The long awaited update to the Australian Standard for concrete structures (AS 3600 – 2009) provides rules for the design of structures with concrete up to a compressive strength of 100 MPa. Unfortunately there are a number of significant typographical errors in the new version of the code, one of the most significant being in the definition of the concrete rectangular compressive stress block, for determination of the ultimate bending strength of beams.
The compressive stress block is an approximation to the actual stress distribution in a reinforced concrete member that takes advantage of the fact that the stress-strain curve of low to medium strength concrete has a wide plateau region where the maximum stress is maintained constant with increasing strain. In high strength concretes this plateau is much narrower, since the maximum stress is developed at a higher strain, and the reduction in stress starts at a lower strain. For this reason both the depth and the stress in the rectangular block must be adjusted so that the resulting bending capacity is accurate. In Section 8 of the final public draft of the code the factors to make this adjustment were defined as:
where a2 is the factor on the depth of the stress block and g is the factor on the compressive stress. By the time the code was released this had been changed to:
Meanwhile in Section 10 of the code (design of columns) the stress block factor equations are repeated, and shown exactly as in the draft code!
The effect of the erroneous formula in Section 8 is to generate a γ value that is at the maximum end of the allowable range (0.85) for concrete grades up to 50 MPa, at which stress the correct formula gives a value of 0.7. The Section 8 formula is therefore unconservative, and the column provisions in Section 10 should be used for all flexural members instead. Another approach is to make use of the code provision that allows the use of any stress-strain curve for concrete “of curvilinear form defined by recognized simplified equations”, subject to the requirement that “the shape of the in-situ uniaxial compressive stress-strain curve shall be modified so that the maximum stress is 0.9f’c“.
Eurocode 2 (EC 2) provides convenient equations for a parabolic-rectangular stress block, which I have added to my spreadsheet for design of rectangular sections. The revised spreadsheet (including full open-source code) can be downloaded from: RC Design Functions.zip.
The design codes available with the new UMom are listed below:
The two formulations of the parabolic stress block give almost identical results. The second (Code = 10) returns equivalent rectangular stress block parameters, which can be compared with the values given in AS 3600.
Output from the new Umom function is shown below for the five different stress blocks, and four high strength concrete grades, from 50 MPa to 100 MPa:
It can be seen that:
- At 50 MPa use of Section 10 in the new code gives results very close to those from the old (2001) code. The Section 8 results are significantly higher, but the parabolic stress block is higher still.
- At 65 MPa the old code provisions had become unconserative, but the Section 8 provisions in the new code are higher still in the range of the balance moment. The parabolic stress block now gives more conservative results than any of the AS 3600 rectangular stress blocks.
- At 80 MPa the old code was no longer applicable. The Section 8 provisions in the new code are the most unconservative, but the Section 10 results are also significantly higher than the parabolic stress block results.
- At 100 MPa the Section 10 results are very close to the parabolic stress block, with the Section 8 results being only a little higher.
In summary there are significant differences between the correct (Section 10) rectangular stress block results and those given by the parabolic-rectangular stress blocks. Since the latter is much closer to the actual stress-strain behaviour of high strength concrete, and since the computation effort for a rectangular section is almost the same, it seems to me sensible to use the parabolic-rectangular stress block as standard.
For non-rectangular sections there is a significant degree of additional computation for the parabolic-rectangular stress block, but since the rectangular stress block introduces a significant degree of error for non-rectangular sections, in my opinion it is better to use the parabolic-rectangular stress block in this case also.