to the width of two or three boards.

Bow the loss of water through the forms and the resulting pore water stand will influence the final strength of the concrete is an interesting question, but a,.eems to have been Httle considered.

"J.

Applications.

The farmulas will be tried on same cases where the results can be checked. We will first consider a wall, siX inches thick, being filled with con- crete at the rate of 10 feet per haur. The concrete is only tamped, 50 hl = O.

Let us take t₅ = 5 haurs. We find

R

=

0,5 sq ft_ 0,25 it, h_s

=

10,5

=

50 it 2it

We will further assurne Kh = 1 and rp = Øl

=

20⁰, which gives A

=

0,5 and tan Øl = 0,36, and f!nd

a = 0,5'0,36 - -50 = 36 0,25

For five feet of concrete, we get h/hs ⁼ 0,10 and formula (12) and Flg. 4 give:

p = (150 - 0,2' 62) x 0.5 x 0.025 x 50 (l - 0.10) = 139 ps!

In order to Hnd the maxlmum pressure, three or faur points must be cal- culated and the pressure curve drawn. In this case 144 psf is the maximum pressure.

•

Most empirical formulas would give more than 500 paunds in this case.

nd yet the above result is well checked by practical experience.

Six inch concrete walls have namely been much us ed in building construe- tion in Norway in the last twenty years, and the formwork, which never seems to have been calculated by engineers, has became standardized by use and habit. It is secured by 0,35 square inch strips, with atensile strength at yield point of 1300 pounds, carrying about 8 square feet.

Evidently, the tensian in the strips cannot be much more than the 144 x 8

= 1150 pounds calculated abave. This gives a gaod check for the formulas.

Radin(2) has given theresults of tests reported by Roby.

Roby used a 2'6" square column, 15 feet high, with a rate of filling from ane to ten feet per hour. We get

2.52

R = - - = 0.625 it 4·2.5

680-7

His" normal" mixture, with a rate of filling of four feet per hour will be compared with the formulas. From the shape of the pressure curves, the puddling seems to have reached about 4,5 feet down. We take ts ⁼ 5 hours,

rp =

^{20°, Øl}

=

^{70 ,} which give A

=

^{0,5, tan Øl}

=

^0,12, _hs ^{= 4.5}

=

20 feet, and a = 1,9. K(hl + h) is estimated at 5 feet. For h = 5 feet, we llnd h/hs ⁼ 0,25 and from formula (12) and Fig. 3 and 4,

p= (150 - 62'0,53) 0,5 (0,7'4,5 +0,21'20)(1 -0,25) = 634psf The pressure line is shown on Fig. 5, where also the result of the test found in Rodin's Fig. 1 is shown.

When the formulas are compared to other lmown tests, the same good agreement as in the two examples above is found.

CONCLUSION

The aim of this paper has been to give a theoretical foundation for the • calculation of the pressure of fresh concrete.

Taking into aceount all factors, the formula (12) has been arrived at. If the frietion against the forms is neglected, the simpler formula (4) may be used.

In order to facilitate the applieation of these formulas, the material con- stants of fresh concrete have been dtscussed. This 15 a mueh neglected fieId, therefore the values given must not be considered as final. But the safe va1.ues indicated for design work may be used with confidence.

APPENDIX I

Calculation of Pressure on Forms, Taking lnto Aceount the Cohesion.

The cohesion of a mass of fine particles (such as a clay) wUl increase with the pressure it is subjected to. We can here write

c=2"(pv -pw) k+k1 _O

where c is the eohesion, Pv the vertical pressure of the mass, Pw is the pore water pressure, and K is a constant which for clays has values between 0,2 and 0,6.

ka

is a constant which we here will consider equal to zero. We . ' write yoK(hl + h) for the pore water pressure, and find

c =

!

[Pv -YO"(hl + h)j k 2

For concrete, the cohesion eVidently also varies with time. For the short time, usually 4 to 6 hours, here in questlon, we can consider it a linear fune- tion of t. This gives finally:

c = 1 2" [kl t + _{k2 (pv} - "OKh - yo"hl)

l

The pressure against a vertical wall, (without the horizontal pressure from the pore water) is for an ordinary cohesive mass:

.

For concrete, we write corresponding to (8) PI = Pv'\' (I

-~)

^{- 2cVx}

hs

= Pv'\' (l -

..h...) - V>:

^{kl t -}

VA

_k2

<Pv -

Yo"h -YOKh_{t )} hs

(13)

In nthe laetor (I - hJbs) ^is not added, con sider ing that the effect ol con- solidation is already taken care of in the expression for c.

In the case of no frictions against the forms,

Pv

⁼ Yl (hl + h), and we find

Pl

=YI['\'(l-~)

^-VAk₂(1-.!lLK)] (hl +h) - -$:klt (14)

hs ^Yl

•

Equatlon (14) corresponds to equaUon (4) lar the case ol no eoheslon.

hen friction against the forms has to be taken into accountJ we can use equatlon (7) and lind wlth the help ol (13) •

k2 h a h

( 1 - ./7 - - ) Pv = Yl' + mh - - (h - - ) Pv

'I ,\. hs ^hs ^hs

The saluttan of this equation is:

, Vxtan

Øl

Yl = Y l - k 2Kh_l^yO

R

,f>:

tan

Øl

kl

m = _R ( - - -_v k2KY

o

^l

b=l-~ kv

(15)

Equation (l5) can be made more manageable with the help of nomograms.

But the se will contain three variables, a, b, and h/hs' instead of the tWQ con- tained in (lO) and (11). It will be correspondingly more complicated to use, and in view of the relatively small importance of the cohesion in most cases, and the uncertainty of the values of kl and k2, it does not seem worth while to work nomograms at the present stage.

680-9

The value of kl is easy to determine in any given case, but the material for finding Us upper and lower limits in the general case is meagre. IT, for instance, we find that the concrete has a compressive strength of 400 psf after 5 hours, then kl

=

400/5

=

80 psl per hour.

k2 is an abstract number. As mentioned befare, for claysitvariesbe- tween 0,2 and 0,6. Here we must expect a smaller value. It will, of course, depend very much on the quality of the concrete, but apparently values near 0,1 may be expected.

APPENDIX Il

The pore water pressure in fresh concrete was recently measured in a test made by the Norwegian Geotechnical Institute. This is probably the first time such a measurement has been carried out. The pressure was measured in a 7" x 40" column, the concrete had a water-cement raUo of 0,7, and the Al \ forms were made with l" x 4" vertical boards. The results are shown on ", \ ,

F~6. .

This test, of eourse, only gives a lirst indication of the size of the pore water pressure, and of the coeffieient K used in this paper. It appears that we can getl(::>l near the surIace, befare the pressure from the reeently dumped concrete has be en equalized. But when the height of concrete giving the maximum pressure is appro~ched, values of I( near those used in this paper are found.

As the eurves show, mueh water was lost through the forms.

1. Teller, L. W.

2. Rodin, S.

3. Hoffmann, R.

4. Ljungberg, N.

5. Koenen, 6. Janssen, 7. Oljord, A.

8. Terzaghi, K.

9. Schjodt, R.

10. v.Oppolzer, T. R.

11. L'Hermite, R.

BIBLIOGRAPHY

"The Effect of VibraUon on the Pressure of Conerete

against Form Work." Public Roads Vol. 12, No. 1.

"Pressure 01 Conerete on Formwork." The Institutlon of Civil Engineers, London 1952.

aDer Sehalungsdruck von frischem Beton. " Beton u.

Stahlbetonbau, 1943, p. 130.

Ll Formar och SfålIningar." Betongtekniska Anvisningar, Stockholm 1945.

in Zentralblatt der Bauverwaltung 1896.

in Zeitschrlft des Vereins deutscher Ingenieure 1895.

ftFastheten hos martelog betong i avbindingsstadiet. "

Oslo 1954.

USoil Meehanies in Engineering Practice." New York 1948.

"Betongs sidetrykk mot forskaling." Teknisk Ukeblad 1951, No. 31.

"Lehrbuch zur Bahnbestimmung der Kometen und Planeten." Leipzig 1880.

Ll The Rheology of Fresh Con er ete. " Cement and Concrete Association, Llbrary translation, London 1949.

'" '"

^o

,

~ ~

• concrde surPace il.

=1,0 <_ i ~

~i ='- 1\

=0

I t=O t=t~ fig .1 Voriot.ion oF 1\1 with time

• h~ spoded or vibrol:.ed concrete -r h=O h h s 5el:tI-ng concref;e

l 'I

fig. ?.

Jncreo5e oF vercical pressure 'liith depl:h

\ \

...,

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680-13

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680-15

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Fig .5

Concrete pressure in

columns ond wall fOrms

'" , - '"

~

cl!

3 I

I I

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5 10 15 20 25 30 35 Minutes Fig.6 Dore water pre~sure in fresh concret;e

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PROCEEDINGS-SEPARATES

The teehnleal papers published In the past year are prcsenled bclow. Teehnlca1-dlvlslon sponsorship Is indicatcd by an abbrcviatlon at the end oC each Separate Number , the symbols reCerrlng to: Air Transport (AT), City PIann!ng (CP), Constructlon (CO), Engineering Meehanics (EM), Hlghway (HW), Hydraullcs (HY), Irrlgatlon and Dralnagc (JR), Power (PO), Sanltary Engineering (SA), Soll Mechanlcs and Foundatlons (SM), Structural (ST), Surveylng and Mapping (SU), and Waterways (WW) dlvlslons. For Utles and order coupons, reCer to the appropriate Issue oC "Civil Engineering" or wrlte Car a eumulativc pr lee list.

VOLUME BO (1954)

MAY: '35(SM), '35(CP)", '37(HY)", '38(HY), '39(HY), 440(ST), 44l(ST), '42(SA), 443(SA).

rUNE: 444(SM)c, 445(SM)C, 446(ST)C, 447(ST)C, 448(ST)c, 449 (ST)c ,450(ST)c, 451 (ST)C, 452(SA)c, e 453(SA)e, 454(SA)e. 455(SAle, 456(SM)e.

rULY: 457(AT1, 450(AT), 459(AT)c, 460(JR), 461 (m), 462(lR), 463(lR)c, 464(PO}, 465(PO)c.

AUGUST: 466(HY), 467(HY), 468(ST),469(ST), 470(ST), 471(SA), 472(SA), 473(SA), 474(SA), 475(SM), 476(SM), 477(SM), 478(SM)C, 479(HY)c, 4BO(ST)c, 481(SA)c, 482(HY), 483(HY).

SEPTEMBER: '8'(ST), '85(ST), '86(ST), 4B7(CP)", '88(ST)", '89(HY), '90(HY), '91 (HY)", '02(SA), '93(SA), 'O'(SA), '05(SA), '96(SA), '97(SA), '98(SA), '99(HW), 500(HW), 50l(HW)", 502(WW), 503[\VW), 50'[\VW)", 505 (CO), 506(CO)", 507(CP), 508(CP), 509(CP), 5l0(CP), 511 (CP).

OCTOBER: 5l2(SM!, 5l3(SM), 5l4(SM), 5l5(SM), 5l6(SM), 5l7(PO), 5l8(SM)", 5l9(m), 5200R), 52I(lR), 522OR) , 523(AT)". 52'(SU), 525(SU)", 526(EM), 527(EM), 528(EM), 529(EM), 530(EM)c, 53] (EM), 532(EM) , 533{PO).

NOVEMBER: 53'(HY), 535(HY), 536(HY), 537(HY), 538(HY)", 539(ST),540(ST), 541 (ST), 5'2(ST), 5'3(ST), 544(ST), 5'5(SA), 546(SA),5'7(SA), 54B(SM), 549(SM), 550(SM), 55l(SM), 552(SA), 553(SM)", 554(SA), 555(SA), 550(SA), 557(SA).

DECEMBER: 558(ST), 559{ST), 560(STl. 561 (ST), 562(ST), 563 (ST)c , 564{HY), 565(HY), 566(HY), 557(HY),568(HY)", 560(SM), 570(SM), 571 (SM), 572(SM)", 513(SM)", 57'(SU), 575(SU), 570(SUI 577(SU), 578(HY), 579(ST), 580(SU), 581 (SU), 582(lnd,x).

VOLUME 81 (1955)

JANUARY: 583(ST), 58'(ST), 585(ST!, 585(ST), 5",(ST), 588(ST),580(ST)", 500(SA), 59l(SA),

~92(SA), 593(SA), 59'(SA), 595(SA) , 595(HW), 507(HW), 598(HW)",599(CP), 600(CP), 601(CP), .-02(CP), 503(CP), 60'(EM), 605(EM), 506(EM)", 607(EM).

FEBRUARY: 608(WW),609(WW), 5l0(WW), 511(WW), 6l2(WW), 51 3 (WW) , 6l4(WW),6l5(\vW), 6l6(WW), 5170R), 6l8OR), 5l00R), 520OR), 821 OR)", 5220R), 023 OR), 62'(HY)", 625(HY), 620(HY), 627(HY), 628(HY), 529(HY), 6'O(HY), 83l(HY), 6'2(CO), 63'(CO).

MARCH: 634(PO), 635(PO), 636(PO), 637(PO), 838(PO), 639(PO), 6'O(PO), 641(PO)", 6'2(SA), 6'3(SA), 544(SA)c 845(SA), 6'6(SA), 6'7(SA)', 5'8(ST), 6'9(ST), 550(ST), 651 (ST), 652(ST), 653(STl, 654(ST) , 655(SA), 656(SM)c, 657{SM)c, 658(SM}c.

APRIL: 659(ST), 660(ST), 661(ST)c, 662 (ST), 663(ST), 664(ST)C, 665(HY)C, 666(HY), 667 (HY), 660(Hy), 669(HY), 670(EM), 671(EM), 672(EM), 673(EM), 674(EM), 675(EM), 676(EM), 677(EM), 678(HY).

MA Y: 67D(ST), 680(ST), 681 (ST), 692(ST)', 683(ST), 684(ST), 685(SA), 5B6(SA), 5B7(SA), GB9(SA), 6aDISA)e, 690(EM), 691 (EM), 692(EMl, 693(EM), 694(EM), 695(EM), 696(PO), 697(PO), 69B(SA), 69D{PO)C, 700{PO), 701(ST)c.

c. Ol8cUssion ol sevcral papers, grouped by Divislons.

c. Presented at the Atlantic City (N.I.) ConvenUon In rWlC, 1954.

AMERICAN SOCIETY OF CIVIL ENGINEERS

OFFICERS FOR 1955

PRESIDENT

WILLIAM ROV GLIDD EN

VICE·PRESIDENTS

Ttrm t:xpirtI OClob~r, 19H: Ttrm lx/,irtJ OtlofJt~r. 19J6:

ENOCH R. NEEOLES

M,\SON C. LOCKWQOD

FRANK L. WEAVER LOUIS R. HOWSON

Term t!xpirt:J OClobrr, 19H:

CHARLES 8. MOLTNEAUX MERCEt J. SHELTON A. A. K. DOQTH CARL G. PAULSEN LLOYD D. KNAPP

DIRECTORS

Ttrm t:xpirtJ Oc/oblr, 1956: Ttrm txpires Oc/ohtr, 19J7:

WILLIAM S. blONDE, JR. JEWElL M. GARRELTS OliVER W. HARTWELL FREDERICK H. PAULSON THOMAS C. SHEDD GEORGE S. RICHARDSON SAMUEL B. MORRIS DON M. CORDETT GLENN W. HOLCDMD

FRANClS M. DAWSON

ERNEST W. CARL TON GRAHAM P. WItLOUGHBY RAYMOND F. OAWSON LAWRENCE A. ELSENER

PAST·PRESIDENTS

MtmbtfJ o/

",t

^Baard

WALTER L. HUDER

EXECUTIVE SECRETARY

WILLIAM H. WISELY

ASSISTANT SECRETARY

E. L. CHANDLER

DANIEL V. TERRELL

TREASURER

CHARLES E. TROUT

ASSISTANT TREASURER

CARL TON S. I'ROCTOR

PROCEEDINGS OF THE SOCIETY

HAROLD T. LARSEN Ml1nl1gC!r o/ TC!chnicl11 Publicl1tioru DEFOREST A. MATTESON, JR.

Editor 0/ Trdmical Publications

PAUL A. PARISI

IISJoc. Editor 0/ Tulrn;cal Publica/ions

97YJ03190

rTEE ON PUBLICATIONS

JEL D. MOR RIS, Clla;rman , M. GARREL TS, YicC!·Chairman

DLIVER W. HARTWELL

•

Proceedi ng s Se parate No.68D Errata : Pag" 1, foot of page: Junior t echn ician, shall be: Dr.techn. " " " " "

3, formula (6) ri' Jr., Il " " t;{ofl 5, " (H) 2 e = h dh " " e- h dh · 6, line 3 from below : 3\0 " " +f 7, " 8, "

17 " " :for mu la shall read: p = (150-0,2' 6 2)'0,5,0,025 ' 50(1-0,10)+62'1 = 139 psf 7 frem above: formula shall read : p = (150-62'0,53)'0,5(0,7'4,5+0,21'20)(1-0,25)+62'5 = 634 psf • •