SEMINARS Sept. 2001
ADVANCED DESIGN™ OF COLUMNS Professor Russell Bridge Dr Andrew Wheeler Centre for Construction Technology and Research University of Western Sydney
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.
1 Fe\Jk\\cI\`e]fiZ`e^
FJI+0(
ADVANCED DESIGN™ OF COLUMNS
500PLUS-CCS SOFTWARE COLUMN CROSS SECTION 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.
2
LOAD-MOMENT STRENGTH INTERACTION - DESIGN φ Nu Locus of φ M u, φ Nu values
φ Nu0
N*
Load
(M*, N*) (Unsafe) (M*, N*) (Safe)
Moment
M*
(φ Mub, φ Nub)
φ Muo
φ Mu
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.
3
CONCRETE AND STEEL MATERIALS
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)
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.
4
CONCRETE STRESS-STRAIN CURVE (CEB) 60
AS3600-2001
f' c = 65 MPa
σc = f (εa)
50
40
f' c = 40 MPa
c
(MPa)
f' c = 50 MPa
σ
f' c = 32 MPa
Stress
30
f' c = 25 MPa 20
10
εo =
0.0022
0 0
0.001
0.002
0.003
0.004
Strain
εa
0.005
0.006
0.007
0.008
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.
5
CONCRETE STRESS-STRAIN CURVE (COLLINS) 80 70
f' c = 85 MPa (Collins et al)
f' c = 50 MPa (CEB)
50
σ
40
Stress
c
(MPa)
60
30
f' c = 25 MPa (CEB)
σc = f ( εa)
20 10
εo =
0 0
0.001
0.0022
0.002
0.003
0.004
Strain
0.005
0.006
0.007
0.008
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
6
STEEL STRESS-STRAIN CURVE 1.4
Strain Hardening Relative Stress σ s/f sy
1.2 1.0 0.8
Design Assumption
0.6
Slope = E s = 200,000 MPa
0.4
εsy = 0.0020 for 400Y Grade εsy = 0.0025 for 500Plus
0.2 0.0 0
1.0
10
20
30
40
50
60
Relative Strain ε s /ε sy
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.
7
Axis
AXIAL FORCE AND MOMENT AT A CROSS-SECTION
Strain Distribution
εa
Axis
Curvature ρ = 1/R
Centre
Cross-section
Neutral
Concrete Stress Distribution
Steel Stress Distribution
Stress Resultants
M N
To determine the capacity of a column the assumption that plane sections remain plane is utilised. An assumed strain distribution is applied to the crosssection, 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.
8
LOAD-MOMENT-CURVATURE DIAGRAM 400 x 400 50 cover 8C24 bars 8N24 Bars f sy = 410 MPa f ′c = 30 MPa
Axial Load N (kN)
5000
4000
3000
4
8
12
2000
16
24
32
40 60 80
1000
120 160 0
100
200
300
Moment M (kNm)
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.
9
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.
10
KEY POINTS ON LOAD-MOMENT INTERACTION CURVE
Axial Load
Nuo
εcu
Mul , Nul
d do
do
εcu
εcu kud
εsy
M ub , Nub k uodo
M uo Moment
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 (M ub, 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 (k oud) 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 (M ub, 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. 11
CAPACITY REDUCTION FACTOR Pure Bending where N u
φ 0 = 0.8
or
φ
=0
φ 0 = 0.8 Mud ≥ 0.6 Muo
Combined Bending and Compression where Nu
< Nub
φ = 0.6 + (φ0 − 0.6)(1− Nu ) N
ub
Combined Bending and Compression where Nu
φ = 0.6
> Nub
Capacity reduction factors (φ ), as defined by AS 3600, are dependent on the applied 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 0.6 at the balance point to 0.8 for pure moment.
12
STRENGTH IN PURE BENDING
800
0.8
700
0.7
600
0.6
500
0.5
400
0.4
300
0.3
200
0.2
100
0.1
Capacity Factor φ
Moment Strength - Pure Bending (kNm)
900 400 x 400 50 cover f sy = 500 MPa f' c = 32 MPa
φ M ud k u = 0.4
M uo
φ M uo
0 0
1
2
3
4
5
6
7
8
9
10
Percentage Steel %
For cross-sections where kuo is greater than 0.4, a reduction factor (φ) is reduced 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.
13
NOMINAL AND DESIGN STRENGTH 8000
400 x 400 50 cover f sy = 500 MPa f' c = 32 MPa
N uo
Load (kN)
6000
Locus M u, N u values
φ N uo
4000
Locus
φ M u, φ N u
M uo
values
2000
Rectangular Stress Analytical Method 0
0
100
200
300
400
500
Moment (kNm)
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.
14
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.
15
MINIMUM REINFORCEMENT IN COLUMN
Min. 1% steel 400Y Grade
0.8% steel 500 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".
16
CREEP AND SHRINKAGE STRESSES IN STEEL 500
Steel Stress (MPa)
400
300
1.0% 400Y Rebar
200
0.8% 500PLUS Rebar
100
0
1
3
10
30
Days
100
1
Time after Loading
3
10
30
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.
17
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.
18
EFFECT OF COVER SPALLING ON STRENGTH 1.00
Strength Factor k
0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50 0
20
40
60
80
100
120
Concrete Grade (MPa)
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.
19
COMPARISON OF HIGH STRENGTH CONCRETE
Axial Load Capacity φ N u (kN)
7000
6000
85 MPa 5000
4000
3000
2000
50 MPa 1000
0 0
100
200
300
400
Moment Capacity φ M u (kN/m)
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.
20
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 (N ub) balanced point • Calculation of maximum value of reduced moment M ud • 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
21
USE 20% LESS STEEL WITH 500 PLUS REBAR 40
700
N u /A g (MPa)
30
450 f' c = 32 MPa
20
0.0% steel 1.0% steel 0.8% steel 2.0% steel 1.6% steel
10
400Y 500PLUS 400Y 500PLUS
0 0
1
2
3
4
5
6
M u /A gD (MPa)
Comparisons between 400Y grade reinforcement are demonstrated here.
reinforcement
and
500PLUS®
In the cases shown, a simple replacement of 20 percent less reinforcement results in a similar column behaviour.
22
500PLUS REBAR AS DIRECT REPLACEMENT 40
700
f' c = 32 MPa
450
N u/A g (MPa)
30
20
10
0% steel 1% steel 1% steel 2% steel 2% steel
400Y 500PLUS 400Y 500PLUS
1
2
0 0
3
M u/A gD (MPa)
4
5
6
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.
23
CONCLUSIONS • 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
24
