## Concrete Stress Blocks

Back in 2010 and 2011 posts here looked at a comparison of alternative stress blocks in the then new AS 3600, and a procedure for calculating parameters for a rectangular stress block exactly equivalent to the Eurocode 2 parabolic-rectangular stress block.

I have now updated the stress block comparisons using the factors in the 2018 version of AS 3600, comparing 3 stress blocks:

• AS 3600 2019, including new stress block factors and capacity reduction factors.
• A rectangular stress block equivalent to the Eurocode 2 parabolic-rectangular stress block (labelled AS 3600-P2 in the graphs below).
• The AS 5100 – 2017 rectangular stress block, which is exactly equivalent to the AS 3600 – 2010 version (including corrections to the 2009 version).

The graphs below are for the following cross section:

• Rectangular section, 1000 mm wide x 350 mm deep
• Compression steel = 10 bars, 16 mm diameter with 40 mm cover
• Tension steel = 10 bars, 20 mm diameter with 40 mm cover

Results below plot axial load against bending moment for a range of concrete strengths, with and without capacity reduction factors:

At 32 MPa  the unfactored results from the two rectangular stress blocks are close, with the new AS 3600 being slightly more conservative at mid to high axial loads.  The P2 results are significantly higher in this range. At 50 MPa  the difference between  the two rectangular stress blocks increases, and the increase in strength for the P2 results is also greater. At 65 MPa the AS 5100 and the P2 results are very close over the full range.  The new AS 3600 results are again lower for axial loads above the balance point. At 90 MPa all three results are close over the full range: The new AS 3600 capacity factors (Phi) are increased as follows:

• For no axial load (or tension) the factor is increased from 0.8 to 0.85 (for normal ductility steel)
• For axial loads above the balance point the factor is increased from 0. 6 to 0.65 when the ratio of live load to dead load (Q/G) is 0.25 or greater.
• The transition between the two factors is unchanged.

In the graphs below the new factors are applied to the AS 3600 and P2 results, but the AS 5100 results use the old factors.

With Q/G = 0

With 50 MPa concrete the new code results are slightly greater than AS 5100 for low axial loads, but remain significantly more conservative for axial loads above the balance point.  The P2 results are greater than AS 5100 over the full range: At 90 MPa all three curves are similar above the balance point, but the AS 3600 and P2 results are greater for low axial loads: For a Q/G of 0.25 or greater the increased Phi factor makes the new AS 3600 results greater than AS 5100 over the full range.  The P2 results are equal to AS 3600 for low axial loads, and significantly higher at mid to high axial loads: At 90 MPa with Q/G = 0.25 or more the AS 3600 and P2 results are close over the full range, with the AS 5100 results lower at all axial loads: The graphs below show the concrete contribution to the bending moment, and the depth of the Neutral Axis, for axial loads up to the decompression point (neutral axis at the “tension” face), for 50 MPa concrete.

Compared with the P2 curve:

• The AS 5100 curve reaches the decompression point at a much lower axial load.  Bending moments are slightly lower over the full range.
• The AS 3600 curve has a higher axial load than AS 5100 at the decompression point, but is still significantly lower than the P2 curve, and bending moments are much lower for axial loads above the balance point:  This entry was posted in Beam Bending, Concrete, Excel, Newton and tagged , , , , , , , , , . Bookmark the permalink.

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