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One steel workshop - design of RC column
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1
ADVANCED DESIGN� OF
COLUMNS
Professor Russell Bridge
Dr Andrew Wheeler
Centre for Construction Technology and ResearchUniversity of Western Sydney
SEMINARS Sept. 2001
The Centre for Construction Technology and Research at the University of
Western Sydney is progressively developing new design rules for OneSteel
Reinforcing�s Guide to Reinforced Concrete Design.
Top-tier design rules that meet the requirements for design by refined
calculation defined in AS 3600-2001 are being released under the trademark of
Advanced Design�. This presentation concerns rules being developed for
advanced design of reinforced-concrete column cross-sections for strength.
The design rules are proprietary and should only be used when OneSteel
Reinforcing�s products are specified.
2
ADVANCED DESIGN� OF COLUMNS
500PLUS-CCS
SOFTWARE
COLUMN
CROSSSECTION
DESIGN
The advanced design rules have been incorporated in a new software package
called 500PLUS-CCS, �CCS� standing for �Column Cross-Section� which
will be demonstrated during the presentation.
The new design rules and software will provide the user with a better
determination of cross-section strength and allowing the safe and economical
use of higher strength materials.
The presentation looks at the design principles used in the determination of the
cross-sectional strength of a conventionally reinforced column.
Also presented are the principles used in advanced analysis which was used in
the development of the software package 500PLUS-CCS.
3
φ Nu
φ Mu
φ Muo
φ Nu0
Moment
Lo
ad
(M*, N*)(Unsafe)
(φ Mub, φ Nub)
Locus ofφ Mu, φ Nu
values
(M*, N*)(Safe)
M*
N*
LOAD-MOMENT STRENGTH INTERACTION - DESIGN
In the design of a reinforced concrete column the designer is primarily
concerned with obtaining a column for which the design action effects
(defined by combination of M*, N*) fall within the load-moment strength
interaction diagram. Typical load-moment strength interaction diagrams as
shown may be generated using either simplified methods or using advanced
analysis. The 500PLUS-CCS software enables the designer to use advanced
analysis methods to derive an accurate interaction diagram for design use.
The load moment strength interaction diagram is dependent on a number of
factors including the geometry of the cross-section, and the material properties
of both the concrete and reinforcement. One of the major advantages of the
advanced analysis is the ability to accurately predict the stress in a cross
section for a give strain distribution, thus providing an accurate means for
determining realistic column capacities.
4
Concrete� Four original Grades; new Grade; high strength
� f′c = 25, 32, 40, 50 MPa; 65 MPa; up to 90 MPa
� Maximum Strength = 0.85 f′c
Steel� 500N grade - 500PLUS (fsy = 500MPa)
CONCRETE AND STEEL MATERIALS
The Australian concrete structures code AS 3600 has previously limited the
maximum concrete strength of the concrete to 50 MPa, and an upper limit of
400 MPa on the nominal yield strength of the reinforcement. However, the
current standard AS 3600-2001 has increased the maximum concrete strength
to 65 MPa and allows the use of 500N grade reinforcement (yield stress
500MPa). In recognition of the industry need and based on current research,
the advanced analysis software also enables the use of high strength concrete
up to 90 MPa.
5
CONCRETE STRESS-STRAIN CURVE (CEB)
0
10
20
30
40
50
60
0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008
Strain εa
Str
essσ
c (
MP
a)
f' c = 50 MPa
f' c = 40 MPa
f' c = 32 MPa
f' c = 25 MPa
εo = 0.0022
σc = f (εa)f' c = 65 MPa
AS3600-2001
To define the concrete stress-strain relationship, the current commentary to the
standard recommends the use of the CEB curve when using advanced analysis
methods.
One key factor of the CEB curves is that the peak stress occurs at a strain of
0.002 and is independent of the concrete cylinder strength. The unloading
behaviour of the varying grades of concrete also differ significantly.
The standard also limits the maximum concrete stress of 85% of the cylinder
strength.
6
CONCRETE STRESS-STRAIN CURVE (COLLINS)
0
10
20
30
40
50
60
70
80
0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008
Strain εa
Str
es
sσ
c (
MP
a)
f' c = 85 MPa (Collins et al)
f' c = 50 MPa (CEB)
f' c = 25 MPa (CEB)
εo = 0.0022
σc = f (εa)
While the CEB curve is considered to be adequate for normal grades of
concrete, the authors recommend the use of the Collin�s concrete stress-strain
curve for high strength concretes.
Unlike the CEB curves, the strain at peak concrete stress is dependent on the
concrete cylinder strength.
As detailed previously, the maximum concrete stress is limited to 85 % of the
cylinder strength
7
εsy = 0.0020 for 400Y Grade
εsy = 0.0025 for 500Plus
STEEL STRESS-STRAIN CURVE
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0 10 20 30 40 50 60
Relative Strain ε s /ε sy
Rela
tive S
tress
σs/f
sy
Design Assumption
Strain Hardening
Slope = E s = 200,000 MPa
1.0
The definition used for the material properties of the steel is the bi-linear
elastic plastic stress strain relationship with a linear elastic region to the yield
point. The modulus of elasticity for the steel is assumed to be constant at
200,000 MPa. Consequently, the strain at this yield point is assumed to be
0.002 for the 400Y Grade steel and 0.0025 for the 500PLUS® reinforcement.
The effects of the strain hardening of the steel are ignored for the advanced
analysis of columns.
8
Stress Resultants
N
M
Concrete Stress
DistributionAxis
Ne
utr
al
Steel Stress
Distribution
Strain Distributionεa
Curvatureρ = 1/R C
en
tre
Cross-section
Axis
AXIAL FORCE AND MOMENT AT A CROSS-SECTION
To determine the capacity of a column the assumption that plane sections
remain plane is utilised. An assumed strain distribution is applied to the cross-
section, defined by the curvature and axial strain at the centroid. From the
applied strain distribution and the pre-defined material properties, the stress
distribution in the concrete may be determined. The same method is use to
determine the stress distribution in the reinforcement. Once the stress
distribution is determined, integration is utilised to determine the axial load (N)
and the moment (M) for the given strain distribution.
9
LOAD-MOMENT-CURVATURE DIAGRAM
5000
4000
3000
2000
1000
0 100 200 300
Moment M (kNm)
Axia
l L
oad
N (k
N)
400 x 40050 cover8C24 bars
fsy = 410 MPa
f′c = 30 MPa
48
12 16 24 3240
60
80
120
160
8N24 Bars
The load-moment strength interaction diagram is determined by selecting a
curvature and varying the applied axial strain. For each value of axial strain, an
axial load (N) and moment (M) is determined and the curve of load-moment
values for a given curvature derived. This procedure is repeated for varying
values of curvature. Plotting values of load and moment for a constant value of
curvature results in the contour chart shown in the slide above. A 3D model of
this behaviour shown in next slide, where load (N) is on the y axis, moment (M)
on the x axis and curvature (r) on the z axis. Viewing the x-y axis, then the
envelope of (N, M) values defines the load-moment strength interaction
diagram.
10
LOAD-MOMENT-CURVATURE DIAGRAM
A 3D model of the load-moment-curvature behaviour of a typical column
cross-section is shown above. This was constructed using the contour diagram
shown in the previous slide. The lines marked on the model are lines of
constant curvature, the vertical axis is the load axis and the horizontal axis is
the moment axis.
11
d
do
εcu
kud
Muo
εcu
kuodoεsy
Mub , Nub
Mul , Nul
do
εcu
Nuo
Moment
Ax
ial L
oa
dKEY POINTS ON LOAD-MOMENT INTERACTION CURVE
When using simplified methods or advanced analysis, a number of key points
are defined on the load moment strength interaction diagram. These points are
used in the determination of the appropriate capacity reduction factors, and
include the axial capacity (Nuo), the bending capacity (Muo) and the balance
point (Mub, Nub).
The axial capacity (Nuo) is the capacity of the section when a constant strain is
applied across the cross-section. For 400Y Grade reinforcement this point
would always corresponds with the strain at which the peak concrete stress is
reached. The pure moment capacity (Muo) is the maximum bending capacity of
the column with zero axial load. The depth to the neutral axis (koud) at this
point is needed, as it is used as a measure of ductility of the cross-section. The
capacity reduction factor (f) at pure moment is dependent on the value of kuo.
As the axial load applied to a column is increased from zero, the moment
capacity will increase as applied axial strains relieve some of the tensile strains
resulting from the bending. As these compressive strains increase, they will
reach a point at which they begin to decrease the bending capacity of the
column. This transition point is considered to be the balance point (Mub, Nub).
For rectangular sections, and particularly those that are singly reinforced, this
point occurs when the steel on the extreme tensile face begins to yield. When
the cross-section is non-rectangular or has multiple layers of reinforcement,
the peak moment may not always occur when the reinforcement on the
extreme tensile face begins to yield. Using advanced analysis methods, the
transition point between applied axial load contributing or degrading the axial
capacity is determined accurately.
12
0.60.8or0.8uo
ud ≥==M
M00 φφ
Pure Bending where Nu = 0
Combined Bending and Compression where Nu < Nub
−−+= ))((
ub
u0
N
N10.60.6 φφ
Combined Bending and Compression where Nu > Nub
0.6=φ
CAPACITY REDUCTION FACTOR φ
Capacity reduction factors (φ), as defined by AS 3600, are dependent on theapplied axial load (N). When the applied load (N) is greater that the axial load
at the balance point (Nub), the column is considered to be predominantly under
axial loading and a reduction factor (φ) of 0.6 is applied. When the axial load
(N) is below the balance point (Nub), bending is considered to be critical so
providing kuo is less than 0.4 the reduction factor (φ) is varied linearly from 0.6at the balance point to 0.8 for pure moment.
13
0
100
200
300
400
500
600
700
800
900
0 1 2 3 4 5 6 7 8 9 10
Percentage Steel %
Mo
me
nt
Str
en
gth
- P
ure
Be
nd
ing
(k
Nm
)
Ca
pa
cit
y F
ac
tor φ
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
M ud
ku = 0.4 M uo
φM uo
400 x 400
50 coverf sy = 500 MPa
f' c = 32 MPaφ
STRENGTH IN PURE BENDING
For cross-sections where kuo is greater than 0.4, a reduction factor (φ) isreduced further to overcome the potential ductility problems. This reduction is
based on the assumed moment capacity Mud which is a theoretical moment
capacity based on a value of kuo = 0.4.
14
0
2000
4000
6000
8000
0 100 200 300 400 500
Moment (kNm)
Lo
ad
(
kN
)
Locus
φM u, φN u
values
Locus
Mu, N u
valuesφN uo
N uo
400 x 400
50 coverf sy = 500 MPa
f' c = 32 MPa
Mu
o
Rectangular Stress
Analytical Method
NOMINAL AND DESIGN STRENGTH
The effect of the reduction factor is very significant on the overall capacities of
the cross-section. Thus optimisation using advanced analysis is critical to
obtain the best performance permitted for the column. The advanced analysis
enables an accurate prediction of the balance point, along with determining the
maximum permitted value of Mud.
15
SLENDER CONCRETE COLUMN
When looking at slender columns, AS 3600 allows the use of moment
magnification factors to take into account the effects of slenderness. The
software included is only for determining the cross-sectional strength, and thus
does not consider slender columns.
16
MINIMUM REINFORCEMENT IN COLUMN
Min. 1% steel400Y Grade
0.8% steel500 PLUS
εsh shrinkage strain = 850 µstrain
φccb creep factor = 7.5
Loading = 0.4φNuo = 40% squash load
Stresses in steel with time
The minimum steel requirements for columns governed by strength as
specified by AS 3600 is 1 percent. The commentary to the concrete standard
suggests that this limit "guards against yielding of the reinforcement due to
shrinkage and to creep under sustained service loading".
17
CREEP AND SHRINKAGE STRESSES IN STEEL
0
100
200
300
400
500
Time after Loading
Ste
el S
tre
ss
(M
Pa
)
1.0% 400Y Rebar
0.8% 500PLUS Rebar
1 3 10 30 30100 1 3 10
Days Years
Studies have shown that for a column with 1 percent 400Y Grade
reinforcement, when compared with an similar column with 0.8 percent
500PLUS® reinforcement and subjected to identical shrinkage strains, the
same creep coefficient and supporting the same sustained service load (see
previous slide) the stresses in the reinforcement of each column are very
similar. Consequently, the advanced analysis will allow the design of columns
with less that 1 percent reinforcement for 500PLUS® reinforcement.
18
COVER SPALLING IN HIGH STRENGTH CONCRETE
Spalled concrete cover
Confined concrete
Nuo = kf´c Ac + fsy As
For f´c ≤ 65 MPa, k = 0.85
The use of concrete grades above those specified in AS 3600 introduce a
number of additional problems. A primary consideration is the effect of
spalling of the concrete cover on the axial strength of columns.
19
EFFECT OF COVER SPALLING ON STRENGTH
0.50
0.55
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.95
1.00
0 20 40 60 80 100 120
Concrete Grade (MPa)
Str
en
gth
Facto
r k
To overcome the effect of cover spaling, the maximum concrete stress allowed
for design is decreased. Numerous experimental studies have demonstrated
that for concretes with cylinder strength up to about 65 Mpa, the peak stress
reduction factor (k) of 0.85 as specified by the standard may be adequate.
However, as the concrete cylinder strength moves beyond this point, the peak
stress reduction factor should decrease to a lower value. A limit of 0.72 has
been suggested in some studies.
20
COMPARISON OF HIGH STRENGTH CONCRETE
0
1000
2000
3000
4000
5000
6000
7000
0 100 200 300 400
Moment Capacity φM u (kN/m)
Ax
ial
Lo
ad
Ca
pa
cit
yφ
Nu
(k
N)
50 MPa
85 MPa
High strength concretes, for a given cross-section, result in an increase in axial
load capacity, including the effects of cover spalling, but have an insignificant
effect on the pure moment capacity.
When using the high strength concrete the designer should also ensure that the
spacing and layout of the confinement reinforcement meet the desired
requirements.
21
ADVANTAGES OF ADVANCED DESIGN� FOR COLUMNS
� Full non-linear material properties
� Numerical integration of stresses for accuracy
� No assumptions for concrete strain at ultimate strength
� High strength concrete HSC included (up to 90 MPa)
� Proper definition of load (Nub) balanced point
� Calculation of maximum value of reduced moment Mud
� Use of maximum values of capacity reduction factor φ
� Reduction in value of minimum reinforcement
� Inclusion of effect of spalling of concrete cover for HSC
22
USE 20% LESS STEEL WITH 500 PLUS REBAR
0
10
20
30
40
0 1 2 3 4 5 6
M u /A gD (MPa)
Nu
/Ag
(MP
a)
0.0% steel
1.0% steel 400Y
0.8% steel 500PLUS
2.0% steel 400Y
1.6% steel 500PLUS
450
700
f'c = 32 MPa
Comparisons between 400Y grade reinforcement and 500PLUS®
reinforcement are demonstrated here.
In the cases shown, a simple replacement of 20 percent less reinforcement
results in a similar column behaviour.
23
0
10
20
30
40
0 1 2 3 4 5 6M u/A gD (MPa)
Nu/A
g
(MP
a)
0% steel 1% steel 400Y
1% steel 500PLUS 2% steel 400Y
2% steel 500PLUS
450
700f' c = 32 MPa
500PLUS REBAR AS DIRECT REPLACEMENT
Further comparisons between 400Y grade reinforcement and 500PLUS®
reinforcement are demonstrated here.
In the cases shown, a simple substitution of the higher grade reinforcement
results in an increase in both axial load and moment capacity.
24
� Practice based on supporting research
� Advanced analysis of concrete cross-sections
� Use of high strength concrete
� Advantages of 500PLUS® Rebar
� Accurate software for design
� Ongoing development and research
CONCLUSIONS