The previous post in this series compared the results of current and previous Australian Standards, and the ACI 318 code, for the ultimate bending capacity of a rectangular reinforced concrete section, subject to combined bending and axial load. I have now extended this analysis to include three European codes: the current Eurocode 2, and the recently superseded British Standard codes: BS 5400 (bridges) and BS 8110 (buildings).
The spreadsheet used in this analysis contains user defined functions (UDFs) that will carry out the section analysis for any rectangular section with 1 or 2 layers of reinforcement, for the following codes:
- AS3600-2010, rectangular stress block (default)
- AS5100, rectangular stress block
- Eurocode 2, parabolic stress block
- BS 5400, rectangular stress block
- BS 8110, rectangular stress block
- Not yet implemented
- ACI 318, rectangular stress block
- AS3600-2001, rectangular stress block
- AS3600-Parabolic1; parabolic parameters to EC 2
- AS3600-Parabolic2; parabolic stress block converted to equivalent rectangular block
The spreadsheet (including full open source code) may be downloaded from RC Design Functions5.zip
All the codes reviewed here adopt the same basic principles, but differences in the method of application of these principles lead to significant differences in the resulting design actions from each code. The major differences are:
- The Australian codes and ACI 318 use the nominal material yield stresses to calculate the section moment and axial load capacity, then reduce these values by a global capacity reduction factor, whereas the European codes apply different reduction factors to the concrete and steel yield stress, and use these reduced values to calculate the design ultimate capacities.
- All of the codes have a greater reduction in capacity for sections where concrete crushing controls the design, compared with sections where steel yield in tension controls, but there are significant differences in the transition range between the different factors.
- All of the codes have an additional reduction factor on concrete stress to account for long term stresses, and differences between the design stress block and the actual stress distribution, but there are significant differences in how this factor is applied.
- All of the codes other than ACI 318 have a minimum load eccentricity for sections that would otherwise have zero or very small design bending moment. ACI has an additional reduction factor on the maximum axial load.
- The European codes allow either rectangular or parabolic-rectangular concrete stress blocks to be used. In this review the parabolic-rectangular stress blocks have been used. The EC 2 stress block has also been used for the AS 3600 calculations, which allow any stress block supported by experimental evidence. For the ACI 318 calculations the specified rectangular stress block has been used.
- The two BS codes are limited to a concrete cube strength of 65 MPa, which is equivalent to a cube strength of a little over 50 MPa. The other codes have modifications to the concrete stress block for higher strength grades, to account for its reduced ductility.
- The reinforcement stress-strain curve is virtually identical for all the codes other than BS 5400, which has a tri-linear curve and a reduced yield stress for steel in compression. The standard yield stress is different in each code, but for comparison purposes the yield stresses have been factored so that each code gives the same bending capacity with no axial load.
- EC 2 has a reduced concrete strain for sections entirely in compression, reducing to the concrete yield strain for sections in uniform compression. AS 3600 reduces the compressive strain for sections in uniform compression to the reinforcement yield strain, and the other codes use the same concrete strain as used for sections in flexure.
The screen-shot below shows the input for the five different codes:
Interaction diagrams for the five codes for concrete grades between 32 MPa and 100 MPa are shown below; note that the AS 3600 results are based on the same parabolic-rectangular stress block as specified in EC 2. See the previous post in this series for a comparison with the rectangular stress block:
The most significant differences between the results from the different codes are summarised below:
For concrete grades up to 50 MPa and axial loads up to about 50% of the balance load the three European codes and ACI 318 give very similar results, but AS 3600 is significantly more conservative, due to the transition of the capacity reduction factor from 0.8 to 0.6 starting at zero axial load. For higher concrete grades the two British codes are not applicable and ACI 318 becomes slightly less conservative than EC 2.
For loads between about 50% and 100% of the balance load the ACI 318 results become closer to the AS 3600 values, and for concrete grades up to 50 MPa the results from these two codes are reasonably close from the balance load up to the maximum design load. For higher strength grades the ACI code design moment values are significantly higher than those from AS 3600, and also exceed EC 2 values for 80 MPa and 100 MPa concrete.
The BS 8110 and EC 2 results are very similar over the whole range (for concrete grades up to 50 MPa), with BS 5400 giving significantly lower capacity for axial loads approaching the balance load and greater.
The maximum axial load under uniform compression given by ACI 318 is similar to AS 3600, and significantly less than the European codes, for low concrete strengths, but becomes progressively less conservative, and is approximately equal to the EC 2 value at 100 MPa.
The AS 3600 results are the most conservative in all cases, except for loads just above the balance load for 40 and 50 MPa concrete, where ACI 318 gives slightly more conservative results.
It should be noted that the ACI results assumed the use of confinement reinforcement consisting of rectangular ties. Where helical reinforcement (complying with the code requirements) is used the ACI code is significantly less conservative. Interaction diagrams are shown below for 50 MPa and 80 MPa concrete, with spiral confinement reinforcement for the ACI code:
It can be seen that for 80 MPa concrete the ACI design bending moments for an axial load of 10,000 kN are of the order of 30% greater than the EC 2 results, and almost 100% greater than the AS 3600 results.