Concrete tensile strength

[Anonymous]

Dear colleagues,

I have a problem with the way SBD calculates concrete tensile strength in flexure.

For example, I use EC1992-2, C35/45 and fctm = -3.21 MPa.

However, when I make a section and try to find cracking moment Mcr by hand (slowly increasing loading until concrete cracks), I get -3.21 MPa stress in concrete only for sections with relatively small height. For higher sections, the tensile strength is reduced and for h = 3000 mm it is 2.14 MPa which is exactly 1.5 times smaller than it should be. If I increase the height, the tensile strength is reduced even more, it goes below 2 MPa.

As far as I know, fctm can only be increased and that is for sections with height smaller than 600 mm, but it can never be less than original value, in my case 3.21 MPa.

Does anyone know which part of EN1992 states this reduction?

Have fun

BJ

[david.geeves · Accepted solution]

Hi BJ,

This is a very interesting question, and thank you for raising it. 

I find that the best way to determine the cracking moment in an RC section is to apply a relatively small moment (not too small) on the section and carry out a strain compatibility analysis on this applied loading which will result in the tensile stresses in the concrete not exceeding the tensile limit specified in the material properties for the concrete.  The section will behave linearly at this point, and up to the point where the tensile limit is reached, so by extracting the tensile stress from the results, a factor can be determined on the applied load that will result in the tensile limit being reached.

However, if this limiting moment is entered as an applied load and a strain compatibility analysis carried out, it is likely that the results show that the section is cracked (no tensile stresses in the concrete.  Even if the moment is reduced slightly, the analysis still shows a cracked section.

The reason for this is that the strain compatibility analysis at SLS is not setting a limit state that limits the tensile strain to the concrete tensile strain limit but is simply trying to find any strain plane where the internal forces and moments balance with the applied moments and forces.  Where the tensile strain in the extreme fibre of the concrete exceeds the tensile strain limit then no tensile force in the concrete is used in the internal forces and moments.

So if the cracking moment, as determined above, is applied to the section, there may be more than one solution that produces balanced forces, one where the section is cracked and the other where it is not. Both are valid solutions with regard to strain compatibility but each may be used separately for checking different conditions.  For max compressive force checks then you would ensure a cracked section approach.  For calculating the cracking moment you would ensure an uncracked section whilst limiting the tensile stresses to the limit specified.

If you wish to use the method of gradually increasing the applied moment to determine the cracking moment you would need to enter a large value for the tensile stress limit in the material properties, which will ensure that the section is always uncracked, then at each stage you can check whether the tensile stress  in the concrete exceeds the limit.

With this in mind it is important also to note that the program does not re-calculate the tensile stress limit for different section and the stress strain diagram used in the SLS strain compatibilist analysis is linear, based on an elastic modulus (short term, long term or interpolated as defined in the Service Calculation Parameters and applied loads) where the tensile stress in the extreme concrete fibre is limited to the value specified in the material properties and where this is exceeded then the tensile force in the complete concrete section is zero.

I hope this helps.  Please mark this post as a solution if this has answered your query.  Thanks

Kind regards

[Anonymous]

Dear David,

Thank you for explanation.

This is one detail which can be solved easily, as you demonstrated, and not a bug. It is important to know how the program works.

Have fun