Cracking Moment at Biaxial Bending and Uniaxial Bending

The cracking moment of a concrete cross-section is calculated from the mean tensile strength of the concrete and the ideal section modulus. The cracking moment describes the internal force that occurs when the tension stress f_ctm is reached in the outermost fiber of the cross-section and crack formation occurs.

For uniaxial bending, it is possible to calculate the cracking moment analytically. For biaxial bending, the introduction of a weight factor k is helpful to determine M_cr from the components M_cr,y and M_cr,z.

Calculation for the attached example:
Bending moment M_y = 20 kNm
Bending moment M_z = 20 kNm

Ideal section modulus W_y = 3,081 cm³
Ideal section modulus W_z = 3,081 cm³
Mean tensile strength of the concrete f_ctm = 0.290 kN/cm²

Member 1: Uniaxial bending M_y:

Member 2: Uniaxial bending M_z:

Member 3: Biaxial bending M_y and M_z: