Calculate neutral axis in SLS where axial compression is combined with bending (Column) 1

[DimzK]

Hi There,

I have been asked to find crack widths in a column. In order to do this , I must find the stresses in the tension steel.
In SLS when column is acting elastically, does anyone know how to calculate the neutral axis correctly when there is an axial force and bending both applied to the section?

Thank you and Regards,
Dimuth

 

[Agent666]

Well it adds/subtracts to the bending induced stresses, you have an additional P/A stress from the axial load that is superimposed on the flexural stress distribution. You can factor this into the cracking moment calculation and allow for it after the concrete is cracked. The concrete compression force in the cross section analysis simply has the axial load added to it, then proceed as you normally would to find the NA depth by looking at the force and moment equilibrium across the cross section to determine a NA depth that satisfies these criteria.

Effectively a compression force would tend to increase the cracking moment, and a tensile force would tend to reduce it.

 

[DimzK]

Thank you very much. Using the below equations:
From force equilibriumfollows:
NEd+ Fs−Fc−F’s= 0
Moment equilibrium around tension reinforcement gives:
MEd+NEd(𝒅 −𝒉/2)−F’s(𝒅 −𝒅 )−Fc(𝒅 −y/3 )= 0

I have numercially solved two non linear simultaneous equations to find the neutral axis (using excel goal seek) and hence I was able to find all the relevant stresses and stains.

 

[Agent666]

Yeah sounds correct for a rectangular member with uniaxial bending and the axial load acting at the centroid (apart from the F's term should be multiplied by (d-d'), but I assume it was just an error in writing it out here)