part 2 tests of reinforced concrete deep beams with …
TRANSCRIPT
lIt) I~CJA
:ftlqS CIVIL ENGINEERING STUDIES c. 3 STRUCTURAL RESEARCH SERIES NO. 193
PRIVATE COMMUNICATION
NOT FOR PUBLICATION
BEHAVIOR AND DESIGN OF DEEP STRUCTURAL MEMBERS
PART 2
TESTS OF REINFORCED CONCRETE DEEP BEAMS
WITH WEB AND COMPRESSION REINFORCEMENT
lti.tz Reference RoOOl ment_ Civil Engineering De BI06 C. E. Building University of Illino Urban~, Illinois 618
By J. R. Winemiller
and
W. J. Austin
Approved by
C. P. Siess
Report to
RESEARCH DIRECTORATE
AIR FORCE SPECIAL WEAPONS CENTER
Air Research and Development Command
Kirtland Air Force Base, New Mexico
Contract AF 29(601 }-468
Project 1 0 8 0
.-
UNIVERSITY OF ILLINOIS
URBANA, ILLINOIS
AUGUST 1960
AFSWC -TR-59-72 Part 2
BEHAVIOR AND DESIGN OF, DEEP STRUCTURAL MEMBERS
Part 2
TESTS OF REINFORCED CONCRETE DEEP BEAMS WITH
WEB AND COMPRESSION REINFORCEMENT
Project, No. 1080
by
J. R. Winemiller and W. J. Austin
Approved by C. P. Sies 8
University of Illinois
Department of Civil Engineering
August 1960
Research Directorate AIR FORCE SPECIAL WEAPONS CENTER Air Research and Development Command
Kirtland Air Force Base New Mexico
Approved:
ERIC H. W AiNG Chief Structures Division
~;:;'~~ Colonel USAF Director, Research Directorate
Contract No. AF 29(601)-468
TR-59-72
ABSTRACT
The results of tests of seven reinforced concrete deep beams with tensile
a.nd web reinforcement and two beams with tensile and compressive reinforce
ment are described in this report. Several patterns of web reinforcement were
used. The beams with web reinforcement had a span-depth ratio of about 3.0
and the beams with compressive reinforcement had a span-depth ratio of 2.32.
All beams were tested under uniform, slowly-applied loading. The general
behavior of the test specimens is described and explanations of the observed
phenomena are given.
PUBLICATION REVIEW
This report has been reviewed and is ~ved.
. y~M. L/ ~ -CA Y ~ANP;;
Colonel USAF Deputy Commande r
I.,
IIo
IIIo
TESTS OF REINFORCED CONcRETE DEEP BEAMS
WITH WEB AND COMPRESSION REINFORCEMENT.
TABLE OF CONTENTS
INTRODUCTION 0 o 0 ., ., ., ., o 0 0 0 ., ., o 0 0 0 • ., f1 000
101 Object and Scope 0 0 • ., 0 ., • ., ., ., ~ 0 ., 00.,
102 Acknowledgment·o o ., ., ., ., ., 0 0 o '0 0 o .
1.3 Notation 0 0 0 0 0 .,
DESCRIPTION OF TEST SPECfIMENS
., ., ., 0 ., ., 0 0 ., ., 0 ., ., ., ., 0 ., 0
00000
201 Description of Beams 0 ., 0 0
202 Materials and Fabrication., 0
TEST EQUIPMENT AND PROCEDURE 0 ., b ., 000
Instrumentationo ., o 000 0
Loading Apparatus. ., 0> 0 0 0
Testing Procedureo 0 ., 0 0 ., 0 .,
o 0 0 0 0 0 0 0 000 0
• o· ., 0 ., ., b
., 0 ., o. 0 0 ., o· ., ., 0 .,
o ., 0 0 a 0 ., 00,000
o 0 - 0 a 00000
000 00" .,. 0 0 ., 0 0
., " 0 0 0 o ., 0 ., 0 0
BEHAVIOR OF BEAMS WITH WEB REINFORCEMENT 0 0 0 .. ., 0 0 0 0 ., 0 0 0
401 Test Results and *odes of Failureo 0 • ., 0 0 ., 0 0 0 ., 0
Deflections., ., 0 o ., ., 000
Steel Strainso-., 0
Concrete Strains •.. 0
o " 0 0 0
., 0 0 0 0
., ., ., 0 0 0 0 0 0 0 0
o ., ., 0 0 • 0 0 o. 0 ., .,
o 0 o ., 0 0 000
iii
Page
1
1
1
2
5
5
7
10
10
~2
13
14
14
15
18
22
405 Total Elongation of Tensile Reinforcement., ., ., ., 0 0 ., 0 24
BEHAVIOR OF BEAMS WITH COMPRESSION REINFORCEMENTo 0 o ., ., 0 0 o· .,
Test Results and Modes of Failureo o • eo. o .. .,
o ., ., 0 0 Deflections 0 0
Steel Strains., ., 0 ., ,0 0 o • 0
Concrete Strains ., 00" 0 0 0
., 0 o . ., 0 o 0 ., 00" .,
., ., 000 • 0 f1 0 0 ., 0
., ., ., 0 ., 0 00., .,
27
27
28.
28
29
.... ..;
iv
TABLE OF CONTENTS (Continued)
VI I> STUDIES OF TEE FLEXURAL STRENGTH AND BEHAVIOR OF DEEP BEAMS \olITH WEB REINFORCEMENT AND WITH COMPRESSION ~INFORCEMENT 0 0 31
601 Effect of Web Reinforcement Upon External Behavior 0 0 31
602 Effect of CompressionReinforc~ment Upon External Behavior 0 • 0 0 0 0 0 0 0 0 I> 0 0 o q 0 000
Prediction of External Behavioro 0 OOOOQOOO
VII. SUMMARY AND CONCLUSIONS. • o b o 0 o 0 0 0 o 000 000
.'
Summary 0 I> 0 • 0 o 0 0 o 0 I> <;> 0 0 o • I>
702 Conclusions 0 00000 I> 0
VIIIo BIBLIOGRAPHY " 0 0 0 0 0 o 0 000 o 0 o 0 O' 0
TABLES
FIGURES
3~
35
10
20
LIST OF TABLES
Properties of A-Series Specimenso
Properties of C-Series Specimenso
Properties of the Reinforcing Steel
CO"
000
o 0'
"'- '.
o 0 0 0 0 l' o 0 o 0
o 0 0
40 Properties of the Concrete Mixeso 0 0 0
50 Test Results of C-Series Specimens 0
OOOO()O 00
o 0 0 0 0 0 0 coo 0
60 Test Results of A-Series Specimenso e 0 () 0
70 Comparative Test Resultso 0 0 0 0 0 0 0 000 000 0 0 0 0
80 Comparison of Measured, and Computed Moments 0 000
Prediction of Steel Strains at Failureo 0 0 o 0 0
v
Page
46
4·1
48
)+9
50
51
52
53
54
Fig., No.,
1
2(a)
3
4
5
6
7
8
9
10
II
12
l3
l4
15
16
l7
l8
19
20
2l
\
LIST OF FIGURES
A-Series Test Specimenso OOOOoocrOO()oO
Nominal Dim~nsi6ns of C-Series Specimens and Location of Concrete Strain Gages and Deflection Dialso 0
Placement of Reinforcement and Location of Steel Strain Gages: Beam C=lo ., 0 0 0 ., 0 ., 0 0
Placement of Reinforcement and Location of Steel Strain Gages: BeamsC-2 and C-3 0 0 0 0 0 () 0 0 0 0 0
Placement of Reinforcement and Location of Steel Strain Gages: Beams c-4 and C-5 0 0 0 0 0 0 0 0
Placement of Reinforcement and Location of Steel Strain Gages: Beams c-6 and C-7 0 0 0 0 0
Typical Stress-Strain Curve for the Reinforcing Steel., .,
Typical Test Set-Upo 0 0 0 0 ., • ., 0 e 0 0 ., ., ., ., e 0 0
Beams without Web Reinforcement After Failure. ., o ., " .,
Beams with Vertical Sti'rrups After Failure
Beams with Inclined Bars After Failure 0 a 0 0 0
Crack Develdpment ~
Crack Development:
Crack Development:
Beam. c-4
Beam. C-5 0
Beam c-6 0
0, .0 0 '0
Load-Deflection Curves for Beams with 1015 P~rcent Longitudinal Steel 0 " ,0 ., 0 0 . .. .. 0 0 ., 0
Load-Deflection Curves for Beams with 1~99 Percent Longitudinal Steel ., 0 0 0 0 0 b . 0 0 .,
Load-Deflection Curve for Beam with 2.09 Percent
o 0 0 0
000 0
0 0 0 0 0
" " 0 0 0
Longi tudinal Steel 0 0 0 " 0 0 0 ., o 0 .,
Deflected Shape of Beams C-l and C-2 .,
Deflected Shape of Beam. C-3o ., ., ., 0 0
Deflected Shape. of Beams c-4 and C.;..5 0
o 0 ,0
Deflected Shape of Beams c-6 and C-7 o ., 0 o 0 0
Load-Deflection Curve for Supports 0 0 .0 0 ., 0 0
000 0
vi
55
51
68
69
10
11
12
73
15
Figo
22
23
24
25
26
27
28
29
30
31
32
33
34
35
37
38
Noo
LIST OF FIGURES (Continued)
Load-Steel Strain Curves for Beam C-l ..
Load-Steel Strain Curves for Beam C-2o
Load-Steel Strain Curves for Besun C - 3~
Load-Steel Strain Curves for ~Beam c- 40 0 0
0 0 0
.. " ..
0<>.. 0
vii
16
11
78
19
Load-Steel Strain Curves for Berun C~5o 0 0 0 . o 0 80
Load-Steel Strain Curves for Beam c-6" 0 ~
Load-Steel Strain Curves for Beam C-7 o "
Load vs 0 Total Tensile Force in Longitudinal Steel at
81
,82
Section 12 in .. 'from Midspan~ Beams C-l, C-2, and C-3" 0 .. " 83
Load vs 0 Total T'ensile Forc'e in Longitudinal Steel at Section 12 ino from Midspa.n~ Beams c-4, C-5, c-6 and C -70 .. 0 0 '0 • 0 0 0 0 0 0 " 0 0 0 0 0 0
Free-Body Diagrams of Cracked Specimens o o 0 "
Distribution of Total Tensile Force in the Longitudinal Reinforcement: Beams C-l, C-2, and C-3o " 0 0 0 • 0 0 "
Distribution of Total Tensile Force in the Longitudinal Reinforceme~t~ Beams c-4, C-5, and c~6o 0 0 " 0 " 0
Load-Steel Strain Curves for the Web Reinforcement 0
Distribution of· Concrete Strain Along Depth: of Beam at Midspan, . Beams· C-l, C-2 and C-3 .; 8 d d 6 a I ~ 8
Distribution of Concrete Strain' Along Depth of Beam at Midsp~ ·Beams ,c-4, C-5,c-6 andC ... 7 <f. 6. (). (). (f. r1' IS
8 ci & 11
Distribution of Concrete Strain Along Top Edge of Beam
Distribution of Concrete Strain Along Top Edge of Beam 0 0 0
84
85
86
87·
88
90
91
92
39 Distribution of Concrete Strain Along Top Edge of Beam 0 93
40 Elongation of Tens:lle Reinforcement: Beams C-l, C-2, and C-3 94
41 Elongation of Tensile'Reinforcement: Beams c-4, C-5, c~6,
42
and C - 7 • 0 0' 0 • 0 " 0 0 0 0 0 0 0 0'" 0 0 • 0 .. o 00 0 95,
Total E~ongation of , Tensile Reiilforce~eJ!.t,v~" Sum,o+, tdngitudinalSteel Strains Below Yield: Beams C-l, C-2, and C - 30 0 " " " '. 0 0 • 0 0 0 0 " O' 0 0 0 <> 0 " 0 0 0 '0
/ Fig" Noo.
44
46
47
48
49
50
LIST OF FIGURES (Continued)
Total Elongation of Tensile Reinforcement vs" Sum of Longitudinal Steel Strains Below Yield: Beams c-4, C-5,
viii
C - 6, BJid C -7 " ., .. . 0' 0 " .. .. " ., .. .. " 0 0 .. • .. G .. • 97
Midspan Deflection vs .. Elongation of Tensile Reinforcement: Beams C;';'l, C-2, and C-3a " .. a ., ., 0 0 0 <) 0, ., ., 0 0 ., .. a" 98
Midspan Deflection VS o Elongation of Tensile Reinforcement: Beams c-4, C-5, and c-6& ., 0 ., .. 0 0 " " ., ., " ., a ., ., .,'.. 099
Beams A-3-4 and A-3-5 After Failureo .... " 0 .. .. . Moment-Deflection Curves for A-Series Beams .. o 0 I 0 0
Load-Steel St~ain Curve~ for Beam A-3-4 .. o 0 000
Load-Steel Strain Curves for Beam A-)~5o 00"
Distribution or'Concrete Strain Along'Depth of 'Beam at Midspan, ,Beams.A~>:4' and A-3-5 ...... 0 • ., ., •
., o· 0, 100
o ., 101
102
103
. ., 104
5l Distribution of Concrete Strain Along lJ]op Edge of Beams' A-3-4 and A-3- 5., ., " 0 " ., " ., ., C> ., 0 ., <) ., ., 0 ., 105
52 Distribution of 'Strain Along Entire 'Depth 'of Beam a.t Midspan: Beams c-4 and c-6 '0 ;, 0 0 o. ., 0 I) ., ., C> ., ., 106 ., '0
53 Strain and Stress Relationships at Flexural Yielding ., ., 101
54 Strain and~Stress Relationships at Ultimate Flexural Capacity 0 ., 0 ., 0 0 " 0 0 0 0 ., ., ., ., 0 ., .,' 0 0 0 0 .. " ., ., 108
1
10 INTRODUCTION
101 Object and Scope
The studies described in this report were performed as a part of
a comprehensive investigation of the strength and behavior of reinforced
concrete deep beamso The object of the investigation reported herein was to
gain information concerning the strength and behavior of concrete deep beams
reinforced in both tension and compression and of' rei.nl'orced concret,e deep beams
with web reinforcemento Several patterns of web reinforcement were tested in
order to obtain some indication of the most efficient, means of reinforcing the
web 0
Two rectangular concrete beams reinforced in both tension and
compression with a sp~/depth ratio of 2032 were tested under uniform load on
a simple span of 36 ino The beams had the same cross-sectional properties,
with the exception of the compression reinforcement, as a beam of a previ9us
test series reinforced in tension only 0
Seven rectangular concrete beams~ designated as C-series specimens,
were also tested under uniform loading on a simple span of 36 ino Two of the
seven beams had only tensile reinforcemento They were reinforced with 1015
and 1099 percent intermediate grade steel barso . The depth to the lower layer
of the longitudinal reinforcement was 12 ino Then two variations of each of
the two beams containing either vertical stirrups or inclined bars were testedo
The seventh C-series specimen tested had no web reinforcement, 'but instead,
had the longitudinal reinforcement distributed along its depth 0
102 Acknowledgment
This investigation was carried out in the Structural Research
Laboratory of the Engineering Experiment Station at the University of Illinois
as part of a cooperative pr6ject between the University and the Air Force
Special Weapons Center, Department of the Air Forceo .General direction of the
2
project was f'urnished by No Mo Ne'WID.a.rk~ Professor and Head, Department of Civil
Engineering, and Dro Co Po Siess j Professor of Civil EngineeriDrgo The project
was under the immediate direction of' Dr 0 W 0 J 0 ,Austinj1 Associate Professor of
Civil En~ineeringo Mro Ro Eo Untrauer, Research. Associate in Civil Engineering,
provided the direct supervisiono The studies described ~n this report also
served as· the basis for an MoSo dissertation by Mro Winemiller 0 ,
1~3 Notation
The following notation has been usedg
A ,= ·total area of tension reinforcement s
An = tdtal area of compression reinforcement s
A = area of web reinforcement .. ·v
a, = -depth of ~tress block in concrete at maximum. load-carrying capacity ,
b = wi dth of m.ember
Cl total compressive force in the concrete
C2 = total compressive force in the compression reinfo~cement
d = effective depths dista.11ce from the top compressive fiber to the centroid of ~he tension reinforcement
d U = distance from the centroid of the compression reinforcement to the centroid of the tension reinforcement '.
E = modulus of elasticity of', concrete· c
E = modulus of elasticity of reinf.Qrc~.ng steel s
f = stress in the concrete c
f9 = compressive:strength of concrete determined from tests of c 6- by 12=ino cylinders 0
f = stress in the tension reinforcement s
fn = stress in the compression reinforcement s
f = stress in the web reinforcement v
t: = ~~eld-point stress of the tension and web reinforcement y
ft = yield-point stress of the compression reinforceme:qt y
f* = fl - 0.85 fl y c
j = ratio of lever arm of internal resisting moment to effective depth, d, for concrete, for elastic section
k = ratio of depth of compression zone to effective depth, d, for fully-cracked elastic section, see Fig. 53
~ = ratio of area of concrete stress block to area of enclosing rectangle at maximum load, see Fig. 54
3
= fraction of depth of compressive zone which determines the position of the compressive force in the concrete at maximum load, see Fig. 54
k3 = ratio of maximum compressive stress in concrete beam to cylinder strength
L = span of simply-supported beam, distance between centers of supports
M = bending moment
Mf = computed ultimate flexural moment (€
M' = computed ultimate flexural moment (€ f
M = measured moment at maximum load u
M = measured moment at flexural yielding y
p = A /bd s
p' = A' /bd s
pf q = reinforcing index = f WY
c
u 0.004)
= 0.008) u
lower critical value of q corresponding to € s
l\.lk € 3 u
T = total tensile force in the tension reinforcement
w = total uniform load
W total uniform load at maximum load u
Wy = total uniform load at flexural yielding
~ = measured midspan deflection at maximum load
6y = measured midspan deflection at flexural yielding
€ • = 0' € + € u 0
4
€ = strain in the concrete c
€ :;:: strain in the tensio'n and web reinforc,ement at beginning o of wbrk..,hardening region'
strain in the co~pression reinforcement at beginning of 'Work~hardening region
€ = strain in the tension reinforcement 5
E U strain in the compression reinforcement 5
€ = crushing strain of concrete u
€ = yield-point stra.in of the tension and web reinforcement y
€o = yield-point strain of the, compression reinforcement y
6
beam c~6J the top layer of the tension steel was bent up at 45 dego beyond
.the point -where it was no longer needed to develop the flexural capacity of
the beamo Since the depth to the bottom layer of steel remained constant at
12 ino throughout this series of tests, the effective depth measured to the
centroid o~ the tensile steel area of these three beams is slightly less
than that for the first group due to the addition of the two top bars d The
effective de~th is 11039 ino j and consequently, the sp'an-depth ratio is 30160
Beam C-7 had the' same t~tal steel area as beam c-4, but instead of
placing the two Noo 4 bars in a horizontal plane they were placed one above
the other as shown in Figo 50 By distributing the longitudinal tension steel
along the depth of the beam in this manner$ it was believed that the reinforce
ment might more effectively retard the development of the inclined cracks than
if it were concentrated near the bottom edge of the specimen 0 Because of the
steel arrangement, the effective depth is decreased to 10082 inoj increasing
the span-depth ratio to 30320
As mentioned previbuslYJ the two top longitudinal bars of 5eam c-6
were bent up beyond the point where they were no longer necessary t~ provide
flexural resistanceo Once this point was established, the diagonal web steel
of beam C-3 was placed in exactly the same positiono The top bars of beam c-6
were bent up at 7 1/2 ino on both sides of midspano In beam C-3 the diagonal
bars intersected ~he longitudinal steel at 6 ino on both sides of midspano
The vertical stirrups were spaced so as to intersect effectively
the inclined cracks observed from'the tests of beams without web reinforcemento
Both the stirrups in beams C-2 and C-5 and the inclined bars of beam. C-3
were welded to the longitUdinal tensio.n steelo
5
II" DESCRIPTION OF TEST SPECIMENS
201 Description of Beams
A-series: The two beams of this series were designed to give in
formation which would supplement the studies made during the previous year (1)0
They have the same properties as beam A-3-2 of the previously mentioned refer
ence except for the addition of compression reinforcemento Their properties
are given in Table 1, and drawings of the two beams are shown in Fig" I" For
beam A-3-4, pI = 1/2 p, and for beam A-3-5, pi = po Since beam A-3-4 failed
by bearing, 6- by 12- by l-ino steel plates were clamped to the sides of
beam A-3-5 above the supports to laterally confine the concrete and thereby
incre~se the bearing strength&
C-series: Two basic rectangular beams without web reinforcement
were first designed, and then variations of these b~sic beams were made by
adding web reinforcement in several different arrangementso The basic beams
had a width 'of 4 1/2 ino, an over-all length of 42 in", and a depth to the
bottom layer of steel of 12 in" The nominal area of the tension reinforcement
was chosen as 0062 s~o ino for the ,one basic beam and 1,,02 sg" ino for the other"
Drawings of the specimens are shown i'n Figs" 2 through 5, and the
properties of the beams are listed in Table 20 Beams C-l, C-2 j and, C-'3 con
stitute one groupo They have the same cross-sectional dimensions and tension
reinforcement 0 The only difference betwe'en them is the manner of reinforcing
the webo Beam C-l had no web reinforcement while vertical stirrups and
inclined bars were provided to reinforce the webs of beams C-2 ~d C-3,
respectively" The effective depth, d j of the three beams is 12 ino,
resulting in a span-depth ratio of 30
Similarly, beams c~4, C-5, and c-6 constitute a groupo The cross
sections of the three beams are the same at midspano Vertical stirrups were
added to reinforce the web of beam C-5o To provide web reinforcement for
8
For the C-series beams the mix was designed for a 14-day strength of 3000 psi;
the actual strength varied from 2970 to 3690 psio Because of expected bear
ing difficulties, the mix for the two beams with compression steel was designed
for a 14-day strength of 5000 psio The actual concrete strengths were 4860 psi
for beam A-3-4 and 5550 psi for beam A-3-5o Properties of the concrete mixes
are given in Table 40 Compressive strengths are the average values obtained
from tests of five standard 6- by 12-ino cylinders. loaded at a rate of
45,000 lb/miri, and the moduli of rupture values are those obtained from bending
tests of two 6- by 6- by 20-ino control beams loaded at the third-points of
an 18"'ine spano Moisture determinations for the sand and gravel were made at
the time of mixingo
Fabrication and Curing~ All the beams were cast horizontally in a
wooden form 0 Before casting, the steel was prepared for the future application
of electric SR-4 strain gages~ Usually this preparation consisted of grinding
the bar smooth at the gage locations and then attaching I 1/2-ino diameter
corks with wire to the bar over the smoothed area to provide access for mounting
the gages by removing the corks after'castingo
The SR-4 gages on the stirrups of beam C-5 and on the top two hori
zontal bars of beam C-7 were attached before casting to avoid cork holes in
the concrete close to or within the compression zoneo This necessitated water
proofing the gages to prevent them from coming in cont~ct with the moist
concrete 0 Waterproofing was accomplished by pouring hot Petro-elastic over
the gages" The performance of the waterproofing was then checked by submerging
each bar in ~ater for several hours before placing it in the specimeno
The concrete was mixed from 3 to 6 minutes in a 6-cuo fto capacity
non-tilting drum ~ype mixer and placed in the previously oiled form with the aid
of a high/frequency internal vibratoro Two 6- by 6- by 20-ino flexural control
beams and five 6- by l2-ino control cylinders were cast at the same timeo
7
202 Materials and Fabrication
Cementg Marquette Type III Portland Cement was used in the concrete
mixes for all specimenso The high-early-strength cement was purchased in
paper bags from a local dealer and stored under proper conditions o
Aggr.eg~tes~ The aggregates employed in the mixes were Wabash River
sand and pea gravel obtained from an outwash of the Wisconsin glaciationo
The gravel is composed mainly of limestone'and dolomite with minor quantities
of quartz, granite, and gneiss, while the sand consists mostly of quartzo Both
aggregates have been used in the laboratory for previous investigations and
have passed the usual specification testse The maximum size of the pea gravel
was 3/8 ino, and the absorption of both the sand and gravel was approximately
1 percent by weight of the surface dry aggregateo
Reinforcing Steel~ Intermediate grade deformed bars were used in
all of the beams e One coupon 2 f't 0 long was cut from e~ch bar and tested in
a 120, OOO-Ib Baldwin-Southwark-Tate'-Emery hydraulic testing machine at a
straining rate of 00005 inc/inc/mino up to yielde Strains into the work
hardening region were measure'd with an 8-ino extensometer employing a Baldwin
nmicroformer l1 coil and recorded by an automatic recording device o The exten
someter was removed from the coupon shortly after entering the strain hardening
region, and the strains beyond this point up to ultimate were determined by
measuring the elongation of an 8-ino gage length with dividerso In each
beam the bars were matched as closely as possible according to their yield
pOints, using bars cut from the same piece of steel to assure identical
properties whenever possibleo Table 3 lists the properties of the reinforcing
steel, and a typical stress-strain curve is shown in Figo 60
Concrete Mixesg The mix design was based on experience obtained
in other investigations conducted in the laboratory using the same aggregateso
10
IIIo TEST EQUIPMENT AND PROCEDURE
301 Instrumentation
Deflectionsg Dial indicators with a smallest division of 00001 ino
were used to determine the vertical. deflections. of' .each "speCimen at· ·VSl'."io'U-S
positions along the spano Locations of the dial indicators are shown in
Figo 20 T.he indicators were mounted to vertical l/4-ino round steel rods
which in turn were attached to heavy base plates resting on the bed of the
testing machine 0
Steel Strains g Strains in the reinforcing ste.el were measured with
Type A-7 SR-4 electri~ strain gageso The gage locations are given in Figso 2
through 50 The gages on the web steel were attached at the point where the
inclined crack was expected to· cross the reinforcemento
Duco cement was used to mcunt the electric gages to the reinforcemento
The drying period was not hastened by the application of heatj for it was
thought that it might influence the concrete strength 0 Therefore? the gages
were applied at least two dBys before the test to allow sufficient drying
time 0
Strains were read to the near~st·5·:iBP.cro.;in/ino 1iith 6 J~al.dw1f!".'
portab1.e strain indicator ~ A temp'uature compensation gage and a check ga.ge
were mounted on an unstressed steel block and connected into the circuito
Strains in the·bottom laye~ of the lon~tudinal tension reinforcemeht
were also measured over continuous~ino gage lengths using a mechanical gage
.em.plo:y""ing an Ames dial 'With a smallest division of 00001 ino The purpose of
these measurements was to obt~ain some indication of the m.a,go.i tude of the steel
strains if the capacity of the electric gages was exceededo While the SR-4
gages were functioning,;; only the strains over the two center 6-ino gage lengths
were measuredo After the electric gage readings became irregular, the strains
Several hours after casting, the top s~f,ace of the beam was
trowelled smooth, and the cylinders were capped with neat cement pasteo The
beam and control specimens were removed from their forms the next day and
wrapped in wet burlap for an additional day 0 They were then stored in the
laboratory until testedo
9
12
plugsc No measurements of elongation of tensile reinforcement were made for
the two beams with compression reinforceme~to It is assumed that the displace-
ments of the tensile reinforcement are equal to the displacements of the
surrounding concrete at the point of measuremento
3 .. 2 Loading Apparatus
A typical test set-up is sho'WIl in Figo7 0 Uniform load was simulated
1?y means of 20..,ton capacity Blackhawk hydraulic jacks mounted to a 10 WF 39
beam which in turn was bolted to the moving head of a 300j OOO -lb Olsen meehan-
ieal tiniY'f2rsa~ .testing machine~ The jacks were joined by high pressure hoses
to a common brass manifold connected to a Blackhawk hydraulic pumpo Eight
jacks spaced ~t 4 ino comprised the uniform load for all the beams except A-3-4,
the first beam testedo For the test of this beamj ten jacks at 4 ino were usedo
However j the first beam failed by crushing of the concrete above the supportso
To reduce the possibility of a bearing failure in the following tests, the
end jacks were eliminatedj making the midspan moment more critical for a given
loado The two center jacks were rigidly attached to the WF beam, but the
other jacks bore against rollers allowing them to rotate as the specimen
deformedo
Load was transmitted from the jacks·to the beam through l-ino diameter
chrome steel balls placed in depressions at the center of 4- by 3 7/8- by 2-ino
steel loading blockso The blocks rested on l/4-ino thick leather pads which
helped to distribute the load uniformlyo
Each beam was supported by two 6~ by 6= by 2~ino steel bearing blocks
which rested on the bed of the testing. machine 0 The top of the blocks ac.commodAted
a 2-ino diameter roller which bore against a 6- by 6~ by 2-ino plate seated in
Hydrocal against the bottom of the beamo The distance between the vertical
center lines of the rollers was 36 ino
I
.. j
I
_J
11
were determined mechanically over all the 6-ino gage lengthso The strain
readings were taken twiceo If they did not agree within 000002 ino/ino~
additional readings were taken until two readings agreed within the prescribed
limit a
Concrete Strainsg Concrete strains along the depth of ea.ch'beam at
midspan were measured by means of a 2-ino Whittemore strain gageo Steel plugs
with gage holes at their centers were cemented to the concrete to establish
the gage lines as shown in Figo 20
The strain readings were taken twiceo If they did not agree within
000001 ina, additional readings were taken until agreement was reachedo
Concrete strains were also measured at various positions along the
span with A-I SR-4 electric strain gageso Locations of the gages are shown
in Figo 20 The method of application of these gages was the same as for the
steel gageso However, since the moisture entrained in the concrete could be
detrimental to the behavior of the gages~ they were mounted only within 48 to
24 hours before the testo Strains were measured to the nearest 5 micro~ino/ino
wi th a Baldwin portable strain indicator 0
Elongation of Tensile Reinforcement~ In order to determine the re~a
tionship between deflection and total elongation of the tensile reinforcement,
the elongation was measuredo Two plugs were cemented to each specimen at
the point where the level of the bottom layer of the tensile reinforcement
intersected the centerlines of the supportso In beam C-l the separation
of these plugs was measured directly with a mechanical gage which employed
a dial indicator with a least reading of 00001 ino At each recording the
gage was read twice or more until the readings agreed within 00001 ino For
the other six specimens of the C..,series, the elongation of the tensile rein
forcement was measured by m;eans of t-wo dial deflection gages mounted horizontally},
as sho'in in Figo 20 These. gages measured the horizontal displacements of the
14
IV" BEHAVIOR OF BEAMS WITH WEB REINFORCEMENT
4,,1 Test Results and Modes of Failure
Test results for the seven beams of this series are given in
Table 5" The most significant properties of the specimens are also listed
for convenient referenceo Values of the load at yield and final collapse
include live load only, the dead load never being "more than about 005 percent
of the total vertical loado In the last column of the table is given the
mode of failure for each beamo
As can be observed from the table, all the beams failed in flexureo
All beams failed by first yielding of the longitudinal reinforcement followed
by crushing of the concrete in the compression zone at midspano
Although all of the specimens failed in flexure, the cracking patterns
developed were somewhat differento Evidence of this can be seen in the photo
graphs of the beams show in Figs 0 8 through 100 The numbers marked on the
specimens are the total load in kips and indicate the observed progress of the
cracks at that loado Three distinct cracking patterns are recognizable, and
the photographs are grouped according to these patterns 0 The manner of crack
ing seems to depend upon the type of web reinforcemento
Beams Without Web Reinforcement~ Well developed inclined cracks
formed, extending from the inside face of the support to top midspan, as
shown in Figo 8" This particular pattern is much more noticeable for beam C-I
than beam c-4o The two inclined cracks practically meet at midspan, giving
the appearance of an arch to the beam: aD.d,as shown in detail later, causing
the specimen to act as a tied arch, the longitudinal steel serving as a tie
between the supports 0 For beam C-7 the cracking pattern is similar to that
of' beam.s C-l and c-4, the arrangement of the top two horizontal bars exerting
little, if any, influence on the cracking patterno
-t
13
303 Testing Procedure
Load was applied in 10 to 17 increments to failureo After a load
increment, all deflection and strain readings were taken, and the cracks
observed through a low power illuminated magnifying glass and marked with inko
A certain amount of drop-off in load and change in deflection occurred while
the readings were being takeno These changes were recorded before the next
increment of load was appliedo
The beams were loaded until they ruptured completely or reached a
condition of unstable equilibrium, ioeo, increasing deflection with decreasing
loado In the vicinity of the expected yield loadj the load was applied by
increments of steel strain (usually a hundred micro-inc/ino) and the load and
midspan deflection read until first yielding was evident from observation of
the steel strainso After yielding, the load was applied by increments of
deflection 0 Between increments several load and deflection readings were
taken simultaneouslyo
Photographs of the test specimens were taken at important stages
during the test and after failureo The control beams and cylinders were
tested the same day 0
forcemento ID, Figo 16 the curve for beam c=4 is replotted for comparative
purposes. The curves are for the deflection measured at the top midspano
Drop-off of load occurring while the readings were being taken is not shown"
All the curves are characteristic of members failing in flexure"
An elastic range is recogniza.ble up to yield;; beyond which considerable
deflection of the beam takes placeo The curves of Figo 14 sho~~a definite
change of slope at yieldo " However!J this sharp break is not present for the
beams with mQltiple layers of steel; the change in slope in the vicinity of
yield is more graduSJ. due to successive yielding of the· layers of longitudinal
steelo Yield load and~~e~l~t.ion were chosen for this report as the load and
corresponding deflectio~ at the intersection of the initial and secondary
slopes of' the curves 0 These iTalues are listed in Table 50
Ultimate deflection is listatt .. ,1x'6 Table 5 as that occurring at
ultimate load)' except for beam c ... 6o Examination of the curve for this specimen
shows that the maximum measured load occurred at a deflection of 0" 343 ino
Beyond this point the load decreased but slightly until a deflection of 00728 ino
was reached the~ dropped off rapidlyo Therefore, it was thought justifiable
to list 00728 ~o as the ultimate deflection for this beam 0
As would be expected~ the smaller the steel percentage the more
ductile was the membero This C~ be seen by comparing the load-deflection
curves for the three beams without web reinforcemento For the specimens
having steel ratios of 000115$ 000199, and 000209;; the midspan deflections
a.t failure were 00875 J 0 0 41.2~ and 0 0 352 ina J respecti velyo The decrease in
ductility with increase in.·longitudinaJ. steel ratio can also be observed by
comparing beams with similar web reinforcement patterns and different percent-
ages of' longi tudina.l steelo
Observation of the elastic portion of the load-deflection curves
shows that the presence of web reinforcement had little effect upon the
__ I
. i
i -~
17
stiffness of the beamso A small difference in stiffness for the beams with
a longitudinal steel ratio of 000199 is noticeableo However j the difference
can probably be attributed mostly to the variation in concrete strengths 0
The web reinforcement also had little effect upon the ultimate
deflectiono Figure 14 shows that beams C-2 and C-3 with vertical stirrups
and inclined bars, respectively, deflected slightly less than beam C-l with
out web reinforcemento However, because of instrumentation difficulties the
deflection of beam C-l near ultimate was extrapolated from measurements of the
deflection of the bottom at midspano The difference in ultimate deflections
could possibly be due· to this extrapolation 0 The curves for beams·C-4j C-5,
and C-7 indicate that the ultimate deflection was increased slightly by the
addition of stirrups and decreased by distributing the longitudinal rein
forcement along the depth of the beamo The only beam in which a pronounced
change in ultimate deflection occurred was beam c-6 which had inclined web
reinforcement 0 The ultimate deflection for this beam was much greater than
the deflections for the companion beams c-4 and C-5 and was almost as large
as the ultimate deflections obtained for beams C-l, C-2, and C-3 which had
less tension reinforcemento The greatly increased ductility of beam c-6 is
believed to be due to the fact that the top layer of the. longitudinal steel
was bent up to form the web reinforcement, leaving a reduced amount of tension
reinforcement in the outer parts of the span and at the anchorageo The strains
in the outer sections were, therefore, much greater than in beams c-4 and C-5
in which both layers of longitUdinal steel ran the full ~ength of the beam,
and the increased strain produced increased deflection and increased energy
absorbing capacity in beam c-6o
The deflected shapes of the specimens are given in Figso 17 through
200 As can be seen from the figures, the deflected shape of the top surface
18
of' the beams can. be approximated by two strai.ght lines 0 This would seem to
indicate that the concrete at top midsp~ is acting as a hinge, resulting
in large strain concen.trations at midsPaJlo It can. also be noted from the
figures that there is a small deflection occurri~g at the centerline of the
supports 0 Ho Ao Ro dePaivaJ Research Assistant in Civil Engineering, performed
compression tests on the support systems used for this series of tests and
obtained the curve shown in Figo 210 For loads of the. magnitude occurring in
the tests of the C...,se:ries beams.., the suppo:e"ts would be expected to compress
as much as 00009 ino Practically the entire deflection shown at the supports
appears J therefo!'e~ t..;o be due t;o the compression of the su.pport systemo
403 Steel Strains
L~ad~steel strain cu-~es for the bottom row of longitudinal rein
forcement are given in Figso 22 through 280 The top figure represents the
full measured ran.ge, while 'the elastic region plotted to a larger scale is
presented in the bottom figureo The locatio~s of the gages are shown in the
partial sketch of the beam i!1 Fig .. 22.. Sira.ce gages 81 and 85 and gages 82
and 84 ar~ symmetries.'! about midspan,? ·t;he stra,i:o.s measured at the two corres
ponding gage locations were nearly identicalo ThereforeJ in order to make
the top fi~xre mor~ easily readJ only the strains measured at each of the
three differe:!lt sections along the spa~ are presentedo In cases where the
strains were different for symmetri.caJ. sections, the greater measured strain
is show. ..
For the three be:ams rei.nforced with 1015 percent longitudinal steel,
the strai!}'s 'Were well into the "Work=hardemng region at failure.. The ultimate
steel strain at mldspan was estimated either by extrapol&tion of the steel
strain=deflection curve or from the results of the strains measured on 6-ino
gage lengths.. For the two beams with web reinforcement, the estimated steel
strain at failure was m~ch greater than that for the companion specimen without
web reinforcemento
The longitudinal steel strains also reached the work-hardening
region for the beams with 1099 percent or more tension steel, except for
beam c-40 However, the maximum strains were not very far into the work
hardening regiono Again the measured maximum steel strains were greater
for the beams with reinforc'ementthan:for. the beam .. wi thout o·
19
The web reinforcement affected to a considerable extent the distri
butions of stress and strain along the tension reinforcement and reduced the
force in the tension reinforcement near the anchorageo The distribution of
stress along the length of the longitudinal re,inforcement indicates to some
extent how the beam is internally acting to resist the applied loado Of
particular interest are the conditions in the outer gages 81 and 850 A plot
of the total tensile force ~s. load is given in Figo 29 for the three beams
with 1015 percent steel and in Fig. 30 for the other four C-series beamso
The total tensile force was plotted in these figure~ instead of stress in
order to take into account the various moduli of elasticity of the reinforce
ment and the variation in steel area in the case of beam c-6 which had
longitudinal steel areas of 1002 sqo inc at midspan but only 0062 sqo ino
at the sections of gages 81 and 850 The total tensile force was computed by
first averaging the measured strains at the two sections and then using the
experimentally determined tensile force-strain curve of the reinforcement
to convert the strain to force 0 For beams with multiple layers of steel,
the strain measured in each layer was used in determining the total tensile
force at the sectiono Also shown in Fi~so 29 and 30 are curves designated as
theoretical beam and arch behavioro The curve for theoretical beam behavior
was obtained by dividing the moment at the gage section by the effective
internal lever a..."Y'J.TI. of an. assumed f'llll y cracked section, jdSl and the curve
labelled theoretical arch behavior, which represents the theoretical tensile
fOl-:ce, eCd.ual for all sections between supports, was obtained by dividing
20
the moment at ,midspan by the same lever armc Since the lever arm depends upon
the concrete strength, it did vary slightly~ but not enough to warrant different
theoretical curves for each specimeno ,
As can be observed from the two figures, the curves for the beams
without web reinforcement follow more closely the theoretical curve for arch
behavior than the theoretical curve for beam behavior 0 Close to yield the
measured tensile force agrees VeF~ well with the theoretical force for
arch behavioro The vertical sti~rups i~~reased the force in the tensile
reinforcement near the anchorage, -,and' the-jjnclined bars were even more
effective in reducing the longitUdinal ~ensile force near the anchorageo For
beam c~6, the measured tensile force agrees very well with the theoretical
curve for beam behavioro
The above-noted effect of the web reinforcement on the longitudinal
tension force can be explained qualitatively by considering free-body diagrams
of the specimenso In Figo 31 are shown free body diagrams of the portions of
beams C-l; C-2, and C-3 to the left of the measured inclined crack at a load
of 50 kips and include the internal forces which are believed to act across
the crack and cut sectionso From statics it is known that the force in the
longitudinal steel must be equal to the external moment divided by the effective
internal lever armJ jdo The external moment causing the tensile' force in the
steel at the location of gages Sl and S5 is equal to the moment at the head
of the crack passing through the gage sectiono As the crack extends more
toward midspanJ the external moment resisted by the longitudinal steel becomes
greater, resulting in a larger tensile forceo The presence of the web rein-
forcement hindered the development of the crack passing through the gage
section for beams C-2 and C-3 so that it did not extend as far toward midspan
as for beam C-lo HenceJl it is easily seen why the tensile force at the gage
section fOl" beam C-l was grea/ljer than -that :.Lor beams C-2 and C- 30
21
Besides retarding the development of the crack, the stresses in
the web reinforcement introduce an additional internal r~sisting moment that
tends to reduce the ~orce in the longitudinal steelo For a given amount of
web rein~orcement, this moment will depend upon how far the crack extends
beyond the web reinforcement, for this furnishes the lever arm when taking
moments about the point where the compressive force acts at the head of the
crack 0 In the case of the beams with vertical stirrups, the crack, as can
be seen in Figo 31, did not extend much beyond the stirrup 0 Hence, the
lever arm developed was sma~l an~ the a~aitional reSisting moment provided
by the web reinforcement could n~t '~pe,*"expected to influence greatly the
\ '. tensile ~orce in the longitudinal steelo Because of the particular location
of the inclined web reinforcement, the lever arm provided by cracking was
greater than that for the vertical stirrupso Thus, the reduction of the
longitudinal steel force::-··w~s. greater 0 .
The above discussion is concerned with the effect of the web
reinforcement upon the longitudinal tensile force near the anchorageo In
order to determine the effect of the web reinforcement upon the distribution
of tensile force along the span, the longitudinal steel force at each gage
location was computed from the measured strains in the same manner as for
the sections at gages 81 and 85 discussed above, and is shown in Figo 32 for
the beams with 1015 percent steel at a load of 50 kips and in Figo 33 for
the three beams with 1099 percent steel at a load of 86 kipso The distribu-
tion is not shown for beam C-7 because instrumentation difficulties were
encountered during the test, and several of the strains recorded for the two
top layers of longitudinal steel are believed to be erroneouso The effect
of the 'Web reinforcement upon the distribution of tensile force along the
span i~ more noticeable in Figo 33 than Figo 320 The tensile force for
beam c-4 is nearly constant along the span, whereas the distribution of force
22
in the longitudinal steel for the beams with web reinforcement is similar to
that of the external moment diagramo The figures indicate, then, that the
addition of' web reinforcement does plI?oduce to some extent the desired effect
of maintaining beam behavioro
Strains in the Web Reinforcement~ Figure 34 shows measured strains
in the web reinforcement vS o applied loado Locations of the gages are given
in the partial sketch of the beamso The inclined bars of beam C-3 were at
yield when the specimen failed, and the bars of beam c-6 which followed the
same straining pattern had, of course, yielded before collapse of the beam.
The strains measured in the vertical stirr~ps of beam C-5 were, however, not
near the yield strain at failureo Stra.ins in the stirrups of beam C-2 were
not measured, but i twould seem logical to assume that they would be very
similar to those measured for beam C-5o
4.4 Concrete Strains
Strains in the concrete were measured both along the depth of the
beam at midspan using a 2-ino Whittemore mechanical gage and along the span
at the top edge of the specimen with SR-4 electric gages 0 The locations of
the gages are shown in Fig. 20
Results of the strain measurements along the, depth of' the beam are
given in Figs. 35 and 360 Although there were five gage lines, at higher
loads cracks usually formed between the plugs of the lower gage lines invali
dating the measured straino This accounts for readings not being shown in
some instances on the lower gage lines of the beams reinforced with 1015 percent
longitudinal steel. At loads near ultimate the concrete at midspan began crush
ing, causing the steel plugs cemented to the beam to become loose and eliminating
further measurements. ,The ultimate concrete strain was therefore obtained by
extrapola~ion of the concrete strain-deflection curve for each beam. As can
be seen in Fig. 2, an electric gage was located between the two plugs forming
the top gage lineo When estimating the ultimate strain, both the strain
measured with the Whittemore gage and that measured with the electric gage
were extrapolated, and the value thought to be more reliable was choseno
23
Although much cannot be said regarding the distribution of concrete
strain along the depth at midspan from a study of Figo 35, since only a few
gage lines are shown, Fig" 36 does shoW, that roe distribution is in good
agreement wi ththe linear strain distriputiqm ordin.arily assumedo
It is interesting to, note the lar-ge values of the estimated ultimate
concrete straino Usually it is assumed that concrete crushes at a limiting
strain o~ 00004, yet all the estimated ultimate strains are greater than ,this
value 0 The lowest strain is 00005 estimated for beam C-5o Estimated ultimate
strains ~or the other specimens are approximately twice that assumed for ulti
mate flexure theory, the values ranging from 00007 to 000100 Since the top
gage line was located 005 ino from the top edge of the beam, the strains at
the extreme fiber can be expected to be even greater than those presented
here 0 A possible explanation of the large strains is that the loading blocks
which covered practically the entire span confined the concrete vertically
and this confinement increased the crushing strain 0
Figures 37 through 39 show the distribution of concrete strains along
the spano Since the specimens had a width of 4 1/2 ino, whereas the loading
blocks were only 4 ino wide, the outer 1/4-ino layer of concrete that was not
confined vertically by the loading block on both sides of the beam tended to
spall off at loads near ultimateo This spalling-off, of course, prevented the
measuring in some instances of the concrete strain near midspan with the
electric gages 0 Therefore, several of the strain readings presented in the
three figures ,are estimated values obtained in the same manner as previously
mentioned 0 The figures are not intended to give quantitative values of the
24
strains, but instead to show more or less qualitatively the distribution along
the span. ~he estimated. values are believed to be sufficiently accurate for
this purpose.
As would be expected of be~s t.ailing by flexure, there is a con
centration of strain near midspan.. Because' of the limited· number of specimens,
no definite conclusion can be formed concerning the effect of web reinforce
ment. It appears from the figures, however, that there is a tendency for the
addition of web reinforcement to distribute the concentration of strain at
midspan over a larger area, thus reducing the peak strain at midspan.. This
is especially noticeable if beams c-4, C-5, and c-6 are compared. It would
seem logical that web reinforcement should affect the strains in this manner,
for it retarded the development of the inclined cracks, and prevented the
cracks from joining or·almost joining at midspan ..
4.5 Total Elongation of Tensile Reinforcement
In order to obtain information on the internal behavior of deep beams
and the relationship between internal strains and deflections, the total
elongation of the tensile reinforcement was measuredo The total elongation of
the tensile reinforcement i~ given as a function of the load in Figs .. 40 and
41. The top graph in the figures shows the :full measured range of values, and
the lower graph is a plot to a larger scale of the values in the elastic region~
The elongation is equal to the sUm of the strains in the longitudinal reinforce
m-ent.. This fact is verified experimentally in Figs .. 42 and 43 in which the
sum of the measured strains in the longitUdinal reinforcement is plotted
against the measured total elongation up to yield. The sum of the steel strains
was obtained by computing the area under the curve of measured distribution
of strain along tpe span, assuming linear distribution between adjacent gage
sections and zero strain at the centerline of the supports.. The dashed line
in the figures represents the theol'et.,ieal condition that the measured
25
elongation is equal to the sum of the strains in the longitudinal reinforce
mento It can be seen that for the majority of the specimens the experimental
curve is in good agreement with the theoretical dashed curve, which indicates
that both the strains and the total elongations were accurately measured
and that the distribution of strains between gage points is smooth as assumedo
These measurements indicate that an accurate prediction of total elongation can
be made if the strains at a number of points along the length can be predicted
ac cur at ely 0
To determine the relationship~ between the midspan deflections and
the total elongations of the tensile reinforcement, the midspan deflections
are plotted versus the total elongations for beams C-l, C-2, C-3, C-4, C-5, and
c-6 in Figso 44 and 450 In each figure the lower graph shows the full measured
range of values and the upper graph is a plot to a larger scale of the behavior
before yieldingo In the upper graph the curve which best fits the post yield
range is reproduced for direct comparisono
In Figo 44 the plots for be.ams C-l, C-2, and C-3 are given 0 It may
be noted that the midspan deflections are proportional to the total elongations
of the tensile reinforcement for both the elastic and post yield ranges. There
is a slight departure in the elastic range, possibly caused by the gradual
cracking phenomenon, etco, but at yield the points are close to the post yield
curve 0 Note that the s·lopes of all three curves are about equal, indicating
no effect on the deflection--elongation relationship due to web reinforcemento
It may be noted that neither the deflection versus load nor elonga
tion versus load curves are linear (see Figso 14, 15.9 40, and 41), but both
have very pronounced yield pointso If the midspan deflections were due to
any extent to shearing or compressive 'strains in the concrete, or to other
effects which are proportional to load, then the deflection versus elongation
curv·cs -would ha.ve an abrupt change of slope at the yield pointo Since these
26
measured curves appear to be 'linear with a constant slope over the entire
elastic and post yield rangesj it appears that the midspan deflection for beams
C-l, C-2, and C-3 is due practically entirely to the elongation of the tensile
reinforcement 0
In Figo 45 are given the curves of midspan deflection versus elonga
tion of the tensile reinforcement for beams C-47 C-5, and c-6o For these
beams there is a definite break in the slope of the curves at the yield pointo
In each beam the graph, for both the elastic and post yield regions is linear,
but the two segments have different slopes; after yielding the deflections
increase less rapidly with respect to the increase of elongationso The ratios
of the slope in the post yield range to the slope in the elastic range are
about 0.62 for beams c-4 and C-5 and 0084 for beam c-6o It may 'be noticed for
each beam that the projection of the curve for the post yield range does not
pass throug~ the origin; the projections intersect the vertical ~is at 0.03 ino
for beams c-4 and C-5 and 00015 for beam c-6o This behavior is possibly due
to the effect of compressive and shearing strains in the concrete and to
compression of the roller supportso The only explanation which can be offered
for the difference in behavior between beams C-l, C-2, C~3 and c-4, C-5, c-6
is that the concrete strains and roller deformations were more significant
in the latter group, beams C-4, C-5, and C-6, because the yield load is about
50 percent greater than for the first group which have, a smaller steel percentageo
From these measurements it can be concluded that the maximum deflections
can be considered to be due entirely to elongation of the tensile reinforcemento
The yield deflection may be partly due to shearing and compressive strains in
the concrete but the major part is also due to the elongation of the tensile
reinforcement 0 'Web reinforcement appears to have little effect on the
deflectio~-elongation relationship 0
27
v 0 BEHAVIOR OF BEAMS HITH COMPRESSION REINFORCEMENT
501 Test Results and Modes of Failure
Test results and the most significant properties of the two beams
reinforced in both tension and compression are given in Table 60 Also listed
are the test results and properties of beam A-3-2 tested during the previous
yeare Since beams A-3-4 and A-3-5 were tested under different loading con-
ditions, it .seems best to present the data, for comparative purposes J in
tel~s o~ midspan moment instead of total loado The uniform load used in the
test of beam A-3-4 was simulated by 10 jacks at 4 ino J while the load for the
test of beam A-3-5 was comprised of 8 jacks at 4 ino Thus, for a given load,
the moment at midspan. for the systems of 10 and 8 jacks is lA-I and 5W, respec-
tively, where W = total loado When computing yield and ultimate moments only
live load vas considered.
Beam A-3-4 definitely failed by crushing of the concrete above the
support at a bearing stress of 0080 flo The manner of failure of beam A-3-5 c
is not definitely knowno At a load of 17902 kips the specimen suddenly dropped
at midspano Computations show that the average bond stress at the anchorage
at ultLffiate load was equal to 005 f V, and since no special anchorage was pro-
. c
vided for the longitudinal tension steel, it is very likely that the failure
of the specimen occurred at the anchorageo In both cases the beams failed
before their full flexural capacities were developed, as is evident from the
photographs shown in Figo 460 The concrete at top midspan had begun to crush,
but the crushing was not so pronounced as to cause failure of the beams by
compressiono
1~ell developed inclined cracks extending from the inside face of
the supports to the top at midspan formed in both beamso At loads near
ultimaie,the inclined cracks had progressed as high as the level of the com-
pression steel, thus greatly reducing the effective concrete areao
Deflections
In Figo 47 are shown the moment-deflection curves for the two beamso
The data are presented in terms of moment since, as mentioned before, the
number of jacks used in the tests of the two beams were differento The curves
are for the deflection measured at top midspano Drop-offs in load which
occurred while readings were being taken are not showno Also sho'WD. for com
parative purposes is the moment-deflection curve for beam A-3-2 of the previous
A-series testso Although both beam A-3-4and beam A-3-5 failed prematurely they
deflected more than beam A-3-2 which failed by flexureo
503 Steel Strains
Measured strains in the longitudinal tension steel are shown in
Figs 0 48 and 490 The fUJi measured range is given in the top figure, while
the elastic region is shown to a larger scale in the lower figureo Only the
steel strains at three gage sections are presented in the top fi~reo When
se~ecting the three sections the same procedure was used as discussed in the
preceding chaptero Locations of the strain gages are shown in the partial
sketch of the beam accompanying Figo 480
The strains in the longitudinal'tension steel were well into the
work-hardening region at failure 0 The estimated ultimate midspan strains
noted in the figures were obtained by extrapolation of the steel strain
deflection curve for each beame HoweverJ the electric gages on the longi
tudinal reinforcement of beam A-3-5 were destroyed long before the ultimate
deflection was reachedo Therefore, the results of the strains measured on
6-ino gage lengths were plotted against the deflections and extrapolated to
obtain the strain at failureo Since the strain measured over a 6-ino gage
length is an average value, the value of the ultimate 'steel strain listed
for' beam ~-3-5 is perhaps some~hat less than the actual strain occurring at
midspan 0
'--
29
From observation of the elastic region of the load-steel strain
curves it can be noted that the curves for all the gage sections fall within
a narrow envelope and progress nearly parallel to each other as the load
increases 0 This indicates that the strains in the longitudinal tension steel
were nearly constant along the span~ Consequently, it may be said that the
specimens behaved as tied arches rather than beams, the longitudinal rein-
forcement serving as the tieo
Shown in the lower figure is a theoretical curve for the steel
strain at midspano The curve was obtained by dividing the moment at midspan
by the effective internal lever arm of an assumed fully cracked section, jd,
and converting the resulting tension force to straino It can be seen that
the measured strains at midspan agree fairly well with the computed valueso
The deviation of the ,strains from the theoretical curves at low loads is due
to the specimen not being fully cracked as assumed when computing the effective
internal lever arm a
504 Concrete Strains
The concrete strains at midspan varied linearly along the depth of
the beam as shown in Figo 500 It was not possible to present the strain dis-
tributions at bigh loads, for cracking had extended as high as the second
gage line eliminating further measurementso
The value of the concrete strain over the top gage line at failure
was estimated by extrapolation of the concrete strain-deflection curves o For
beams A-3-4 and A-3-5 the estimated concrete strains at failure were of the
order of 00009 and 00007, respectivelyo The strains at the extreme fiber
could be expected, then, to be even greater, since the top gage line was
located 005 ino from the top edge of the specimens~ Because the two beams
faile~ prematurely, the value of the concrete strain at midspan at failure
~
of the beams by flexure is not known, although the strain would be much
greater than the value of 0.004 normally assumed for shallow beams failing
by compression.
The variation of the concrete strains along the top edge of the
specimens is shown in rig. 51. As can be seen from the distribution of
strains for beam A-3-4, there is a great concentration of strain at midspan&
The distribution of concrete strains for beam A-3-5 is similar to that of
beam A-3-4 up to a load of 130 kips. Upon applying another lo~d increment,
the gage at midspan was destroyed. Unfortunately, it was impossible to
estimate the strain beyond this load. However, it seems logical that the
strain distribution at higher loads would be similar to ,the distributions at
lower loads and to that of beam A-3-4.
31
VIo STUDIES OF THE FLEXUHAL STRENGTH AND BEHA,VIOR OF DEEP BEAMS HITH
WEB REINFORCEMENT AND WITH COMPRESSION REINFORCEMENT
601 Ef~ect of Web Reinforcement Upon External Behavior
Yield Moment~ Listed in Table 7, Column (4), are the yield moments
computed from the test yield loads J and. in COJ.l1.:ml (5) are listed the ratios
of the yield moments of the beams with web reinforcement to the yield moment
of their companion specimen withol1t we"b steely M 1M " Beam C-l is the yw ywo
companion specimen of beams C-2 and C~ 3J and beam c-4 is the companion. speci-
men of beams C-5 and C-6., The maximum deviation in yield m.oments :Lg, only
7 percent, and therefore it c,an be concluded that the addition of web rein~
forcement had no effect upon the yield strength of the specimenso
Ultimate Moment ~ The effect of web reinforcement upon ultimate
moment can be studied in the same manner as for the moment at yielding of
the beamo Ultimate moments computed from the ultimate test loads are given
in Column (6), and the ratios of the ultlmate moments of the beams with web
reini'orcement to the ultimate moment of their compa.:o.ion specimen are listed,
in Column (7) of Table 7. The ultimate moment was' increased by reinforcing
the web, the greatest increase in load-carrying capacity occurring ~or beams
It has been noted previol~ly tbatthe ~ddition of web reinforcement
retarded the development of the inclined crackso Since the inclined cracks
cause concentrated concrete strains at midspan, any retard~tion of the cI'acks
allows the steel strains to reach a higher value before the lJJmiting concrete
strain is attainedo If the steel strain, is in the work-hardening region, any
increase in strain will produce a greater tensile force resulting in a greater
resisting momento
32
In Fig. 52 are shown the strain distributions along the entire depth of
the beam near midspan at loads near ultimate for beam C -4, which had no web
reinforcement, and for beam c-6, 'which had inclined web reinforcemento The strain
distribution for beam c-4 is non-linear. A non-linear strain distribution at
midspan is always obtained for deep beams without web reinforcement, for loads
greater than the transition cracking load, for the following reason. In such
beams extensive diagonal cracks develop and run from the bottom edge near each
support almost to the top edge near midspan. Because of these cracks the
strains in the tensile reinforcement are roughly constant from support to support.
This typical behavior has been likened to that of a tied arch or a beam with
reinforcement which is not bonded to the concrete between supportso The strain
in the reinforcement at every cross section is roughly equal to the separation
of the supports divided by the distance between supportso It is meaningless to
compute curvature at a section from the tensile reinforcement strains because
the extensive cracking has invalidated the assumption of continuity of member
upon which such a computation would be based. In contrast, the compressive
concrete strains are highly concentrated at midspan. The distribution of com-
pressive concrete strains through the depth to the neutral axis is roughly I
linear. The curvature' at a section can be computed from the distribution of
concrete strains. However, because of the concentrated nature of the concrete
strains at midspan and the distributed nature of the steel strains} for any
given deflection the curvature indicated by the distribution of concrete strains
will always exceed the "apparent curvature" computed by dividing the steel strain
by the distance to the neutral axis 0 In other words) the strain distribution
through the depth is non-linear, as shown~
The strain distribution through the depth is linear for beam c-6o This
linear distribution, which is typicaJ. of true flexural behavior, was obtained in
this beam because of the web reinforcement) as discussed fully in Section 4.3.
'..,.
33
The type of strain distribution" non-linear as in beam c-4 or linear
as in berun c-6" may affect the ultimate moment, because when the limiting
concrete strain is reached the steel strain for deep beams with linear distribu
tions will be greater than for similar deep beams with tJ~ical non-linear
distributions. Due to instrumentation difficulties at loads near ultimate, it
",as impossible to obtain strain distributions along the entire depth of the
beam for other C-series specimens. However" it seems that the addition of web
reinforcement would affect the strain distributions of the other beams in the
same manner as noted in Fig. 52.
Since the steel strain at midspan for beam C -1 which had no web
reinforcement "las wi thin the work-hardening region at failure" the increased
strain in beams C-2 and C-3 caused by the inclusion of web reinforcement
increased the longitudinal tensiJ.e force and resulted in greater load-carrying
capacities for these beams. The longitudinal steel of beam c-4 was not strain
hardened at failure , although the ultimate steel strain was close to the work
hardening region. . The ultimate strengths of beams C-5 and c-6 1.;rere not
appreciably greater than their companion specimen, be&~ c-4, because the
increased steel strains did not result in increased steel stresses.
Ductility and Energy-Absorbing Capacity: Ductility is an important
property of beams subjected to blast loads. It is defined as the ratio of
ul timate deflection to yield deflection and is sh01·m in Column (8) of Table 7.
The values range from 402 to 17.1. Beam C-7 ,.;rhich had the longitudinal tension
steel distributed along the depth vTas the least ductile" vThile the three beams
having a longitudinal steel percentage of 1.15 exhibited t.he greatest ductility.
In all cases" I{eh reinforcement increased the ductility of the members 0 vleb
reinforcement in the form of inclined bars increased the ductility considerablY
more than vertical stirrups.
Listed in Column (9) of Table 7 are values of the energy-absorbing
ca.paci ty. The values were determined by a.pproximating the load~deflectio:n
curves by two straight lines, one from the origin to yield load and deflection,
and the other from yield load and deflection. to ultimate load and deflec.tioll.!l
and then computing the area under the approximated curve multiplied by a
factor depending upon the loading condi,tiollo Beam c-6 which had inclined web
reinforcement e.xhibi ted the greatest energy-absorbitl.g capacity.!l while beam C-7
exhibi ted the least v The addi tioD. of web rei.r .... :forcement increased the energy
absorbing capa.city of' the beam in every case, aithough the increase was very
sma.l1. for the specimens with 1.15 percent longi t,udinal steelo
602 Effect of' Compression Reinforcement Upon External Behavior
In order to determine the effect of compression reinforcement upon
the e~terna1 behavior of the beams) the test data of beam A-3-2 obtained from
the previous series of' tests (1) are presented along with the data for beruns
A-3-4 and A-3""5o
Yield 1vbrnent~ VeJ.ues of t,he ratios of' the yield moments of the
beams with compression reinforcemen.t to ·the yield moment of the companion
specimen w2thout compression steel are presented in Column (5) of Table 70
It can be seen that there ius a marked increase in the yield· moments of
beams A-3-4 and A-3-5~ The increase is believed t.o be due mostly to the
variation in the yield stress of the tension reinforcement. The yield stresses
of the steel used "in beams A-3-4 and A~3""5 were 9 and 1,3 percent, respectively.,
greater than the yiel,d stress of the tension steel. of beam A-3-2o It appears.,
theref'ore~ that compression. reinforcement had little} if any) effect upon the
yield moment.
Ultirnat·e M:>ment~ A comparison of moments at failure for the three
beams is of only limited value since beams A-3-2) A-3-4., and A-3~5 faiJ.ed by
.35
flexure ~ bearing, and anchorage J respecti.vely 0 However, the ratios of uJ..t·iTn.at.e
moments of the two beams with compression reinforcement to the ultimate mement.
of beam A-3-2, listed in Column (7) of Table 7, are of some interest in that
they show that even though the two beams reinforced in both tension and com
pression failed prematurely:; the moments at failure ~lere greater t,haD. that
causing the flexure failure of beam. A~3-2o It seems, therefore, that the
flexural. strength of beams with a Lid ratio of 2032 may be increased consider,~
ably by the addition of compression steel if t.hey are proportioned so as t.o
prevent them from failing by other modes before their full flexural capaci ti.es
are developed.
Ductility and Energy-Absorbing Capacity~ Because of the different
modes of failure of the three beams, no direct comparison,s caY). be made to
determine the effect of compression reinforcement upon ductility and energy~
absorbing capacityo Nevertheless, the values of ductility are listed in
Colum..'YJ. (8) of Tallle 7. It can be seen that the ductil.i ties of the two spec.i
mens reinforced in both tension and compression are almost as great as t.hat for
beam A-3-2 which was reinforced in tension oIlly and fail.ed by flexure.., The
deflections at yield of beams A-3-4 and A-3-5 were somewhat greater than the
yield deflection of beam A-3-2" ca;lsi.ng the lower values of ductili tyo
The energy-absorbing capacities of the three beams are li.sted i.n
Column (9) of Table 70 It can be seen that, even though beams A-3 .... l.j. and A-)-5
failed prematurely J the en.ergy,~absorbi.ng capacities of these two speclJ]lens
were greater than that for beam A-3-2o
603 Prediction of External Behavior
l-bment at Yielding~ In Table 8 are listed the values of computed
moments a.t first yielding of the tension reinforcement 0 The m.oments for the
seven C-series beams were computed by the convent.ional stra.ight~line theory.,
The strain and stress di.stributions axe assuriled to be as sho'wn in Fig 0 ~:;3{ a) 0
For the two beams reinforced in both tension and compression, the moment at
first yielding was computed by consideration of the strain and stress relation-
ships shown in Fig. 53(b). A summary of the theoretical expressions for the
moment at yielding is given in Appendix A of Part 3 of this final reporto
Shown in Table 8 are the yield moments determined from the test
loads at yielding of the specimens in Column (2), the computed yield moments
in Column (3), ~d the ratios of the test yield moments to the computed yield
moments in Column (4). The ratios are all greater than 1000, rangi.ng from
1004 to 1.l4. It should be remembered that the test yield loads were de-
termined by the intersection of the primary and secondary slopes of the load-I
deflection curves. In general, this method of determining the yield load
over-estimates slightly the actual loeA at which the longitudinal reinforcement
yields. Although the ratios of the test yield-moments to the computed yield
moments are all greater than one, the computed moments at first yielding are
in good agreement with the actual moments at flexural yielding of the specimens 0
Ultimate MJment: It isknovro. that the ultimate moment of shallow
reinforced concrete beams failing by compression at midspan after yielding of
the longitudinal tension reinforc~ment can be predicted with reasonable accuracy
by consideration of the strain and stress distributions shown in Fig. 54(a) for
beams reinforced in tension only and in Fig. 54(b) for beams reinforced in both
tension and compressiono A summary of the theoretical. expressions for ultimate
moment is given in Appendix A of Pru:t 3 of this final. report.
In view of the fact that at the- present time there is no available
theory to predict the ultimate strength of deep reinforced concrete members,
the procedure for beams of normal proportions was applied in an attempt to
predict the ultimate moments of the test specimens 0 The theoretical ultimate
moments, ¥~, the ultimate test moments computed from the test loads, and the
ratios of the test moments at failure t.o the theoretical moments are listed i.n
37 Table 8. :.:1; can be seen that the actual moments were great.er in every c.aJ38,~
the ratios ranging from 1001 to 10390 It is interest.ing to note that al thoi~gh
the two beams reinforced in both tension and compression failed prematurely" the
flexural moments at failure were greater than the predj,cted values Q
It appears that the ultimate strength theory for shall.ow beams under~
estimates the strength of the test specimens" and especially the ultimate
strength of the beams with web rei,nforcement in which the longitudinal t.ens:i,on
steel had strain-hardened pri.or to failure ~ However., ,,(·rhen comput.ing the
theoretical moments, the strain at which the concrete crushes) ~ J was assumed u
to be 00004 ino/in. As was pointed out in Chapter DJ" the estiraated concrete
strains at failure of the C-series specimens were of the order of 00007 to
00010 in./in. If an average value of 00008 is assumed for the limit,ing con~
crete strain) and the ultimate flexural moments of the C-series beams are
computed using this value) the moments, Mr, listed in Colunm (8) of Table 8
are obtained 0 In Column (9) are given the ratios of the actual. moments at
failure to the theoretical moments 0 The ratios range between 0098 and 1 n 20 J
indicating that the theoretical moments computed by assruning E = 0,,008 are 11
in much better agreement with the test results than the theoreti.cal momeut.s
obtained under the assumption that € = 00004. 1.1
The assumption that the concrete crushes at a liwiting strAin of
00008 in./in. affects) of cO'I.:trse;J the critical value of the reinforcing index)
~) corresponding to €s = eo' used to determine whether the steel strai,n at
failure vrill be in the yield or vlark-hardening regiono By assuming € = 00004 , 11
when computing %) only the q v~ues for the beams reinforced 1·li,t.h 1015 percent
longi t.udinal steel indicated that the st.eel Foulct be strain~bardened at faj_lure)
as can. be seen in Table 90 However) the load-steel strain curves presented :Ln
Chapter IV 'sho'w that the longitudinal steel strains at midspan reached the
work,;.;'hardening region prior to failure in all the specimens except beam c-4o
For this beam the steel strain vras very close to the '\·rork-hardening region
when the specimen failed. The comparison in Table 9 between q and the value of
% obtained by assuming Cu = 00008 indicates that the strain at midspan in the
longitudinal reinforcement of all the specimens should enter the work-hardening
region. This appears to agree more closely with the test results.
Due to the limited number of specimens, no definite conclusions can
be drawn regarding the value of the limiting strain at which the concrete
crushes 0 The value of 0.004 usually assumed for .the ultimate strength theory
of shallow beams does not, however, agree with test results. Possibly a
larger limiting concrete strain should be assumed, as above, for beams tested
under uniform loads that confine the top surface of the beam.
Deflections: There are insufficient data from this series of tests
to. develop formulas for the prediction of the yield and ultimate deflections.
A comprehensive study of the calculation of deflections is 'given in Part 3
of tgis final report. However, the following qualitative inferences can be
dra.wno
(l) Web reinforcement does not affect appreciably the yield
deflection.
(2) . Web reinforcement has two somewhat counterbalancing effects
on the deflection at maximum lqad, as follows:
(a) Web reinforcement, by reducing the concentration of concrete strain at midspan, increases the steel strain at midspan at failure; this effect tends to increase the deflection at maximum load.
(b) Web reinforcement changes the distribution of internal stresses and strains in the beam and tends to restore beam. action and to reduce arch action 0 A deep beam wi thout web reinforcement behaves at ultimate as i.f the steel is anchqred only at the ends and isunbonded between ends. A deep beam with web reinforcement acts more like a normal bonded beam. This partial restoration of beam behavior tends to decrease the ultimate deflections.
The net result of these two effects in the case of beams C-l,
C-2, and C-3, with P = lo15 percent, was to produce essentially
39
no change in the deflections at maximum load, while in the
case of beams c-4 and C~5., with p = 1099 percent, the deflection
at max~um load was increased by web reinforcement. The ultimate
deflection of beam c~6 was greatly increased owing to another
effect discussed previously.
40
VIIo SUMMARY AND CONCLUSIONS
7 I> 1 Sumrna.:r:y
Nine rectangular reinforced concrete deep beams were tested under
uniform load on a simple span of 36 ino Two of the beams (A-series specimens)
were reinforced in both tension and compression 'an.d had a span-depth ratio of
20320 The other seven beams (C-series specimens) wer,e tested,' to investigate
the effect of web reinforcemento Two of the seven beams had different percentages
of longitudinal tension, steel and no web 'reinforcemento Then two varia.tions of
each of the two beams were made by adding vertical stirrups and inclined barso
The last beam had the longitudinal reinforcement distributed along the deptho
Since the depth to the centroid of the bottom layer'of the longitudinal steel
was kept constant'at 12 ino for the seven C-series specimens, the span-depth
ratios ranged from 3000 to 30320
The deflections at top and, bottom at midspan, the strains in the
longitudinal tension steelJ and the concrete strains along the depth of the
beam at 'midspan and a.long the top edge of the beam were measured for all nine
specimens 0 For beams that were reinforced with multiple layers of longitudinal
tension steel~ the strains were measured in one bar of each layero In addition,
the deflections at various positions along the span and the total elongation
of the tensile reinforcement were deter.minedo Strains in the web reinforcement
of three of the C-series s~ecimens were also measuredo
The two beams reinforced in both tension and compression failed before
their maximum flexural capacities were developedo One beam failed in bearing, '
and the other one failed at the anchorageo In both beams, inclined cracks
extending ~rom the inside face of the supports to midspan at the level of the
compression reinforcement formed, greatly reducing the effective concrete area
and causing the beams to behave as tied archeso
41
All the C-series spec~ens failed in flexure by first yielding of
the longitudinal reinforcement followed by crushing of the concrete at midspano
In the two beams without web reinforcement and the beam with the longitudinal
steel distributed along the depth, inclined cracks developed and extended very
near to the top edge of the specimens at midspano The presence of vertical
stirrups retarded the development of the inclined cracks and forced them to
progress more verticallyo Inclined -web reinforcement confined the major cracks
to \vithin the middle portion of the spano The inclined web reinforcement seemed
to be most effective in reducing the· extent of the diagonal cracking and the
influence of this cracking on the distribution of strains in the tension rein
forcemento
The concrete strains along the depth of the beam at midspan varied
linearly in all nine beams 0 A great concentration of concrete strain occurred
at midspan in the beams reinforced in both,tension and compreSSion and in the'
beams without web reinforcemento The' addition of web reinforcement appeared
to distribute the concrete strains more uniformly over a larger area near
midspan 0 The average estimated midspan concrete strain at failure was 00'008
iUo/ino,twice that usually assumed for the strain at which concrete crushes 0
This larger value of the strain is believed to be due to the vertical confine~
ment of the top surface of the specimen by the uniform loado
702 Conclusions
The following conclusions may be drawn from the results of the tests
described hereino These conclusions are of course limited by the fact that
only a very small range o~ each variable was investigatedo In particular,
only one span/depth ratio, 2032, was considered for beams reinforced in both
tension and compressiono The span/depth ratio for the C-series specimens
varied only between 3000 and 3.320
42
1. Neither the compression nor the web reinforcement had any
effect upon the yield'stre~gth or corresponding yield de=
flection of the membero
20 Compression reinforcement appeared to increase the ultimate
flexural strength of deep beams, although how much so cannot be
determined because the two beams tested failed prematurelyo
3. Web reinforcement had two major effects on the internal strain
distributions at failure in the deep beams testedo First, the
concentration of compressive strain in the concrete at midspan
w~s reduced; for this reason the strains in the tensile reinforce
ment at midspan at failure were increased. Secondly, normal
flexural a.ctibn was partially restored and the typical arch
action of deep beams without web reinforcement was reducedo In
deep beams without web reinfoxcement the straln distributions in
the beams at failure are like those which would exist if the
tensile reinforcement were anchored at the ends and 1J.u.bonded
between endsc With sufficient web reinforcement the strain distribu
tions are more like those of a norma~ beam.
4. Web reinforcement.~ by increasing the strain in the tensile rei.n
forcement at midspan at failure, increased the ultimate strength
of the beams which failed when the strain in the ten.sile reinforce~
ment was in the strain-hardening range, but it did not affect the
ultimate strength of the beamS which failed when the strain in
the tensile reinforcement was in the yield rangeo
5.. The defl.ections at maximum loa.d of beams C-2 and C .... 3, with l.l5
percent tensile reinforcement, were not apprec.iabl.y affected by
the web reinforcemento The two effects of web reinforcement on
the internal strains at maximum load approximately counterbaJ..anc.ed
each other insofar as the deflections of these beams were concernedo
However., the midspan deflection at maximum load for beam C ~ 5 , with
1099 percent reinforcement, was substantially greater than for
the companion beam without web reinforcement 0
6. The midspan deflection of beam c-6, which had inclined web rein
forcement formed by bending up the top layer of tensile reinforcement
bars" had a greatly increased maximum value over that of beam c-4
due primarily to the very large strains developed in the tensile
reinforcement in the region between the ends and the bend-up point.
This design appears to be very advantageous for blast-resistant
construction as it gives both high strength and great ductility
and energy-absorbing capacity 0
7 . Ductility and energy-absorbing capacity of the beams were increased
by the addition of web reinforcement and decreased by distributing
the longitudinal reinforcement along the depth. The increase in
ductili ty and energy-absorbing capacity was very small for the
beams reinforced with 1.15 percent longitudinal tension steel
but was considerable for the beams reinforced with 1099 percent
longitudinal steel.
80 The moment at flexural yielding can be predicted with reasonable
accuracy by the usual straight-line theory for beams reinforced
in both tension and compression and for beams with web reinforce
mento
9. The ultimate strength theory for shallow beams under-estimates
the maximum flexural capacity of the members when the value of
?o004 ino/in. is assumed for the crushing strain of the concreteo
When the average test value of 00008 ino/inc is used for the
lind ting concrete strain, along with the ultimate strength theory
44
tor beams of normal prop~rtio~s, the predicted values of ultimate
flexural capacity agree very well with the test results of the
C-series specimens except for' the two beams with web reinforcement
whoa~longitudinal tension steel wa.s greatly stra.in-hardened prior . .'
to fa.ilureo BecaUBe of the premature failure of the two A-series
specimens p no conclusion can be formed regarding the agreement
between predicted and test values of the ultimate flexural capa-
city of beams reinforced in both tension and compressiono
VIII & BIBLIOGRAPHY
1. Austin, W. J., Untrauer, R. E., Egger, W., and Winemiller, J. R., "An Investigation of the Behavior of Deep Members of Reinforced Concrete and Steel ll
" Technical Report to Air' Force Sp'ecial Weapons Center, AFSWC-TR-59-18, 1960
2. Sozen, M. A., "Strength in Shear of Prestressed Concrete Beams Without Web Reinforcement", Ph. D. Thesis, University of Illinois, August 1957 •. Issued as a part of the Sixth Progress Report of the Investigation of Prestressed Concrete for Highway Bridges, Civil'Engineering Studies, Structural Research Series No. 139, August 1957.
3. Gaston, J. R., Siess; C. P., and Ne'WInark, N. M., nAn Investigation of the Load-Deformation Characteristics of Reinforced Concrete Beams up to the Point of Failuren
, Civil Engineering Studies, Structural Research Series No. 40, University of Illiriois, December 1952e
4. Laupa, A., Siess, C. P., and !fe'WInark, N. M., "Strength in Shear of Reinforced Concrete Beams 11 , University of Illinois Engineering Experiment Station Bulletin No. 428, March 1955.
Beam d d' Mark . in. . in .
A-3-4 15.5 ;14.125 ,:
A"'3-5 15. ~ ;14.125 1
TABLE 1 FROPERTIES OF A-SERIES SPECIMENs
. Lid
2·32
2·32
. b' = 4 in.; L = 36 in.
f' c psi
4860
5550
r" I
Tension Reinforcement No. & P f Size y
ksi
2-#5 0.0100 56.13
2- #5 0.0100 58.06
Compression Reinforcement Noo & p' f' Size y
1- 1/=5 0.0050 56.13
2- #5 0.0100 58.06
~: ..
8\
:f
TABIZ 2 PBOPZRr:r&<J OF C-.9R I IS SPBCDID8
b a 4 1/2, in.i L a 36 In.
Tension Re1nf'orcellent Web ReinrorceMnt
Be_ d t' 1'0. &. t .0. & f e P l'
Mark in. ,Lid psi " Size ka! Type Size ,-
C-l 12.00 ,.00 ,2910 2- #5 0.0115 --'.55, !fODe
0-2 12.00 3.00 '250 ,2- #5 0.0115 4'.'55 lr,ertleal 6-#3 54·54 Stirrups
C-3 12.00 }.oo 3520 2-#5 0.0115 ~3,·55 Inclined 4- #4 116.50 Bars '
C-4 11·'9- 3.16 3690 2-$4 0.0199 ltB.OO ' 2- 5 43.87 Bone
, C-5 1l·39 ,.16, 3060 2 -#4 0.0199 48.00 Vertical 6-13 54.54 2 - 5 43.87 Stirrups
c-6 1l·39 3.16 3530 2-$4 lJ6.50 Inclined ~-14 46.50 2 - 5 ' 0.0199 43.87 Bar.
C-7 lO.82 '·32 ,1 lao 2-$4 0.0209 ~.OO None 2- 5 45.16
~
TABLE 3 PROPERTIES OF THE REINFORCING STEEL
.:Beam Tension Reinforcement Compression Reinforcement
f-1ark f E € f t € • € I Y Y 0 Y Y 0
k~~.~ _____ i~.Lin--"--_ in./~n. ksi in .. /il1 . in.j!n.
A-Series Specimens
A-3-4 56.13 0.0018 0.0108 56.13 0.0018 0.0108
A-3-5 58.06 0.0022 0.0071 58.06 0.0022 0.0071
Beam Mark
C-1
C-2
C-3
c:-4
C-5
c-6
C-1
Tension Reinforcement Web Reinforcement
f € E f € € Y Y 0 Y Y 0
ksi in.jin. in.jin. ksi in.jin. in.jin.
C-Series Specimens
43.55 0.0015 0.0152
1~3· 55 0.0015 0.0152 54.54 0.0018 0.0166
43·55 0.0015 0.0152 46.50 0.0016 0.0169
(#4)48.00 0.0015 0.0137 (lf 5)43·81 0.0017 0.0143
(~L4) 48 .00 0.0015 0.0137 54.54 0.0018 0.0165 (#5)43.81 0.0017 0.0143
(#4)46.50 0.0016 0.0169 46.50 0.0016 0.0169 (115) 43 .81 0.0017 0.0143
(#4) 4B .00 0.0015 0.0137 (#5)45.16 0.0014 0.0130
if,
t'~:
TABLE 4 EROPh!RTIES OF THE CONCRETE MIXES
I·
Beam Grave1:Cement:Sand W/C Ratio S1map Comp. str. Mod. ot Rupt. Age at Test .- Mark by Weight by Weight in. psi psi days
A-8eries SR!c1Mns
A-3-4 3·53:1.00:3.26 0.68· 1/2 It860 JKi5 12
A-3-5 3·56:1.00:3·29 ·0.62 1/4 5550 570 12
C-8eries Specmena
C-1 4.52:1.00:4.22 0.81 1/2 2970 430 21
C-2 4.51:1.00:4.22 0.82 1/2 3250 470 11
C-3 4.51:1.00:4.22 0.84 3/4 3520 365 15 C-4 4.52:1.00:4.13 0.85 3/4 3690 415 17 C-5 4.50:1.00:4.20 0.86 1 3060 330 11
c-6 4·51:1.00:4.16 0.84 1/2 3530 390 22
C-1 4.50:1.00:4.18 0.89 1 3140 410 15
$
'(g
TABLE 5 ~T RESULTS OF C-SERIES SPECIMENS
Yield Ultimate Yield Ultimate Beam Web wad Load 'Deflection Deflection Mode of Mark f' f p Reinforcement W W D. ~ Failure c y y u y u
psi ksi % kips kips. in. in.
C-I 2970 43·6 1.15 None 64.5 16.2 0.060 0.875 Flexure
C-2 3250 43~6 1.15 Vertical 61.0 89·5 0.056 0.828 Flexure Stirrups
C-3 3520 43·6 1.15 Diagonal 60.0 94.5 0.048 0.823 Flexure Bars
c-4 3690 46.0 '1·99 None 99·5 102.0 0.081 0.412 Flexure
C-5 )060 46.0 1·99 Vertical 93.8 106.0 0.091 0.512 Flexure Stirrups
c-6 3530 45.2 1.99 Diagonal 98.2 102.6 0.078 0·128 Flexure Bars
C-1 3140 46.6 2.09 None 90.6 95·9 0.084 0·352 Flexure
I . , "
i .. !
TABLE 6 TEST EESULTS OF A-BERIES SPECIMENS
Yield Ultimate Yield Ultimate Beam Moment Mcaent Deflection nefiection Mode of Mark t' f P r t p' M M 6 /)., Failure c y. y l' u y u
psi kai 1i kai ~ In.-kips in.-kips in. in.
A-3~4 4860 56.1 1.00 56.1 0.50 552 145 0.080 0.608 Bearing
A-3-5 5550 58.1 1.00 58.1 1.00 565 896 0.095 o.~ Anchorage
A-3-2* 5610 51.4 1.00 0 480 659 0.064- 0.570 Flexure
* Data obtained from previous A-series teats.
~
TABLE 1 COMPARATIVE TEST RESULTS
(1) ( 2) ( 3) ( 4) ( 5) ( 6) (1)
Beam f' f M M M M Mark
c y y J:::!..-. u uw M M
psi ksi In.-kips ywo In.-kips uwo
C-Series Specimens
C-l 2970 43·6 322 381 C-2 3250 43·6 305 0·95 448 1.11
C-3 3520 43·6 300 0·93 472 1.24
c-4 3690 46.0 498 510
C-5 :;060 46.0 469 0·94 530 1.04
c-6 3530 45.2 491 0.98 513 1.01
C-7 3140 46.6 453 480
A-Series Specimens
A-3-4 4860 56.1 552 1.15 - 745 1.13
A-3-5 5550 58.1 565 1.10 896 1.36
A-3-2* 5610 51.4 480 659
-)(. Data. obtained. from previous A-series tests.
L. , L
(8)
Ductility
1:1 /6 u y
14.6 14.8
11·1 4·7 5.6
9·3 4.2
1.6 8.8
8·9
l'
(9) Energy-
Absorbing Capacity in.-klps
32·9 33·2 34.0 20.6
25·7
31·9 16.0
45.5 63.5
37·9
\J1 I'\)
[ _ . L '~J
TABLE 8 COMPARISON OF MEASURED AND COMruTED MOMENTS
( 1) ( 2) (3) * ( 4) ( 5) (6)* (7) (8)* Beam Test Compo Test M Test ~>1f Test M ~.i'
Mark M M l M u f
y y Compo M u (€ =0.004) Mf
(€ =0.008) y u u
in.-kips in.-kips in.-kips in.-kips in.-kips
C-Series S~cimens
C-1 322 284 1.13 -381 328 1.16 381
C-2 305 285 1.07 448 332 1·35 387
C-3 300 286 1.05 472 339 1·39 394
c-4 498 451 1.10 510 472 1.08 521
C-5 469 450 1.04 530 465 1.14 497
c-6 491 445 1.10 513 465 1.10 504
C-7 453 434 1.04 480 441 1.07 483
A-Series Specimens
A-3-4 552 486 1.14 145 600 1.24
A-3-5 565 508 1.11 896 831 1.08
* A summary of the theoretical expressions for the computation of the values of M , Mf , and Mf is given in Appendix A of Part 30f this final report. Y
(9) Test M
u '"""M'
f
1.00
1.16
1.20
0·98
1.06
1.02
0·99
\J1 Vl
54
TABLE 9 PREDICTION OF STEEL STRAINS AT FAILURE
Beam Mark
C-1
C-2
C-3
c-4
C-5
c-6
C-7
q
0.169'
0.154
0.142
0.246
0.296
0.253
0·309
~ (€ =0.004)
U
0.220
0.210
0.205
0.217
0.233
0.215
0.243
Expected Strain Range
W.H.*
W.H.
W.H.
Yield
Yield
Yield
Yield
0·364
0·348
0·339
0.354
0.380
0.353
0·393
* W.R. indicates vork-hardening region.
q = Pfy
f' c
'1a= klk3€U € + €
U 0
Expected Measured Strain Strain Range Range
W.H. W.H.
W.H. W.H.
r;.H. H.H.
W.H. Yield
W.H. W.H.
W.H. W.H.
W.H. \Ol.H.
...,-
I: \0
~ "" ~
~{1- No. 5 ?-"'4~ 2- No. 5 A- 3-5
I
, 2- No. ", -.
5
W//~ I
I'
4"
M •
I 4 at 6" :II 24"
42"
l/8"-round ties at 4"
. T
I ,t(h V~
• I ' 6" ~ I I ,..
I 3/4" Cl. ',/4" Cl.
Beam A-~4 Bed A- 3-5
FIG. 1 A-SlRIES TEST SPECIM!l(S
55
t t
,
I: (\J
,~ lI'\ M
~ ___ .. _ .. ___ .. _. __ .. 4 at 911 .= .. ;!6" .. ,_ ...... ' ._., . .. -1
6" 4 at 3" = 12" 611
L...... .____._ ....-. - .•. -"-- -.J
.~ -....... r-I
I cD I 0 1- ..
I I
"r,........-..:~~~IIo.L-~""""="'-.~g~. -=T=----=-=l _____ O~_ :.-. -:::::7"-:-.---~O ldj I , i
(0. _: __ : .~ I ~ I :... ... - 4 at 111= 4 It ! ,-{: 211~ 1;_
I "",' ,-{
·-t --p._. L ----------~ o
1_. ~f--__ ------- .-.. --.---.-
__ SR-4 strain gage () Deflection dial .. Whittemore gage point
FIG. 2(a) NOMINAL Dr{EN~~ION3 OF C-SERIES SPECIMENS AND LOCATION OF CONCRETE STRAIN GAGES AriD DEFLECTION DI."i.L3
-_._-------l i
r
~ , I i I I
" ~ , •
I I I i I
I s
Ii ~ j 1 ! i I I
3/4" Cl. f'4" CL 1
l .. J,1 I I
1 2- No. 5 / I I
......
,j a
I o SR-4 strain gage I
Beam C-l
FIG. 2(b) PLACE~··1E~T OF REI~RCEI'-1..]1TT AND LOCATION I .... _____________ O_F_3::~, GAGE3: B~:~_.~
+- t/7"""""/1/' ~~/ /-::'1 "j' .. / " /. / '
4 at 611 = 2411
: (\J .....
-
I
... i--
. .... t> ,...
.l
--r-NO. :3 Stirrups
~
z: r-f
2- Bo. 5
" 4 "
...
.~ ,;.
o SR-4 strain -gage
5" -5" 4"
.
I - .
--:
--
4 at 6" 1111: 24"
Beam C-2
2- 110.
6" 6" A
4 at 6" lilt 24"
:se_ C~,
4" I
~ t2~ J~o .• -5
~ffR
nG. :3 PLACIMDT OP REIN10RCEMDT AND -IJ)CATION OJ' STBL STRAIN GAGE& BUMS 0-2 AID 0.,
5'"(
1" Cl.
Sict"lOa~;
.I.~ - A'.
4" C
//<;: 'i~';J .'//, ',!
. r-i o
r-i
I
! i ./2-i
"'" - -I 2- No.- 5/ !
..... I
! --;---_ ....... __ .
1 !
J 4 at 6" = 2411 : h-.------.... ........ - ..... :Jooo-I
Beam c-4
I
No. 4 I
[7'-' .-
~
NO.3', stirrups I
L 2- No. 41 __ --~~~~~--~~~-----' 2- No.
I 4 at 6" = 24" ~.--.-.- .. -.... ,... ............ ..
o SR-4 strain gage
Beam C- 5
FIG. 4 PLACEMENT 'OF REINFORCEMENT AND LOCATION OF STEEL STRAIN GAGES: BEAMS c .. ~ Ann C .. 5
n ! ! I 1 I ; I
~l"
I t I i . I
I ~ I
I •
f
Cl. I
i ~
! J
Cl.
i;
. ,....f o
C\I
'"
2- No.5.
6" 6" .'
Beam c-6
I
I ,,1- No. 4 '. I 1
'. , 2'; No. '5.,..,.,.. I
V//~ J t)////h
4. at 6" = 24" -o SR-4 strain gage
Beam C-7
YIG. 5 PLACEMENT OJ! REINFORCEMENT AND LOCATION OF MDL STRAIN GAGES: BEAMS e-G AND 0 .. 7
Section A-A
Cl.
2 1/4"
• I • t • •
,80
60 OM
0'.1 ..!>4
... I1l CJ}
OJ H
+> 40 rn +' oM ~
:::>
20
o
~ .
IV ~
1/: I I ; I
i I ! I
i
i I ; I I
I
/ ! I ! I
/ V o o
! ! i
:
:
\
I
I i ! I I i i
.1
I I
i
! ,
! J
i , I
! !
, I , ;
I
i 0.4 8
-----
:
-
i I
I I
I
i 0.8 16
I
I I
I I
"
Unit Strain, percent
""'" '\
1.2 24
FIG. 6 TYPICAL STRESS-STRAIN CURVE FOR THE REINFORCING STEEL
I . '
-
I I
-
1.6 32
-
3'
1/4"
Moving Head of Testing MaChine
Test Specimen
Bed of Testing ~h1ne
mOWF'9
Roller
4"x .3 1/8" x 2" Loading
Block
Hydraulic Pump
FIG. 7 TYPICAL TEST SET-UP
1" Chrome Steel Ball
J?l
Beam C-l k W = 76.2
u
Beam C-4 k W = 102.0
u
Beam C-7 k '\01 = 95.9
u
FIG. 8 BEAMS WITHOUT WEB REINFORCEMENT AFTER FAILURE
62
Beam C-2 k W = 89.5
u
Beam C-5 k W = 106.0
u
FIG. 9 BEAMS WITH VERTICAL STIRRUPS AFTER FAILURE
FIG. 10 BEAMS WITH INCLINED BARS AFTER FAILURE
Beam C-3 W = 94. f u
Beam c-6 k
W = 102.6-" u
64
FIG. 11 CRACK DEVELOPMENT: BEAM c-4
k W = 92.2
(Yielding of tension ·steel)
W = l02.0k
u
FIG. 12 CRACK DEVELOPMENT: BEAM C-5
k W = 30.0
W = 85.0 k
(Yielding of - tension steel)
W = lo6.ok u
FIG. 13 CRACK DEVELOPMENT: BEAM c-6
k W..: ~.O
67
W ::: 88.f (Yielding of tension steel)
k W = 102.6 u
100
80
fa
.!f 60 ~
i .s
40
20
o o
"
Jd r
I
~
;,
~ ~ ~C-3
V V ~ """" t'- C-2 ~
~ ~ ,,-V
iO'"
i
/. ~ ~ -..:-~ 1\
~ ~ ~ - ~ ~
~C-l
-
0.4 0.8 1.2 1.6 Midspan De!1ection,_in.
FIG. 14 LOAD-DEFLECTION CURVES roR BEAMS Wrnr 1.15 PERQENT LONGITUDINAL STEEL
100
80
art 60 ~. ~.
i .3
40
20
o o 0.2 0.4 0.6 0.8
Midspan Defiection, in. $
FIGo 15 LOAD-IlEFI.BCTION CURVES FOR BEAMS WITIl 1.99 PERCENT LONGITUDINAL S'mEL
0) p. .,; ~
rc1~
al
S
c5
lOO~--~--+---~~~~~~~~4===~~~--~--~---+---+----+--~--~--~
++~~ __ ~ __ ~r-_~r-_C_-~7 __ -r~~ -~I--~-~~~~
I I 80 I -- T---+-i ---+-1 ---+-1 ---t-----t----'i
, 1 , I I
I----+I---I-----t----+---t--_r---L .--1--1--1--~ ~---+-: ' I ---i
i I I·! ~ I I : I ; I 60 I-- -H--+-. --l--~- L--- _-~-i __ ' --i------1---t------i------1
I I ! : ! ; ! I : . ! I
I . I I I Ii' I I I 1 I i ----1 --... -t- I --+- --+ I -; ---~-- I - --~. ------.;-------t I I I . . I I· I I - -I I' I II : i I ; . : I .
lJ- .. --1--+-' -L - --l .. --- -l---J - -- ~-lj.· -- t---~------~-- --+---11--+--! I I' I I, I -: I
: I I I ! I I Ii! : i I
i I : I i I Ii' i ! I I ,--T----l--"--i -:-----t------t-----J------t---i- ! t~ i ; I I I . I I I I
- Ii! ! i - i, I !.: 20 H------T---i--,----t------,---- --y -----,- --:-- ------t-- - ---~- - t it -f "-----,-----
I I I ! : : iii ii, ! I I I f--:----- -- ----- r- -i- - r .. -----~---t- ---I ---t -I 1--1-1---1 o! I I I I I I I I I U
40
. -'----
o 0.2 0.4 0.6 0.8
Midspan Deflection, in.
FIG. 16 LOAD-DEFLECTION CURVE FOR BEAM '-lITH 2.09 PERCENT LONGITUDINAL STEEL
---,--- .......
! ~.. ..
i I- l
n 4 a.t 9" :z 36" f'" - ~ I
d 0.2' I---~~-+--~--""'" "I"'f
... ~ o ..,.. ...,
Beam C-l --,c..-+--+---I W m 76. ~
u CJ V
~ . o. 4 I-----~~~-+_____:lf__-~-----_t
0.6 ~------~----~~--~----~------~
0.2
. ~ .. s:l 0
.,.; 0.4 .., CJ
" ~ ~
0.6
0.8 a....-___ --'--______ ~---...:..----.....
FIG. 17 DEFI.BCTED SHAPE OF BEAMS C-l AND C-2
Beam C-2 k w ::: 89.5
U
----. -- --_._--!IIIIIIBIIIIiI 72
4 at 9" = 3611
I~ ·-~~I o ~----------------~--------~------~
0.2
Q OM
~
Q Beam C- 3 k 0 0.4 OM W = 94.5 +' u () (!) M ~
8
0.6
0.8 "--------1-----
FIG. 18 DEFLECTED SHAPE OF BEAM C-3
. d
.,-4
. d
....-4
co. d 0
.,-4 ..., (J
" (j ~
4 at 9" s .. 36"
Beam c-4 ---,,,.c--7t'-------t W U :: 102. ok
0.4 L-----__ ~ ______ ~~~ ______ ~ ______ ~
0
0.2 Beam c-5 W c 106.ok
u
0.-4
rIG. 19 DEFLECTED SHAPE OF B!AMS C-4 AND c- 5
... J:l o
4 at 9" = 3611
+J O. 2 1'---___ ~----3~-_-~
C) Q)
r-{ 'H
~
... Q o
''-;
Beam c-6 k W = 102.6
u
+:l C)
Q) O. 2 1------o --...,,-L--f-------i Beam C -7 k
W = 95.9 r3
u
FIG. 20 DEFLECTED SHAPE OF BEAMS c-6 AND C-7
120
/ - /
/ 100
80 1:1)
P1
lJ ...
s... G)
~ 60 ~ g
/ /
V I
.~ .s
40 / V
/ ,/ /
20
~ v
o o . 0.008 0.016
Deflection, in.
FIG.·21 LOAD-IBFLECTlOK CURVE lOR SUPPOR;rS
..... ___________ ~ ........ .,.J:Jr1'\dIIOCI'._J!liAJWU7I ••
roO'"' oj
80
I ---- t··~·_-·
I -... f -1-' ... - •
1 ;
I i 82 85
S 40 t----#*-+-+---,--.. ;-.-.- ...
._-' -- -.. -.. +-- -._- .. "1 . t ..... -. • --- .. " .... -.. - .- j ! S3 I EOI
I t I Est. ult. €s I
to
~
i. i 1 1
1_ at midspan
I = 0.0230 in.jin. I
o 400 800 1200 1600 2000
Strain, in.jin. x 10- 5
80 ,..------------------,.--
81
~ ~ ~--+---~--~ rd ~
~
20
s3
~~~----+---
H"-I'---;-- -._.. -.- ---- - ._.. . _. . ... - " .
o 40 80 120
strain, in.jin. x 10- 5 168
FIG. 22 LOAD-STEEL STRAIN CURVES FOR BEAM C-l
....... -------__ ".. ____ 1II1I'2i'Wfo:<¥~ __ • ..... ~ ..... ·~·~.,.... ...... ~~ ... 1I. "5:,
200
__ , __ .J
1.20 I T
! I I 1 V V I / I
-----. - ------. 85 ---- t-""'" ~
.,-.
I ~ ( 82 ~ I
I
80·
~I 83 "1
I E:o I I
I . • 1
iA I C' . I Est. ult. 's .'1 I at aiclepan -, I
I - 0.0420 in·/in. I I I I I I o
o 400 800 l~ l~ 2000
Strain, in. lin. x 10-5
80 120 160 200
strain, in./ln. x 10-5
FIG. 2' LOAD-STEEL STRAIN CURVES FOR BEAM C-2
78
~~~--~----~---+----~---~---4---~+----4-------85
84 80 1----1--+----- .. ---.- ----.-.- --- --r-i -t-~-~ -- -~j-~--
40
~~~~~~~~~~~I~~ . - 4~ .
IE ~---f- -. I !
I I Est. ult. € i S
.. -t -.i- at midspan --I
I I = 0.0600 in. lin.
--+--_.- --_ .. _ .. -- ....... - .. _- .--. -.
o~~ ________________________ ~ __ ~~~ ____ ~ ____ ~ __ _
o 400 800 1200 lWO 2000
Strain} in./in. x 10- 5
40
O~ __ ~ __ ~ ____ ~ __ ~ ____ ~ __ ~ __ ~ __ ~~ __ ~ ____ ~ __ ~
o 40 80 120 160 200
Strain, in./in. x 10- 5
FIG. 24 LOAD-STEEL STRAIN CURVES FOR BEAM C- 3
80
80
60
o o
19.. I
~ 1 81 .-AJ.L LoA
I ...----~
I s, I
I I • I • . I • I ,- 1° I . I I Bst. ult. « I 8
I I at midlpan
- 0.0138 in./in. ---IF
I I I I I I I .. 800 1200 1600
strain, in. lin. x 10-5
~ l7 ~ ~ -~ S3
~0 " I J
~~ V I I
~ , I
85 ... I
~~ ~ I I
~~~S3. I I
~ 'S2andS4 Ie ) I Y
/I ~ I I
V I . I
40 80 120 160 200
Strain, in. lin. x 10-5
FIG. 25 WAD-STEEL STRAIN CURVES FOR BEAM c-4
80
o----~ __ ~ __ ~ ____ ~_ o 400 800 1200
Strain, in./in. x 10-5
80~--~---+----~--4---~~~----~
E.:3t. tilt. € .:3
at midspan
== 0.0170 in./in.
2000
~~--4----+----~--~---h~~----+---~-~-+----~-~
20
o
I ---- t· __ · ... ---
I
40 80 120 160 S~rain, in./in. x 10- 5
r€ I
y' -L~---.. - --_. I f-+-------t--I
200
FIG. 26 LOAD-3TEEL STRAIN CURVES FOR BEA'1 C- 5
- : 80
I
~ -~ ~ I'
I I
o : rd m :3 4.0
I ! o o
lEy I I I
400
81.
s5 1 .
-"'/ I s3 S2
I I I I I EO
--I Est. bt. E
I s at midspan
I -
= 0.0270 in./in.
.. -----~ I I ~~ __ I 800 1200 2000
strain, in./in. x 10- 5
83 '-S5 80t-----+---+---+---+-- -l--L~~tJ8~::S4::' ~~
60 r----+---+-
en Pl ~rl ~
i40r----+S
o 40 80 120 160
Strain, in./in. x 10- 5
FIG. 27 LOAD-STEEL STRAIN CURVES FOR BEAM c-6
200
,..,..-------______ ....... ____________ ... __ .' .... _~ .. r ......... ~~' ___ .."..".....
82
I ____ d===~~~==~~J ~ Jl'SlEL!P~~=5 ==l==-=-+_-+-~S4=-_t_-------- .oCt--
80~~~·~--~--~s3~--~--~--1~~--~--/' I
~#J'J~--_4----~--~ __ +---4_-1~r_--~--~-__ --~-.--
hI I' ll€o, I i 40~~~+---4---~---+--~--~--r_r_-o 1 ,I Est ul t. €
H I j ,! €y I, I 1 s
1 1----; = O.Ol}:J in.jin. --. ti at midspan
ttl A
.,-i
..!:4 ... ~ S
a "---10...1 ~--t.~ ______ '.' _ . ....I.-.-i -J-...-I ~I ~l~. ___ o 400 800 1200 1600 2000
Strain, in. lin. x 10- 5
=-§2. r. -w-_-+
80 ~--~--~---~~~--.~--~--~~*--- -.~~ l~~
+-+-T--~-t-·--j-------! ------t
~_l--_t---~ ! : I! :
I I I I i
-+1--~------'·--I I l I I
-J -__._ -. -- -~- -'._ --~ -___ ~-_ ---+ .--~ I I I . I I ! ! I I I I . :
--.~--.-t_----- ----- ··----t--·-+-·-·-r--j --1 ~~~+-----+---+-- --- -- .-. ry--t---t-----~- .
-'- -_ .. _----+----- -----+-~--± !
o ~-""_~ ___ """""----::~ __ '- I I _. j ~ 40 80 120 1&J
60
I 40 ~-
i I I
20
o 200
Strain, in. lin. x 10- 5
FIG. 28 LOAD-STEEL STRAIN CURVES FOR BEAM C-7
i __ f
; t._/
, "J.l
I • ~ ! I -4
100
UJ PI ·rl ~
i
80
60
840
20
o
/
1,// I -----1----- r--- . - ,L- f-- Vrv i I ,// V
I ~7 / ./ i / /" C-2 J .-'.-/' Theoretical .I
~ ~I-'" I ... Ioi"
~~. I beam behavior
y'/ , / . "/',,.
~~ ,,'" /' I !
V C-l ....... I I -7
~ ~ I V~ .". ~ I
I +y ~ . -' ~/
,// ~~ vV' ../ I I
I I Y j I I
K .., ....
~~ ~ ...- "" Theoretical
I _l----~ ~ .//
,,// arch behavior ~ ,
~b;~ v ,.// I
// I .-
~V~ a / _~ ./ V ....
~ [7./"", ~
""'" o 8 16 24 32
Total Tensile Force, kips
FIG. 29 LOAD vs. TOTAL TENSILE FORCE IN LONGITUDINAL STEEL AT SECTION 12 in. FROM MIDSPAN: BEAMS C-l, C-2, AND C-3
()) \.)l
, rz ... ~~.........-.-- '
100
80
Ol
~ 60 ~
.,. td cd o H
40
20
o
, /
/ / It /~ /' /'"
Theoretical j U~ ,/ / beam __ ~
-C-';;""5 L ------/
~V , 1--------
tlehavior ~V 1/ ;
n c-6 ~ -----
I / /
c-y ~ // ./ ~ I / / 0~~ / ~ ~ Theoretical
V
~ ~~ ---arch behavior (C-7)
/ // ---1 --r---
V ~' ~'~Theoretical /- r7' arch behavior 1 L/ (c-4, C-5, C(6) _ /f~ V~
'/ ~
/y l/;~/ 1------- -
~ /;.~ ~
I
~~'r ---~-----r-_-----I~-t------ --- - I
/ , ~~
------ f------ --/ ~ ~
YI/ " ---1------~.
~----- ----- --- -- - --- ---------------
o 16 32 48 64 Total Tensile Force, kips
FIG. 30 LOAD vs. IDTAL TENSILE FORCE IN LONGITUDINAL STEEL AT SECTION 12 in. FROM MIDSPAN: BEAMS C-4, C-5, c-6, AND C-1
". r-i;". _ !: .
. i,
ex> ~
[
15"
13 1/211
13 1/2"
T
~I
A f vv
Beam C-1
Ml T =-
jd
M1 = external moment
Beam C-2
M - aA f T = 2 v v
jd
M2 = external moment
M2 < M1
Beam C- 3
M2 - bA f T= vv
jd
b > a
FIG. 31 FREE-BODY DIAGRAMS OF CRACKED SPECIMENS
~
24 I ~ =--I I Theoretical arch behavior
1:_ I ~ I - ~I ~ I ......... {J}
~ -r-I ~
'" Q)
CJ ~ . 16 ~
~/ 1'-Theoreti c al ~ beam behavior r-i
oM {J}
I=l Q)
8
r;d 8 +' 0 8
6" ~ .. 2~1 ~. 4 at 6" = 24" • LIE II'I~
FIG. 32 DISTRIBUTION OF TOTAL TENSILE FORCE IN THE LONGITUDINAL REINFORCEMENT: BEAMS C-l, C-2, AND C-3
.. . i 1 l
'1 ..•.•• ,' ~..Ih;).""':"'';:.1 6;.. ••• .: •• ; .. ~.... .;"';.; .. ~t..).<, It ........... ~~j.\ ....... '.:r' ....... ii..:.tJ ~;~·jb·u.:..WI ..(~.:.iI-'.:::.U·H
4D " "' I'\. / I / r/ """"-
Theoretical arch behavior P' "I cij~eoretiCal I ~,\ '''1
CIl Pi ~ .r-f ~
--Q) u H 0 ~
Q) .. 20 .r-f til Q Q)
E-f
~ +' 0 E-f
10
I-<-__ .§'.~ ._-.+ --- --.--------.-- 4 at 6" 24" ~ I.. 6"
FIG. 33 DISTRIBUTION OF TOTAL TENSILE FORCE IN THE LONGITUDINAL REINFORCEMENT: OJ -l
BEAMS c-4, C-5, AND c-6
~
100 I---t----+----+----+---~
80 1--1 J 1 7/ A #
€ 71' I I y (C-3 and C-6)~
Ui 60 l~u_ I I I / I 1'1 / I ~ ::;;:f .~..-- I / 7:7 ,!4
rd aJ
S o p ··M
40 r- II 7r 17" I I ~I
·1 Beam C-5 I
20
~r I 7'1 ~I I € = 0.0018 in./in. y
I I 1 __ I I
~/ I In"m "" ... 1 ~~9 spYl--4--8 ~ I BeamC-6~ 40 80 120 160
strain) in./in. x 10- 5
FIG. 34 LOAD-STEEL STRAIN CURVES FOR THE WEB REINFORCEMENT
i:!:" r
C\I
ff\ ~r,.....--_II
C\I r-l
I
~I
-;l I
Strains at loads of
57.5k
65. -;k 67. ()< 76.~ = ult.
1 r .- .. Beam C-l
o Estimated ult. strain
r· 0100 _:;,n.Jin.---..
strains at loads of
6J.Ok
65.5k
74.2k 89.5k = ult.
Beam C-2
~.Q986 J.n.li,n.
strains at loads of
?JJ. Ok
5O.0k
6o.ak 94.0= ult.
Beam C-:3
FIG. 35 DISTRIBUTION OF CONCRErrE STRAIN AWNG DEPTH OF BEAM AT MIDSPAA
BEArviS C-l, C-2 .AND c-3
0-
OJ
'"
: (\f
" r-f
1_ ~
.::t • ~ f"'4
~ ..:t
:;
:;
. ~
0.0086 in. in.
Strains at loads of
~.ok 92.~ 96.
102.0& z: ult.
. Beam c-4
strains at loads of
6o.~ 88.r 98.5lt
lOl.~ loo.Ok sa u.lt.
Beam c .. 6
o Estimated ul.t. strain
0.0050 in.jiIi
strains at loads of
45.0k
75.~ 95.0
lo6.ok :a: ult •
Beam C-5
Strains at loads o.f
70.0k
85.ok 92.ok 92.f>1t ..Jr.
95. y- :: ult. ........---.... Beam C-7
nG. 36. 'DISTRIBUI'ION OF CONCRETE STRAIN ALONG DEPrH OF BEAM AT MIDSPAN I
BEAMS C .. 4. C~5, c-6 AIm C-7
~
.... ~..: ..
..... ..J
~ I !
I
l!"\ I 0 M
><
):1 -r-I
.............. . ):1
.r-!
~
Q -r-l ttl H +' U)
Q)
+' Cl> H CJ ):1 0 0
680
400
200
800
600
400
200
600
400
200
Beam C-l k W = 76.2
u
Beam C-2 k W = 89.5
u
91
_ - _ Estimated
Beam C-3 k W = 94.5 u
FIG. 37 DISTRIBUTION OF CONCRETE STRAIN ALONG TOP EDGE OF BEA\f
92
000 t-----+---+--+--~,
400 ~---+---+"7"'<--
611
Beam c-4 k W = l02.0
u
. FIG. ;8 DISTRIBUTION OF CONCRETE STRAIN ALONG IDP EDGE OF BEAIv1
93
101. -f 400
Beam c-6 k = 102.6 W
u
200
If''\ I 0 r-I
X . 0 .r;
............. . Q on
"" Q ..-l oj H
-I-' m d)
-I-' Cl.> ~
400 c.> s:1 0
92.0k u
Beam C-7 k VI = 95.9 u
200
6" 4 at 3" =12" I 6" ., 6" ....... .. ...
FIG. 39 DI3TRIBUTIO:'J OF CONCRETE STRAIN ALONG TOP EDGE OF BEAA
120
C-3 ...-.... ~ ............. ---~ ~ ----.-"""" --
~ V" ~~ ~ C-2
80
.............: ~
40
o o
80
40
20
I( ~
/; !/ 1/ ~~ o
o
-
0.2 0.4 0.6 0.8
Elongation, in.
-- -------.- ._- . -_.
,,- ._.- ._-c-v ~ ~--~. ___ . . C-2
7 ~ V
/.
/~ W V .- ------ ------
// V
----I
---. -... - ---
0.02 0.04 0.06 0.08
Elongation, in.
~
1.0
---,...._--
.-.
0.10
FIG: 40 ELONGATION OF TENSILE REIiUi'ORCEr..ffiNT: BEAHS Cal, C-2, .rum c .. 3
.. "'"
120 95
C-5 c-6 -k:::-~ ...
C-4 ~ ~ : c-7
J.~
~V 80
#1 :
~ V 40
v o
o 0.1 0.2 0.3 0.4 Elongation, in.
80~--~--~----~---+~~~~~--~----~---+----r---~
... ~ ~r---+--+'H-~~---+--~--~ S
20 I---ff---+
0.02 . 0.04 0.06 0.08 0.10
Elongation, in.
~
0~5
0.04
s:1 0.03 ·rl
... 5:l 0 .r! +> cO ~) 0
.--t 0.02 r:i1
0.01
o o 0.02 0.04 0.06 0.08
Total Longitudinal Steel Strain, in.
FIG. 42 TOTAL EWNGATION OF rrENSILE REIHroRC:ElvIENT VB. SUM OF WNGI'I'UDINAL STEEL STRAINS BELOVI YIELD: BE.AMS C-l, C-2, AND c-3
"Ii
s:1 -r-!
d 0
.r-! +l cd bO C 0 r-l f:i1
0.')5 ~ I.
I- Elongation =}sdTJ -+----+---+----+--~
I o. 04 ~ -+- . ·-t----t--.--t-----t-.---+
I- -t- .. -.-.. - -+----.- . \--- -_ .. --_ .... -----~- .. --- -.. ..._ ........ ------
0.03
1----+--.---- -- C-4 i ------r-T --,_-- _+-------+--+----+---+---+------I
0.02
r- -- --r ---~ -r~-----t-·-·-··+__--_+_-··--__t_____· 4~
0.01 1..---- - .. --t----t-------t---- -" - .. t- . "'- ·t·_····· -t ....... ·f···· ·1· -.. - ~
o 0.02 0.04 0.06 0.08
Total Longitudinal Steel Strain, in.
FIG. 1-1-3 '.eOTAL ElDIJGATION OF TEl>TSlLE REIl··l'FORCThIElTT vs. SUH OF LONGlTUDNIAL STEEL STRAIl'IS BEL01-; YIELD: BE.ru1S c-4, C-5, c ... 6, AND C-7
\Q ,-J
tI)
.~ t)
~ .,-t
'" " 0 .,-t ..., 0 v ~ ~
~ PI
~ ~
tf.)
.8 (J
= '" ... s::: 0
"r"I .p 0
~ ~ 5 t=lt
~ '" ::E!
0.10
0.08
0.06
0.04
0.02
0
Elongation, inches
0.80
0.70 / 0.00
0.50
O.lto
0.30
0.20
0.10
0
/ ~
V / /
C-2 V c-y V /
V / V
/ V
/ 7
/ V
/ V
/ i/
V
V 0.10
Elongation, inches
.' FIG. 44 MIDSPAN DEFLECTION VS. ELONGATION OF TENSILE
REINFORCEMENT: BEN'1S C -1, C - 2, AND C - 3
/
/
[?
[7
to I!J
..!:! t)
~ -,-4
po,
t:: 0
ol""i +' v cv ,..; r;~
8 § P-I ,§ .,..; ~
m
~ CJ P OM .. ~ 0
'.-i ~ 0 V
H t'j..f tU ~
a·, r4
~ ~
99 0.12 /
, /
/ / 0.10
// V / /~
0.08
0.06
0.04
0.02
0
/' ~'
V / 1/ ./'
v /
,/ C"'5 I if ( I c-Gj //f C-4/,
V / 1 / /' /
/
'/ f I 0.02
Elongation, inches
0.80
0.70
0.60
0.50
0 V /
/ V
/ /'
c-6 / 0.40
0.30
0.20
0.10
0
/ /
/ /v / C-5
/
/ ~ / / /
c-4 ./
V / / /
/
/7 /F I if
/ 0.10 / 1I /
Elongation, inches
FIG. 45 HIDSPAN DEFLECTION VS. ELONG.NrrON OF TENSILE
REINFORCEMENT: BEAMS c-4, C-5, AND c-6
/
Beam A-3-4 W z: 186.;k
u M = 745in ... k
u
Beam A-3-5k Wu - 179.,2
~ = 896in .-k
100
'I.
1000
800 LI----~----~--~----~----~----i_----~--~----_+--~~~~=--;~~~~-----;----------;_--------l U)
A .,-j
~ I
Q 600 .,-j
.... +l Q Q)
§ ::g
§ 400 A U)
rcj -rl ~
200
/ ~-dfFf l-r_
i yl ---~---+----+---~----~--+I----+-----~----'~----~-
I I !/ i I J I I L I 1,1 iii --1-----+-__ -----, __ -----'---
• ! I /1 I
1/ ! I . i
I I I I ".: ; I i i' I I ! r---~-l-----~--i III Unloaded to I !! ----if -r:lease; rOlle~s i --;
r : i I t--f----+---~II --+--t----+------ir- j---t---t-·---t--
I I I 1 I ! ;
-l- 3-2
a a 0.2 0.8
Midspan Deflection, in. b J-l
FIG. 41 MOMENT-DEFL!~CTION CURVES FUR A-SERIES BEAMS
102
m Pc
J I
!r( I
I L...----' ...--U
120
j i 11
/ 1£ I Y I
( , i I
40
I I I o
,0 400
- --Sl S2 -120
~ ~ 6 at
: I
s3 i ~ ~
....& ~
s5 t=::: t2: S2
~ ~
... I
I I I ! EO
I I I I
I I Est. ult. € I s
I at midspan
I = 0.0308 in./in. ___ I
I I
800 1 roo 1~0 2000
strain, in./in. x 10- 5
- --
83 s4 S5 ..... -I'i' /.: r/// -
6"= 36" ,
] 80 ~--~---4----+----+----~--~~~~--~---+--~r---~
I I ~ ~--~--~~~~---+----r---~--~----4----+--IE ----~
I Y
~~-+---.;tC--j Theoretical strain --+---f-----f----+-....L.-+-----I
at mi ~spa.n I o K-__ ~ __ ~ ____ ~ __ ~ ____ ~ __ ~ __ ~ ____ ~ __ ~ __ ~ ____ ~
04080 120 200
strain, in./in. x 10-5
FIG. 48 LOAD-STEEL STRAIN CURVES FOR BEAM A- 3- 4
I I _V--~ LL
!j I ~ t:;:--
v--I
L---:j ~ ~ 82 I -
l20
I ~ ~
~ I ? I
11 83 I
:1 ~ ~ I
I 1/ J€ JV I 0
II I
11 I I
j I€ I I Y I I ,
I I Est. ult. €
I I s I at midsp'ID J I
= 0.0377 in./in.-I 1
I I I J I
40
o o 400 800 1200 1600 2000
Strain, in./in. x 10- 5
l20 ~--~--~--~----~--~--~--~--~----.---.---"
40 S2
/" I ~~:r--~"f- Theoretical strain --f---f----+--t----t---H
o~ __ ~ __ .~ __ ~ ____ ~ __ ~ __ ~ __ ~ __ ~ ____ ~ __ ~ __ _ o 40 80 120 160 200
Strain} in./in. x 10- 5
FIG. ~ LOAD-STEEL STRAIN CURVE8 FOR BEAM A-3-5
104
OJ
0.0022 in. in.
1--~7"'9~=------------.-' ....
IH---..... --.-... -...... _.- .-----------------
strains at loads of
6o.ok
120.0k
140.Sk Beam A- 3-4
k W = 186.3
u Est. E = 0.009 in./in.
c
~ ,~ ______ -O-.-O-O-28--in~./-i-n-.-------~,~ I r I
....---1-_
C\J
ri
Strain3 at loads of
5o.ok
IOO.Ok
120.0k
-
·1
Beam A-3-5k W = 179.2 u Est. € = 0.007 in./in. e
FIG. 50 DISTRIBUTION OF CONCRETE STRAIN ALONG DEPTH OF BEAM AT MIDSP fu"'T,
BEAMS A- 3-4 kllD A .. 3-5
8001
U"\
• ~, H . 600 Q .,...
'-..... . d ..n .. s:1 ~400 J.. .~
.p m 4J .p G)
J.. 0 d 0 u. 200
174.ak , I I
'''-12"
Beam A-;-~ W == 186.,· u
I . 800
U"\
• ~
~000 Q .,...
......... •
d ...... ...
Q
-.1400 J.. .p tr.l
~ t v d
8200
I 150.0k
Beam A-3-~ VI =119.~ u
'ne. 51 DISTRIBUTION OF CONCRETE STRAIN ALONG IDP EIXlE OF BE.Ale At-3- 4. AND A-3-5 ...... o V1
106
N Strain, in. lin . ............ r-i
o 0.004 0.008
Beam C-4
O.Ol2 0.008 OJ I ............ Strain, in. in. r-I
Beam c-6
o.Ol6 0.012 o
FIG. ~ DISTRIBUTION OF STRAIN ALONG ENTIRE DEPTH OF BEAM AT MIDSPAl"if :
BEAMS c ... 4 AND c-6
b
A s
------+--'. Cross section Strains
107
c ~ 0.5 f bkd c
T:::: A f s y
Stresses
T ~
(a) Beams Reinforced in Tension Only
-,..-- ,-
• ~~ AI S
-rQ
A " s •
Cross section Strains
f n C :::: Af(fl-E E:')
2 $ S C S
T = A f s y
-rd
Stresses
(b) Beams Reinforced in Tension and Compression
FIG. 53 STRAIN AND STRESS RELATIONSHIPS AT l!"1.EXURA.L YIELDlllG
~~
.. ro
,~
b
1
Cross section Strains Stresses
(a) Beams Reinforced in Tension Only
b
l • Al
S
As • Cross section Stxains Stresses
(b) Beams Reinforced in Tension and Compression
T ::: A f s s
T::: A f s s
FIG. ;4 ~ STRAn~ AND STRESS .RELATIONSHIPS. AT ULTIHATE F'l..EALJRAL CAPACITY
TR-59-72
DISTRIBUTION
No .. Cys.
HEAD QUAR TERS USAF
1 ,Hq USAF (AFCOA), Wash 25, DC
1 Hq USAF (AFOCE), Wash 25 1 DC
1 Hq USAF (AFDRD), Wash 25 J DC
1 Hq USAF (AFCIN), Wash 25, DC
1 USAF Dep IG for Inap (AFCDI-B -3), Nortan:-AFB, Calif
MAJOR AIR COMMANDS
1 ARDC (RDR) , Andrews AFB, Wash 25, DC
AFBMD, AF Unit Post Office, Los Angeles 45, Calif
1 ATTN: Dr. George Young
1 ATTN: Space Technology Lab
1 SAC (DINC), Offutt MB', Nebr
1 TAC (TDA), Langley AFB, Va. J
1 AMC (MCW7), Wright-Patterson AFB J Ohio
1 ADC (Ops Anlys), Ent AFB, Colorado Springs, Colo
'I AUL, Maxwell AFB, Ala
I USAFA, United States Air Fo.rce Academy, Colo
ARnC CE!'-lTERS
WADD, Wright-Patterson AFB, Ohio
1 (Director of Sys Mgt, Lt Col J. Stone)
1 (WCOSl}
1 (RDSIW)
KIRTLAND AFB
AFSWC, Kirtland AFB, N Mex
1 (SWNH)
3 (SWRS)
5 (SWOI)
OTHER AIR F~RCE AGENCIES
1 USAF, Project RAND, ,Via AF Liaison Office, (Nuclear Energy
Division), The RAND Corporation, 1 700 Main Street, Santa Monica, Calif
1 / USAF IT , Wright-Patterson AFB, Ohio
'TR-59-72
DISTRmUTION (Cont'-d)
No. {.;ya.
ARMY ACTIVITIES
1, 'Chief of Research and Development, Department of the Army, ATTN:
Special Wea.pons and Air Defense'Division, Wash 25, DC
1 Director, Ballistic Research Laboratories, ATTN: Library,
Aberdeen Proving Ground, Md
1 Commanding Officer, US Army Engineers, Research and Development
Laboratories J Ft. Belvoir. Va
1 Director, Waterway. Experiment Station, ATTN:, W. J. Turnbull,
Box 631, ViCKsburg, Miss
1 Chief of 'Eng'ineers, Department of the Army, ATTN: Protective
Construction Branch, Wash 25, DC
NA VY ACTIVITIES
1 Commanding Officer, Naval Research Laboratory, Wash 25, pC
1 Chief,. Bureau of Yards and Docks,: ATTN: D-440, Wash 25, DC
1 'CanuDapOjng Officer and Director, Naval ,Civil Engineer~
Laboratory, Port 'Huenem,e" Calif
OTHER DOB ACTIVITIES
1 Director, ~ea.pon Systems EvalUation Group, Office of Assistant , \
Secretary of Defen.se, Room 2E1006, The Pentagon, Wash 25, DC
3 Chief, Defense Atomic S~pp~~t Agency, ATTN:"'lS1.a.at and Shock
Division, Wash' 25, DC
1 Commander, Field Command. Defense Atomic Support'Agency,
ATTN: WET, Sandia Ba.Be, N Mex
1 ASTlA (TIPDIl), Arlington Hall Sta, Arllneton 12, va
AEC ACTIVITIES
1 US' Atomic Energy Comma/.ion, ATTN: Technicallleporta Library
{Mrs., J. otLeary~ for ,DMA}, 'Wash 25, DC
1 'Prea.ident, Sandia Corporation, ATTN: T. B. Cook, Div S111,
/Sandia Bailie, N Melt
1 A •• iatant Secretary of-Defe1lft, ATTN: H. Facei, W'.ah ZS, DC
TR-59-72
DISTRIBUTION (Cont'd)
No. Cys.
OTHER
1 American Machine and Foundry Company, ATTN: T. G. Morrison,
1104 South Wabash Ave., Chicago 5, III
1 Massachusetts Institute of Technology, Dept of Civil and Sanitary
Engineering, ATTN: Prof. R. J. Hansen, 77 Massachusetts Ave.,
Cambridge 99, Mass
1
1
1
University of Massachusetts, Dept of Civil Engineering J ATTN:
Prof. Merit P. White, Amherst, Mass
Holmes and Narver, Inc., ATTN: Sherwood B. Smith, 824 S. Figueroa
St., Los Angeles 14, Calif
E. H. Plesset Associates, Inc., ATTN:' ~rc Peter, Jr., 6399
Wilshire Blvd., Los Angeles 48, Calif
'--')
I
........ 1
'--