NATIONAL BUREAU OF STANDARDS REPORT

4396

TESTS OP PRESTRESSED CEUOULAR SLABS

(Slab Nos. 1 , 2 , 3 , and 4)

by

M. Chi and D. Watsteln

Report to

Bureau of Yards and Docks

Department of the Navy

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
U. S. DEPARTMENT OF COMMERCE

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NATIONAL BUREAU OF STANDARDS

A. V. Astin, Director

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NATIONAL BUREAU OF STANDARDS REPORT

NBS PROJECT NBS REPORT

1001-10-4811 October 28, 1955 4396

TESTS OF PRESTRESSED CELLULAR SLABS

(Slab Nos. 1, 2, and 4)

by

M. Chi and D. Watsteln

To

Bureau of Yards and Docks

Department of the Naby

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

The publication

unless permissi 25,D.C. Such

cally prepared

Approved for public release by the

Director of the National Institute of

Standards and Technology (NIST)

on October 9, 2015.

I or In part, is prohibited

f Standards, Washington

a report has been speclfiir report for its own use,

TESTS OF PRESTRESSED CELLULAR SLABS

(Slab Nos. 1, 2, 3 , and Ij.) by

M, Chi and D. Watsteln

Abstract

Pour 5- by ^-ft prestressed cellular

slabs were tested under concentrated

loads. Deflections and strains were

measured and were compared with the

computed values. Maximum load carrying capacities and crack patterns were

recorded. Data obtained thus far indicated that elastic theory for solid

slabs is applicable to slabs of this

type. Welded wire reinforcement in the

blocks and good contact between blocks

such as would be provided by grouted

joints, were essential to insure a high

load carrying capacity of such slabs.

The slabs tested on a relatively short

span and carrying a moderate prestress

of 1000 psi failed by "punching" shear

under a centrally applied load.

1. INTRODUCTION

At the request of the Bureau of Yards and Docks, the Structural Engineering Section initiated a study of the properties

of slabs composed of 6- by 6- by 6-ln. cellular concrete blocks

arranged in a checker-board fashion and prestressed in two

directions. The current report presents the results obtained

in tests of four 5- by 5- ft slabs made of cells procured by

Preload Corporation while under contract with the Bureau of

Yards and Docks.

The first two slabs were fabricated with cells assembled

with ungrouted joints. It became apparent upon assembling the

ungrouted slabs that the dimensional tolerances of these cells

were such that close fitting and tightly closed joints could

not be obtained. Accordingly, it was decided to grout the
2o

joints in subsequent test specimens in order to secure uniformly

intimate contact between all bearing surfaces and the second pair

of slabs described in this report were fabricated in this mannerc

2, DESCRIPTION OP TEST SPECIMENS

2.1 Cells

The cells were hollow 6 in. cubes having an opening hy

5- in. in cross section. There was a 1- by 2-in. elliptical hole

on each web through which the prestressing unit could pass. The

principal dimensions of the cellular unit are shown in figure 1.

The cells utilized in the tests of these four slabs vjere

furnished to the National Bureau of Standards by Preload Corporation which procured these units from a commercial concrete

products plant. For these reasons, the proportions of the concrete used in the cells are not known.

The outside dimensions of the cells selected at random

were found to vary as much as l/8 in, from the specified dimensions. The reinforcement in cells consisted of a single layer

of 1- by 1-ln. galvanized welded wire fabric of l5/l5 gage.

A 3/4” tiy 2- by 6-ln, strip of concrete removed from a cell was tested to determine the modulus of elasticity and compressive strength of concrete. The results of sonic and static

tests are given in the following table:

Method of

testing

Modulus of

elasticity

Compressive

strength

Poisson* s ratio

10 ^

Static 2.

2 .

p si psi

91 4710

97

0.12

Soni c
3.

2.2 Prestressing steel

The prestressing units in the test slabs were 5/8 in.

"Stressteel” bars. The anchorage for these bars consisted of

hexagonal nuts 1 l/4 in. long which bore on 5 3/k~ 5 3/4“

by 3/4“in. anchor plates.

The tensile strength of unthreaded Stressteel bars was

found to be 163»000 psi, whereas threaded bars supported by

fully tightened nuts developed a tensile strength of 152,000

psi. The yield strength of the steel, determined by the

"offset” method (offset = 0.2^) was ll|2,000 psi. The stressstrain characteristic was a straight line up to 65,000 psi,

giving a Young’s modulus of 30 x 10° psi; the secant modulus

at 100,000 psi was 28.2 x 106 psi. The reduction in area at

point of fracture was 35 percent.

2.3 Description of prestressed slabs

Each slab consisting of 100 cells was nominally 5- by 5-ft

in plan and 6 in. thick. The cells were arranged in such a

fashion that the axis of the cell through the open ends was

perpendicular to the axis of each adjacent cell. This arrangement resulted in equal strength in both directions of the slab.

The holes in the cell webs were also arranged in such a manner

as to enable the prestressing tendons to be staggered with

respect to the mldplanef of the slab. Thus, the resultant prestressing force produced axial prestressing in both directions

of the slab.

The dimensions of the slabs with ungrouted joints were

approximately 5- t>y 5-ft. The first slab with ungrouted

joints designated as Slab No. 1 was made of cells wlch appeared

to be sound in texture and free from shrinkage cracks. It was

quite evident that the cells had very poor contact with one

another. Some of the joint openings were as wide as l/4 inch.

The second slab with ungrouted joints, designated as Slab

No. 2, was made of cells which were selected with greater care

as to their dimensions and shape. However, on account of

limited stock of units, some of the blocks were honeycombed

and had shrinkage cracks. Nevertheless the assembled slab presented a better appearance and its joint openings were much

narrower than was the case in Slab No. 1.

The first grouted joint slab, designated as Slab No. 3,

was constructed in two stages. First, the cells were assembled

into 5-ft beams with about l/8 in. mortar joints. The beams

were then assembled together with l/8 in. mortar joints between
them„ The finished slab was approximately 6l„5 by 62 inches

The shorter dimension was the length of the beams „ The slab

was a true plane before it was prestressed. The second slab

with grouted joints, designated as Slab No. 4, was made of

cells which w’ere inferior in concrete quality compared with

those in previous slabs. Its general appearance, however, was

similar to Slab No. 3.

After prestressing, the slabs became slightly warped

with one corner curled up.

2.[|. Prestressing procedure

Experience in prestressing operations indicates that it

is neither necessary nor practical to apply prestress simultaneously to all bars. Large amounts of prestress may be

sa_fely applied if the prestressing force is applied in small,

equal increments to all tendons.

In the current tests, a portion of the prestress was

applied by tightening the anchorage nuts with a wrench. Approximately half of the specified prestress of 1000 psi was

applied with a wrench and the remainder was applied with a hydraulic jack. In order to maintain the stress in the slab

as uniform as possible, the following sequence of prestressing

with a jack was adopted?

1. The third bars from the edges of slab.

2. Edge bars.

3. Center bars.

Ij.. The rest of bars symmetrically.

The tensioning force was applied to the prestressing tendons through an adaptor having suitable threaded connections.

Two SR-1| strain gages were mo'onted longitudinally and two

transversely on the adaptor bar. Each pair was connected in

parallel and the two pairs served as measuring and compensating

gages, respectively. The calibration curve for the adaptor is

shown in figure 2.
5 .

3. TESTING PROCEDURE

3.1 Test set-up

All slabs were tested in a 600,000 lb capacity hydraulic

testing machine to failure. The specimen was simply supported on 3/k pip© rollers which rested on suitable

frames. Two- by 6-in. timbers were used for the frame in

testing Slab No. 1. This frame was found to be lacking in

rigidity and accordingly it was replaced by one consisting

of 6 in. I-beams in tests of Slabs Nos. 2 and 3. With this

arrangement, however, it was impossible to observe the cracking pattern in the bottom of specimens during the tests. It

was decided, therefore, to test Slab No. [j. elevated about

5 ft above the machine platen. The frame for supporting the

slab was made of 6- by 12-in. reinforced concrete members

which, in turn, were supported by seven 6- in, concrete

cylindrical pillars about I; ft high. This permitted not

only visual observation of the bottom face of the specimen

during the test, but also the Installation of Tuckerman optical gages to measure tensile strains and widths of cracks.

3.2 Instrumentation

In the test of Slab No. 1 only the deflections were

measured. During this test 0.0001-in. micrometer dial

gages were used. However, in the tests of Slabs Nos. 2, 3>

and [|., 0.001- in. dial gages were used and were found to be

sufficiently accurate. The location of the dial gages is

shown in figure 3.

The variation of strain in prestressing bars was measured

by SR-I). strain gages attached to the bars. Pour bars in each

direction in Slabs Nos. 2, 3» and were each equipped with

a pair of A-IT gages connected in series. They were designated

as bar gages Nos. 1 through 8 and their locations are shown in

figure 3. All bars with gages were calibrated in a testing

machine.

Strain in concrete surfaces was measured by A-11 gages.

In Slabs Nos. 3 and 4> four such gages were mounted on top

and four on bottom surface of each slab. The locations of

these gages are also shown in figure 3.

Pour Tuckerman optical gages were installed on Slab No.

4

and their locations are shown in figure 3- They were intended
to measure the width of cracks. Unfortunately, cracks occurred

elsewhere and these gages were used only to check the tensile

strains recorded by SR- 1), gages,

3 . 3 Testing procedure

All slabs were first flexed by applying a load of 5000 lb.

This load was then removed, the slab was allowed to recover

for several minutes and a set of readings of all gages for

zero load was recorded. The load was applied to the slab

through a 6- by 12- by 12- in, concrete loading block located

at the center of the specimen. The load was generally applied

in increments of 5000 lb, but sometimes the Increments were reduced to 2500 lb when an extra set of readings appeared to be

advisable. As the maximum load was approached, the indicated

strains and deflections increased noticeably. As soon as

these signs of impending failure were observed, readings of

the gages were discontinued and the load was Increased until

the maximum value was reached. This value was recorded as the

load carrying capacity of the slab,

i|. TEST DATA

i|,l Deflections of slabs

All deflection measurements were made with reference to

the lower platen of the testing machine. The four dial gages

placed directly over the edges of the slab indicated the

settlement of the supports. The observed deflections of the

slabs were corrected for the settlement of the supports by

assuming that the edges of the slab remained straight during

the test and that, consequently, the settlement of the supports

varied linearly between these four points.

The relation between center deflections and applied load

is shown in figure 4- Tt is noted that Slab No, 2 had a much

larger deflection than Slabs Nos, 3 and 4» This indicates

that imperfect contact between cells in the ungrouted slab produced extra deflection due to the adjustment of the contact of

cells

.

Figures lj.A and 4^ show the deflection profiles of Slabs

Nod, 3 and 4 obtained by averaging the deflections along two

rows of dial gages disposed symmetrically and adjacent to the

loading block. The location of the dial gages is shown in

figure 3 . The gages at the ends of these two rows served to

determine the datum plane of the supported edges of the slab.
7.

lj..2 Variation of prestressing force during test

After the prestress is applied to the slab it may diminish

slowly due to the following causes: (l) readjustment of contact of cells, (2) relaxation of steel, ( 3 ) creep of concrete,

and (L|.) shrinkage of concrete. In view of the fact that the

cells were about a yearold, concrete would be expected to

shrink only a negligible amount. Since Slabs Nos. 3 and i|

had grouted joints, they were monolithic structures and no readjustment of cells occurred. The loss indicated by the decrease in strain of bars in these slabs must be attributed to

causes (2) and ( 3 ). The loss was rather small because of the

low prestress; this is illustrated by data obtained for Slab

No. 3 shown in table 1. In the case of Slabs Nos. 1 and 2,

however, the loss of prestress due to readjustment of the cells

was observed from the time when the anchorage nuts were

tightened by wrench. ¥hen the full prestress was applied to

Slabs Nos. 1 and 2, most of the readjustments of the cells had

already taken place but the process continued for a few days

before it tapered off. Since SR-1]_ gages were installed on some

prestressing bars in Slab No. 2 these losses were measurable.

It was noted that the loss of prestress in Slab No. 2 due to

its being moved from the working platform to the test frame constituted 25 percent of total strain due to prestressing.

Since the prestressing bars were placed either at the neutral

plane or 0.^ in. above or below it, it was expected that the application of transverse load to the slab would have little or no

effect on the strain in the bars. The observed increments of

strain in the bars in Slabs Nos. 3 4 were all under 4 percent

of the initial prestress. The variation of prestress is given

in table 2.

In Slab No. 2 the maximum loss of strain during the test

was 96 X 10“° in. /in., which was more than four times as much as

that for corresponding load in Slabs Nos. 3 and 4* The larger

loss of prestress in Slab No, 2 can be attributed to the readjustment of the cells. This excessive loss of prestress probably had a direct bearing on the extraordinarily large deflection

mentioned in 4«1 and low load carrying capacity as will be described in 4*^*
8 ,

3 Concrete strain

Concrete strains due to prestressing were measured in Slab

No, 3* '^Ne average strain corresponding to 1000 psi prestress

was observed to be 313 x 10"8 in, /in.

The variation of strain on the surface of the concrete

with the applied load is illustrated in figures 5 and 6 for

Slabs No, 3 and 4? respectively, I>uring the test of Slab No.3<p

it was observed that the strain gages on the bottom face of the

slaby that were connected to a common ground lead had a low resistance to ground. The tensile strain data obtained for Slab

No. 3 were, therefore, discarded. All strain gages in Slab

No. 4 separate leads and the data obtained appeared reasonably good,

4,4 Width of cracks

Tuckerman gages were Installed to measure the width of

cracks on the bottom face of Slab No, 4 they were located

directly under the edges of the loading block where the maximum moment was expected to occur. Since the slab presumably

failed due to punching shear, the crack occurred about a foot

from the loading block. However, the Tuckerman gages served to

check the tensile strains measured by SR-4 gages. The concrete

strains measured by Tuckerman gages are also shown in figure 6,

4«5 Load carrying capacity

Slabs Nos, 1 and 2 which were assembled with ungrouted

joints supported maximum loads of 11,800 and 16,2^0 lb, respectively, It will be recalled that Slab No, 1 contained units

which made poor contact with one another and had joint openings

as wide as l/4 in. The units used in Slab No, 2 were selected

with greater care as to their dimensions and shape and its

joint openings were much narrower than in Slab No, 1,

Slabs Nos, 3 and 4 were grouted and w^ere both fabricated

in the same manner. During the test, Slab No, 3 was loaded to

35yOOO lb at which point signs of approaching failure were indicated, The load was then removed, and readings after recovery were recorded. The slab was then loaded again and

failed at a load of 30?500 lb. Slab No, 4 supported a maximum

load of 34,240 lb.
9.

4.6 Crack pattern

In Slab No. 1 the four cells under the loading block were

pushed down about 3/4 cells adjacent to them had

crushed corners. ‘this can be attributed to the failure of

frictional forces between the cells to resist the shear.

Figure 7 showing bottom view of slab, clearly Illustrates

this type of failure.

In Slab No. 2 the four cells directly under the loading

block along with two rows of cells surrounding them were

pushed down. There was some slipping between cells but the

bottom surface formed essentially a convex surface. Cracks

were Irregular and did not form any definite pattern on the

surface. The cells adjacent to the loading block and having

a web parallel to its edge developed horizontal cracks near

the top shell of the unit; for cells further away from the

loading block, the horizontal cracks developed near the bottom

shells. Webs of cells perpendicular to the edge of the loading block had diagonal cracks. Cells one foot or more away

from the loading block appeared undamaged except for the presence of some horizontal hair cracks in the webs. The top surface of the slab remained intact but the loading block was

forced into the slab about l/4 inch, (See figures 8 and 9).

In Slabs Nos, 3 and 4 a circular crack approximately 3 ft

in diameter appeared at the bottom surface. Figure 10 shows

the crack pattern observed in Slab No, 4- Slabs Nos. 1

and 2, the loading block was pushed approximately l/4 in, into

the slab. The top shells of the cells adjacent to the loading

block cracked slightly. There was a circular hair crack in the

top surface of Slab No, 3 with a diameter of approximately 3 ft.

(See figure 11 ) . No similar crack was observed in Slab No, 4*

On the other hand, a hair crack approximately 14 in, in diameter

was observed in the bottom face of Slab No, 4? tnt not in Slab

No, 3. Cracks in the webs of cells were essentially similar to

those in Slab No. 2. Typical diagonal crack patterns in sections

of a slab are shown in figures 12 and 13 ; diagonal cracks in individual units are shown in figure 14 .
10 .

5. COMPARISON OP TEST DATA WITH THEORY

5,1 Theory

The deflection of a square plate under a partially distributed load is given in S, Timoshenko’s ’’Theory of Plate and

Shells,” p, l53> as follows:

hn-J

W =

4^<3

D7I“

CO

VI = f, 3, 5,

(- 1 ) 5m YY]

yriTT 9,

2 a

cosh

C 05 h o( ^

[cosh ^r„) -t S\nh (o<^.2r^)+oi^ 5 in 2 Yin 2 Cos In Vm.

C05 h 3 0 5,n h -!21Z>

]

jroj_

2 cos h a a j a

The following notation is used in the equation above and

the following discussion:

w =

q

a = D

at = m =

o(, (i,r =

p

V

E

X, y

M = X

deflection

intensity of a uniformly distributed load per

unit of loaded area,

length of edge of square slab,

flexural rigidity of the slab,

edge length of the loaded square,

positive odd integers ranging from 1 to

infinity

dimensionless constants,

total load on the slab

Poisson’ s ratio

Young’ s modulus

coordinates of a point in the slab,

bending moment along x - axis

bending moment along y

- axis
h

11.

= thickness of a solid slab with flexural

strength equal to that of the cellular slab.

m = moment along x - axis due to a unit load,

m = moment along y - axis due to a unit load.

y

Maximum deflection occurs at the center point of the slab

where the coordinates are,

X = £ - y = 0

2

In this case, a = 54 in.

at = 12 in.

and o<' = m TT m 2

Y = m T

Tn 18

and c< - ?X = in ^ ' m

7

18

vn TT

Substituting into the equation and taking only first two terms

of the series, we obtain

w = 0.041 6 ^ ^ %

D TT^

and substituting Q = £ h

\2 (\-v^)

P <a" E

w = 0.131 (I- yV
12 .

For . 3 w = . I ig P

E h"

which is comparable with w = .12^5

as given by Timoshenko in table 20, p

P a'

£

158 ,

for point load

For 1/ = . 15 j w = .128 P3^

E

Also, -D (

yv

-h 1/

w \

9

^

Combining the two expressions for and w , the bending moment

at any point can be found. The final expression for maximum

moment can be reduced to the following equation:

^ ^max ~ P ^ ~ ^ P

The value of P can be found in table 1? of the above

reference, for 1/ =0,3? as approximately 0,2. Values of C 0 “ efficient p can also be found in Reynolds’ "Reinforced Concrete Designer’s Handbook", p. 233? from which

= 0. 13 is obtained for

12

54 o. 2^2

hence, = My = P ( -I- 0. 1 5 rriy

)

0,17 P
13 . This value is applicable to material with Poisson’s ratio

of 0.15 which is a commonly used value for concrete.

It is noted that the foregoing formulas are valid under

the following conditions:

(1) Material in the slab is homogeneous and elastic.

(2) The rigidity of the loading block is negligible

and (3) The four edges of slab are restrained against

vertical movement but are free to rotate.

In the laboratory tests of the slabs, it can hardly be

claimed that any of these conditions were completely fulfilled.

Nevertheless, it was assumed that the deviations from ideal conditions during these tests produced only minor changes in the

behavior of the test specimen. It was also assumed that the

deflections and strains measured at a point 3 from the loading block were essentially the same as those values at the center

of the slab.

In the following discussion of the properties of the slabs,

the section modulus of the cell was computed to be 22.05 in. 3 , Prom this, the thickness of equivalent solid slab was found to

be 4*7 in. Young’s modulus determined for a 3/4

- I’M 2- by 6- in.

concrete strip, cut from a cell was 3 x 10° psi. The theoretical maximum deflection of the slab based on these properties of

its section was calculated and is shown in figure 4»

It is recalled that the relation between the bending moment

M and the applied load P is given by the expression

M= 0.I7P

Prom this expression and the flexure formula M = f^ _ ,

the load P corresponding to f^ = 1000 psi is 21,600 lb.

The strain in concrete corresponding to 1000 psi with

E = 3 X 10^ psi is 333 X 10“^ in, /in. The average strain observed during the prestressing operation was 313 x 10“° in. /in.

The relationship between the applied load and the strain

in the concrete is Illustrated in figures 5 and 6.
14 .

Comparing the calculated strains and deflections with observed data, it can be seen that they agree fairly well for

Slabs Nos. 3 and Ij, which had grouted joints. The observed loaddeflection relationship for ungrouted Slab No. 2 was markedly

different from the computed relationship.

5.2 Discussion of test results

From the data given in section 5.1j it is evident that

prestressed grouted slabs do not exhibit any sharply defined

transition from uncracked to cracked slabs at the point where

the initial prestress at the bottom fibers is reduced to zero.

There is, rather, a gradual transition as evidenced by both

the load-deflection and load- strain relationships in figures

i|, 5> and 6 , In Slabs Nos. 3 and I4. there was a gradual increase

in the center deflection up to a load of about 30>000 lb, or

about 85 percent of the load carrying capacity. As the loads

approached the maximum values, cracking progressed over the

tension face of the slab and deflections Increased rapidly. It

is probable that at this stage of loading the cracking around

the elliptical holes in the cells was extensive. Examination of

the cells after test revealed the presence of diagonal tension

cracks extending into two or three rows of blocks adjacent to

the loading block. This is Illustrated in figures 12 and I 3 . The failure of the slabs was primarily caused by punching

shear around the periphery of the loaded area. The failure in

every case was accompanied by the loaded area being "punched”

out. This is strikingly demonstrated in figure 7 where the

central group of four ungrouted cells is shown displaced about

3/4 in. below the adjoining cells and a similar view of the

top is shown in figure 8. The displacement of the central

loaded area is not quite as severe for the grouted slab as can

be seen in figure 12.

At ultimate load, the prestress was completely nullified

and the slab behaved as an ordinary non-prestressed concrete

slab. The diagonal tension in this case is numerically equal

to vertical shear. The effective web area of the cells

immediately adjacent to the central loaded area was 3 in.

for each cell, or 38 in.^ for the entire periphery of the loading block. The shear strengths of the grouted Slabs Nos. 3 and

4 were, thus, 98 O and 950 psi, respectively. The Slabs Nos. 3

and !(_ were able to develop diagonal tensile stresses of nearly

1000 psi because of the presence of closely spaced welded wire

reinforcement in the webs and flanges of the cells.
15 .

6 . CONCLUSIONS

Although the study of prestressed cellular slabs is still

In progress the following conclusions may be drawn from the

test results obtained so far:

(1) A prestressed slab made of precast hollow cells

may be expected to behave like a homogeneous

material in flexure and shear.

(2) A simply supported slab made of these cells, subjected to concentrated load, with short span and

nominal prestressing falls in punching shear,

( 3) Welded wire reinforcement in the cell webs contributed a considerable amount to the load carrying

capacity of the slab.

(I4.) lt)r a structure of this type, intimate contact

between the cells is of utmost importance.

( 5 ) With reasonably rigid anchorage plates for prestressing bars, solid end blocks are not necessary,

provided the anchorage plates are nearly equal in

area to the cell with which they are in direct contact .

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j>i fA

•H vO cO vO P 1 d 1 d A S o o 1 M t—1 (—i {—1 o o

rH <H •'ri •'TJ P> p> 0 A 0

cd

d -p

d -p

fn

H 0 Ih 0 p

•H P, fi o S O

cti 0 0 ft P tiD !h P, p ft

p>

d o p o p 0 -H p 0 p 0 d •H •H 1—1

fA (A

aJ o a

H ^ rH

•H ;s •H ft •H ft

p>

p s P

•H P ^ ‘H P *H C O p> 0 A 0 H ta ca - - ~ - - - - - - _ -

Pj- o

CO Ift o OO A —1 1—1 + +

fA lA lA

ift "LA vA 1 1 A + +

1A 1 vA CO cr fA A 1—1 + + 0A0 1A 1A P lA Pt A A O A 1 1 i d + + o »- ft. •_ ». o- «. ^ ft- ft- o A % P P± fA ft O o fA 1 00

«- *-

— ^

bO Pf P fA fA pt

A

CP (A 4" +

lA

O

A O- ftA

fA 4" 4" A r- A 1 1 1 1 1—1 1 1 - - A 4" - +

ft ft p P

ft 1—1 1 1 P 0 0 1 1 ^ 0

ft ft p P

ft •H

A P P •H ft ft 1 1 p P'-- 0 ft •H ' •H 0 p fA k:> ft ft P A P o 1 ft 1 ft A o O p 1 P 1—1 ( ( 1 o O O

•H ft ft ft ^ ft

ft ft ft 0 ft 0

•H ft\ P p ft P ft P 1 0 P 0 P p •H ft El o S o o p 0 ft 0 ft o p bO P ft P ft ft P o p o p 0 »|—} p 0 P 0

•H •H f—1 P fA p O G H r-l •H |2 H ft •H ft ft p s P S

•H P p •t—i•H

p

O ft 0 ft 0 H ca ca

O- ft-

—— o*— 0 0 0 0

p> p>

aj aj o o

•H *H d t:*n

•H «H + I

an

increase

in

strain,

a

decrease

in

strain.

Table 2. Strain increments in prestressing bars due to

applied loads.

f t

’ Slab’

’No. ’

t I

I

T,na<i ’ -

- 8 Strain Increments, 10“ in. /in. , in bars

\ Nos . , kips ’

t 1

!

, 2

I

, 3

'

1

’

t 4 , 5 ; 6

t

. 7 : 8 :

5 5 8 _ 3 13 -5 15 -1

o 10 0 5

- 0 23 -24 19 -21

13 -19 -11 - -20 16 -60 14 -57

15 -43 -32 - -39 11 -96 7 -85

5 4 7 4 3 6 -1 8 0

10 3 5 4 3 10 -6 9 -6

15 3 5 3 -1 13 -10 14 -10

3 20 -2 4 3 -6 17 -17 19 -20

25 0 8 4

-6 21 -17 24 -21

30 6 14 10 4 27 -26 35 -31

32.5 13 22 18 0 36 -26 45 -32

35 34 44 — — — ~ — —

2.5 2 -8 -7 0 -9 0 -7

5 1 -4 — -3 8 -19 0 -7

7.5 2 -3 -- -4 8 -10 9 -4

10 3 -3 — -5 7 -16 8 23

4 15 10 -4 -7 18 -14 10 29

20 12 -3 — -8 19 -19 18 —

25 18 0 — -5 29 -19 20 -28

30 42 10 2 6 -20 40 -22

Note: Total strain due to prestressing was approximately

1200 X 10“° in. /in.

Bar 5 and 7 were l/2 in. below centerline.

Bar 6 and 8 were l/2 in, above centerline.
I 0

HI

I'

‘1A

•)

‘-i ' ' u j ' '-f ; :
l"x l" - 15/15

WELDED WIRE FABRIC

i ii n 1

*^’"= 1

11

^ ii

~s.

1

1

_l

1

pHj

1

2 -

^ 2

1 V

.. 6

2 2

II

EFFECTIVE SECTION PROPERTIES OF A CELL IN A SLAB!

A =11.25 IN.^

1 = 66.22 IN.*^

^

= 22.05 IN?

Q = 13.1 IN.^

h = THICKNESS OF EQUIVALENT SOLID SLAB

= 4.7 IN.

FIGURE DIMENSIONS AND SECTION PROPERTIES OF A

CELLULAR BLOCK. .

sdix ‘soaod

STRAIN
,11

•a

K )

• ^

¥

f . £# --1 *. J ..iiy

I'1
4'- 6"

LEGEND

X INDICATES MICROMETER DIAL GAGES

T " TUCKERMAN GAGES

C '« SR4

GAGES

GAGES I THROUGH 4 ON BOTTOM SURFACE OF SLAB

• • 5 " 8 " TOP •• "

FIGURE 3. LOCATION OF MICROMETER DIAL DEFLECTION GAGES,

STRAIN GAGES ON CONCRETE AND PRESTRESSING
I
APPLIED

LOAD,

KIPS

40

A-SLAB NO. 2

X - " " 3

- II II 4

O-THEORETICAL CURVE FOR

EQUIVALENT SOLID SLAB.

0

2 3 4 5

CENTER DEFLECTION,

6

IN.

7x 10’^

FIGURE 4. COMPUTED AND OBSERVED CENTER DEFLECTION

IN SLABS NOS. 2, 3, AND 4.

.01

.02

.03

.04

.05

.06

.07

.08

.09

.10

.11

SLAB NO. 3

LOADING BLOCK

FIGURE 4A. DEFLECTION PROFILE OF SLAB NO. 3 AT A

SECTION ADJACENT TO THE LOADING BLOCK.

DEFLECTION,

IN

SLAB NO. 4

LOADING BLOCK

FIGURE 4B DEFLECTION PROFILE OF SLAB NO. 4 AT A

SECTION ADJACENT TO THE LOADING BLOCK

DEFLECTION
f

'

I

;

r *

'.Hm •

VMi

'V

1

v»

I

I

\M

.V'

i

I
APPLIED

LOAD,

KIPS

FIGURE 5- COMPUTED AND OBSERVED STRAINS IN CONCRETE

IN SLAB NO. 3.
;<w . v;,..'" . ' i
APPLIED

LOAD,

KIPS

0 100 200 300 400 500 600 700xl0‘®

STRAIN

FIGURE 6. COMPUTED AND OBSERVED STRAINS IN CONCRETE

IN SLAB NO. 4.
•-

l!

. I

i

%

. ,-v;
Pig. 7. Bottom of slab No, 1 after failure.

Pig. 8. lop of slab No. 2 after failure^


*•1

V

1
note:

LOADING BLOCK PENETRATED 1/4 IN. BELOW TOP SURFACE OF SLAB,

(SHOWN BY DOTTED LINE). THERE WAS LITTLE OTHER DAMAGE ON

TOP OF SLAB.

BOTTOM VIEW OF SLAB NO. 4

FIGURE 10. CIRCULAR CRACK PATTERN IN BOTTOM OF SLAB NO. 4.

ng 11, Cii*cular crack in top of slab No, 3<
f* 1


N

n

(T' r

oJ: 0

SECTION AA

FIGURE 13. CRACK PATTERN IN SECTIONS OF SLAB AT

VARIOUS DISTANCES FROM THE LOADED AREA.
.r

•

» . (.

t

I I
Hg. ll4-« Diagonal crack pattern in individual units

THE NATIONAL BUREAU OF STANDARDS

Functions and Activities

The functions of the National Bureau of Standards are set forth in the Act of Congress, March

3, 1901, as amended by Congress in Public Law 619, 1950. These include the development and

maintenance of the national standards of measurement and the provision of means and methods

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publications should be addressed to the Office of Scientific Publications, National Bureau of

Standards, Washington 25, D. C.
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