NATIONAL BUREAU OF STANDARDS REPORT

5704

FLEXURAL TESTS OF BEAMS WITH REINFORCEMENT

OF DIFFERENT PROPERTIES

by

Robert G. Mathey and D. Watstein

Report to

American Iron and Steel Institute

<S>

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
THE NATIONAL BUHEAIJ OF STANDARDS

Function** 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

for making measurements consistent with these standards; the determination of physical constants and properties of materials; the development of methods and instruments for testing materials,

devices, and structures; advisory services to Government Agencies on scientific and technical

problems; invention and development of devices to serve special needs of the Government; and the

development of standard practices, codes, and specifications. The work includes basic and applied

research, development, engineering, instrumentation, testing, evaluation, calibration services, and

various consultation and information services. A major portion of the Bureau's work is performed

for other Government Agencies, particularly the Department of Defense and the Atomic Energy

Commission. The scope of activities is suggested by the listing of divisions and sections on the

inside of the back cover.

Reports and Publications

The results of -the Bureau's work take the form of either actual equipment and devices or

published papers and reports. Reports are issued to the sponsoring agency of a particular project or program. Published papers appear either in the Bureau's own series of publications or in the

journals of professional and scientific societies. The Bureau itself publishes three monthly periodicals, available from the Government Printing Office: The Journal of Research, which presents

complete papers reporting technical investigations; the Technical News Bulletin, which presents

summar) and preliminary reports on work in progress; and Basic Radio Propagation Predictions,

which provides data for determining the best frequencies to use for radio communications throughout

the world. There are also five series of nonperiodical publications: The Applied Mathematics

Series, Circulars, Handbooks, Building Materials and Structures Reports, and * Miscellaneous

Publications.

Information on the Bureau’s publications can be found in NBS Circular 460, Publications of

the National Bureau of Standards (#1.25) and its Supplement (#0.75), available from the Superintendent of Documents, Government Printing Office, Washington 25. D. C.

Inquiries regarding the Bureau's reports should he addressed to the Office of Technical Information. National Bureau of Standards, Washington 25, D. C.
NATIONAL BUREAU OF STANDARDS REPORT

NBS PROJECT NBS REPORT

1001-12-4814 December 30, 1957 5704

FLEXURAL TESTS OF BEAMS WITH REINFORCEMENT

OF DIFFERENT PROPERTIES

by

Robert G. Mathey and D. Watstein

To

American Iron and Steel Institute

IMPORTANT NOTICE

NATIONAL BUREAU OF ST

Intended for use within the

to additional evaluation and

listing of this Report, either the Office of the Director, N

however, by the Government

to reproduce additional copl

Approved for public release by the

Director of the National Institute of

Standards and Technology (NIST)

on October 9, 2015.

progress accounting documents

irmally published It Is subjected

, reproduction, or open-literature

islon Is obtained In writing from Such permission Is not needed,

t prepared If that agency wishes

<NBS>

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

Contents

page

1. Introduction 1

2. Description of Materials and Test Specimens 2

2.1 Beam specimens

2.2 Reinforcement 3

2 . 3 Concrete 4

2.4 Fabrication and curing 4

3. Testing Procedure 4

3.1 Test Setup 4

3.2 Instrumentation 5

3.3 Test procedure 6

4. Test Results 7

4.1 Mode of failure and load carrying capacity 7

4.2 Deflections of beams 8

4.3 Stress in reinforcement 8

4.4 Concrete strains 9

4.5 Widths and spacing of cracks 9

5. Comparison of Experimental and Theoretical Results 11

6. Discussion of Results lS

7. References 18

Tables

1. Description of Beam Specimens

2. properties of Reinforcing Steel

3. Properties of Deformations on Reinforcing Bars

4. Grading of Aggregates

4. Values of 0

6. Comparison of Computed Maximum Steel Stresses with

Observed Yield Strengths

Figures

1. Illustration of Flexural Test Specimen and Instrumentation.

2. Stress-Strain Characteristics of Reinforcing Bars.

3. Typical Reinforcing Bars Used in Beams.

4. Method of Loading Beam Specimen and Arrangement of

Tuckerman Gages for Measurement of Width of Cracks.

5. Beam In Testing Machine Prior to Testing.

6. Views of Beams after Failure.

7. Views of Beams after Failure.

8. Load vs. Mid-Span Deflection.

9. Load vs. Mid-Span Deflection to Point of Failure.

10. Comparison of Mid-Span Deflection in Beams Supporting

Equal Loads.

11. Load vs. Observed Stress in Reinforcement.

12. Load vs. Compressive Strain in Concrete.

13. Comparison of Compressive Strains in Beams Supporting

Equal Loads.

14. Load vs. Average Width of Cracks.

15. Comparison of Average Width of Cracks In Beams Supporting

Equal Loads.

16. Theoretical Stress In the Reinforcement vs. Average Width

of Cracks.

17. Theoretical Stress In the Reinforcement vs. Spacing, and

Maximum and Average Width of Cracks.

18. Comparison of Theoretical and Observed Mid-Span Deflections.

19. Comparison of Theoretical and Observed Stresses in the

Reinforcement

.

20. Comparison of Theoretical and Observed Concrete Strains.

21. Comparison of Theoretical and Observed Width of Cracks.

22. Cross-Section of Beam Illustrating the Parameter 0 .

FLEXURAL TESTS OF BEAMS WITH REINFORCEMENT

OF DIFFERENT PROPERTIES

by

Robert G. Mathey and D 0 Watstein

Abstract

The effect of magnitude of steel stresses on

the center deflection, strain in the concrete,

widths and spacing of cracks in the region of

constant bending moment, maximum load carrying

capacity, and the manner of failure was investigated in a series of flexural beam tests. This

series consisted of 12 beams having a cross

section of 6- by l5~in. and a span of 10 ft with

the load applied at the quarter points.

Six types of deformed bars with yield strengths

ranging from 40,000 to 100,000 psi and different

stress- strain characteristics were used as tensile reinforcement. The ratio of reinforcement

in the beams was proportioned inversely to the

yield strength, thus providing equal resistance

to yielding under tensile forces. Failure

occurred in all of the beams at approximately

the same load. The relationship between the computed steel stresses and the center deflections,

width and spacing of cracks, and strain In the

steel and concrete was determined for the six

types of steel.

1. INTRODUCTION

The current interest in the properties of reinforced

concrete beams containing high-strength deformed steel

bars has prompted the National Bureau of Standards to

undertake a study of the effect of magnitude of steel

stresses on the behavior of flexural members. This study

is being supported at the National Bureau of Standards by

a grant made by the Committee on Reinforced Concrete Research of American Iron and Steel Institute. The present

report representing a completed initial phase of this study

deals with the effect of steel stresses on the flexural

rigidity, width and spacing of cracks and the strains in the

concrete and steel.

Tests described in this report were carried out with

beams reinforced with six types of deformed bars which

differed both in their yield strengths and in their stressstrain characteristics. The yield strengths ranged from

40,000 to 100,000 psi; some of the steels had well defined

yield strengths while others exhibited gradual yielding.

The modulus of elasticity of one of the bars was significantly lower than that of the other five types of bars.

The beams were all of the same size, and concrete of

the same quality was used for all beams. The ratio of

longitudinal reinforcement was proportioned inversely to the

yield strength so that the total resistance to yielding of

the tensile reinforcement was practically constant in all

specimens. The beams were designed to fail in tension, and

bond and shear failures were precluded by the use of adequate

shear reinforcement and anchorage. Observations were taken

under load to determine deflections, strain in the steel and

concrete, widths and spacing of cracks in the region of uniform bending moment, and the maximum load which was sustained.

2, DESCRIPTION OF MATERIALS AND TEST SPECIMENS

2,1 Beam specimens

The specimens were reinforced concrete beams having a cross section of 6- by 15-in, and an effective depth of 12.8

in. The beams were 13 ft long and were tested over a span of

10 ft. The arrangement of the reinforcing bars, dimensions

of the beams and the method of loading are illustrated in

figure 1. The specimens were loaded at the quarter points

and tested as simply supported beams.

The test beams are described in Table 1. The first

symbol (P) in the beam designation signifies a flexural beam

specimen. The second symbol (Roman numeral from I to VI)

designates the type of steel bar;

and V indicates that the original

to be unsuitable and a second lot

these two cases. The last number

the letter A following I

steel shipment was found

of steel was procured in

in the designation denotes

the serial number of the beam specimen,

2 .
>

‘
The ratio of longitudinal reinforcement ranged from a maximum of 2.55 percent for steel IA having a nominal yield

strength of [j.0',000 psi, to a minimum of 1.12 percent for

steel having a yield strength of 100,000 psi. The actual

total force causing yielding of the tensile reinforcement,

f A , as determined by tests of coupons of the reinforcing

bars ranged from 8l,600 to 90,300 lb.

Stirrups placed in the shear portion of the beam span

and tied to the longitudinal reinforcement were used to safeguard against diagonal tension failures. Steel plates,

[)__ by 6- by l/4 in. were welded to the ends of the tensile

reinforcement to prevent bond failures.

2.2 Reinforcement

Six types of deformed bars with various stress strain

characteristics were used for longitudinal reinforcement.

The nominal yield strengths of these steels were 1|0 j 000 psi

for Type IA, 65*000 psi for Types II, III, and IV, and

100,000 psi for Types VA and VI. A tensile coupon from

each bar size was tested to rupture. Tensile properties of

the bars are listed in Table 2, and a typical stress- strain

curve for each bar is given in figure 2. The yield strengths

of the steels varied from +8.5 percent for Type IV steel to

-1.2 percent for Type VA steel from the specified or nominal

values. Types IA and II steels exhibited a well defined

yield strength, and that was determined by ’’halt of the gage

method." Steels III, IV, VA, and VI, exhibited gradual

yielding and their yield strengths were determined by the

"0.2 percent offset method." Type VA steel was specified to

have a well defined yield strength, but did not fully meet

this requirement. While steel VA did not exhibit a sharply

defined yield strength, its stress- strain characteristic was

essentially linear up to a stress well above 80,000 psi.

Nevertheless, its yield strength was determined by the "offset" method in order to avoid ambiguity.

All of the bars were conventional round reinforcing bars

with diamond shaped deformations except the bars of Type IV

steel. The Type IV bar was a cold twisted, ribbed bar with

a dumbbell shaped cross section (Pig. 3)- Height, width,

spacing, and projected length of the deformations were

measured on one coupon from each bar size. The properties

of deformations appear In Tables 2 and 3- Deformations of

all the reinforcing bars met the requirements of ASTM A 305-

53T.

3 °
*
2, 3 Concrete

The concrete was made from a mix of Type I cement, sand,

and gravel proportioned approximately 1:3°2:4°1 by weight

„

The sand and gravel were silicious aggregates from White

Marsh, Maryland, The maximum size of the coarse aggregate

was 1 in, and the fineness modulus of the sand was 2 . 71 . Grading of these aggregates is given in Table 4- Water content of the concrete was about 7-7 gab per sack and the

slump ranged from 3 to 6 in. The average compressive strength

obtained from tests of control cylinders was 3&50 psi; values

for individual specimens tested for each beam are given in

Table 1,

2„4 Fabrication and curing

The stirrups and ties were fabricated in the laboratory

and the reinforcement was assembled into a unit before it was

placed in the forms. The deformations were filed off for a length of about 3/4 in. on each side of the bars at the center

of span to facilitate the placement of bonded wire electric

strain gages. Two gages were placed on each longitudinal

reinforcing bar and the gages and lead wires were waterproofed

with Petrosene wax.

Specimens were cast in steel forms with the tensile

reinforcement near the bottom. After five days they were removed from the forms and moist- cured until two days prior to

testing at 28 to 30 days. One control cylinder was cast from

each of the three batches that were used to cast a beam specimen. The three standard 6- by 12-in. cylinders were stored

and cured in the same manner as the specimen. The cylinders

were tested at the same age as the specimen to determine the

compressive strength and the modulus of elasticity of the

concrete. All concrete was mixed in a tilting drum type

mixer of 7 cu ft capacity and placed with the aid of a laboratory type internal vibrator.

3. TESTING PROCEDURE

3.1 Test setup

The specimens were tested as simply supported beams over

a span of 10 ft In a 600,000 lb capacity hydraulic machine.

To facilitate the placement and reading of Tuckerman optical

strain gages on the tension face of the beam, the beams were

placed in the testing machine in an inverted position. A

sketch of the method of loading and location of Tuckerman
-
strain gages is shown in figure 4° Rockers were used to support the beams at the quarter points and the load was applied

through a steel loading beam with knife edges attached at

each end. The forces were distributed at the load and reaction points through steel bearing plates 3 l/2 in. wide

that covered the entire width of the specimen. The bearing

plates at the reaction points were 1 in. thick. The bearing

plate was 1 l/2 in. thick under one of the knife edges and

under the other, three l/2 in. steel rollers rested on a 1-in.

bearing plate. A photograph of a beam in the testing machine

prior to testing is shown in figure 5.

3.2 Instrumentation

The widths of cracks were measured with 11 Tuckerman

optical strain gages arranged in two rows located at equal

distances from the longitudinal center line of the specimen.

The gages in the two rows were staggered and overlapped 0.5 in.

to include every crack which formed in the region of constant

bending moment. (Location of the Tuckerman strain gages on

the specimen is shown in figure 4) ° The Tuckerman gages had

a gage length of 6 In. and a 0.5 in. lozenge. The gages were

placed on brass bearing strips attached to the surface of the

concrete with epoxy resin cement. The gages were held firmly

in place with rubber bands attached to brass anchorage disks

cemented to the concrete in a similar manner. These gages

were equipped with 45 degree prisms to enable observations to

be made with the auto- collimator in a horizontal position.

The Tuckerman gage readings after formation of a crack

were taken to represent the width of crack spanned by the

given gage and no attempt was made to correct the crack width

for the tensile strains observed in the concrete prior to

formation of cracks within the gage length. In some of the

test specimens two or three cracks occurred in the same gage

length while no cracks would occur in another gage length.

Compressive strains were observed in a few cases on the tensile face of the beam where there were no cracks through the

gage length, while the adjoining gages spanned cracks. The

compressive strain continued to increase with the tensile

stress in the reinforcement as long as no additional cracks

formed between the original pair of adjacent cracks. This

phenomenon was also observed by Clark Cl]* and investigated

more fully by use of tensile bond specimens [2D . Figures in brackets indicate literature references at the

end of the paper.

5 .

The average spacing of cracks was determined from the

number of cracks and the distance between the two outermost

cracks that occurred within the region of constant bending

moment

.

Deflections at the center of span and 2 ft from the

center were measured with 0. 001-in. dial gages attached to

aluminum bars whose ends were supported at the sides of the

beams under the loading points. The gages were located as

shown in figure 1. The gages bore on angle clips attached

to the concrete by screws. The aluminum bars with the

attached dial gages were removed prior to failure. Deflections were then measured at the center of span by scales

attached to the specimen and a taut wire stretched between

two points on the side of the beam directly under the loading

points

.

Strains in the tensile reinforcement were measured with

bonded wire electrical resistance strain gages attached

diametrically opposite at mid plane of the longitudinal bars.

The gages were of type AB-7, with a gage length of l/ip in.

and were located at mid span. The gages were attached with

epoxy resin cement and waterproofed with Petrosene wax.

The compressive strains in the concrete were also

measured with bonded wire electric resistance strain gages.

These gages were of type A-l, with a gage length of 13/16 in.

They were located at the center and at positions of 2 ft on

either side of the center of span along the longitudinal

center line of the specimen on the compressive face of concrete, These gages were located as shown in figure 1. The

gages were attached to the concrete with epoxy resin cement.

3.3 Test procedure

The loading beam was placed in position, as shown in

figure 5s and the gages were read at zero machine load. A

load of 1000 lb was applied and released and the gages were

again read at zero machine load. The load was then applied

in increments of 2500 lb up to a load of l5»000 lb and then

in increments of 5000 lb to failure. Each increment of the

load was applied at a rate of i|000 lb per min. The following

measurements were recorded after each increment of applied

load: deflections along beam, the strains in the reinforcement,

the strains in the concrete, the width of cracks in the region

of constant bending moment, and the applied load at which the

measurements were observed. In addition to these measurements

the location and extent of cracks were recorded immediately

after the application of each Increment.

6 .
»
The loading beam was placed in position before attaching

the Tuckerman strain gages to the beam specimen. This procedure was followed to prevent any damage to the Tuckerman

gages. The steel loading beam weighed 1300 lb and the beam

specimen weighed ll|00 lb. At zero machine load, the summation

of moments at the center of span was equal to 21^0 ft-lb,

corresponding to an effective initial load of 1,72 kips. In

the computations a correction factor of 1.72 kips was added to

the machine load.

Observed strains in the steel and concrete were very

small for the first increment of the applied load; therefore,

no attempt was made to correct the strain measurements for the

initial load. However, the deflections were corrected for

the deflection corresponding to the initial load. The corrections were computed using the formula given on page 11 ; their

values ranged from 0.00% in, in beams with Type IA steel to

0.0179 in. in beams with Types VA and VI steels.

4, TEST RESULTS

i|.l Mode of failure and load carrying capacity

The control beams were reinforced with Type 1A steel and

were designed to fail by yielding of the tensile reinforcement.

Tensile failures occurred In all the beams except the beams

that were reinforced with steels having nominal yield strengths

of 100,000 psi. Beams P-VA-17 and F-VI-18 failed by compression of the concrete while tensile and compressive failures

occurred simultaneously In beams F-VA-19 and F-VI-9. The use

of adequate shear and bond reinforcement limited the mode of

failure In this Investigation to tension or compression. Photographs of all the beams after failure occurred are shown in

figures 6 and 7 » The maximum load carrying capacity of the beams ranged

from 61,700 to 67,500 lb with an average maximum load of

64,000 lb; the deviation of loads at failure from the mean

ranged from +5° 5 to - 3.6 percent. Since all of the beams failed

at approximately the same load, the maximum load carrying capacity of the beams was not affected by the type of longitudinal

reinforcement whose areas were proportioned to give a constant

total yield strength of the tensile reinforcement. The maximum

load and mode of failure for the individual beams are given in

Table 1.

7 .

4.2 Deflections of beams

The relationship between the applied load and the midspan deflection is shown in figure 8. Each curve plotted on

this graph represents the average results obtained with two

beam specimens. As expected, the deflections increased as

the percentage of longitudinal reinforcement was reduced.

The deflections of beams reinforced with Type IV steel departed considerably from the deflections of beams reinforced

with comparable steels of Type II and Type III. This departure is explained by the fact that the modulus of elasticity of Type IV bars was 12 percent lower than the modulus

of Types II and III bars. (See Table 2).

Load vs. midspan deflection curves to the point of

failure are shown in figure 9 for individual beam specimens.

The effect of higher steel stress on the deflection is

shown more directly in figure 10. This graph presents relative deflection values for loads of 28 . 5 , 42 . 9 , and 57.1

kips which produce respectively theoretical steel stresses of

20,000, 30,000, and 40,000 psi in beams with Type IA steel.

Similarly, at a load that produces a steel stress of 20,000

psi in beams with Type IA steel, the computed stress in the

steel with a 65,000 psi yield strength will be 32,500 psi

and the computed stress in 100,000 psi yield strength steel

will be 50,000 psi. For the purpose of direct comparison,

the deflections are taken as unity in beams with Type IA

reinforcement. For a stress equal to one-half the nominal

yield strength of the steel, deflections in beams with 65,000

psi reinforcement ranged from 40 to 53 percent greater than

the control beams. The deflections in beams with 100,000 psi

reinforcement ranged from 80 to 93 percent greater than In the

control beams.

Similar comparisons of the deflections for stresses of

75 and 100 percent of the nominal yield strengths of the

steels are also shown in figure 10.

4.3 Stress in reinforcement

The relationship between the applied load and the observed

stress in the reinforcement is shown In figure 11. Each curve

on this graph is an average of the observed values for two beam

specimens. The data for beams reinforced with Type VA steel

are omitted because of faulty performance of the strain gages.

8 .

The strains in the reinforcement were measured at the center

of span. The observed strains were converted into stresses

by means of the stress- strain curves shorn in figure 2.

Beams reinforced with Types IA, II, III and IV steels

failed by yielding of the steel. The maximum observed

stresses in steels IA, II, III and IV approached the yield

strengths determined in the tensile tests. However, the observed stress In the reinforcement in beams with Type VI

steel was 80,000 psi at a load equal to 95-7 percent of the

maximum load; the theoretical stress at this load was 94, 000

psi o 4.4 Concrete strains

The applied load- compressive strain data are presented

'graphically in figure 12. Each curve on this graph represents

the average results obtained with two beam specimens. The

compressive strains were measured on the surface of concrete

and the strain gages were located as shown in figure 1. As

expected, the compressive strain in the concrete increased as

the percentage of longitudinal reinforcement was reduced. The

compressive strains In beams with Type IV steel were considerably greater than In beams with comparable steels of Types II

and III. This is attributed partly to the lower modulus of

elasticity of Type IV bars.

A comparison of compressive strains in beams supporting

equal loads Is shown in figure 13» The effect of higher steel

stresses on the compressive strains Is brought out clearly in

this graph. At a stress of one-half the nominal yield strength

bf the reinforcement the compressive strains in beams with

65>000 psi reinforcement range from 5 to 24 percent greater

than in the control beams. In beams with 100,000 psi reinforcement, the compressive strains ranged from 25 to 37 percent

greater than in the control beams. Similar comparisons of the

compressive strains for stresses of 75 and 100 percent of the

nominal yield strengths of the steels are also shown in figure

13.

4.5 Widths and spacing of cracks

The relationship between the applied load and the average

width of cracks is shown in figure 14 . Each curve in this

figure represents the results obtained from two beam specimens.

The cracks were measured on the tensile surface of the beam

in the region of constant bending moment. (See Pig. 1). The

9 .
'

.
effect of higher steel stresses is brought out particularly

clearly in figure 14 , where the load-width of crack curves

fall into three distinct groups corresponding to the nominal

yield strengths of 40,000* 65,000, and 100,000 psi. As expected, the width of cracks increased markedly as the percentage of longitudinal reinforcement was reduced.

The ratio of the average width of cracks in beams

reinforced with high yield strength steels to the width of

crack in beams with steel of Type IA and supporting equal

loads is shown in figure 15 = For the purpose of direct comparison the widths of cracks are taken as unity in beams with

Type IA steel. For a stress of one half the nominal yield

strength of the steel In beams with 65,000 psi reinforcement

the average width of cracks ranged from 60 to 76 percent

greater than in the control beams. In beams reinforced with

100,000 psi steel, the width of cracks ranged from 164 to

168 percent greater than in the control beams. Similar comparisons of the widths of cracks for steel stresses of 75 and

90 percent of the nominal yield strengths of the steels are

also shown in figure 15 . The relationship between the average width of cracks and

the computed stress In the reinforcement is shown in figure

1 6 ; this figure Includes the crack data for all the beams.

The slopes of the stress- crack width curves varied within

narrow limits and appeared to be independent of the ratio of

reinforcement and in case of Type IV steel, of the modulus of

the steel. The effect of lower modulus of elasticity in Type

IV steel was probably minimized by the somewhat smaller average spacing of cracks In beams containing that steel than the

spacing in beams with steels of Types II and III,

The relationship between the theoretical stress in the

reinforcement and spacing and width of cracks is shown in

figure 17 , Each curve represents the average results obtained

with two beam specimens. The minimum average spacing of

cracks in the control beams was 4° 2 in. For beams with 65,000

psi yield strength reinforcement this minimum spacing of cracks

ranged from 4-2 to 4*8 in,, and for beams with 100,000 psi

reinforcement, this minimum spacing ranged from 4*7 to 5=3 in.

This is an Indication that the minimum average spacing of

cracks will increase with a decrease In the percentage of

longitudinal reinforcement and higher tensile stresses. The

minimum spacings of cracks for the individual beams are given

in Table 1.

10 .
.* '
In view of the consistently greater spacing of cracks

observed in beams with reduced ratios of reinforcement, it

would be expected that at a given stress in steel the average width of cracks would be somewhat greater in beams

containing the lesser amounts of reinforcement „ It is believed that the effect of greater spacing of cracks on the

width of cracks was offset by the fact that the reduction of

steel ratio was achieved by using smaller diameter bars; it

is known that the effective modulus of elasticity of embedded

deformed bars is materially increased as the diameter of

bars is reduced [2]

5. COMPARISON OP EXPERIMENTAL AND THEORETICAL RESULTS

The comparisons of experimental and theoretical values

of the midspan deflections, stress in reinforcement, and the

compressive strain in the concrete are shown graphically in

figures 18 , 19, and 20 respectively. The theoretical values

of the variables were determined by the conventional "straightline” theory. A comparison of the experimental and theoretical results of the average width of cracks is shown in figure

21. The theoretical values for the average width of cracks

were determined from an expression developed by Chi and

Kirstein , and a brief explanation of this expression is

given on page 13«

In computing the theoretical values of the variables the

observed values of moduli of elasticity of steel and concrete

were utilized. The modulus of elasticity of concrete was

the secant value determined for 0„5 f

! c > while the modulus of

steel was the value corresponding to the linear portion of the

stress-strain curve.

The load-deflection curves for beams reinforced with

steels of Types IA, II, and III show good agreement between

observed and theoretical values (Pig. 18 ). The theoretical

deflections were determined from the expression,

where E c I

L

M

n

A 11 M L

2

96 E c

I

modulus of elasticity of concrete

moment of inertia of beam cross section

transformed to concrete = l/3 bk3d3 + nA q ( 1-k) ^d‘~

length of beam span

bending moment

observed modular ratio

11 .
'
The theoretical midspan deflections plotted in figure 18 are

terminated at the calculated yield point of the beam as indicated on the graph. The maximum observed load is also shown

in each case by a short dash at the extremity of the loaddeflection curve.

It was observed that the agreement between the computed

and observed deflections was better for steels having a linear

stress-strain characteristic than for comparable steels exhibiting gradual yielding. Thus, beams with steel of Type IV

showed a greater departure of computed from observed deflections than did beams with steels of Type II and III, while

beams with steel of Type VI showed a greater departure than

did beams with steel of Type VA. The observed deflections of

all the beams were less than the calculated values up to a stress of one-half the nominal yield strength of the reinforcement . A comparison of the theoretical and observed stress in the

steel reinforcement is shown in figure 19. Each curve represents the results obtained from two beam specimens. Steel

stress data from beams reinforced with Type VA steel were

omitted from this figure because of unreliable strain data.

The observed strains were converted into stresses by means of

the stress- strain curves shown In figure 2.

The observed and theoretical values of steel stresses show

good agreement for beams reinforced with Type IA steel. However, the observed stress in the reinforcement Is considerably

less than the theoretical stress in beams reinforced with the

higher yield strength steels. This is particularly true In

beams reinforced with Type VI steel. The use of the "straight

line" theory thus yielded calculated stresses that were in excess of observed stresses in all cases; the difference between

the observed and computed stresses increased as the diameter

of bar decreased.

The theoretical and observed strains in the concrete are

compared in figure 20. Each curve represents the results obtained from two beam specimens. The theoretical strain was

determined from the calculated compressive stress at the surface of concrete and the observed modulus of elasticity of the

concrete. One control cylinder that was cast with each beam

specimen was used to determine the stress- strain characteristics

of the concrete. The value of the modulus of elasticity, E,

was determined by the slope of a line passing through the

origin of the stress- strain curve and a point on the curve

corresponding to one-half the compressive strength of the

J c

»

12 .
s * .
cylinder, 0.5 f'

c

. The values of the observed compressive

strains in the concrete in all cases are less than the

theoretical values up to the load producing a stress in the

reinforcement of one-half the nominal yield strength.

As in the case of load-deflection relationship, the departure of the observed compressive strains from the computed

values at high steel stresses was greater for steels IV, VA,

and VI, than for steels IA, II, and III. The departure of

observed strains from computed values was particularly marked

for steels IV and VI whose strain- strain characteristics showed

the greatest departure from linearity.

The observed and theoretical values of the average width

of cracks are compared in figure 21. Each curve represents the

results obtained from two beam specimens.

The paper, ’’Flexural Cracks in Reinforced Concrete Beams,"

by Michael Chi and Arthur F. Kirstein has not yet been published.

Therefore, a brief explanation of the equation for determining

the width of cracks In reinforced concrete flexural beams is

given in the following pages.

The average width of crack at the reinforcing steel is

>y the equation:

p^00

ws = 5 0 D

f

s

' 0 D (D

E s

0

= V (2) w

area of reinforcing steel

area of concrete effected by the extension of the steel

diameter of reinforcing bar

modulus of elasticity of the steel (linear portion of

the stress- strain curve)

steel stress

factor determining the diameter of the concrete area

effected by the extension of the reinforcing steel.

ratio of the assumed effective area to the fully

developed area of concrete

given d

where

D

E c

m

0

13 .
,

*

.
A constant conversion factor was used to convert the

average width of crack at the reinforcing steel to the average width of crack at the surface of concrete. The average

width of crack at the surface of concrete is given by the

equation

:

¥

c h-kd

d-kd

( 3 )

where d = effective depth of specimen

h = total depth of specimen

kd - depth of compressive concrete in the specimen.

The Chi-Kirs tein formula is a semi-empirical expression

in which the factors m and 0 are derived from the hypothesis

that only a portion of the cross section of the beam below

the neutral axis resists the tension in the concrete induced

by bond stresses. This portion of the tensile cross section

is termed "the effective area,” and its ratio to the "fully

developed area” determines the value of 0, These terms are

defined in figure 22 in terms of the properties of the cross

section of the beam. The values of 0 determined for all

beam specimens are listed in Table 5> . Chi and Kirstein estimated that m = 1| for the Bethlehem bar which they used in

their study. It was assumed by the authors that this value of

m was also applicable to the deformed steel bars used in this

investigation.

In the application of Chi and Kirstein 1 s expression for

the average width of cracks, the nominal dimensions of the

reinforcing bars were used. For the purpose of computing

the coefficient 0 in the formula, bars of Type IV steel were

assumed to be round and their effective diameters were determined from their cross-sectional areas. While the deformation

of the bars used in this investigation had a pattern different

from that used by Chi and Kirstein in their development of the

expression for predicting the average crack width, no attempt

was made to modify the coefficients in their formula to take

into account the surface characteristics of the bars.

Comparison of the theoretical and observed crack widths

in figure 21 indicates that the mean crack width was predicted

with reasonable accuracy for bars of all six types. The shape

of the s tre s s- strain curve did not appear to have a consistent

effect on the relationship between the mean crack width and

the stress in the reinforcement.

14 .
'

-
The maximum values of steel stresses computed by both the

’’straight line" and the "ultimate strength design" ±7 theories

are compared in Table 6 with the actual yield strengths obtained in tensile tests of the steel bars. The yield strengths

given in the Table are the values obtained by the "halt of the

gage" method for steels IA and II. while the values given for

the other steels are based on an "offset" of 0.2 percent.

The agreement between the observed yield strengths and the

maximum computed steel stresses was better for the straight line

theory than for the ultimate strength design theory. Ratios of

the maximum stresses computed by the straight line theory to

the yield strengths ranged from 0.956 to 1.088, while for the

ultimate strength design theory these ratios ranged from 1.05?

to 1.180.

6. DISCUSSION OP RESULTS

This series of flexural beam tests was designed to study

the effect of magnitude of steel stresses and the nature of the

stress- strain characteristics on the performance of reinforced

concrete beams.

It will be recalled that the beam specimens were designed

so that the nominal total yield strength of the reinforcement

(f

y

A s ) was a constant. The control beams were designed to fail

by yielding of the reinforcement and were reinforced with

Type IA steel. Beams reinforced with 1+0,000 and 65,000 psi

steel failed in tension, but beams with 100,000 psi reinforcement failed in compression or simultaneous compression and

tension. All the beams failed at approximately equal loads.

The effect of the magnitude of steel stresses and the shape

of the stress- strain curves on the center deflections, compressive strains in concrete and the average widths of cracks is

shown in figures 8, 12, and 1 4 respectively. Attention is called

to the fact that only in the case of the load-crack width relationship do the curves fall in three distinct groups corresponding to three nominal yield strengths of 40 , 000 , 65,000 and

100,000 psi. In the case of deflections and particularly in the

\J Ultimate strength design theory is that given in the Appendix —

of the ACI Building Code, ACI 318-56.

15 .
. -

Ip .
case of compressive strain in the concrete, the effect of

the differences in the stress- strain characteristics and

the corresponding differences in the moduli of steels became sufficiently pronounced to affect the relative standings of the several types of steel. This is brought out

more clearly in figures 10, 13, and 15. As can be seen in

figure 15, the effect of increasing the steel stress on the

average width of cracks is essentially linear. Thus, at a given load causing stresses of 20,000, 32,500, and 50,000

psi in steels having nominal yield strengths of 1+0 , 000 , 65,000, and 100,000 psi, respectively, the observed increases

in crack widths were approximately 60 and 160 percent, or

nearly the same as the increases in stress. The same relationship between increases in steel stresses and crack

widths was observed for stresses ranging up to 90 percent of

the nominal yield strengths of the steels. However, the relationship between the increases in the steel stresses and

the observed increases in compressive strains, as well as in

center deflections, is roughly linear only when the comparison is confined to the four steels having fairly linear

s tre ss- strain characteristics (steels IA, II, III and VA)

.

For steels IV and VI, the effect of the curvilinear stressstrain characteristic on the deflections and compressive

strain in the concrete can be clearly seen in figures 10 and

13. The effect of the lower modulus of steel on the increases

in concrete strains is particularly pronounced for the twisted

bar of Type IV steel. Reference to figure 2 indicates that

the modulus of elasticity of steel bars of Type IV is 12 percent less than that of a conventional bar at a stress of

30,000 psi, while at a stress of 60,000 psi this difference

increases to 28 percent. Similarly, for steel bars of Type

VI, the modulus at stresses of 50,000 and 95,000 psi is

about 13 percent and 27 percent less than that of a bar with

a well defined yield strength.

Comparison between the observed values of steel stress

and those computed by the straight line theory is indicated

in figure 19. The agreement between the computed and observed

stresses was closest for Type I steel. The difference between

the computed and observed values became larger as the ratio of

reinforcement and diameter of bars decreased.

Comparison of computed and observed values of deflections

and compressive strains in the concrete is shown in figures

18 and 20. The deflections can be fairly accurately predicted

provided the stress- strain characteristic of the steel does

not depart significantly from a straight line and the crack

pattern of the beam is substantially uniform along the entire

span length, as shown in figures 6 and 7. The observed

16 .

deflections depart considerably from the computed values for

steels exhibiting curvilinear stress-strain curves and gradual

yielding, as in case of steels IV and VI. The comparison of

observed compressive strains in concrete with the theoretical

values shown in figure 20 indicates that the limitation of the

"straight line theory” is more severe with respect to calculation of compressive stress than with respect to deflections.

The departure of the observed compressive strains from the

computed values becomes quite pronounced at higher loads,

particularly for steels exhibiting gradual yielding.

The observed mean crack widths were compared with the

theoretical values computed by means of Chi-Kirstein formula

Ol • Comparison of the theoretical and observed crack

widths shown in figure 21 indicate s that the mean width of

crack can be predicted with reasonable accuracy for all the

steels used in this study. The shape of the stress-strain

curve did not appear to have a consistent effect on the relationship between the crack width and the stress In the

reinforcement

.

The agreement between the computed maximum steel stresses

and the observed yield strengths of the steels was better for

the "straight line" theory than for the "ultimate load design"

theory. Thus, the ratios of the maximum loads predicted by

straight line theory to the observed loads ranged from 0.956

to 1,088, while for the ultimate load design theory these

ratios ranged from 1.057 to l.l80. In general, the agreement

between the computed and observed maximum loads was best for

the steels with the highest yield strengths Irrespective of

the s tre s s- strain characteristic.

17 .
'

*

,
7 . References

[1] Arthur P. Clark, "Cracking in Reinforced Concrete

Flexural Members," American Concrete Institute

Journal, April 1956, Proceedings of, Vol. 52,

page 851

.

[2] D. Watstein and R» G-„ Mathey, "Evaluation of Width

of Cracks in Concrete at the Surface of Reinforcing

Steel by Means of Tensile Bond Specimens," Proceedings, Symposium on Bond and Crack Formation in

Reinforced Concrete, Stockholm, 1957, pp . 253-260,

[3] Michael Chi and Arthur F, Kirstein, "Flexural Cracks

in Reinforced Concrete Beams," (Manuscript has been

submitted to the American Concrete Institute),

18 .

Table

1,

Description

of

Beam

Specimens.

- - - - - - - - - - - ~ - - - - - - - - - - - - - - - - -

rHj rH]

CD d d

i •H •H 1 CD 3 d d d d £ d d d TO cd cd TO d CH i—

1

O O O O o o o O © -p -p ©

O O «H •H *H •H °rH •H «H •H *H Ph d Ph d Ph d

S 05 TO TO TO TO TO TO TO TO p. O © © P o d d d d d d d d d E -H O O £ *H © © © © © © © © O o/. d d O TO -p -p -p -p -p -p -p -p o d P5 O •

»- to to a- to to to to C- to — to — to- c- «=- to to- ^ c- o- to- to to d

£ to 1

1 d d m TO e th d a

i—1 VO mm r- o i—l cO m NO o m d H O Ph O d oo i—i m O GO o m m CO CO NO o

C cd O a! •H ©

•H P Ph m m -d m d

S 03 O cd — o_o~ o- to «_ to «- to «- t- •» c- e- to- c- e- •- to— to— to- c- to- to- to- to- o- to -p O PH rd 1—

1

-P © -P d

CD d bO o o O O o o o o o o o o £

p. d d - o •H C\J o vO o 1—1

1—

1

co m 1—

1

m mm •H O *H CD P to mm -dCM m o mm CO vO mm TO ^ i—I £h P m o mm mm m m m m mm

O >5-P •O O O 00 ©

to to to to to to e-- •- — — o-a- to e- c- «- o- «- to- to- to- e~ to- 0- «>- o- e- to to Ph

1 mm mm nO vO CM CM mm Ph O 1 CD mm mm mm mm I 1

1 1

i—1 l

1 d

•H d O -P c\j c\j i—1 i—

1

i—1 i—

1

i—1 i—

1

1

1

1

1

1—1 i—

1

©

p !h 'H Ph d ft o o o o o o o o O O oo O

Cd O CD O CD o • • a o a a a o a a o K Ph P £ o o O O O O O O o O OO e. t. ». e- «> ». c to o- to to to to to to e- to- to- e- to- to- to- to- •- to- e- e- (to to ©

£ ^ >

d o o o o o o o o o o o OO cd £ £ o o o o o o o o o o oo d

•H d cd d UMA CM O i—1 ”LP\ m m CM 1—

1

mm

K Cd © 1 1 to\ on On On ON on On o

cd o d l>— m m m-d 1 1 I 1 m CM mm -p S i—

i

vO v0 nO vD vO vO nD vO vO vO mm ;*a~ »>-• to to o- to —

.

to «- ®- e- *_ to to e- b_ e- to- to- to- to- •- »>- o- c- a- e- to d

-P ©

d i d Ph -p d CD o o O O o o o o o O oo cd bO-H g o o o o o o o o o O oo ©

rH d d © ® P d mm NO vO H rH mm -d -d mm P

! d rH CD pH O 00 rH ON On •n as «S ON •v on On On On On P

-P CD Ph Ph <£, ro m i—1 rH CM CM m m OO cd O "H -P p O coco CO CO CO CO CO CO CO CO oo

B Sco od TO

** •- — - - — e- *- e»- — ^ *- Cto to- to- to- to- to- «>- «- to to CD

c.

1 CD CVJ O O CM CM mm CO CO -d m nOnO d

d d o -p o vO NO CO CO m cr O' O' d vO vOvO r—

H

0 ft -H Ph d CO d o o rH i—1 l

1 I

1 1—1 1—1 CO CO COCO •H

Ph O CD O CD d •H o a a a o o o a « O a a cd < fnft g i—1 i—1 1 1 I

1

1—1

1—

1

1

1

1

1 o O OO d

to to to o_ to t- *- to to to •“ to- «- to- to- to- o- a- •- to- to- to- «>- to to to to -p © d did o o o o O O O O o o oo >

CD -P d CD o o o o O O o o o o oo •rH > bO-H g •H mm o o CO CO mm CO CO com TO

Ph d d CD CD !>> 00 •N *\ •n *N on on on On On ON On On TO

CD i—1 CD Ph O ft p CM CM o o CO CO O O CO CO mm ©

CO © Ph Ph vO MD vQ vO m m cr o oo Ph £> -H -P P O rH i—1 P O S® Oft £ »* e** 1 fe— . to b— o— e-— *— o- b- «>- «»- to- c- to- to- e- to- to- «- to- *>- •- to- to- b- t>- to o

O' O' o

o d d

00 o i i d

CD id o o o- c— r- m I—1 i—1 vD mm d

o d o o o o o o ON »n • • o a cd © d Ph O O O O O 0 CO CO o O O O

•r~1 Gj Ctf d d d d d d d d dd © d d i i i i 9 ! 1 1 i i i i 1—1 CM CM CM CM CM CM 1—1 1—1 CM CM CM CM •rH

to to. to c- o- to to to to o- *»- — to- e- e- to- to- to- to— to—* to— a- to- e- to* to to to' TO m d

cm m CM CO i—1 O i—1 D- O' CO ©

i d CM CM d-h 1 1 CM CM I 1 1 1 OrH Eh bO O 1 1 1 i H H 1 t 1 1 1 1 S *H *H < < H H H H > > < HH \ cd to -p M H H H 1—1 H H H > > » rH 1 © © d 1 i 1 1 1 1 1 1 1 1 1 1 W d d d (x, d d d d d d d d dd ^ b- «** •-« t~' ^ *- — ' -1 — 1 — a- - to to

- - |- - ~ P

®H - - - - - - - - - - - - - - i M3 o- M3 Pp Pp CO Pp P cd pp o pp M3 to M3 CO

cd bO© oj • pp CO co Pp to OJ OJ

©

p P P P »h cd •rH o O

O

O o O

O

T3©

© -P

bfl ojj pp M3 1 1 CM M3 CM CM

cd© -p • 1—1 O 1 1 CO OJ CO CO

P'nbC P ©op •H co CVJ CM CM co 1 1 1 1 CO > P © P < PH o — to- «- •- — c— — *- o- e- to- o- o- r— •- toa H ©

-p bfl-P r- M3 M3 CM CO CO o

cd cd p) • M3 1-0 to Pp pp Pp to & P bO p o o O O o o o P © »H •rH o • • G • to o O > © O o O o o o O

<M < rP ©P © bO

bD P OJ M3

H Pp CO Pp 1—1

q6 *H « ro- Pp to CO OJ CM P o P pp CO CO CM CM co co © cd •rH o • © • o * © > P O o O o o o O • < ra 1—1

C- c- «*- «- o- •- e- to. to- to- o_ C- to- to- *-

© CO M3 M3 o- CO CM o © -p • CO M3 M3 M3 CO Pp M3

-p O'h

p

p

O o 1 1 O o 1 1 1 1 CO •H o cd •H ® • • ® ® «» ®

bO ^ bO o o O

O o OO

to- o- to- *_ «>- o- e-

— o- e- o- •- to- to- to- e-

— e- c- P o •H 1 P o Cd •H p bO p CO o CM to o to co o P O CO • • • • © • CH o M3 M3 0- 1—1 o M3 M3 p 1—1

-p

p 1—1 1 1 1 1 H

H

•H

p •H

© c- o- 0-0-0- o- «— to- e— to- to- to- o- *— •- to- to- K CQ f •rH P •H CQ Qm 1 1 -p lx P to co co r 0- -d- H CO o P <M CQ -P • O c • • rO O Cd •H O CO CO co to to CO CO

CQ o H

O o OJ CM CM CM OJ CM OJ

© S ©

H

•H >o t- C— e— t— o- «- o_ *- to— to— to- to- to- ®- «- to- -p rP p © -P o O O O o O

O

© i—1 bO o O o o o o o

Pi • H P •rH o 1—1

Pp M3 1—1M3 to

O

m

© CQ •s •s ®\ P P P P CO O- CO co M3

O

H

Ph

© -P 0- o 10- CO CO CM 1 1 E—i m H 1 1 H a- 6- to- to- to- o- o- o- o- to- to- to- to- to- to- *- ©- to- b- to—

C\J ,P P r-T| ool ctTl CM| CM| bl

-P o o o o o o o © bO o o o o o o o 1—1 no P •H tO o GO to CM CO CO

P3 i—1 CD CQ •N to <o cd © p P CM co CO o H CO Pp

EH • H -P Pp M3 M3 M3 r- CO o

>H CQ 1—1

to* o- o-> e- - to- o_

—,

to- t- to- to- to- to- toO 1—1 0- to CO CM co

cd

M CO o CO OJ 0- CO co

© o CO tO UA to M3 Pp Pp P P o • * e o •rH o o o o O o O — ^ — t— to- to- to. to- to- - to- to-

© co 0- c

M3 M3

N <M P o o C • » •H o cd o o o CO O O

to rQ P; Pi pH 13 Ph Ph - c- o- to- to- — to- to- to-, to- to-' *-* to- 1—1 © © H H > > H

CVH

©

H

HH

H

H > >

lx o -P

H

Eh CQ - - *- - — - o- to-

— to- to- to- to- to-, toTdo

-p

CDB©

bO

cdbOO

-Pi—I

cd W

T3O

r-P -P

CDb

-p

CDmH

<+hO

-P£

CDO

Pi

CDPi OJo Eh <U

'his

value

is

high

compared

to

other

size

bars

of

Type

III

steel,

-verage E=

28.5 x

10^

psi

for

Type

III

steel.

Table

3.

Properties

of

Deformations

on

Reinforcing

Ba - - - to - ~ - - - - - - - - - - - - - - - - - -

bO

>-* •H ft ft ft ft ft ft-ft

OO ftft £ cd \ -ft- ft O v*'0 1—1

ftft ft CM CO CM

cd 0 CM -ft CM ft CM ft CMft CM ft CM ft 0 £

FQ cti £ 0 O

OOO OOOO

OO

130 © -P bO O ft -ft ftft ft

O CO ft CM

O CM ft 0

cd 0 ft 0 1—1

ftft CO ft

O CM CO ft CO ft > £ "“a b£ £ 0 •H 0 O £ > £ 0 ^ P-11—I

•H 1—1

CM 1—1

CM CM ft 1—1CM 1—1

CM -p0©

ft

O ft

© -P £ © 0 © rH|rH | cd -P -P 0 -fto CO -ft 1—1

ft ftft ftft £ © 0 ft © O 0 ftft r^— __rj~ -^f~ 1 1 ~f r ft ft •rH £ £ bOg -H ft ft -ft LfUA -ftft ft in ft ft 0 cd 0 •H Cd -P 0 0 0 • 0 O O 0 0 • • r£

•H 0 “H cd 0 0 0 0 0 O

O 0 0 0 0 ft 1—1

-p ft no £

nO

cd £ •— •*- to- to- »>- to- to. to- to- to- to- to*. »- to- •- «>- £ g £ 0 £ 0 cd •H O bO-P ft ft CM _~j~ ,—1

ftCO CO

H 0 0 +3

ft cd ft « ft -ftft -ftft CM -ft _ftft ftft no 0 0 £ bO £ 0 O O 0 0 O O O O 0 0 £ © Q 0 « a 9 9 © 0 © 0 £ to > © 0 O O 0 0 O O O O 0 0 0 1 < r£ £ CO

to- to- to- to- to*' »* to- to* to- to* to- to- to. to* •to to* to- to- 0 0 0 0 bO ft £

bD £ CM ftcO CO ft ftft rH CM 0 0 ft CM -ft 0 rH OCO CM rH CM rH O £ 0 £ -ft ft_ft ftft CM CM ftlTN ftft -P £ © cd 0 0 a 0 • 0 0 • . • © > ft O O O 0 0 O O O O O O nO ©

<J 0 0 ft

to- to* e- to- to- to- to* to- to- to- to- to* to- to- to- *- e- to- to- tg -P £

ot

g

ft CQ -ftft ftft CM CO CM

OO ft 0 0

-P « CO ft

O ft 0 ftCQ -ftoO ft

O cd £

TO ft ft £ O

O 1 1 rH CMO

O rH rH

H CM ft

•H OCti •H 0 • O 0 o • . • « ©

© ^ bC O O O O O O O O O O O £ no 0 ©

ft t- to- to- *- b- to*-. to- b- to- to- to- to* to* to- to- to- to- to* to*' to- to* to- ft £ £

•H

H

H £•

O

O CM ft ft ft -ftft CM ft ftft 0 Jh 0 .h CM ft ft O ftoo ft ft ftft ftco 0 © 0 -p cd ft -fto -ftft CM vO -ftft -fto -P -p 000 £ • 0 0 e e © 0 © 0 » 0 © £ © £ O 0 aj •H O O 1—1 O O O O O O 0 0 >

no

ft O- to- to- to. to-- to*. to* to- to- to- to* to* to- to- to- to- to* to- to- to- to- ft

H 0£ 0 0 0 Ph £ N ft £ ft ft ft ft ft ft ft ft o ft

•H

O cd <* • 0 » 0 • • « • Eh 0

cq ft

OOOOO ft ft

O

O 0 0 £

ft ft ft! ft ft! ft; ft ft ft Oi 0 O ft

** *-' «~ to. to* a- to-' to*. to*' to* to- to- to* to- *>* to* to. to* to- to* to- to*. 0 0 g £ cd 1 1 cd •rH 0 0 < H H H H > > <1! < H H FQ ft ftft 0 H H H H H H H > > t> >

ftO -P ft

H \ EH 0 H - - ~ - - — - - to* to* to- - - - to- to* to- ** to - - to

Table 4* Grading of Aggregates

(White Marsh sand and gravel)

Sieve size

Cumulative Percent Retained » Sand ' Gravel

1

”

r 0.0 » 0.0

3/4"

0

0

•

e

O

O 27.00

1 /2

" 62.50

3/8" 0.0 t

t 0.0 t

t 1.98 t

83 .IO

11 100.0

No. 4

17.53

31.49

49.19

76.55

93.96

Fineness

Modulus

2.71

Table 5- Values of 0

? Beam !

1

Pieces

and

Bar No

i

t

7

F--IA-22

1

’ 2

i - No. 9

7

7

p--IA-23 i 2

j

- No. 9

T

* F--II-7 ' 2

7

- No. 7

*

f P--11-12 > 2 - No. 7

7

P--III-8 » 2 - No. 7

7

P--HI-13 t 2 - No. 7

T

P-IV- 20 » 1--W8, 1- ¥9 7

F- IV-21 T 1--W8, 1- W9 7

F- o- r

—

1

><1 ’ 2 - No. 6 t

P--VA-19 » 2 - No. 6 7

P--VI-9 ’ 2 - No. 6 7

P--VI-18 t o

i

- No. 6 I

7

!

7 0.757 '

7 0.757 »

! 1.012 >

! 1.012 *

t 1.012 i

i 1.012 »

7 0.895 1

? 0.895 ’

0.964 «

7 0.964 i

i 0.964 »

! 0.964 '

Table 6. Comparison of Computed Maximum Steel

Stresses With Observed Yield Strengths.

Type

of

steel

Observed

yield

strength

f

y

Straight line theory

Maximum ’ p~

? s steel stress „ h ;

Ultimate load

design theory

Maximum f

! !

’ steel stress

f

? ! T

y

psi !

t psi !1

!

t psi t?

I

’ 42,500 t

1 46,200 ’ 1.088

t

1

? 50,200 ’ 1.180

1 II

’ 69,000 t

T 72,800 ; 1.0551

I

1 78,900

; 1-143

III ’ 68,800 I

t 73,000 1 1.062t

!

1 79,800 1 1.160

? IV ’ 70,500 t

! 68,800 ’ 0.975 t! 75,700

; 1.074

VA ’ 98,800 1

I 94,500 1 0.957 t! 104,500 1 1.057

t VI ' 104, 300 t

1 99,700 ’ 0.956

?

1

1 110,500 ’ 1.060

t

Note: Yield strengths of steels I A and II were determined by

"halt of gage" method; "offset" method was used for the

other steels, with offset of 0,2 percent. Only those

beams containing steels VA and VI (F-VA-19 and F-VI-9)

which appeared to fail In tension were Included in the

above tabulation. For all other types of steel, the

results of duplicate beam specimens are presented.

toz<

DC

I-to

Ui>

tOCO

UJ

Q£Q.2Ooo

Ui

UJo

3

V)<

UJ2

(TO

CO

UIo<

CD2<

DCh-(0

UJa*Q

UJQZo

CD

U.Ozo<oo 4»

FIGURE

I.

DESCRIPTION

OF

FLEXURAL

TEST

SPECIMEN

AND

INSTRUMENTATION

IIOxlO

z

<

a:H

<n o

o

o

o

o

o

o

ISd *SS3dlS

FIGURE

2.

STRESSSTRAIN

CHARACTERISTICS

OF

REINFORCING

BARS.

FIGURE 3. TYPICAL REINFORCING BARS USED IN BEAMS.
1
FIGURE

4.

METHOD

OF

LOADING

BEAM

SPECIMEN

AND

ARRANGEMENT

OF

TUCKERMAN

GAGES

FOR

MEASUREMENT

OF

WIDTH

OF

CRACKS

.

• , r

FIGURE

5.

BEAM

IN

THE

TESTING

MACHINE

PRIOR

TO

TESTING.

F-IA-2N09-ZZ

FIGURE

6.

VIEWS

OF

BEAMS

AFTER

FAILURE.

FIGURE

7.

VIEWS

OF

BEAMS

AFTER

FAILURE

70

60

50

40

30

20

10

0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

MID -SPAN DEFLECTION, IN.

FIGURE 8. LOAD VS. MID - SPAN DEFLECTION.
I

I

I

I

I

I

I

I

I

I

I

I

I
CM 2 - 9. i

o o - UJ

u_

UJQ£

toi o5

Sd I >4 WV99 NO QVO") SdIX ‘ INV39 NO OVOl o

i-o

UJ

UJo2

0)I o2oo

iij u_UJo2

if) 2OHO

UJ-J

u.UJo2

tni Q

UJ

cr

Z>O

l—2O

0.O

UJ

UJQ

<£

CL

if)I o

CO>Q<O

CD

UJ

CC~o

u.

RATIO

OF

MID

-SPAN

DEFLECTION

TO

THE

DEFLECTION

IN

BEAMS

WITH

STEEL

OF

TYPE

IA

STEEL TYPE

-o - I A

O - H

. -IE

- TV"

x - 3C A

a - 31

AVERAGE VALUES FOR BEAMS REINFORCED WITH THE SIX DIFFERENT TYPES OF STEELS.

AVERAGE VALUES FOR BEAMS REINFORCED WITH STEELS HAVING A WELL DEFINED YIELD STRENGTH.

FIGURE 10. COMPARISON OF MID-SPAN DEFLECTION IN BEAMS

SUPPORTING EQUAL LOADS .
I
70

60

50

40

30

20

10

0

10 20 30 40 50 60 70 80 90xl0 3

STRESS IN REINFORCEMENT, PSI

II. LOAD VS. OBSERVED STRESS IN REINFORCEMENT

70

60

50

40

30

20

10

0

IGURE 12. LOAD VS. COMPRESSIVE STRAIN IN CONCRETE.

RATIO

OF

COMPRESSIVE

STRAIN

IN

CONCRETE

TO

THE

STRAIN

IN

BEAMS

WITH

STEEL

OF

TYPE

I

A

AVERAGE VALUES FOR BEAMS REINFORCED WITH STEELS HAVING A WELL DEFINED YIELD STRENGTH.

FIGURE 13. COMPARISON OF COMPRESSIVE STRAINS IN BEAMS

SUPPORTING EQUAL LOADS .

70

60

50

40

30

20

10

0

AVERAGE WIDTH OF CRACKS, IN.

FIGURE 14. LOAD VS. AVERAGE WIDTH OF CRACKS

RATIO

OF

AVERAGE

WIDTH

OF

CRACKS

TO

THE

WIDTH

OF

CRACKS

IN

BEAMS

WITH

STEEL

OF

TYPE

IA

fs

= 30,000 PSI IN TYPE IA STEEL'

LOAO ON BEAM - 42.9 KIPS , 40,000 65,000 100,000

NOMINAL YIELD STRENGTH OF STEEL, PSI

fs = 36,000 PSI IN TYPE IA STEEL"

LOAD ON BEAM = 51.4 KIPS

40,000 65,000 100,000

NOMINAL YIELD STRENGTH OF STEEL, PSI

STEEL TYPE

o - IA

o - n

. -m

- I

V

X - 3C A

a - 3ZE

FIGURE 15. COMPARISON OF AVERAGE WIDTH OF CRACKS

IN BEAMS SUPPORTING EQUAL LOADS.

80x

10

toiO

<n*o<

tro

u.o

LsJ o<

or

LU><

</> XLO<

<ro

UloX

h-Q

LUO<

ccLU><

(O>

I- 2 2 uj LU 5 2 5 8 s g « o 5 2 <

LLl m * <

LU = X 9

I- >Q 7 Z

tr (0 £ co

LU

a:

>—co<o

K-LU

q:o

UJX

hID

LUX3O

ISd ‘ 1N3W3DU0JNI3U Nl SS3U1S

28x10'?

1

1

1

1

1

14

.

28x

I0"

3

|

,

r

T

l'4

•

28x10'

' Nl ‘SXOVdO JO ONIOVdS 39VH3AV «o

J — 9 (O (O t N Ox

Nl ‘SXOVdO JO ONIDVdS 39VM3AV «O O oo ir* Ok

‘XOVdO JO H1QIM

M- o <x> cm go d- o

CM C\J

* N I ‘XOVdO JO HiaiM

to

CL

UJ

UJhtO

CO

if) UJ

DC

<n

a.

UJ

inin

UJ

irh-co

tn

CL

UJUJh

w

in

in

UJ

QC

CO

*NI ‘SXOVdD JO 9NI0VdS 39VH3AV «o 19 9 ® to d- CO o X

to

CL

UJUJ

I—

to

toCO

UJ

DC.

I

to

’Nl ‘SXOVdO JO 9NI9VdS 39VH3AV roo 2 9 ® to 'f cm Ox

to

CL

UJ

UlF-

(OZ

to

CO

UJ

DC

J—

CO

• Nl

d-

* SX9Vd9 JO ONIOVdS 39VJ3AV io 9 9 ® ® d" CM Ox

O

o

UJ Q W

o z d- —

to o to

CM LU

DC

I

o M

FIGURE

17.

THEORETICAL

STRESS

IN

THE

REINFORCEMENT

VS.

SPACING,

AND

MAXIMUM

AND

AVERAGE

WIDTH

OF

CRACKS.

(DATA

AVERAGED

FOR

TWO

BEAM

SPECIMENS

WITH

EACH

TYPE

OF

STEEL)

— zo

UJ

-I

u.UJ0z2

CO1 95 O . — Z o 2i

o

co uj

UJo<CL<o zooz2

COo5 o co uj

CL- UJoz2

co95 <o £h

u, o

CO UJ

CDX

O Isdix ‘qvot o

UJ

_J

LlUJa2

CO92

co £2

CO92

sdiM ‘avcn

FIGURE

18.

COMPARISON

OF

THEORETICAL

AND

OBSERVED

MID

-SPAN

DEFLECTIONS

roOx to

Cl

uj

LlI h

to

(O

(0UJo:

hCO

x

to0.

UJ

UJ

<0

to

UJa

to > Si! tc oc

UJ o

co uj

CD

X

O IIOo

to

Q.

UJUJ

(O

to

UJ

£Eh

(O

FIGURE

19.

COMPARISON

OF

THEORETICAL

AND

OBSERVED

STRESSES

IN

THE

REINFORCEMENT .

yjliuacozoo<

CtI-CO

sd i>i ‘avcn «*oO IU

CM (EO

co Z ~ Oo

CO

UJ

IUJ

CHOOO<

£C

CO

sdix ‘avcn

M-Io

UJIUJ

croo

c_> <0c

CO < SP

SgUJ O

CO Ul

CD

X

O

H

CO<

cr

J-co

Ul

JUl

CToooO

Ul>

acUJ

co

CDoaz<<o

UJ

cr0

UJ1

51- Io

UJ

crozooz<

cr

h-co

MUJ

hUJITOOO<

cr

co o

co

crsoo6

CM

Ul

cr3

e>

01*08

c0l*08 £

0I*08

K)

FIGURE

21.

COMPARISON

OF

THEORETICAL

AND

OBSERVED

WIDTH

OF

CRACKS

-e~

FIGURE

22.

CROSS

SECTION

OF

BEAM

ILLUSTRATING

THE

PARAMETER

U. S DEPARTMENT OF COMMERCE

Sinclair Weeks, Secretary

NATIONAL BUREAU OF STANDARDS

A. V. Astin, Director THE NATIONAL BUREAU OF STANDARDS

T'he scope of activities of the National Bureau of Standards at its headquarters in Washington,

D. C., and its major field laboratories in Boulder, Colorado, is suggested in the following listing of

the divisions and sections engaged in technical work. In general, each section carries out spe- cialized research, development, and engineering in the held indicated by its title, A brief

description of the activities, and of the resultant reports and publications, appears on the

inside front cover of this report,

WASHINGTON, D. C.

Electricity and Electronics. Resistance and Reactance. Electron Tubes. Electrical Instruments. Magnetic Measurements. Dielectrics. Engineering Electronics. Electronic Instrumentation

Electrochemistry.

Optics and Metrology. Photometry and Colorimetry. Optical Instruments. Photographic

Technology, Length Engineering Metrology.

Heat and Power. Temperature Physics. Thermodynamics. Cryogenic Physics. Rheology

and Lubrication. Engine Fuels.

Atomic and Radiation Physics. Spectroscopy. Radiometry. Mass Spectrometry. Solid State Physics. Electron Physics. Atomic Physics. Nuclear Physics. Radioactivity. X-rays. Betatron. Nucleonic Instrumentation. Radiological Equipment. AEC Radiation Instruments. Chemistry. Organic Coatings. Surface Chemistry. Organic Chemistry. Analytical Chemistry.

Inorganic Chemistry. Electrodeposition. Gas Chemistry. Physical Chemistry. Thermochemistry, Spectrochemistry Pure Substances.

Mechanics. Sound. Mechanical Instruments. Fluid Mechanics. Engineering Mechanics.

Mass and Scale. Capacity. Density, and Fluid Meters. Combustion Controls.

Organic and Fibrous Materials. Rubber. Textiles. Paper. Leather. Testing and Specifications, Polymer Structure Organic Plastics. Dental Research.

Metallurgy. Thermal Metallurgy. Chemical Metallurgy. Mechanical Metallurgy, Corrosion

Metal Physics

Mineral Products. Engineering Ceramics. (Bass. Refractories. Enameled Metals. Concreting

Materials. Constitution and Microslructure

Building Technology. Structural Engineering. Fire Protection. Heating and Air Condi

tioning. Floor, Roof, and Wall Coverings, Codes and Specifications.

Applied Mathematics. Numerical Analysis. Computation. Statistical Engineering. Mathematical Physics

Data Processing Systems. SEAC Engineering Group. Components and Techniques. Digital

Circuitry, Digital Systems Analogue Systems. Application Engineering.

• Office of Basic Instrumentation • Office of Weights and MeasureBOULDER, COLORADO

Cryogenic Engineering. Cryogenic Equipment. Cryogenic Processes. Properties of Material:-. Gas Liquefaction

Radio Propagation Physics. Upper Atmosphere Research. Ionospheric Research. Regular

Propagation Services Sun-Earth Relationships.

Radio Propagation Engineering. Data Reduction Instrumentation. Modulation Systems

Navigation Systems Radio Noise Tropospheric Measurements. Tropospheric Analysis Radio

Systems Application Engineering.

Radio Standards. Radio Frequencies Microwave Frequencies. High Frequency Electrical

Standards. Radio Broadcast Service High Frequency Impedance Standards. Calibration

Center Microwave Physics. Microwave Circuit ‘standards.