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Flexural behaviour of reinforced and prestressed solite structural lightweight concrete beams
Build. Sci. Vol. 10, pp. 43-56. Pergamon Press 1975. Printed in Great Britain
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Flexural Behaviour of Reinforced and Prestressed Solite Structural Lightweight Concrete Beams R. N. SWAMY* A. B. IBRAHIM~"
The structural behaviour of reinforced and prestressed concrete beams made of expanded slate lightweight aggregate (Solite) concrete is discussed in relation to strength, cracking and deformation characteristics. The beams were designed to have permissible concrete stresses of 15.0-26-0 N/mm 2, and the cube strength of the concrete was 35-40 N/mm 2 in one day and about 50 N/mm z at 28 days. The deflection, cracking and the strength characteristics of the beams have been studied throughout their flexural loading range, and their mode of failure. It is shown that Solite lightweight concrete beams possess adequate ductility and load factor, and satisfy all the serviceability requirements of current Codes of Practice.
Tests are therefore reported here on the shortterm flexural behaviour of reinforced and prestressed concrete beams made of expanded slate lightweight aggregate. The beams were designed to have a working stress of 17.3 or 26.0 N / m m 2. The beams were tested to failure in flexure and their structural behaviour in terms of strength, cracking and deformation is discussed.
INTRODUCTION
E X P A N D E D SLATE (Solite) is a relatively new addition to the list of lightweight aggregates currently available in the U.K. It is manufactured in N. Wales from the slate deposits of the Silurian period of the Palaeozoic era by an expansive rotary kiln process. The resulting aggregate is chemically inert, stable and of good quality with a highly vitrified internal pore structure. The aggregate is strong and possesses low water absorption. With the current shortage of good quality natural aggregates in several parts of the country, lightweight aggregates are being increasingly used in reinforced and prestressed structural members, and design data and an understanding of their structural behaviour are necessary to establish their serviceability in practice. Because of the lower modulus of elasticity of lightweight concrete, the short- and long-term deflection of lightweight concrete beams will be greater than that of normal concrete beams. Also, for a given load the strain in the reinforcement is likely to be greater which is likely to produce more and wider cracks. The deformation and cracking characteristics of structural members are therefore important in design. Although data on the flexural behaviour of lightweight aggregate concretes in U.K. are available, these are confined to aggregates other than Solite.
EXPERIMENTAL
PROGRAMME
The aim of this investigation was to study the flexural behaviour and to establish the serviceability characteristics of reinforced and prestressed concrete beams made of Solite lightweight aggregate. Altogether 13 beams were tested and their details are given below. DETAILS OF REINFORCED
BEAMS
Five reinforced beams were tested. Three beams were of all Solite concrete (mix S1) having steel ratios of 1.14, 2.03 and 3.16%. The other two beams having a steel ratio of 3"16% were made from Solite with sand concrete (mix $2) and normal gravel concrete respectively. All the beams had the same width and effective depth and adequately reinforced for shear as shown in figure 1. The details of these beams are shown in Table I. DETAILS OF PRESTRESSED
*Department of Civil and Structural Engineering, University of Sheffield. tUniversity of Mosul, lraq; formerly of the Department of Civil and Structural Engineering, University of Sheffield.
BEAMS
Eight prestressed beams were tested--four at 28 days and one at three months (series P). The other 43
44
R. N. Swamy and A. B. lbrahim 752
F~ . . . . . . . . . . . . . . . . . . .
H
_
~'~J
-
%
2286 2438
I"-
~-6mm at lO0mm C/C
- Etectrical Resstonce Strain Gouge • Dernec Strain Gouge Disc (a) Typical Longitudinal Section I'
Beams R1, RS1 and 01 'Aste 2-12rnm Top 2-16mm Bottom
127 ~.j
127
I"
--fl
Beam R3
Beam R2 Ast,, 2-6ram (b) Cross Section All Neesurements in mm
Fig. 1. Details o f reinforced test beams.
three beams (PS1, PS2 and PS3 of series PS) were tested after they had been subjected to a sustained design load corresponding to an extreme fibre concrete compressive stress of 26-0 N / m m 2 for four days, and then left unloaded for one year exposed to the outside environment covered with polythene sheet. These latter beams were exploratory tests, tested particularly to study their ultimate load and deflection characteristics under permissible concrete compressive stresses of 26.0 N / m m 2. All the beams were prestressed such that the stress at the top fibre was zero. Beams P1, P2 and P4 were identical--Pl and P4
P
being from all Solite concrete, and beam P2 from Solite with sand concrete. These beams were stressed with wires with a concrete stress at transfer of 17.3 N / m m 2. Beam P3 made from all Solite concrete was also stressed with wires but with a concrete stress at transfer of 26.0 N/mrn z. All the other four beams were prestressed with Dyform strands. Beam PS had a stress at transfer of 17.3 N / m m 2 while the three beams of the PS series, retested after sustained loading, had a stress at transfer of 26.0 N / m m 2. Details of these beams are shown in figure 2 and Table 1.
762
;i0 -
'4
-I-I-I-I-I-L-I-t-I!1 PI
Electrical Res,st ..... Stra,n4Gouge • Demec Strain Gauge D~c
at 10Omm C/C
(o) Typical Longitudinal Section ~, 127
Beams R1, RS1 and 01 AstO 2-12rr~n Top 2 16ram Bottom
F 127~-"1
I" 127
Beam R2 Asto 2q6mm
Beam R3 AstO2-12mm
(b] Cross Section AU Measurements in mm
Fig. 2. Details o f prestressed test beams.
.~
S1 S1 S1
S2
O.C.
S1 $2 $1 S1 S1 S1 Sl S2
R3 R2 R1
RSI
O1
P1 P2 P4§ P3 PS PSlll PS211 PS3II
42.5 48'5 51.2 50.9 48.3 47.0 48'0 54'5
59'6
51.0
44.4 42.5 44.5
36"0 41"2 39.5 40'4 40-5 ----
44.0
36'3 36'0 37"6
Cylinder strength ( N / m m 2)
*S1 = All Solite mix. $2 = Solite with s a n d mix. O.C. = O r d i n a r y concrete. t U l t i m a t e tensile strength for prestressed steel. :]:Zero stress at T e p Fibre. §Tested at 3 m o n t h s . ]tTested at one year. All o t h e r b e a m s tested at 28 days.
Mix* type
Beam No.
Cube strength ( N / m m 2)
17.93 35.36
2.9 --
127 x 156
127 x 156
127 x 156 127 x 156 127 x 156
17.61 19'50 17"00 16.50 18'06 ----
127 x 127 x 127 x 127 x 152 x 127 x 127 x 127 x
135 135 135 135 135 135 135 135
Prestressed b e a m s
17"40 17'60 16.80
2.9 3"0 2-9 2'9 2.8 ----
Bxd (mm)
Reinforced b e a m s
Y-modulus E ( k n / m m 2)
2"5 2"9 2"9
Flexural strength ( N / m m 2)
5-7 5-7 5-7 8-7 2-12.7 2-12.7 2-12-7 2-12.7
2-12 2-16 2-16~ 2-12J 2-16~ 2-12J 2-16~ 2-12J
Reinforcem e n t No. a n d size (mm)
1.122 1'122 1.122 1-795 1"09 1'308 1.308 1'308
3.16 628.6
410
192.5 192.5 192.5 308.0 224 224 224 224
3-16
628.6
410
1730 1730 1730 1730 1960 1960 1960 1960
1"14 2"03 3"16
(%)
Steel ratio As/bd
226"3 402-3 628'6
Area of steel As ( m m 2)
410 410 410
Yield stress? ( N / m m 2)
Table 1. Details of Solite concrete reinforced and prestressed beams
17'3 17'3 17"3 26"0 17"3 26"0 26"0 26"0
m
Prestress~ at b o t t o m fibre ( N / m m 2)
4~
9
t~
¢5
~o
t~
t~
t~
R. N. Swamy and A. B. lbrahim
46 MATERIALS
The Solite concrete mixes S 1 and $2 were designed to give a cube strength of 35-40 N/mm 2 at one day and about 50 N/mm 2 at 28 days. To achieve the high early strength a finely ground Portland cement with a surface area of over 700 m2/kg was used. The cement content of the mixes was 540 kg/m 3. The total aggregate-cement ratio was 2.0 by weight with a ratio of fines to coarse of 0.44, and a watercement ratio of 0-55. Mix SI consisted of both lightweight coarse and fines whilst for mix $2 67 % of the lightweight fines were replaced by natural sand of Zone 2 grading[l]. The plastic density of the concrete varied from 1740 to 1860 kg/m 3 and the dry density at 28 days from 1680 to 1730 kg/m 3. The workability of the mixes varied from 4.0 to 4.5VB seconds immediately after mixing. The strength properties of the concrete used in the beam tests and its elastic moduli are shown in Table 1. One reinforced beam 01 was made with graded crushed gravel aggregate with a maximum size of 19ram (3/4in.), natural sand and very fine Portland cement. The mix proportions used were l: 1.05:2.45 with a water-cement ratio of 0-39. The reinforcement for the tensile steel in the reinforced beams and the web reinforcement in both reinforced and prestressed beams consisted of high tensile hot-rolled deformed bars with a minimum yield strength of 410N/ram 2. For prestressed beams, Bridon low-relaxation 7 mm indented wires and Dyform low-relaxation 12.7 mm seven wire strands having a minimum tensile strength of 1570 and 1920N/mm 2 respectively were used. The properties of the steel reinforcement used in the tests are shown in Table 1.
M A N U F A C T U R E AND TESTING OF BEAMS All the beams were cast in steel moulds. With each beam control specimens for compressive strength, modulus of rupture and modulus of elasticity were also cast. In the prestressed beams, the prestress was transferred at seven days. All the beams and the control specimens were cured in the laboratory under polythene sheets. The strain on the reinforcement bars and wires was determined through electrical resistance gauges. In addition, the concrete tensile and compressive strains in the pure bending region were also determined by electric resistance gauges. The strain distribution on the vertical face of the beams in the flexural region was determined through a de-
mountable mechanical extensometer with a sensitivity of 3 - 5 x 10 - 6 m/m. Further, the central deflection and maximum crack widths at the extreme tensile face were also measured. All the beams were tested at 28 days except P4 which was tested at three months, and beams PSI, PS2 and PS3 (of series PS) which were tested at one year. The beams were loaded under two point loads 762 mm apart on a span of 2286 mm (figures I and 2). The reinforced beams were loaded in three cycles, the first to the calculated design load, the second to hail-way between the design and ultimate load, and the third extending to the ultimate load. The prestressed beams of series P except beam P2, were loaded in two cycles. The prestressed beams of series PS were all tested to ultimate load in one cycle. All strain measurements, deflection and maximum crack widths were measured at every load increment. All electrical strain gauges were recorded through a data logger.
TEST RESULTS The main objective of this series of tests was to investigate the flexural behaviour of structural lightweight concrete beams throughout the loading range up to failure. The results obtained from the tests regarding deflection, cracking and load capacity are discussed and compared with the corresponding Solite with sand concrete beams and normal concrete beams.
DEFLECTION CHARACTERISTICS The load-deflection characteristics of typical reinforced and prestressed beams are shown in figures 3-6, which also show the number of cracks and the maximum crack width in the flexural region measured during each cycle of loading. In the tests on the reinforced beams the first loading cycle extended to the design load corresponding to a
9of
,~b
80 70
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z 60
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c u 50
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', I
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I I '~ r
30
. . . . . . . . . ~. 2 5
10 Deflection - mm
•
~ 15
2
2 20
Fig. 3. Deflection and cracking characteristics o f all Solite reinforced concrete beam RI.
Flexural Behaviour of Reinforced and Prestressed Solite Structural Lightweight Concrete Beams
9O
80
el- maximum crack width rnm xlO 2
7O
~/" zu\ ~ . . ~ ' o ~ b~, _
z 50
115 [
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~ 5c
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3[
/ -x
2[
~1
10 0
2
-.
6
8 10 12 Deflection rnm
1l.
15
16
20
Fig. 4. Deflection and cracking characteristics of Solite with sand reinforced beams RS1.
b.
a
102"3 00
a-- maximum crock width: mm x 102 ~
9oi
b-- no. of cracks ~
2
7.5 ~] !
60
20 10 0 0
11
12.~.
7c
3O
11
17 5
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I/,
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6
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10
7=,
,
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,
,
,
,
,
15 20 Deflection --ram
,
25
,
30
Fig. 5. Deflection and cracking behaviour of Solite prestressed beam P3.
o.
7£
a. maximum crock
6(
b nc ~f crocks
w,~fh. . . . 102
jj~-
8
//7. .o
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~
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~11 2
[ 4
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I 1/,
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Fig. 6. Deflection and cracking behaviour of Solite prestressed beam PS with strands.
whereas in the prestressed beams the second cycle (except in beam P2) extended to the ultimate load. The prestressed beams of the PS series were all tested to destruction in one loading cycle. In all the tests visible cracking occurred during the first cycle, and the deflection curve of the second cycle, after cracking, generally followed the continuation of that of the first cycle. Similar behaviour also occurred during the third cycle before yielding commenced (figures 3-6). The data obtained from the tests, such as, the deflection at the design moment, the residual central deflection on unloading after the first cycle of loading up to the design load and the final deflection measured prior to failure are shown in Table 2. In the tests with the prestressed beams, the tendons were stressed against the moulds in which the beams were cast and it was impractical to measure the camber of the beams at transfer. The calculated and measured deflections shown in Table 2 are therefore, due to external load only. Under the permissible working loads, the deflection in the reinforced and prestressed beams of series P varied between 4.95 and 7.85 mm, the maximum value being for the reinforced beam R2 with low amount of tension steel. For a nearly balanced section, the deflection at the design load for the reinforced beams of all Solite, Solite with sand and gravel concrete beams was respectively 5-26, 7.20 and 6.04 ram. In considering deflection it must be remembered that Solite concrete had about half the Young's modulus of gravel concrete. The residual deflection after the first cycle of loading up to the design moment during which visible cracking had occurred was above 1 mm for the reinforced beams, and less than 1 mm for the prestressed beams of series P. The data show that the Solite beams, except beam R3 with very low tension steel (1"14~o), recovered nearly 8 0 ~ of their deflection compared to 75% of its deflection recovered by the gravel concrete beam. For all the beams the deflection at the beginning of the second cycle at the design load was nearly the same as that at the first cycle as shown in the typical figures 3-6. Table 2 also shows the predicted deflections at the design moment. These deflections were calculated from the basic formula. = K4'L 2
permissible tensile stress of 210 N / m m 2 in the steel reinforcement and a compressive stress of cube strength/2.73 in concrete. In the tests on the prestressed beams of series P, the applied load in the first loading cycle corresponded to a permissible concrete stress of 17.3 N / m m 2. The second cycle for the reinforced beams generally extended to about half-way between the design and ultimate load,
47
0)
where K = a factor depending on the type of loading q~ = curvature of the beam, and, L = effective length of the beam the curvature ~b was calculated according to both the Draft Unified Code[2] and the A.C.I. Code [3].
6515 10370 12330 14730 15740 15000 15000 15000 15000 22500 18000 15000 15000 15000
*Beams tested at one year
PS PSI PS2 PS3
R3 R2 R1 RS1 Ol P1 P2 P4 P3
Beam No.
Design moment M (N-M)
5-35 7.85 5-26 7.20 6.04 7-57 6.70 6.95 4.95 7.27 6.29 14-30 5"90 9.50
(1) Deflection at M (mm)
-
0.67 ----
-
1-88 1-45 1 '05 1'55 1.52 0.89 0.67 0.63 0.80
Residual deflection (unloaded) (mm)
35"0 18.5 20.0 21 '5 25-0 11.7 10-0 9"1 16.2 11.0 10"6 ----
Percentage o f residual deflection on deflection at M
4.79 6'69 6-09 7.42 5.74 7.02 7-02 7.02 5.24 8.2 5.46 5.44* 5-44* 5.44*
(2) Deflection at M (unified code) (mm)
5-0 6.4 5-7 6.9 5"64 6.51 6"51 6.51 5.25 8.3 5'4 5.39 5-39 5-39
(3) Deflection at M ( A C I code) (mm)
1'12 1.18 0.87 0.97 1'05 1.08 0"95 0.99 0.95 0.88 1"15 2.62 1.08 1.74
C o l u m n (2)
C o l u m n (1)
1-06 1.22 0.925 1.04 1'07 1.16 1.03 1.06 0-95 0.87 1.16 2.65 1"09 1'76
C o l u m n (3)
C o l u m n (1)
Table 2. Deflection characteristics of Solite reinforced and prestressed concrete beams
427 291 434 317 378 302 341 329 462 314 363 160 387 241
Deflection at M
Span
33.07 31"85 18.93 20.78 22-83 19.33 23.55 15.60 25.64 -18-64 21.31 12.25 17.55
Deflection prior to failure (mm)
4~ o0
3700 3700 3700 3700 6370 13860 13860 13860 22300 18100 ----
No.
R3 R2 R1 RS1 O1 P1 P2 P4 P3 PS PSI PS2 PS3
Beam
Moment at first crack mcr (N-M)
4-4 4"4 4"2 4.2 7.2 2.84 2-67 3.08 4'82 2.90 ----
Flexural stress at first crack ( N / m m 2)
2.5 2.9 2.9 2.9 -2-9 3.0 2"9 2.9 2.8 ----
Flexural stress (prisms) ( N / r a m z)
6515 10370 12330 14730 15740 15000 15000 15000 22500 18000 15000 15000 15000
Design moment M (N-M)
17626 24065 35590 38980 38130 23810 20340 25420 39830 27455 19490 26780 21185
Ultimate moment Mu (N-M)
15 5 6.5 7.5 6 5 5 5 5 5 ----
Maximum crack width at M ( × 102mm)
109 96 58,6 58.6 54.4 95.2 108.9 127 108"9 108.9 108.9 127 127
Average crack spacing at M (mm)
7 8 13 13 14 8 7 6 7 7 7 6 6
No, of cracks between loading points at M
60 108 89 102 102 165 140 165 83 159 229 330 197
Maximum crack spacing at M (mm)
Table 3. Crack characteristics of Solite reinforced and prestressed concrete beams
15 44 13 44 57 22 95 19 38 57 32 25 76
Minimum spacing at M (ram)
1-76 2"80 3-32 3"96 2"46 1-08 1'08 1.08 1'005 0.995 ----
mcr
M
4,75 6-50 9'6 10-5 6"00 1-72 1'46 1'82 1,78 1.52 ----
mcr
Mu
r~
e~
%
t~
50
R. N. Swamy and A. B. lbrahhn
From Table 2 it is seen that the deflection at the design load predicted by both methods compares well with the experimental results. Although the number of beams tested are limited to give a final comparison with ordinary concrete, the results show no significant difference in deflection between Solite and gravel concrete beams having the same steel ratio. In general, at the same applied moment, the deflection in ordinary gravel concrete beam was about 15-20 ~ less than that of Solite concrete beams. The span-deflection ratios under the permissible working load varied cetween 291 and 434 for the Solite reinforced beams compared to the value of 378 for the gravel concrete beam. For the Solite prestressed beams of series P, this ratio varied between 302 and 462. Tests by Evans and Orangun[4] on Lytag concrete beams with square twisted bars and a cube strength of 44.5 N/mm 2 showed span-deflection ratios between 487 and 671. However, the steel stress for the Lytag concrete beams was 196 N/mm 2 and the span-depth ratio 7.6 whereas the corresponding values for the Solite concrete beams in this investigation were 207 N/mm z and 14.6 respectively. The typical deflection diagrams shown in figures 3-6 indicate that all the Solite concrete beams had adequate ductility and showed substantial deflections at failure. The final deflections shown in Table 2 were measured prior to failure as near to collapse as poss ble. For the reinforced beams the measured final deflection varied between 1/70 to 1/120 of the span compared to 1/ 100 of the span for the gravel concrete beam. For the prestressed beams of series P, the measured final deflection varied between 1/90-I/150 of the span. These values are characteristic of those obtained by the yielding of the tension steel and even after failure, the beams showed appreciable recovery. The deflection properties and the span-depth ratios of the prestressed beams of series PS should not be interpreted too severely. These were exploratory tests with a concrete stress at transfer of 26.0 N/mm 2. Further, the beams had initially been subjected to a sustained load corresponding to 7 0 - 8 0 ~ of the ultimate load, and cracked, and retested after one year of exposure and prestress losses. These beams had inadequate transmission length as explained later, and all the beams failed prematurely.
CRACKING B E H A V I O U R The maximum crack widths at the tensile face and the crack spacing were measured at every load stage in all the tests, and the cracks marked on the beams. These are shown in figures 3 and 4 for typical prestressed beams P3 and PS. The experimental
data on maximum crack width and crack spacing at the design load are tabulated in Table 3. It is shown that with Solite reinforced beams the crack width at the design load varied between 5 and 1 5 × 1 0 - Z m m , the maximum value corresponding to a highly under reinforced beam. The ordinary gravel concrete beam had a crack width of 6 x 10 -2 mm compared with a crack width of 6.5x 10 . 2 and 7.5x 10 -2 mm at design load for the two Solite beams R I and RSI respectively having the same steel ratio. These working load crack widths are by no means excessive, and are well within the acceptable limiting crack widths necessary for durability. The flexural stress at first crack has also been calculated for the reinforced and prestressed beams from the load at first crack when it was first visually observed and shown in Table 3. For the prestressed beams, the net concrete compressive stress due to prestress was calculated by allowing elastic, shrinkage, creep and relaxation of steel losses from the 7 days, when the stress was transferred, up to the age of test. Tests by Hardwick[5] showed that the crack width of Aglite and ordinary concrete beams with mild steel bars of different percentages was 7.1 x 10 - 2 and 5"3 x 10 2 mm respectively when the steel stress was 207 N/mm 2. The average crack spacing was between 62.5 and 110 mm for Aglite concrete and between 97 and 134 mm for ordinary concrete. These tests were carried out one year after casting when most of the shrinkage would have taken place. Tests by Evans and Orangun[4] on Lytag concrete beams have shown a maximum crack width between 7 . 9 x 1 0 . 2 and 1 7 . 0 x l 0 - 2 m m and an average spacing between 125 and 188mm for beams reinforced with mild steel and between 8.9 x 10-2 and 25.4 x 10-2 and 62.5 and 157 mm respectively for beams reinforced with square twisted bars. These beams were also tested after several months when a substantial part of the shrinkage had taken place. These tests[4] have shown an increase of 15-500/o in crack width and a decrease of 20-40 o/ in crack spacing by using twisted bars instead of mild steel reinforcement. The results of Solite beams compare well with the results on other lightweight aggregate concretes--being between 5 × 10- z and 15 x 10-2mm, and between 58.6 and 109 mm for maximum crack width and average spacing respectively for the reinforced beams. For the prestressed beams these were 5 x l0 -2 mm and between 95.2 and 127 mm respectively. The small difference in crack width and crack spacing between the Solite beams and the gravel concrete beam of this investigation was mainly because they were tested at 28 days and cured under polythene sheet so that the shrinkage
Flexural Behaviour of Reinforced and Prestressed Solite Structural Lightweight Concrete Beams at the age of testing was by no means complete. Similar tests at 28 days[6] have shown that lightweight and ordinary concrete beams have similar crack characteristics. All the reinforced and prestressed beams in this investigation showed no cracks after unloading from the first cycle, and except for beams R3, P2 and P4, the beams gave the same maximum crack widths in the second cycle at design load as in the first cycle. The moment at first crack is further related to the design moment and ultimate moment for all the beams and tabulated in Table 3. For the reinforced beams, the ratio of the design to the first cracking moment varied from 1.80 to 4.0 while the ratio of the ultimate moment to the first cracking moment varied from 4.8 to 10.5. Comparing the Solite concrete beams R1 and RS1 with the gravel concrete beam O 1 having the same tensile steel ratio, the ratio of the design moment to the moment at first crack was respectively 3.32, 3.96 and 2.46. The corresponding ratio of ultimate moment to the moment at first crack was 9.6, 10-5 and 6.00 respectively. For the prestressed beams of series P, the ratio of the design moment to the moment at first crack was just about 1"00 in all cases while the ratio of the ultimate moment to the moment at first crack varied between 1.46 and 1.82. The maximum and minimum crack spacing in the pure flexural region for all the beams tested in this programme is also shown in Table 3. Considering the reinforced beams and the prestressed beams of series P, the maximum crack spacing varied between 60 and 165 mm whilst the minimum crack spacing varied between 13 and 95 mm. Crack spacings and crack widths are notoriously subject to wide
51
experimental scatter; nevertheless, the values obtained from these tests show a reasonable degree of consistency. The results of this investigation and those of others show that the cracking behaviour of lightweight aggregate concrete beams depends, to some extent, on the type of aggregate and the nature of the aggregate-matrix bond in addition to the percentage of reinforcement, the steel strain and the cover. In sintered clay concrete beams, for example, the cracks were about 4 0 ~ wider than in gravel concrete beams, and the cracks spaced about 60 closer[5]. In Solite beams, the maximum crack widths were about 8 and 2 5 ~ wider in all Solite and Solite with sand beams respectively than in gravel concrete beam with the same amount of tension steel. The average crack spacing was similar in all the three beams, but the minimum crack spacing varied widely. STRAIN D I S T R I B U T I O N The strain distribution over the depth of the beam was measured for each load increment in all the tests. From this data the variation of neutral axis depth with load was observed. Typical values of the depth of the neutral axis at the design moment and at the last load increment before failure obtained from the tests are shown in Table 4. The data showed that the strains were distributed approximately linearly above the neutral axis throughout the loading range, whereas the strain distribution below the neutral axis remained linear until cracking after which the strains tended to become rather erratic (figure 7). All the beams showed a progressive decrease in the neutral axis
Table 4. Strain characteristics of reinforced and prestressed Solite concrete beams
Beam No.
Tensile strain before cracking ( × 106m/m)
(1) Effective depth (mm)
R3 R2 R1 RS1 O1 P1 P2 P4 P3
302 242 118 170 270 753 694 800 1330
156 156 156 156 156 135 135 135 135
PS PS1 PS2 PS3
890
135 135 135 135
-
-
-
-
-
-
(2) Depth of neutralaxis at design M (mm)
Column (2)
74'5 80"0 99"0 83'5 78"5 96"0 93"0 99"0 100"2 (96"0) 102'0 102"0 104"0 96.0
0"475 0"51 0"63 0"535 0-505 0'71 0'69 0"73 0'74 (0.71) 0-755 0'755 0-77 0'71
(3)
Column (1)
Depth of neutralaxis at last reading (mm)
Column(3) Column (1)
Compressive strain at last reading ( x 106m/m)
51'0 63-0 95"0 74"0 74'0 82-5 81"0 86"0 76-0
0-325 0"41 0"61 0.475 0-475 0'61 0"60 0'64 0.56
2797 2437 3175 3250 2250 2555 1723 1506 2564
88'0 73-5 97"0 77-0
0.65 0'545 0-72 0'57
1740 2456 1808 1631
52
R. N . S w a m y a n d A. B. I b r a h i m
C O N C R E T E AND STEEL STRAINS
depth with increase in load. It was observed in the tests that immediately after the application of the first increment of load, and near failure, the neutral axis showed rapid decrease in depth. Further, Solite beams had generally a greater neutral axis
Load in KN
I
I
6000
P
1
i ,t"1
1/I
5000
AO00
Tensile
I
i
3000
2000 Strain
,/i
r
i
1000
i
|
0
I
i
I
1000
2000
Compr ess+ve
m/m x 105
(a) u~ t'-- trJ c~ ~o ~ Load in KN
I
8000
7000 6000 5000 Tensile
4000 3000 2000 1000
0
Strain --m/rn x 106
I
I
I
1000 2000 3000 4000 Compressive
(b) Fig. 7. Strain distribution on the vertical face o f test beams: (a) reinforced concrete beam R3 (b) prestressed concrete beam P3.
depth than that of the comparable ordinary concrete beam, and this was also the case near failure. This explains the validity of using Whitney's Theory[7] in calculating the ultimate moment of both lightweight and normal concrete beams because, while in the normal concrete beam, the top fibre stress at failure is generally higher than that in the comparable lightweight concrete beam, the neutral axis depth will be in reverse order in the two beams such that the concrete compressive area for both lightweight and normal concretes is equivalent to the rectangular stress block suggested by Whitney. Similar differences in neutral axis depth have also been observed between Lytag and ordinary concrete beams[4]. Tests on Solite and ordinary concrete prisms under constant strain showed that the ultimate stress of Solite prisms occurred at a strain of 0.3-0-35 % compared to a strain of about 0.2 % in gravel concrete. In Lytag concrete, this strain varied from 0.3 to 0.4 %[4].
The concrete compressive strain at the top fibre of the beams, and the strain in the steel reinforcement (except in beams with strands) was measured at every load stage in all the beams. Further, the concrete tensile strain up to flexural cracking was also measured. The concrete tensile strain before cracking and the concrete compressive strain prior to failure are shown in Table 4. The concrete tensile strain in the reinforced beams varied between 120 and 300x 10 -6 mm. The concrete compressive strain prior to failure in the reinforced beams varied between 2250 and 3 2 5 0 x 10 - 6 mm, the lowest value being in the gravel concrete beam. In the prestressed beams of series P, the concrete compressive strain varied between 1500 and 2 5 6 0 x 1 0 - 6 m m . The final measured values reported in Table 4 are necessarily conservative, a~ rapid changes in strain took place near failure, and the actual test values are likely to be much higher than those quoted in the table. The concrete compressive strain and the steel strain at the design load were almost the same for the first and second cycles of loading. Even during the third cycle, the difference in the strain values between the second and third cycles was negligible. The tension steel had reached yield strain in all the beams. In beams with two rows of reinforcement. the top steel generally took less strain, but after the bottom steel had yielded, their strain increased rapidly, and this happened at about 85-90 ~o of the ultimate load. The measured final steel strain varied from 2400 to 4000 x 10 -6 mm in the reinforced beams and from 1600 to 4 5 0 0 x 1 0 - 6 m m in the prestressed beams with wires. These values are again necessarily conservative as they were measured prior to failure and rapid changes of strain occur during failure. The lightweight aggregate concrete beams generally develop greater strains in the steel reinforcement than in normal concrete beams, because of the greater deflection due to their lower modulus of elasticity. A higher steel stress is therefore developed to compensate for the smaller lever arm.
DESIGN L O A D S The experimental moment at first crack and the calculated design moments for the reinforced and prestressed beams tested n this programme are shown in Table 5. The calculated design loads are based on the load factor method of CP11418] for reinforced beams and on permissible compressive strength in bending according to the Unified Code[2] and CPII0[9] for the prestressed beams.
Flexural Behaviour of Reinforced and Prestressed Solite Structural Lightweight Concrete Beams
53
Table 5. Experimental and calculated moments of Solite beams
Beam No.
Moment at first crack (N-M)
Design moment M (N-M)
Ultimate moment (unified) code Mr (N-M)
Ultimate moment (Whitney) Mu (N-M)
R3 R2 R1 RS1 O1
3700 3700 3700 3700 6370
6515 10370 12327 14734 15738
10963 17703 20192 24133 26790
PI P2 P4 P3*
13860 13860 13860 22300
21362 21362 22534 34180
25256 27052 27863 33643
23810 20340 25420 39830
PS PSI PS2 PS3
18100 --
15000 15000 15000 15000 22500 18000 15000 15000 15000
26910 26910 26910 26910
33200 29303 29668 32102
27455 19490 26730 21185
Experimental ultimate moment M exp (N-M)
Load factor (M exp/M)
M exp
M exp
Mr
Mu
2'70 2.32 2.89 2.65 2.42
1.61 1"36 1.76 1-61 1.42
1.30 1"07 1-11 1-16 1.11
1.59 1.36 1.70 1.77 2.65 1.52 1'30 1.78 1.41
1.11 0.95 1.13 1-16
0.94 0'75 0-912 1.18
1.02 0-73 0.99 0.79
0'827 0-66 0-90 0.66
Reinforced beams
-
-
--
13544 17626 22432 24065 32103 35590 33500 38980 34420 38130 Prestressed beams
*Design moment at concrete compressive stress of 17.3 N/mm 2 and 26-0 N/mm 2 respectively. F o r beam P3 which was stressed at transfer to 26.0 N / m m 2, the design moments are calculated for concrete compressive stresses of 17-3 and 26.0 N / m m 2. The experimental ultimate moments of all the beams are also shown in Table 5. The load factor o f Solite concrete reinforced beams varied from 2.32 to 2.89. F o r balanced steel ratio, these were 2.89 and 2.65 for all Solite and Solite with sand concrete beams respectively while the corresponding value for gravel concrete beam was 2-42. These results show that the load factor for Solite concrete beams in flexure is between 30 and 60% more than that recommended by C P l l 4 and 10-20% more than that of the corresponding ordinary gravel concrete beam. F o r the prestressed beams of series P the load factor for the design m o m e n t is a b o u t 1.6 for all the beams except for P2 for which the load factor was 1.36. This low value for beam P2 is probably due to the fact that when the beam was being unloaded in the second cycle it was already near failure, and it could not reach the same load in the third loading cycle. The load factor for the prestressed beams is generally less than that for reinforced beams mainly because the steel stress at the design m o m e n t in the prestressed beams is about 70% of the ultimate tensile strength o f the steel. For the prestressed beams of series PS, the load factor varied from 1.30 and 1.80. As was pointed out earlier these beams failed rather prematurely, and the experimental load factors for these beams are not a true indication o f their strength characteristics.
ULTIMATE MOMENTS Table 5 also shows the calculated ultimate moments for all the reinforced and prestressed beams tested. The ultimate moments were calculated according to both C P I I 0 [ 9 ] and Whitney's theory[7]. For the reinforced beams, the experimental ultimate moments are on average 10 % higher than that predicted by Whitney's theory (excepting beam R3 with very low tension steel). The ultimate moments of all Solite and Solite with sand concrete beams compare well with that o f the gravel concrete beam having the same reinforcement. The ultimate m o m e n t s predicted by CP110 appear to be generally conservative, the experimental values being 35-75 % higher than the predicted values. For the prestressed beams, Whitney's theory appears to overestimate the ultimate moment, whereas the values predicted by C P I I 0 were mostly the same as the experimental results. In beams with low a m o u n t of tension steel (1.12~), the small steel ratio results in a smaller stress block with consequently a longer lever arm, giving an unrealistically higher predicted value. In beam P3, the steel area (1.8%) was about 60% higher than in beams P1, P2 and P4, and both Whitney's theory and CP110 gave similar results which were about 17% less than the experimental moment. The results o f beams PSI, PS2 and PS3 do not show g o o d correlation between experimental and predicted moments because the beams were originally stressed and subsequently loaded to a design m o m e n t corresponding to a concrete stress o f
54
R. N. S w a m y and A. B. Ibrahim
26-0 N/mm 2 which made the transmission length at both ends longer than the length of the beam. On testing therefore by two point loads, the strands slipped resulting in premature failure. Even then, these three beams had an average load factor of 1.50.
la)
~a)
(b)
(b)
(c)
(c) Fig. 8. Cracking and mode of failure of Solite and normal aggregate reinforced concrete beams: (a) beam RI, p = 3-16~ (all Solite concrete) (b) beam RS1, p = 3.16% (Solite+sand concrete) (c) beam 01, p = 3"16 % (gravel concrete).
(d) M O D E OF FAILURE All the beams tested were under-reinforced and failed by yielding of the tension steel with considerable ultimate deflection followed by crushing of the compression concrete. Typical failure patterns are shown in figures 8 and 9.
Fig. 9. Cracking and mode of failure of Solite prestressed concrete beams: (a) beam P1 (wires, all Solite concrete)," (b) beam P2 (wires, Solite + sand concrete); (c) beam P3 (wires, all Solite); (d) beam PS (strands, all Solite); beams PI, P2 and PS stressed at 17.3 N/mm ~, beam P3 at 26.0 N/mm z.
Flexural Behaviour o f Reinforced and Prestressed Solite Structural Lightweight Concrete Beams Failure of Solite concrete beams generally tended to occur more rapidly than that in normal concrete beams, and often resulted in breaking up of the compression zone. The failure zone was generally larger both in extent and in depth than that of the ordinary concrete b e a m - - u p to 4 times in length and 2-4 times in depth (figures 8 and 9). In most failures, secondary shear cracks developed from the compression zone as failure of the beams fully materialised. Nevertheless, all the beams showed adequate ductility at failure, and the crushing of the compression zone was preceded by substantial deflection, visible cracking and ample warning of collapse.
CONCLUSIONS The following conclusions are drawn from the results reported in this paper. !. Solite reinforced and prestressed beams with concrete working stresses of 15.0-26.0 N / m m z can be satisfactorily designed according to C P l l 4 or CP110. For the reinforced beams the load factors against failure ranged 30-60% more than that required by the Code. For prestressed beams the load factors ranged between 1.50 and 2-65. 2. Deflection at design load of Solite lightweight concrete beams compares well with that of gravel concrete beams and is well within the calculated values according to the Draft Unified Code and the A.C.I. Code. It was about 15-20% more than the deflection of the normal aggregate beam of identical properties. The beams recovered on unloading 80-90 % of their deflection at design load. 3. The span-deflection ratios under permissible design moments varied between 291 and 434 for Solite reinforced beams compared with a value of 378 for gravel concrete beam. For the Solite prestressed beams, this ratio varied between 302 and 462.
55
4. The Solite reinforced and prestressed beams showed adequate ductility and substantial deflections prior to failure. The final measured deflection for all the beams varied between 1/70-1/150 of the span. 5. The crack width of reinforced beams at design load varied from 5 to 15 × 10 -2 m m and for prestressed beam the crack width was 5 × 10- 2 mm. The beams showed good crack distribution, and the crack spacing in the flexural zone varied between 59 and 109 m m and between 95 and 127 m m for reinforced and prestressed beams respectively. These values compare well with other lightweight aggregates, and the maximum crack width is less than the limiting crack width recommended by C P l l 0 . Almost all the cracks closed on unloading from the design load, and the crack widths at the design load in the second cycle of loading were the same as those in the first cycle. 6. The strain distribution over the depth of the Solite beams was similar to that in normal aggregate concrete beams throughout the loading. They were linear above the neutral axis, and the neutral axis depth decreased as the load increased. 7. The steel strain at design load remained the same for the first and second cycles of loading. 8. The ultimate moment of Solite beams agreed well with those calculated from Whitney's theory for both reinforced and prestressed beams except for prestressed beams with low tension steel. The calculated ultimate moments according to C P l l 0 underestimated the ultimate moments of the reinforced beams while they agreed well with the experimental results for the prestressed beams. 9. Solite beams had adequate ductility but tended to fail more rapidly than normal aggregate concrete beams. The failure zone was distinctly larger in Solite than in gravel concrete beams. Acknowledgements--The authors wish to express their gratitude to both Solite Ltd., Bwlchgwyn, N. Wales and to British Ropes Ltd. for their generous supply of raw materials.
REFERENCES 1. British Standards Institution: BS882 and 1201, Specification for Aggregates From Natural Sources for Concrete (Including Granolithic), London (1965). 2. British Standards Institution: Draft British Standard Code of Practice for the Structural Use of Concrete, London, Sept. (1969). 3. American Concrete Institute, Building Code Requirements for Reinforced Concrete (ACI 318-71), Detroit (1971). 4. R.H. EVANSand C. O. ORANGON,Behaviour in flexure of reinforced lightweight aggregate (Lytag) concrete beams, Civ. Engng Publ. Wks Rev., 59, May and June (1964). 5. T.R. HARDWICK,Lightweight structural concrete, Ph.D. Thesis, The University of Leeds (1961). 6. A. SHORT, The use of lightweight concrete for reinforced concrete construction, Reinf. Concr. Rev. 5, Sept. (1959).
56
R. N. Swamy and A. B. lbrahim 7. C. S. WHITNEY, Plastic theory for reinforced concrete design, Proc. Am. Soc. Test Mat. 66, Dec. (1940). 8. British Standards Institution, CP114, The Structural Use of Reinforced Concrete in Buildings, London (1969). 9. British Standards Institution, CPll0, The Structural Use of Concrete, Part 1, Design, Materials and Workmanship, London (1972).
I
I
I i
I
p
I
Flexural Behaviour of Reinforced and Prestressed Solite Structural Lightweight Concrete Beams R. N. SWAMY* A. B. IBRAHIM~"
The structural behaviour of reinforced and prestressed concrete beams made of expanded slate lightweight aggregate (Solite) concrete is discussed in relation to strength, cracking and deformation characteristics. The beams were designed to have permissible concrete stresses of 15.0-26-0 N/mm 2, and the cube strength of the concrete was 35-40 N/mm 2 in one day and about 50 N/mm z at 28 days. The deflection, cracking and the strength characteristics of the beams have been studied throughout their flexural loading range, and their mode of failure. It is shown that Solite lightweight concrete beams possess adequate ductility and load factor, and satisfy all the serviceability requirements of current Codes of Practice.
Tests are therefore reported here on the shortterm flexural behaviour of reinforced and prestressed concrete beams made of expanded slate lightweight aggregate. The beams were designed to have a working stress of 17.3 or 26.0 N / m m 2. The beams were tested to failure in flexure and their structural behaviour in terms of strength, cracking and deformation is discussed.
INTRODUCTION
E X P A N D E D SLATE (Solite) is a relatively new addition to the list of lightweight aggregates currently available in the U.K. It is manufactured in N. Wales from the slate deposits of the Silurian period of the Palaeozoic era by an expansive rotary kiln process. The resulting aggregate is chemically inert, stable and of good quality with a highly vitrified internal pore structure. The aggregate is strong and possesses low water absorption. With the current shortage of good quality natural aggregates in several parts of the country, lightweight aggregates are being increasingly used in reinforced and prestressed structural members, and design data and an understanding of their structural behaviour are necessary to establish their serviceability in practice. Because of the lower modulus of elasticity of lightweight concrete, the short- and long-term deflection of lightweight concrete beams will be greater than that of normal concrete beams. Also, for a given load the strain in the reinforcement is likely to be greater which is likely to produce more and wider cracks. The deformation and cracking characteristics of structural members are therefore important in design. Although data on the flexural behaviour of lightweight aggregate concretes in U.K. are available, these are confined to aggregates other than Solite.
EXPERIMENTAL
PROGRAMME
The aim of this investigation was to study the flexural behaviour and to establish the serviceability characteristics of reinforced and prestressed concrete beams made of Solite lightweight aggregate. Altogether 13 beams were tested and their details are given below. DETAILS OF REINFORCED
BEAMS
Five reinforced beams were tested. Three beams were of all Solite concrete (mix S1) having steel ratios of 1.14, 2.03 and 3.16%. The other two beams having a steel ratio of 3"16% were made from Solite with sand concrete (mix $2) and normal gravel concrete respectively. All the beams had the same width and effective depth and adequately reinforced for shear as shown in figure 1. The details of these beams are shown in Table I. DETAILS OF PRESTRESSED
*Department of Civil and Structural Engineering, University of Sheffield. tUniversity of Mosul, lraq; formerly of the Department of Civil and Structural Engineering, University of Sheffield.
BEAMS
Eight prestressed beams were tested--four at 28 days and one at three months (series P). The other 43
44
R. N. Swamy and A. B. lbrahim 752
F~ . . . . . . . . . . . . . . . . . . .
H
_
~'~J
-
%
2286 2438
I"-
~-6mm at lO0mm C/C
- Etectrical Resstonce Strain Gouge • Dernec Strain Gouge Disc (a) Typical Longitudinal Section I'
Beams R1, RS1 and 01 'Aste 2-12rnm Top 2-16mm Bottom
127 ~.j
127
I"
--fl
Beam R3
Beam R2 Ast,, 2-6ram (b) Cross Section All Neesurements in mm
Fig. 1. Details o f reinforced test beams.
three beams (PS1, PS2 and PS3 of series PS) were tested after they had been subjected to a sustained design load corresponding to an extreme fibre concrete compressive stress of 26-0 N / m m 2 for four days, and then left unloaded for one year exposed to the outside environment covered with polythene sheet. These latter beams were exploratory tests, tested particularly to study their ultimate load and deflection characteristics under permissible concrete compressive stresses of 26.0 N / m m 2. All the beams were prestressed such that the stress at the top fibre was zero. Beams P1, P2 and P4 were identical--Pl and P4
P
being from all Solite concrete, and beam P2 from Solite with sand concrete. These beams were stressed with wires with a concrete stress at transfer of 17.3 N / m m 2. Beam P3 made from all Solite concrete was also stressed with wires but with a concrete stress at transfer of 26.0 N/mrn z. All the other four beams were prestressed with Dyform strands. Beam PS had a stress at transfer of 17.3 N / m m 2 while the three beams of the PS series, retested after sustained loading, had a stress at transfer of 26.0 N / m m 2. Details of these beams are shown in figure 2 and Table 1.
762
;i0 -
'4
-I-I-I-I-I-L-I-t-I!1 PI
Electrical Res,st ..... Stra,n4Gouge • Demec Strain Gauge D~c
at 10Omm C/C
(o) Typical Longitudinal Section ~, 127
Beams R1, RS1 and 01 AstO 2-12rr~n Top 2 16ram Bottom
F 127~-"1
I" 127
Beam R2 Asto 2q6mm
Beam R3 AstO2-12mm
(b] Cross Section AU Measurements in mm
Fig. 2. Details o f prestressed test beams.
.~
S1 S1 S1
S2
O.C.
S1 $2 $1 S1 S1 S1 Sl S2
R3 R2 R1
RSI
O1
P1 P2 P4§ P3 PS PSlll PS211 PS3II
42.5 48'5 51.2 50.9 48.3 47.0 48'0 54'5
59'6
51.0
44.4 42.5 44.5
36"0 41"2 39.5 40'4 40-5 ----
44.0
36'3 36'0 37"6
Cylinder strength ( N / m m 2)
*S1 = All Solite mix. $2 = Solite with s a n d mix. O.C. = O r d i n a r y concrete. t U l t i m a t e tensile strength for prestressed steel. :]:Zero stress at T e p Fibre. §Tested at 3 m o n t h s . ]tTested at one year. All o t h e r b e a m s tested at 28 days.
Mix* type
Beam No.
Cube strength ( N / m m 2)
17.93 35.36
2.9 --
127 x 156
127 x 156
127 x 156 127 x 156 127 x 156
17.61 19'50 17"00 16.50 18'06 ----
127 x 127 x 127 x 127 x 152 x 127 x 127 x 127 x
135 135 135 135 135 135 135 135
Prestressed b e a m s
17"40 17'60 16.80
2.9 3"0 2-9 2'9 2.8 ----
Bxd (mm)
Reinforced b e a m s
Y-modulus E ( k n / m m 2)
2"5 2"9 2"9
Flexural strength ( N / m m 2)
5-7 5-7 5-7 8-7 2-12.7 2-12.7 2-12-7 2-12.7
2-12 2-16 2-16~ 2-12J 2-16~ 2-12J 2-16~ 2-12J
Reinforcem e n t No. a n d size (mm)
1.122 1'122 1.122 1-795 1"09 1'308 1.308 1'308
3.16 628.6
410
192.5 192.5 192.5 308.0 224 224 224 224
3-16
628.6
410
1730 1730 1730 1730 1960 1960 1960 1960
1"14 2"03 3"16
(%)
Steel ratio As/bd
226"3 402-3 628'6
Area of steel As ( m m 2)
410 410 410
Yield stress? ( N / m m 2)
Table 1. Details of Solite concrete reinforced and prestressed beams
17'3 17'3 17"3 26"0 17"3 26"0 26"0 26"0
m
Prestress~ at b o t t o m fibre ( N / m m 2)
4~
9
t~
¢5
~o
t~
t~
t~
R. N. Swamy and A. B. lbrahim
46 MATERIALS
The Solite concrete mixes S 1 and $2 were designed to give a cube strength of 35-40 N/mm 2 at one day and about 50 N/mm 2 at 28 days. To achieve the high early strength a finely ground Portland cement with a surface area of over 700 m2/kg was used. The cement content of the mixes was 540 kg/m 3. The total aggregate-cement ratio was 2.0 by weight with a ratio of fines to coarse of 0.44, and a watercement ratio of 0-55. Mix SI consisted of both lightweight coarse and fines whilst for mix $2 67 % of the lightweight fines were replaced by natural sand of Zone 2 grading[l]. The plastic density of the concrete varied from 1740 to 1860 kg/m 3 and the dry density at 28 days from 1680 to 1730 kg/m 3. The workability of the mixes varied from 4.0 to 4.5VB seconds immediately after mixing. The strength properties of the concrete used in the beam tests and its elastic moduli are shown in Table 1. One reinforced beam 01 was made with graded crushed gravel aggregate with a maximum size of 19ram (3/4in.), natural sand and very fine Portland cement. The mix proportions used were l: 1.05:2.45 with a water-cement ratio of 0-39. The reinforcement for the tensile steel in the reinforced beams and the web reinforcement in both reinforced and prestressed beams consisted of high tensile hot-rolled deformed bars with a minimum yield strength of 410N/ram 2. For prestressed beams, Bridon low-relaxation 7 mm indented wires and Dyform low-relaxation 12.7 mm seven wire strands having a minimum tensile strength of 1570 and 1920N/mm 2 respectively were used. The properties of the steel reinforcement used in the tests are shown in Table 1.
M A N U F A C T U R E AND TESTING OF BEAMS All the beams were cast in steel moulds. With each beam control specimens for compressive strength, modulus of rupture and modulus of elasticity were also cast. In the prestressed beams, the prestress was transferred at seven days. All the beams and the control specimens were cured in the laboratory under polythene sheets. The strain on the reinforcement bars and wires was determined through electrical resistance gauges. In addition, the concrete tensile and compressive strains in the pure bending region were also determined by electric resistance gauges. The strain distribution on the vertical face of the beams in the flexural region was determined through a de-
mountable mechanical extensometer with a sensitivity of 3 - 5 x 10 - 6 m/m. Further, the central deflection and maximum crack widths at the extreme tensile face were also measured. All the beams were tested at 28 days except P4 which was tested at three months, and beams PSI, PS2 and PS3 (of series PS) which were tested at one year. The beams were loaded under two point loads 762 mm apart on a span of 2286 mm (figures I and 2). The reinforced beams were loaded in three cycles, the first to the calculated design load, the second to hail-way between the design and ultimate load, and the third extending to the ultimate load. The prestressed beams of series P except beam P2, were loaded in two cycles. The prestressed beams of series PS were all tested to ultimate load in one cycle. All strain measurements, deflection and maximum crack widths were measured at every load increment. All electrical strain gauges were recorded through a data logger.
TEST RESULTS The main objective of this series of tests was to investigate the flexural behaviour of structural lightweight concrete beams throughout the loading range up to failure. The results obtained from the tests regarding deflection, cracking and load capacity are discussed and compared with the corresponding Solite with sand concrete beams and normal concrete beams.
DEFLECTION CHARACTERISTICS The load-deflection characteristics of typical reinforced and prestressed beams are shown in figures 3-6, which also show the number of cracks and the maximum crack width in the flexural region measured during each cycle of loading. In the tests on the reinforced beams the first loading cycle extended to the design load corresponding to a
9of
,~b
80 70
a
w2, f.... ,°2
q' 25 ,
z 60
~,, I
////
c u 50
b
/1/a.,/b
I I
13
- J LO
', I
] I
I I '~ r
30
. . . . . . . . . ~. 2 5
10 Deflection - mm
•
~ 15
2
2 20
Fig. 3. Deflection and cracking characteristics o f all Solite reinforced concrete beam RI.
Flexural Behaviour of Reinforced and Prestressed Solite Structural Lightweight Concrete Beams
9O
80
el- maximum crack width rnm xlO 2
7O
~/" zu\ ~ . . ~ ' o ~ b~, _
z 50
115 [
\
~ 5c
,//O ~7~5°~b
b
3
7"5~13
I
1\0~-~13
3[
/ -x
2[
~1
10 0
2
-.
6
8 10 12 Deflection rnm
1l.
15
16
20
Fig. 4. Deflection and cracking characteristics of Solite with sand reinforced beams RS1.
b.
a
102"3 00
a-- maximum crock width: mm x 102 ~
9oi
b-- no. of cracks ~
2
7.5 ~] !
60
20 10 0 0
11
12.~.
7c
3O
11
17 5
8[
i 50 /,0
I/,
/,5355~
//~'/,
6
5
6
2.= 4
,
5
10
7=,
,
10
,
,
,
,
,
15 20 Deflection --ram
,
25
,
30
Fig. 5. Deflection and cracking behaviour of Solite prestressed beam P3.
o.
7£
a. maximum crock
6(
b nc ~f crocks
w,~fh. . . . 102
jj~-
8
//7. .o
50
~
-
b.
2~2~ 1076 ~ 8 ~ 8
b.
~5~
7
Z
z /,o c_
N o, 30 2C 10 0
~11 2
[ 4
I 6
~ i I 8 10 12 DefLection - mm
I 1/,
I 16
t 1B
I 20
Fig. 6. Deflection and cracking behaviour of Solite prestressed beam PS with strands.
whereas in the prestressed beams the second cycle (except in beam P2) extended to the ultimate load. The prestressed beams of the PS series were all tested to destruction in one loading cycle. In all the tests visible cracking occurred during the first cycle, and the deflection curve of the second cycle, after cracking, generally followed the continuation of that of the first cycle. Similar behaviour also occurred during the third cycle before yielding commenced (figures 3-6). The data obtained from the tests, such as, the deflection at the design moment, the residual central deflection on unloading after the first cycle of loading up to the design load and the final deflection measured prior to failure are shown in Table 2. In the tests with the prestressed beams, the tendons were stressed against the moulds in which the beams were cast and it was impractical to measure the camber of the beams at transfer. The calculated and measured deflections shown in Table 2 are therefore, due to external load only. Under the permissible working loads, the deflection in the reinforced and prestressed beams of series P varied between 4.95 and 7.85 mm, the maximum value being for the reinforced beam R2 with low amount of tension steel. For a nearly balanced section, the deflection at the design load for the reinforced beams of all Solite, Solite with sand and gravel concrete beams was respectively 5-26, 7.20 and 6.04 ram. In considering deflection it must be remembered that Solite concrete had about half the Young's modulus of gravel concrete. The residual deflection after the first cycle of loading up to the design moment during which visible cracking had occurred was above 1 mm for the reinforced beams, and less than 1 mm for the prestressed beams of series P. The data show that the Solite beams, except beam R3 with very low tension steel (1"14~o), recovered nearly 8 0 ~ of their deflection compared to 75% of its deflection recovered by the gravel concrete beam. For all the beams the deflection at the beginning of the second cycle at the design load was nearly the same as that at the first cycle as shown in the typical figures 3-6. Table 2 also shows the predicted deflections at the design moment. These deflections were calculated from the basic formula. = K4'L 2
permissible tensile stress of 210 N / m m 2 in the steel reinforcement and a compressive stress of cube strength/2.73 in concrete. In the tests on the prestressed beams of series P, the applied load in the first loading cycle corresponded to a permissible concrete stress of 17.3 N / m m 2. The second cycle for the reinforced beams generally extended to about half-way between the design and ultimate load,
47
0)
where K = a factor depending on the type of loading q~ = curvature of the beam, and, L = effective length of the beam the curvature ~b was calculated according to both the Draft Unified Code[2] and the A.C.I. Code [3].
6515 10370 12330 14730 15740 15000 15000 15000 15000 22500 18000 15000 15000 15000
*Beams tested at one year
PS PSI PS2 PS3
R3 R2 R1 RS1 Ol P1 P2 P4 P3
Beam No.
Design moment M (N-M)
5-35 7.85 5-26 7.20 6.04 7-57 6.70 6.95 4.95 7.27 6.29 14-30 5"90 9.50
(1) Deflection at M (mm)
-
0.67 ----
-
1-88 1-45 1 '05 1'55 1.52 0.89 0.67 0.63 0.80
Residual deflection (unloaded) (mm)
35"0 18.5 20.0 21 '5 25-0 11.7 10-0 9"1 16.2 11.0 10"6 ----
Percentage o f residual deflection on deflection at M
4.79 6'69 6-09 7.42 5.74 7.02 7-02 7.02 5.24 8.2 5.46 5.44* 5-44* 5.44*
(2) Deflection at M (unified code) (mm)
5-0 6.4 5-7 6.9 5"64 6.51 6"51 6.51 5.25 8.3 5'4 5.39 5-39 5-39
(3) Deflection at M ( A C I code) (mm)
1'12 1.18 0.87 0.97 1'05 1.08 0"95 0.99 0.95 0.88 1"15 2.62 1.08 1.74
C o l u m n (2)
C o l u m n (1)
1-06 1.22 0.925 1.04 1'07 1.16 1.03 1.06 0-95 0.87 1.16 2.65 1"09 1'76
C o l u m n (3)
C o l u m n (1)
Table 2. Deflection characteristics of Solite reinforced and prestressed concrete beams
427 291 434 317 378 302 341 329 462 314 363 160 387 241
Deflection at M
Span
33.07 31"85 18.93 20.78 22-83 19.33 23.55 15.60 25.64 -18-64 21.31 12.25 17.55
Deflection prior to failure (mm)
4~ o0
3700 3700 3700 3700 6370 13860 13860 13860 22300 18100 ----
No.
R3 R2 R1 RS1 O1 P1 P2 P4 P3 PS PSI PS2 PS3
Beam
Moment at first crack mcr (N-M)
4-4 4"4 4"2 4.2 7.2 2.84 2-67 3.08 4'82 2.90 ----
Flexural stress at first crack ( N / m m 2)
2.5 2.9 2.9 2.9 -2-9 3.0 2"9 2.9 2.8 ----
Flexural stress (prisms) ( N / r a m z)
6515 10370 12330 14730 15740 15000 15000 15000 22500 18000 15000 15000 15000
Design moment M (N-M)
17626 24065 35590 38980 38130 23810 20340 25420 39830 27455 19490 26780 21185
Ultimate moment Mu (N-M)
15 5 6.5 7.5 6 5 5 5 5 5 ----
Maximum crack width at M ( × 102mm)
109 96 58,6 58.6 54.4 95.2 108.9 127 108"9 108.9 108.9 127 127
Average crack spacing at M (mm)
7 8 13 13 14 8 7 6 7 7 7 6 6
No, of cracks between loading points at M
60 108 89 102 102 165 140 165 83 159 229 330 197
Maximum crack spacing at M (mm)
Table 3. Crack characteristics of Solite reinforced and prestressed concrete beams
15 44 13 44 57 22 95 19 38 57 32 25 76
Minimum spacing at M (ram)
1-76 2"80 3-32 3"96 2"46 1-08 1'08 1.08 1'005 0.995 ----
mcr
M
4,75 6-50 9'6 10-5 6"00 1-72 1'46 1'82 1,78 1.52 ----
mcr
Mu
r~
e~
%
t~
50
R. N. Swamy and A. B. lbrahhn
From Table 2 it is seen that the deflection at the design load predicted by both methods compares well with the experimental results. Although the number of beams tested are limited to give a final comparison with ordinary concrete, the results show no significant difference in deflection between Solite and gravel concrete beams having the same steel ratio. In general, at the same applied moment, the deflection in ordinary gravel concrete beam was about 15-20 ~ less than that of Solite concrete beams. The span-deflection ratios under the permissible working load varied cetween 291 and 434 for the Solite reinforced beams compared to the value of 378 for the gravel concrete beam. For the Solite prestressed beams of series P, this ratio varied between 302 and 462. Tests by Evans and Orangun[4] on Lytag concrete beams with square twisted bars and a cube strength of 44.5 N/mm 2 showed span-deflection ratios between 487 and 671. However, the steel stress for the Lytag concrete beams was 196 N/mm 2 and the span-depth ratio 7.6 whereas the corresponding values for the Solite concrete beams in this investigation were 207 N/mm z and 14.6 respectively. The typical deflection diagrams shown in figures 3-6 indicate that all the Solite concrete beams had adequate ductility and showed substantial deflections at failure. The final deflections shown in Table 2 were measured prior to failure as near to collapse as poss ble. For the reinforced beams the measured final deflection varied between 1/70 to 1/120 of the span compared to 1/ 100 of the span for the gravel concrete beam. For the prestressed beams of series P, the measured final deflection varied between 1/90-I/150 of the span. These values are characteristic of those obtained by the yielding of the tension steel and even after failure, the beams showed appreciable recovery. The deflection properties and the span-depth ratios of the prestressed beams of series PS should not be interpreted too severely. These were exploratory tests with a concrete stress at transfer of 26.0 N/mm 2. Further, the beams had initially been subjected to a sustained load corresponding to 7 0 - 8 0 ~ of the ultimate load, and cracked, and retested after one year of exposure and prestress losses. These beams had inadequate transmission length as explained later, and all the beams failed prematurely.
CRACKING B E H A V I O U R The maximum crack widths at the tensile face and the crack spacing were measured at every load stage in all the tests, and the cracks marked on the beams. These are shown in figures 3 and 4 for typical prestressed beams P3 and PS. The experimental
data on maximum crack width and crack spacing at the design load are tabulated in Table 3. It is shown that with Solite reinforced beams the crack width at the design load varied between 5 and 1 5 × 1 0 - Z m m , the maximum value corresponding to a highly under reinforced beam. The ordinary gravel concrete beam had a crack width of 6 x 10 -2 mm compared with a crack width of 6.5x 10 . 2 and 7.5x 10 -2 mm at design load for the two Solite beams R I and RSI respectively having the same steel ratio. These working load crack widths are by no means excessive, and are well within the acceptable limiting crack widths necessary for durability. The flexural stress at first crack has also been calculated for the reinforced and prestressed beams from the load at first crack when it was first visually observed and shown in Table 3. For the prestressed beams, the net concrete compressive stress due to prestress was calculated by allowing elastic, shrinkage, creep and relaxation of steel losses from the 7 days, when the stress was transferred, up to the age of test. Tests by Hardwick[5] showed that the crack width of Aglite and ordinary concrete beams with mild steel bars of different percentages was 7.1 x 10 - 2 and 5"3 x 10 2 mm respectively when the steel stress was 207 N/mm 2. The average crack spacing was between 62.5 and 110 mm for Aglite concrete and between 97 and 134 mm for ordinary concrete. These tests were carried out one year after casting when most of the shrinkage would have taken place. Tests by Evans and Orangun[4] on Lytag concrete beams have shown a maximum crack width between 7 . 9 x 1 0 . 2 and 1 7 . 0 x l 0 - 2 m m and an average spacing between 125 and 188mm for beams reinforced with mild steel and between 8.9 x 10-2 and 25.4 x 10-2 and 62.5 and 157 mm respectively for beams reinforced with square twisted bars. These beams were also tested after several months when a substantial part of the shrinkage had taken place. These tests[4] have shown an increase of 15-500/o in crack width and a decrease of 20-40 o/ in crack spacing by using twisted bars instead of mild steel reinforcement. The results of Solite beams compare well with the results on other lightweight aggregate concretes--being between 5 × 10- z and 15 x 10-2mm, and between 58.6 and 109 mm for maximum crack width and average spacing respectively for the reinforced beams. For the prestressed beams these were 5 x l0 -2 mm and between 95.2 and 127 mm respectively. The small difference in crack width and crack spacing between the Solite beams and the gravel concrete beam of this investigation was mainly because they were tested at 28 days and cured under polythene sheet so that the shrinkage
Flexural Behaviour of Reinforced and Prestressed Solite Structural Lightweight Concrete Beams at the age of testing was by no means complete. Similar tests at 28 days[6] have shown that lightweight and ordinary concrete beams have similar crack characteristics. All the reinforced and prestressed beams in this investigation showed no cracks after unloading from the first cycle, and except for beams R3, P2 and P4, the beams gave the same maximum crack widths in the second cycle at design load as in the first cycle. The moment at first crack is further related to the design moment and ultimate moment for all the beams and tabulated in Table 3. For the reinforced beams, the ratio of the design to the first cracking moment varied from 1.80 to 4.0 while the ratio of the ultimate moment to the first cracking moment varied from 4.8 to 10.5. Comparing the Solite concrete beams R1 and RS1 with the gravel concrete beam O 1 having the same tensile steel ratio, the ratio of the design moment to the moment at first crack was respectively 3.32, 3.96 and 2.46. The corresponding ratio of ultimate moment to the moment at first crack was 9.6, 10-5 and 6.00 respectively. For the prestressed beams of series P, the ratio of the design moment to the moment at first crack was just about 1"00 in all cases while the ratio of the ultimate moment to the moment at first crack varied between 1.46 and 1.82. The maximum and minimum crack spacing in the pure flexural region for all the beams tested in this programme is also shown in Table 3. Considering the reinforced beams and the prestressed beams of series P, the maximum crack spacing varied between 60 and 165 mm whilst the minimum crack spacing varied between 13 and 95 mm. Crack spacings and crack widths are notoriously subject to wide
51
experimental scatter; nevertheless, the values obtained from these tests show a reasonable degree of consistency. The results of this investigation and those of others show that the cracking behaviour of lightweight aggregate concrete beams depends, to some extent, on the type of aggregate and the nature of the aggregate-matrix bond in addition to the percentage of reinforcement, the steel strain and the cover. In sintered clay concrete beams, for example, the cracks were about 4 0 ~ wider than in gravel concrete beams, and the cracks spaced about 60 closer[5]. In Solite beams, the maximum crack widths were about 8 and 2 5 ~ wider in all Solite and Solite with sand beams respectively than in gravel concrete beam with the same amount of tension steel. The average crack spacing was similar in all the three beams, but the minimum crack spacing varied widely. STRAIN D I S T R I B U T I O N The strain distribution over the depth of the beam was measured for each load increment in all the tests. From this data the variation of neutral axis depth with load was observed. Typical values of the depth of the neutral axis at the design moment and at the last load increment before failure obtained from the tests are shown in Table 4. The data showed that the strains were distributed approximately linearly above the neutral axis throughout the loading range, whereas the strain distribution below the neutral axis remained linear until cracking after which the strains tended to become rather erratic (figure 7). All the beams showed a progressive decrease in the neutral axis
Table 4. Strain characteristics of reinforced and prestressed Solite concrete beams
Beam No.
Tensile strain before cracking ( × 106m/m)
(1) Effective depth (mm)
R3 R2 R1 RS1 O1 P1 P2 P4 P3
302 242 118 170 270 753 694 800 1330
156 156 156 156 156 135 135 135 135
PS PS1 PS2 PS3
890
135 135 135 135
-
-
-
-
-
-
(2) Depth of neutralaxis at design M (mm)
Column (2)
74'5 80"0 99"0 83'5 78"5 96"0 93"0 99"0 100"2 (96"0) 102'0 102"0 104"0 96.0
0"475 0"51 0"63 0"535 0-505 0'71 0'69 0"73 0'74 (0.71) 0-755 0'755 0-77 0'71
(3)
Column (1)
Depth of neutralaxis at last reading (mm)
Column(3) Column (1)
Compressive strain at last reading ( x 106m/m)
51'0 63-0 95"0 74"0 74'0 82-5 81"0 86"0 76-0
0-325 0"41 0"61 0.475 0-475 0'61 0"60 0'64 0.56
2797 2437 3175 3250 2250 2555 1723 1506 2564
88'0 73-5 97"0 77-0
0.65 0'545 0-72 0'57
1740 2456 1808 1631
52
R. N . S w a m y a n d A. B. I b r a h i m
C O N C R E T E AND STEEL STRAINS
depth with increase in load. It was observed in the tests that immediately after the application of the first increment of load, and near failure, the neutral axis showed rapid decrease in depth. Further, Solite beams had generally a greater neutral axis
Load in KN
I
I
6000
P
1
i ,t"1
1/I
5000
AO00
Tensile
I
i
3000
2000 Strain
,/i
r
i
1000
i
|
0
I
i
I
1000
2000
Compr ess+ve
m/m x 105
(a) u~ t'-- trJ c~ ~o ~ Load in KN
I
8000
7000 6000 5000 Tensile
4000 3000 2000 1000
0
Strain --m/rn x 106
I
I
I
1000 2000 3000 4000 Compressive
(b) Fig. 7. Strain distribution on the vertical face o f test beams: (a) reinforced concrete beam R3 (b) prestressed concrete beam P3.
depth than that of the comparable ordinary concrete beam, and this was also the case near failure. This explains the validity of using Whitney's Theory[7] in calculating the ultimate moment of both lightweight and normal concrete beams because, while in the normal concrete beam, the top fibre stress at failure is generally higher than that in the comparable lightweight concrete beam, the neutral axis depth will be in reverse order in the two beams such that the concrete compressive area for both lightweight and normal concretes is equivalent to the rectangular stress block suggested by Whitney. Similar differences in neutral axis depth have also been observed between Lytag and ordinary concrete beams[4]. Tests on Solite and ordinary concrete prisms under constant strain showed that the ultimate stress of Solite prisms occurred at a strain of 0.3-0-35 % compared to a strain of about 0.2 % in gravel concrete. In Lytag concrete, this strain varied from 0.3 to 0.4 %[4].
The concrete compressive strain at the top fibre of the beams, and the strain in the steel reinforcement (except in beams with strands) was measured at every load stage in all the beams. Further, the concrete tensile strain up to flexural cracking was also measured. The concrete tensile strain before cracking and the concrete compressive strain prior to failure are shown in Table 4. The concrete tensile strain in the reinforced beams varied between 120 and 300x 10 -6 mm. The concrete compressive strain prior to failure in the reinforced beams varied between 2250 and 3 2 5 0 x 10 - 6 mm, the lowest value being in the gravel concrete beam. In the prestressed beams of series P, the concrete compressive strain varied between 1500 and 2 5 6 0 x 1 0 - 6 m m . The final measured values reported in Table 4 are necessarily conservative, a~ rapid changes in strain took place near failure, and the actual test values are likely to be much higher than those quoted in the table. The concrete compressive strain and the steel strain at the design load were almost the same for the first and second cycles of loading. Even during the third cycle, the difference in the strain values between the second and third cycles was negligible. The tension steel had reached yield strain in all the beams. In beams with two rows of reinforcement. the top steel generally took less strain, but after the bottom steel had yielded, their strain increased rapidly, and this happened at about 85-90 ~o of the ultimate load. The measured final steel strain varied from 2400 to 4000 x 10 -6 mm in the reinforced beams and from 1600 to 4 5 0 0 x 1 0 - 6 m m in the prestressed beams with wires. These values are again necessarily conservative as they were measured prior to failure and rapid changes of strain occur during failure. The lightweight aggregate concrete beams generally develop greater strains in the steel reinforcement than in normal concrete beams, because of the greater deflection due to their lower modulus of elasticity. A higher steel stress is therefore developed to compensate for the smaller lever arm.
DESIGN L O A D S The experimental moment at first crack and the calculated design moments for the reinforced and prestressed beams tested n this programme are shown in Table 5. The calculated design loads are based on the load factor method of CP11418] for reinforced beams and on permissible compressive strength in bending according to the Unified Code[2] and CPII0[9] for the prestressed beams.
Flexural Behaviour of Reinforced and Prestressed Solite Structural Lightweight Concrete Beams
53
Table 5. Experimental and calculated moments of Solite beams
Beam No.
Moment at first crack (N-M)
Design moment M (N-M)
Ultimate moment (unified) code Mr (N-M)
Ultimate moment (Whitney) Mu (N-M)
R3 R2 R1 RS1 O1
3700 3700 3700 3700 6370
6515 10370 12327 14734 15738
10963 17703 20192 24133 26790
PI P2 P4 P3*
13860 13860 13860 22300
21362 21362 22534 34180
25256 27052 27863 33643
23810 20340 25420 39830
PS PSI PS2 PS3
18100 --
15000 15000 15000 15000 22500 18000 15000 15000 15000
26910 26910 26910 26910
33200 29303 29668 32102
27455 19490 26730 21185
Experimental ultimate moment M exp (N-M)
Load factor (M exp/M)
M exp
M exp
Mr
Mu
2'70 2.32 2.89 2.65 2.42
1.61 1"36 1.76 1-61 1.42
1.30 1"07 1-11 1-16 1.11
1.59 1.36 1.70 1.77 2.65 1.52 1'30 1.78 1.41
1.11 0.95 1.13 1-16
0.94 0'75 0-912 1.18
1.02 0-73 0.99 0.79
0'827 0-66 0-90 0.66
Reinforced beams
-
-
--
13544 17626 22432 24065 32103 35590 33500 38980 34420 38130 Prestressed beams
*Design moment at concrete compressive stress of 17.3 N/mm 2 and 26-0 N/mm 2 respectively. F o r beam P3 which was stressed at transfer to 26.0 N / m m 2, the design moments are calculated for concrete compressive stresses of 17-3 and 26.0 N / m m 2. The experimental ultimate moments of all the beams are also shown in Table 5. The load factor o f Solite concrete reinforced beams varied from 2.32 to 2.89. F o r balanced steel ratio, these were 2.89 and 2.65 for all Solite and Solite with sand concrete beams respectively while the corresponding value for gravel concrete beam was 2-42. These results show that the load factor for Solite concrete beams in flexure is between 30 and 60% more than that recommended by C P l l 4 and 10-20% more than that of the corresponding ordinary gravel concrete beam. F o r the prestressed beams of series P the load factor for the design m o m e n t is a b o u t 1.6 for all the beams except for P2 for which the load factor was 1.36. This low value for beam P2 is probably due to the fact that when the beam was being unloaded in the second cycle it was already near failure, and it could not reach the same load in the third loading cycle. The load factor for the prestressed beams is generally less than that for reinforced beams mainly because the steel stress at the design m o m e n t in the prestressed beams is about 70% of the ultimate tensile strength o f the steel. For the prestressed beams of series PS, the load factor varied from 1.30 and 1.80. As was pointed out earlier these beams failed rather prematurely, and the experimental load factors for these beams are not a true indication o f their strength characteristics.
ULTIMATE MOMENTS Table 5 also shows the calculated ultimate moments for all the reinforced and prestressed beams tested. The ultimate moments were calculated according to both C P I I 0 [ 9 ] and Whitney's theory[7]. For the reinforced beams, the experimental ultimate moments are on average 10 % higher than that predicted by Whitney's theory (excepting beam R3 with very low tension steel). The ultimate moments of all Solite and Solite with sand concrete beams compare well with that o f the gravel concrete beam having the same reinforcement. The ultimate m o m e n t s predicted by CP110 appear to be generally conservative, the experimental values being 35-75 % higher than the predicted values. For the prestressed beams, Whitney's theory appears to overestimate the ultimate moment, whereas the values predicted by C P I I 0 were mostly the same as the experimental results. In beams with low a m o u n t of tension steel (1.12~), the small steel ratio results in a smaller stress block with consequently a longer lever arm, giving an unrealistically higher predicted value. In beam P3, the steel area (1.8%) was about 60% higher than in beams P1, P2 and P4, and both Whitney's theory and CP110 gave similar results which were about 17% less than the experimental moment. The results o f beams PSI, PS2 and PS3 do not show g o o d correlation between experimental and predicted moments because the beams were originally stressed and subsequently loaded to a design m o m e n t corresponding to a concrete stress o f
54
R. N. S w a m y and A. B. Ibrahim
26-0 N/mm 2 which made the transmission length at both ends longer than the length of the beam. On testing therefore by two point loads, the strands slipped resulting in premature failure. Even then, these three beams had an average load factor of 1.50.
la)
~a)
(b)
(b)
(c)
(c) Fig. 8. Cracking and mode of failure of Solite and normal aggregate reinforced concrete beams: (a) beam RI, p = 3-16~ (all Solite concrete) (b) beam RS1, p = 3.16% (Solite+sand concrete) (c) beam 01, p = 3"16 % (gravel concrete).
(d) M O D E OF FAILURE All the beams tested were under-reinforced and failed by yielding of the tension steel with considerable ultimate deflection followed by crushing of the compression concrete. Typical failure patterns are shown in figures 8 and 9.
Fig. 9. Cracking and mode of failure of Solite prestressed concrete beams: (a) beam P1 (wires, all Solite concrete)," (b) beam P2 (wires, Solite + sand concrete); (c) beam P3 (wires, all Solite); (d) beam PS (strands, all Solite); beams PI, P2 and PS stressed at 17.3 N/mm ~, beam P3 at 26.0 N/mm z.
Flexural Behaviour o f Reinforced and Prestressed Solite Structural Lightweight Concrete Beams Failure of Solite concrete beams generally tended to occur more rapidly than that in normal concrete beams, and often resulted in breaking up of the compression zone. The failure zone was generally larger both in extent and in depth than that of the ordinary concrete b e a m - - u p to 4 times in length and 2-4 times in depth (figures 8 and 9). In most failures, secondary shear cracks developed from the compression zone as failure of the beams fully materialised. Nevertheless, all the beams showed adequate ductility at failure, and the crushing of the compression zone was preceded by substantial deflection, visible cracking and ample warning of collapse.
CONCLUSIONS The following conclusions are drawn from the results reported in this paper. !. Solite reinforced and prestressed beams with concrete working stresses of 15.0-26.0 N / m m z can be satisfactorily designed according to C P l l 4 or CP110. For the reinforced beams the load factors against failure ranged 30-60% more than that required by the Code. For prestressed beams the load factors ranged between 1.50 and 2-65. 2. Deflection at design load of Solite lightweight concrete beams compares well with that of gravel concrete beams and is well within the calculated values according to the Draft Unified Code and the A.C.I. Code. It was about 15-20% more than the deflection of the normal aggregate beam of identical properties. The beams recovered on unloading 80-90 % of their deflection at design load. 3. The span-deflection ratios under permissible design moments varied between 291 and 434 for Solite reinforced beams compared with a value of 378 for gravel concrete beam. For the Solite prestressed beams, this ratio varied between 302 and 462.
55
4. The Solite reinforced and prestressed beams showed adequate ductility and substantial deflections prior to failure. The final measured deflection for all the beams varied between 1/70-1/150 of the span. 5. The crack width of reinforced beams at design load varied from 5 to 15 × 10 -2 m m and for prestressed beam the crack width was 5 × 10- 2 mm. The beams showed good crack distribution, and the crack spacing in the flexural zone varied between 59 and 109 m m and between 95 and 127 m m for reinforced and prestressed beams respectively. These values compare well with other lightweight aggregates, and the maximum crack width is less than the limiting crack width recommended by C P l l 0 . Almost all the cracks closed on unloading from the design load, and the crack widths at the design load in the second cycle of loading were the same as those in the first cycle. 6. The strain distribution over the depth of the Solite beams was similar to that in normal aggregate concrete beams throughout the loading. They were linear above the neutral axis, and the neutral axis depth decreased as the load increased. 7. The steel strain at design load remained the same for the first and second cycles of loading. 8. The ultimate moment of Solite beams agreed well with those calculated from Whitney's theory for both reinforced and prestressed beams except for prestressed beams with low tension steel. The calculated ultimate moments according to C P l l 0 underestimated the ultimate moments of the reinforced beams while they agreed well with the experimental results for the prestressed beams. 9. Solite beams had adequate ductility but tended to fail more rapidly than normal aggregate concrete beams. The failure zone was distinctly larger in Solite than in gravel concrete beams. Acknowledgements--The authors wish to express their gratitude to both Solite Ltd., Bwlchgwyn, N. Wales and to British Ropes Ltd. for their generous supply of raw materials.
REFERENCES 1. British Standards Institution: BS882 and 1201, Specification for Aggregates From Natural Sources for Concrete (Including Granolithic), London (1965). 2. British Standards Institution: Draft British Standard Code of Practice for the Structural Use of Concrete, London, Sept. (1969). 3. American Concrete Institute, Building Code Requirements for Reinforced Concrete (ACI 318-71), Detroit (1971). 4. R.H. EVANSand C. O. ORANGON,Behaviour in flexure of reinforced lightweight aggregate (Lytag) concrete beams, Civ. Engng Publ. Wks Rev., 59, May and June (1964). 5. T.R. HARDWICK,Lightweight structural concrete, Ph.D. Thesis, The University of Leeds (1961). 6. A. SHORT, The use of lightweight concrete for reinforced concrete construction, Reinf. Concr. Rev. 5, Sept. (1959).
56
R. N. Swamy and A. B. lbrahim 7. C. S. WHITNEY, Plastic theory for reinforced concrete design, Proc. Am. Soc. Test Mat. 66, Dec. (1940). 8. British Standards Institution, CP114, The Structural Use of Reinforced Concrete in Buildings, London (1969). 9. British Standards Institution, CPll0, The Structural Use of Concrete, Part 1, Design, Materials and Workmanship, London (1972).