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New Formula for Maximum Crack Width and Crack Spacing in Reinforced Concrete Flexural Members

By: Byung Hwan Oh

Check the following reference Please.. it might's assist you in your question … Regards…

https://hal.archives-ouvertes.fr/hal-00683652/document

Hello,

in my eyes this is a really difficult topic. Outside of science they simulate a smeared crack distribution because the results deliver the best quality / the best conformity with the experimental values. In my project I also used the smeared distribution, but the experimental input comes from a 4-point-bending-test. This way I implemented the whole experimental curve (stress-strain curve of bending) and not only (as common) the compressive- and tensile strength (peak).

Please find here an abstract concerning my simulation: https://tu-dresden.de/zih/hochleistungsrechnen/hpc-monat?set_language=en

For detailed informations there are all informations within my project:

https://www.researchgate.net/project/CC-Technology-Conserving-resources-with-light-weighted-concrete-constructions-for-slabs-and-walls

Dear Jürgen,

in your case fibre-reinforced concrete is used. Therefore the residual tensile strength of concrete is also required for the modelling of cracking behaviour. In fib Model Code 2010 there is a equation for calculating crack spacing and crack width of FRC. You may try this equation to estimate crack spacing and crack width for your FRC plate.

If you have already experimental results, firstly for one-way plate (or a bending beam). I can make an estimation of crack spacing and crack width and we can compare the results.

Best regards

Dear Ngoc Linh Tran,

thank you for your reply. I did not use the (uniaxial) tensile or compressive strength at all - the coefficient of variation of the tensile strength is pretty high (bad quality).

Only 20 normalized pairs of values from my experimental deformation-controlled 4-point-bending-test have been used, including the pre-peak- and the post-peak-behaviour ; of course also including the bending strength. (flexural modulus ; secant modulus)

The reinforcing steel has been modeled with bilinear behaviour.

Dear Jürgen,

for any concrete material the uniaxial strengths (tensile and compressive strengths) are normally required. The multiaxial behaviour (also failure criterion) is formulated based on the uniaxial strengths.

I aggree that the scatter of concrete tensile strength is pretty high, depending on the size of sample used in the test. However, if you have a large number of specimens you will get a relative good mean value of the tensile strength, also the variation coefficient. These parameters are very useful for the recalculation of tests on concrete structures.

I suggest that you may try to use an analytical calculation before you model your structures with the use of a numerial method (FEM). For calculating the bond behaviour of concrete and reinforcement, the analytical model is often better than numerical model due to the fact that the numerical model based on the analytical results regarding bond behaviour. For flexural behaviour of reinforced concrete members, also with FRC, analytical calculations are quite accurate. The numerical calculation can be carried out later.

@ Jürgen: just comment that the large variation coefficient of tensile strength of concrete is normal and correct. Note that the mean value of fct shows a smaller scatter than fct itself. Therefore, you can use your results of concrete properties (mean values) in the calculation. An explanation of the scatter of fct can be found in the following paper.

Article Influence of material spatial variability on the shear stren...

Dear Ngoc Linh Tran,

refering to a numerical solution the quality of simulation results (output) should improve with the quality of the input. As you mentioned for concrete the uniaxial strength (tensile and compressive strength) are required as (minimal) input values (experimental values). The multiaxial strength and the failure criteria are just calculated by theory - experimental values for multiaxial strength are usually not available (only 2 machines in Germany). In my simulation the input values are 20 pairs of values stress-strain, calculated from the experimental recorded force-displacement values. The bending test takes a long time 20-30 min ; the recorded force-displacement-curve should represent static behaviour - so the values shoud have a good quality. The only uncertainty is located within the theory of statics, but in my eyes the theory for a beam is better than the theory for a slab / ceiling.