DELR UNIVERSITY OF TECHNOLOGY
DEPARTMENT OF CIVIL ENGINEERING
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Report 5-78-5 The behaviour of bar and steel-fibre-reinforced concrete beams in static testing Dr. ing. Traian One| Associated professor of the Polytechnical Institute Cluj-Napoca (Romania)
STEVIN LABORATORY
CONCRETE STRUCTURES
CT7 8 - 0 1
Bibliotheek
o^ix ^^^ Civiele Techniek T.M. s - O ^ ^ • • ... Stevinweg .1. = Delft
5 - 7 8 - 5
THE BEHAVIOUR OF BAR-REINFORCED STEEL FIBRE CONCRETE BEAMS IN STATIC TESTING
"oy
Dr. Ing. Traian ONET Associated Professor
Polytechnic Institute of Cluj-Napoca (Romania)
Delft, June 1978 (^
-0-Contents page
1. Introduction • 1
2. Analysis for the ultim.ate stage 1 3. Analysis for service stage 5
3.1. Before cracking , 5
3.2. After cracking 8
h. Experimental tests 10
5. Comparison of calculated and test data 12
5.1. The ultimate stage 12 5.2. The service stage 13 6. Summary and conclusions 15
7. Acknowledgements 16
8. References 17 9. Notations 18
10. Appendix • ' 20 The tables are given in the appendix.
-2-b) The tensile contribution of the fibres is represented by a rectangular stress block.
c) The effective tensile stress in the fibrous concrete (o ) is given according to R.N. Swamy f 1 ~| and C.H. Henager p 3 ] by equation:
a^ = 0.00772 -T- p F,
t a„ -^ oe (1)
in which:
- fibre length, d - fibre diameter,
p - percentage by volume of fibres, F, - bond efficiency factor.
be •^
d) The tension bar reinforcement is reaching the yield strength of steel (f ). a 1) o -- Aa b 2) X Ox . ^ a , 0.85 f'b * . . • -^ -^.
Fig. 1. Assumed stress distribution (l) and simplified (2) representation.
The equation for the equilibrium of compressive force (C), tensile force of fibrous concrete (l' ) and tensile force of bar
reinforce-f c ment (T ) from fig. 1 is:
a
C = T^ + T
-3-or:
0.85 bx f' = b(h - x)a, + A f . (2a) b t a a
With the notations:
the position of neutral axis is given by the equation: w f + a,
^ 0.85 f' + a^ • ^^'
b t
Equating moments about C we obtain the ultimate moment strength:
^ = Va^^ - f) ^ ^^^ -
-K^H^ '
f)
= f w f^(6 - 0.5 C) + 0,5(1 -5)a,
I o a t bh2 (5)
where:
In the equation (5), the second term represents the tensile contribution of the fibres to increasing of moment strength. For B 37,5 concrete and FeB i+00 steel | 5 | this contribution is shown in figure 2. It's easy to see that the tensile con-tribution of the fibres is greater when the effective tensile stress in the fibrous concrete (cf ) is greater and when rein-forcement percentage ratio (o) = 100 w ) is smaller.
a)
M/bh^(N/mm^)
2.5 3.0
a)(%)
Fig. 2. The tensile contribution of the fibres: a capacity increasing due to steel fibres).
b) 28 2A 20 16 12 AM(7o) 0 IC: M / r o r „2 \ \ '^ \ \ \ \ ^ 2 1 = i.u IN/ m nn
K.,
=0.5 N / m m 'v\
^ 0 05 1.0 1.5 2.0 Z5 3.0 ü3o(7o) I I-5-Analysis for service stage
1. Before cracking
The following assumptions can be made for the analysis method: a) The strains in the concrete and reinforcing steel are directly
proportional to the distance from, the neutral axis.
b) The stress distribution in both compressive and tensile zone is triangulare (fig. 3).
c) The modulus of deformation of concrete in tension is the same as in compression. -C ' o L Aa b 1 1. -«^2 tl-^Ö b --*ib(h-x)G5 ->-Aa O Q assumed stress
distri bution diagram strain
Fig. 3. The assumptions for the analysis before cracking
The equation for the equilibrium of forces shoxm in fig. 3 i;
bx o' = I b(h - x)a. + A a
a a (7)
Bibliotheek
afd. Civiele Techniek T.H. Stevinweg 1 - Delft
-6-By similar triangles in strain diagram we find:
s
s
=: a e a h o h -h o - X X - X (8) (9)and further we obtain the values of stresses;
X b a h - X o h - X „ b a h - X o (10) (11)
Above, E represents the modulus of deformation according to a-e diagram
of fibre reinforced concrete. Such a diagram is obtained by S.P. Shah, P. Stroeven, D. Dalhuisen and P. van Stekelenburg P ^ ~| .
Put a' from (10), a, from (ll) and a = e E (E - elastic m.odulus
b b a a a a
of steel) 'in equation ( 7 ) , use the notations (3) and (6) and solve
for 5 : • S = E 1 + 2a) 6 „ o E a 12)
2(^^%r)
The sum of moments in respect to the axis of the compressive force of concrete is:
M = A a (h - - ) + 1 b(h - x)a^
a a o 3 b
2 2
- (h - x) + — X 13)
With ( 3 ) , (6) and (ll), the equation (13) becomes:
M =
% ( ^ - f ) ^ ^
S-,
1E a
bh-^a
The curvature of a deformed element (see fig. h) can be calculated, as it is known, using the equation:
Fig. h. The scheme for'calculating the curvature of a deforraed element.
_!
^
do
^ 3
R dx X :) ~ (h - x) (15) With a from (l^), the eauation become;
a
where the modulus of rigidity (K) is given by the equation:
(16)
K =
'"o^ '6
I) +-1-^
3^ 3 6 E 6 - 5)bh^EThe value of deflection (f) can be obtained with the relati on:
-8-in which:
S - coefficient depending on the type of load and on the kind of supporting | 6 ~| ,
1 - span of the element.
3.2. After cracking
The analysis method, after cracking, is based on the next assumptions (see fig. 5 ) :
a) In the compressive zone the stress distribution is triangulare. b) The bottom of cross section is reaching the tensile strength (f., )•
Thus the fibre concrete has an elastic-plastic behaviour and the stress distribution in the tensile zone is a second degree parabola. c) After cracking, only the compressive strain of the concrete and
the strain of reinforcing steel are directly proportional to the distance from the neutral axis.
d) The deformation modulus (E) in the compressive zone depends on the shape of the a-e diagrarn of fibre concrete 1 ^t | •
JC . o L Aa . b , -«i^jbxo'b |b(h-x)fb •Aa G Q assumed stress
distribution diagram strain
-9-From the equilibrium of compressive and tensile forces shown in fig. 5 we get:
i bx a' = 4 t'(h - x)f^ + a A .
b 3 b a a (19) With the equations (8) and (10) resulted from similar triangles in strain diagram and with the notations (3) and (6) we obtain the position of the neutral a:<;is:
^E 3 o '^ a a ^ ^ (1 + 6) + 20) 3 a o (^ — 6 + 2ca 6) = 0 3 a o a (20;
The bending moment is given by the equation:
M = A a (h _ |) + I b(h - x)f.^
a a o 3 3 b
I (h - x) + 3 X
a
bh^a (21)
The curvature and the deflection can be obtained by the equations (l6) and (18) respectively, taking for the modulus of rigidity the following value:
K
,'*-f) - f ' ' - « > ' ! r i ï ^ „
b (6 - C)bh3E . (22)a
In the equations (20), (21) and (22) the — ratio is known only if
°a
the a value is known, for example by experimental measuring of the steel strain. Otherwise an iteration proccdare is necessary, taking
•^b
primarily an approximate value for the — ratio according to the 3.1. a assumption (see fig. 3):
_b ^ 1 - g E_
-10-Example
For the beam number 8 in table 5 we have the following data: BK fibres, E, = 20800 N/imn2, Ü = 2.09/^, E =21000 N/mm^, M, , = 7.51 x 10 N.mm
t o a test and f, , = 6 . 1 1 3 mm.
test
Put the equation (23) in (20):
TT TP TT TP
(^ - 1.33 ^ ) S 2 + 2(1.33 ^ + üj^)S - (1.33 ^ + 2 oj^6) = 0 a a a a and with above data solve for 5 obtain E, =
0.59-From the equation (21) we obtain a = I90 N/mm^. a
A new value for E, we obtain from the equation (20): g = 0.1+7^. 11
Using the equation (22), we find K = 6.IU5 x 10 N.mm^ and 23
further using the equation (18) with S = — 7 - we obtain f = 5.205 nm.
_ ^ I D C 3J-L C
calc
The ratio -; • = O.85 and the value of this ratio obtained with known test
value of a (by measuring) are very close to each other (see table 5).
3.
Experimental tests
The validity of the analytical method was verified by a testing program carried out in the Stevin-Laboratory, Delft University of Technology | 8 "] .
Four sets of beams were tested in flexure. First a conventional set was made without fibres. The types of fibres used in random distribution for other three sets were a straight one ( A R ) , a hooked one (BK) and a straight one with paddles on both ends ( T H ) , like is shown in figure 6.
-11-00,4 m m _r- 0 0,4 m m •*i—-• %_-1 0 0,8 m m 50 ' 1
Fig. 6. Types of steel fibres used p 8 ~| .
The percentage by volume of fibres (p) was 0.89^ for AR; 1.27/^ for BK and 1.53?^ for TH fibres.
Each set of beams included one beam without bar reinforcement and three beams reinforced with 2 ?$ U, 1+ (z5 6, and ^i ^ 10 respectively. The steel
quality was a FeB 500 Hi bond.
The concrete m.ix consisted of i+00 kg/m^ type A portland cement, round sand, gravel aggregate with a marcimiium size of l6 mjn and 0.^8 water-cement ratio. Data of concrete are given in table 1 (see appendix).
The beams were 100 x 150 imn^ m cross-section and 2200 mm long. The free span during testing was 2000 m;?i with a pure bending zone of 800 m!7i long.
The top and bottom concrete strain was measured by electrical extenso-meters and the deflection by dial gauges.
In order to obtain a supplementary confirmation, the author's method was applied on the experimental results of C.H. Henager [ 3 ~] .
1,5
1^
25 30
-12-5. Com-parison of calculated srd test data
5.1. The ultimate stage
The moment strength of beams calculated by the proposed method (M ) calc are given in ta,ble 2 and compared with test values (M, ^ ) .
test
Note that, fo.r non-reinforced beams we used the assumption shown in figure 7 and the following equation:
M = (1 - C) ^ ^ ^ bh^f, :2k: where: C ^ f = 0 . 5 , f , = (1 + — f ' ) x O . 8 7 , N/mjTi^ , a c c o r d i n g t o | 5 "] O b < f b
H
— — f b • * — » *r
1 X X JZ stressdistribution diagram strain
Fig. 7. The assuniptions for the calculation of ultimate bending moment of non-reinforced beams.
-13-Therewith, for non-fibrous beams the a value in the equations (^, and (5) is set equal to zero.
For the bond efficiency factor (F ) in the equation (I) we used the following values: 1.1 for BK fibres, 1.0 for AR fibres and 1.2 for TH fibres.
h
The value of 5 = :;— for reinforced beams was equal to 0.93. h
M ,
The results, given syntheticaly in table 2 by — ratio, show ^'^test
good agreement of the calculated moments with test moments. The average value of this ratio was I.OU for the fibrous beams and 1.09 for all the beams. The main difference between the calculated and test values presented the non-fibrous beams without reinforce-ment (number 1 in table 2). Note that such beams don't represent
actual cases in practice.
In table 3 are presented the calculated values of ultimate moment strength by the author's method comparatively with the experimental values obtained by C.H, Henager | 3 |. Calculated strength agree
Mcalc
well with experimental values, the average — ratio being 1.02. test
So, we can conclude that the method presented in paragraph 2 predicts the ultimate moment strength of fibre reinforced concrete beams with a good accuracy.'
The service stage
In table k are given the values of the top and bottom concrete strain measured at a medium level of loading. The values of compressive and tensile concrete stress and tensile steel stress, obtained from the measured strains multiplied by the moduli of deformation, are given also in this table.
The values of bending moment obtained according to paragraph 3 (M )
CQ,J_C
are presented in the table h comparatively with test values ( M ).
-1U-b
stress
distribution strain diagram
Fig. 8. The assumptions for the analysis of non-reinforced elements under service loads.
For the non-reinforced beams we used the assumptions shown in fig. and the following equation:
M = •:^ ( 1 - fjbh^a.^^ :25) in which: ? = 0.5 - vhen a, < 0.5 f^ b b • - • ) • . E 5 2 ( ^ _ 1) + 2 5 - 1 = 0 - when a^> 0.5 f^.
Calculated moment values agree well with experim.ental values. The M
average M calc ratio is 1.02. test
In table 5 a comparison of calulated and test deflections under service loads (about half of ultimate load) is done. For the non-reinforced beams, according to assumptions from fig. 8, the stiff-ness was calculated with the equation:
-15-The agreement between calculated deflections and experimental values
O file
is also good. The — ratio has an average value equa.l to 1.01. test
This m^eans that according to the method of analysis, presented in paragraph 3 we can predict accurately the value of bending moment or the value of deflection under service loads.
Summary and conclusions
The method of ana.lysis described here is suitable for predicting the behaviour of reinforced steel fibre concrete beams, regarding: - the ultimate moment,
- the moment value in service stage when the values of stresses are known (e.g. by measuring),
- the magnitude of deflection caused by a given bending moment.
There is a good agreement between predicted values and experimental values in ultimate stage as well in service stage.
It can be seen that fibre reinforcement (in random distribution) increases the ultim.ate moment strength of bending elements. The influence is the more distinct the smaller the steel bar reinforce-ment ratio and the higher the effective tensile stress in the fibrous concrete.
The fibre reinforcement increases also the post-cracking stiff-ness of the reinforced fibrous beams. However, an increase of deflections is caused by the higher moment values.
The crack width and the crack spacing of fibre reinforced concrete, analysed in the report p 8 "] , were less than in non-fibrous concrete. The crack load in fibrous concrete is greater than in conventional concrete. Thus, the crack width of fibre reinforced concrete will be probably not a condition for the serviceability limit state.
-16-7. Acknowie dgement s
This report represents a partial result of the author's specializing work in Delft University of Technology, Department of Civil Engineering, during three m.onths (22th March to 22th June 1978). The author is
indebted to the Nederlandse Ministerie van Onderwijs en Wetenschappen for this opportunity.
Useful advices and helpful suggestions of Prof. ir. A.S.G. Bruggeling and ir. J. Brakel are gratefully acknowledged.
The tests used in order to establish the analysis method were carried out in the Stevin-Laboratory, Concrete Structure. The author wish to
thank Dr. Ing. H.W. Reinhardt for his generous help in this investigation. Thanks are also extended to Ir. H.A. Körmeling for useful discussions pertaining to experimental results.
-17-References
1. X « K Fiber Reinforced Concrete , symposium held at Ottawa, Canada. ACI Publication SP - UU, I97U.
2. X JC H RILEM Symposi-um 1975 "Fibre Reinforced Cement and Concrete". The Construction Press Ltd.
3. H X 3€ Fibre Reinforced Materials: design and engineering applications. Proceedings of the conference held in London,
1977-k. X X M RILEM, ACI, ASTM International Symposium "Testing and Test Methods of Fibre Cement Composites", held in Sheffield, I978.
5. X X X Voorschriften Beton VB 197^. Nederlands Normalisatie-Instituut.
6. X X X STAS IOIO7/O-76: Non-Industrial and Industrial Buildings. Design of plain, reinforced and prestressed concrete members
(in Romanian).
7. Onet, T. Contributions to the Study of Deformations of Light-Weight Reinforced Concrete Beams Subjected to Short-Time Bending. Doctor degree thesis. Polytechnic Institute of Cluj-Napoca,
1972 (in Romanian).
8. Reinhardt, H.W. , Köi-meling, H.A. Static and D3mamic Testing of Concrete Beams Reinforced with Steel-Fibres and Continuous Bars. FIP 8th Congress 1978 - written contribution to the discussion.
•
18-Notations
A = area of tension bar reinforcement, mm^ a
b = width of cross section, mm
C = compressive force in concrete, N d = fibre diameter, mm
E = modulus of deformation of concrete, N/mm^ E = modulus of elasticity of concrete, N/ram^
E = modulus of elasticity-plasticity of concrete, N/mm^ E = modulus of elasticity of tensile steel, N/mm^
f = deflection of beam, mm
f = yield strength of steel (characteristic value), N/mm^
3.
f, = tensile strength of concrete, N/mm^
f,' = cylindrical compressive strength of concrete, N/rma^
f' = characteristic cylindrical compressive strength of concrete, N/mm
uK.
F, = bond efficiency factor be
h = depth of cross section, mm h = effective depth, mm
K = modulus of rigidity, Nmm^
1 = span of beam as well as fibre length, mm
M = applied moment as well as internal moment, Nmm M = ultimate moment, Nmm
u
p = percentage by volume of fibres , %
R = radius of curvature, mm
1 -1 — = curvature of beam, mm
R
S = coefficient for calculus of deflection T = tensile force of bar reinforcement, N
a
T^ = tensile force of fibrous concrete, N f c
-19-X = distance from extreme compression fibre to neutral axis, mm h
6 = ratio -— h
e = steel strain, mm/m a
e, = tensile strain of concrete, xmn/m b
e' = compressive strain of concrete, mm/m Ü) = steel bar reinforcement ratio
o
0) = steel bar reinforcement percentage ratio, %
a = tensile stress of bar reinforcement, N/mm a
a = tensile stress of concrete, N/mmi^ a' = compressive stress of concrete, N/imn^
a = effective tensile stress of fibrous concrete, N/mm^ 5 = ratio — .
-20-10. Appendix
Table 1. Data of concrete
type of concrete plain with BK fibres with AR fibres with TH fibres f' bk N/mm2 31.15 35.88 35.17 35.63 E o N/mm2 3U 800 36 100 3h 200 37 100 N/mm^ 22 800 20 800 19 000 15 800
-21-Table 2. Comparison of calculated and test values of the ultimate bending moment N r . 1 2 3 k 5 6 7 8 9 10 11 12 13 1U 15 16 "to o af /o -0 . 1 7 0 . 7 5 2 . 0 9 -0 . 17 0 . 7 5 2 . 0 9 -0 . 1 7 0 . 7 5 2 . 0 9 -0 . 1 7 0 . 7 5 2 . 0 9 f i b r e s -BK BK BK BK AR AR AR AR TH TH TH TH P -0 . 8 9 0 . 8 9 0 . 8 9 0 . 8 9 1.27 1.27 1.27 1.27 1.53 1.53 1.53 1.53 ^ t N/mm2 -0 . 5 7 0 . 5 7 0 . 5 7 0 . 5 7 0 . 6 1 0 . 6 1 0 . 6 1 0 . 6 1 0 . 8 9 0 . 8 9 0 . 8 9 0 . 8 9 f a N/mmi^ -716 531 U8U -716 531 lt8U -716 531 U8U -716 531 U8U 5 0 . 5 0 0 . 0 5 0 . 1 5 0 . 3 8 0 . 5 0 0 . 0 6 0 . 1 5 0.3U 0 . 5 0 0 . 0 6 0 . 1 5 0 . 3 5 0 . 5 0 0 . 0 7 0 . 1 6 0 . 3 5 M , c a l c X 1 0 - ^ Nmm 1.U6 2.U5 7 . 7 2 1 6 . 9 1 1.59 3.0U 8 . 2 8 1 7 . 7 7 1.57 3 . 0 8 8 . 3 0 1 7 . 7 0 1.58 3 . 3 6 8.5U 1 7 . 8 9 t e s t X 1 0 " ^ Nmm 0 . 8 3 1.03 2.U5 -1 7 . 0 0 I . U 9 I . I U 2 . 9 9 8 . 2 5 1 7 . 2 0 1.1+9 1 .)49 3 . 1 2 9 . 5 5 1 7 . 3 0 1 , 2 0 1.51 3 . 8 6 9 . 2 5 1 8 . 5 0 M , c a l c t e s t 1.75 1 .U2 1 . 0 0 -0 . 9 9 1.07 1.39 1.02 1.00 1.03 1.05 1.05 0 . 9 9 0 . 8 7 1.02 1.32 1.05 0 . 8 7 0 . 9 2 0 . 9 7
2 2
-Table 3 . Comparison of c a l c u l a t e d moments and C.H, H e n a g e r ' s t e s t v a l u e s
Nr. 1 2
3
k5
6
7
8
mm -0.6U 0.51 0.36 -0.51 0.51 0.51 1 mm -57 38 Ul -33 33 33 P % -1.22 1.52 1.36 -1.36 1-59 1.81 ^be -1.0 1 .2 1 .1 -1.2 1.2 1.2 N/mm 2 -0.8U 1.05 1.32 -0.82 0.95 1.08 f a N/mm2 3U3.9 3U3.9 3U3.9 3U3.9 3U6.9 3U6.9 3U6.9 3U6.9 N/mm2 2U.6 U0.9 hk 3 I1I.2 29.U 53.3 5U.I 52.15
0.15 0.11 0.11 0.12 0.13 0.09 0.09 0.09 M ^ calc N.m U3.87 52.06 53.96 55.63 UU.97 53.25 5U.32 55.21 M, , xest N.m U2.3I 52.00 53.50 55.35 UU.18 52.75 53.50 53.87 M , calc test I.OU 1.00 1.01 1 .00 1.02 1.01 1 .02 1 .02
-23-Table U. Co.mparison of calculated and test moments under service loads
N r . 1 2 3 1+ 5 6 7 8 9 10 11 12 13 iU 15 16 f i b r e s -BK BK BK BK AR AR AR AR TH TH TH TH ió o % -0 . 1 7 0 . 7 5 2 . 0 9 -0 . 1 7 0 . 7 5 2 . 0 9 -0 . 1 7 0 . 7 5 2 . 0 9 -0 . 1 7 0 . 7 5 2 . 0 9 M M u 0.6U 0.1+3 0.1+6 -0.1+5 0 . 9 7 0 . 8 l 0.1+5 0.U8 0.1+3 0 . 7 5 0 . 8 5 0 . 5 3 0 . 5 7 0 . 5 2 0 . 9 3 0 . 9 0 0 . 5 2 0 . 5 8 0 . 5 7 mm/m 0 . 0 2 0 . 0 1 0 . 3 2 -1.00 0 . 6 5 0 . 2 2 0 . 2 2 0 . 6 5 1 . 0 7 0 . 2 2 0 . 2 2 O.II+ 1.07 1.22 0 . 2 2 0 . 1U 0 . 2 2 1.00 1.28 ^b N/mm^ 0 . 7 0 0 . 3 5 1 1 . 1I+ -2 -2 . 8 0 1 3 . 5 2
7.9U
7.9U
1 3 . 5 2 2 2 . 2 6 7 . 5 2 7 . 5 2 U.79 1 9 . 7 6 2 3 . 1 8 8 . 1 6 5 . 1 9 8 . 1 6 1 5 . 8 0 2 0 . 2 2 e., 0 mm/m 0 . 0 5 0 . 0 5 0 . 1 6 -1.31+ 0 . 5 3 0 . 2 2 0 . 1 9 1.16 1 .31+ 0 . 1 9 • 0 . 2 2 0 . 2 2 1.93 1.U6 0 . 3 3 0 . 17 0 . 3 7 1.69 1.61L a a < % ) N/mm^ ( I . l l l ) ( 1 . 1 U ) 26.5U -2I17.OO ( 2 . U 3 ) (2.1+3) 3 3 . 8 7 2 1 6 . 9 9 2I+5.97 (2.1+0) ( 2 . U 0 ) 1+0.91 3 6 1 . 2 0 2 6 7 . 2 0 (2.1+2) (2.1+2) 6 9 . 0 3 3 1 5 . 3 6 301.1+8 ? 0.1+5 0.1+5 0 . 5 1 -0.1+3 0.1+3 0.1+3 0.1+1 • 0.1+2 0.1+7 0.1+3 0.1+3 0.1+3 O.3U 0.1+8 0 . 3 9 0 . 3 9 0 . 3 3 0 . 3 9 0 . 5 1 M ^ c a l c x l O - ^ N.mm 0.1+7 0.1+7 1.31 -9 . 1 3 1 . 0 3 1.03 I . U 3U.88
1 0 . 1 3 1.02 1.02 1.1+6 6.1+6 1 0 . 8 2 1. 10 1.10 1.7I+5.67
1 1 . 8 6 t e s t x l O - ^ N.mm 0 . 5 3 0 . 5 6 1.12-7.63
1.11 1.20 I.3U 3 . 9 3 7 . 5 1 1 . 12 1.27 1.61+ 5.1+18.96
1.12 1.36 2 . 0 1 5.Ui 1 0 . 5 0 M ^ c a l c t e s t 0 . 8 9 0.8U 1.17 -1.20 0 . 9 3 0 . 8 6 1.07 1 .2U I.3U 0 . 9 1 0 . 8 0 0 . 8 9 1.19 1.20 0 . 9 8 0 . 8 1 0 . 8 6 I.0U 1.13
-2U-Table 5. Comparison of calculated and test deflections under service loads
Nr. 1 2 3 U 5 6 7 8 9 10 11 12 13 1U 15 16 fibres -BK BK BK BK AR AR AR AR TH TH TH TH 0 % -0.17 0.75 2.09 -0.17 0.75 2.09 -0.17 0.75 2.09 -0.17 0.75 2.09 M M u 0.6U 0.U3 0.U6 -0.U5 0.97 0.81 0.U5 0.U8 0.U3 0.75 0.85 0.53 0.57 0.5? 0.93 0.90 0.52 0.58 0.57 a a <%) N/mm2 (1.1U) (1.1U) 26.5U -2U7.OO (2.U3) (2.U3) 33.87 216.99 2U5.97 (2.U0) (2.U0) U0.9I 361.20 267.20 (2.U2) (2.U2) 69.03 315.36 301.U8 M xlO"^ N.mm 0.53 0.56 1.12 -7.63 1.11 1.20 I.3U 3.93 7.51 1.12 1 .27 1.6U 5.U1 8.96 1.12 1.36 2.01 5.UI 10.50
