You can use the Wood&Armer method (the European code supplement [ENV 1992-1-1 EC2 Design of Concrete Structures - Appendix 2, point A.2.8 Reinforcement in Slabs]). The conception of determining equivalent moment is authored by Wood and Armer. Details concerning the method can be found, for instance, in R.H.Wood, "The reinforcement of slabs in accordance with a pre-determined field of moments", Concrete, February 1968, August 1968 (correspondence)].
When calculating reinforcement of a slab structure or switching on the option of panel design for simple bending in a shell structure, design moments are calculated according to the method by Wood and Armer.
For a selected directions x and y, two types of design moments M* are calculated: the lower ones (negative, causing mainly tension in the bottom parts) and the upper ones (positive, causing tension in the upper parts). The general procedure takes the following form:
Determination of the moments M xd *, M yd * with a greater impact on top reinforcement ( + ).
M xd * = M x + |M xy |
M yd * = M y + |M xy |
However, if M x < -|M xy | (i.e. the calculated M xd * < 0)
M xd * = 0
M yd * = M y + |M xy *M xy /M x |.
Similarly, when M y < -|M xy | (i.e. the calculated M yd * < 0) → (*)
M xd * = M x + |M xy *M xy /M y | → (*)
M yd * = 0 → (*)
If any of thus obtained moments M xd *, M yd * is smaller than zero, you should assume zero (the design moments for tension in the upper layers are determined further on in the text).
Determination of the moments M xg *, M yg * with a greater impact on bottom reinforcement ( - ).
M xg * = M x - |M xy |
M yg * = M y - |M xy |
If M x > |M xy | (i.e. the calculated M xg * > 0) → (*)
M xg * = 0 → (*)
M yg * = M y - |M xy *M xy /M x | → (*)
Similarly, when M y > |M xy | (i.e. the calculated M yg * > 0)
M xg * = M x - |M xy *M xy /M y |
M yg * = 0.
If any of thus obtained moments M xg *, M yg * is bigger than zero, you should assume zero (such moments would design the lower reinforcements, which is already guaranteed by the formerly calculated 'lower' moments M xd *, M yd *).
Analogously, design forces are calculated from the formulas given below for a plane stress structure or for the activated option of panel design for compression/ tension in a shell structure.
For the selected directions x and y, two types of design forces N* are calculated: the tensile (positive, causing main tension in a section) and the compressive (negative, causing section compression). The general procedure takes the following form:
Calculation of 'tensile' forces N xr *, N yr *.
N xr * = N x + |N xy |
N yr * = N y + |N xy |
However if N x < -|N xy | (i.e. calculated N xd * < 0)
N xr * = 0
N yr * = N y + |N xy *N xy /N x |.
Similarly, if N y < -|N xy | (i.e. calculated N yr * < 0) → (*)
N xr * = N x + |N xy *N xy /N y | → (*)
N yr * = 0 → (*)
If any of thus obtained forces N xd *, N yd * is less than zero, one should assume the zero value (forces designing a section by reinforcement compression are determined further on).
Calculation of 'compressive' forces N xs *, N ys *.
N xs * = N x - |N xy |
N ys * = N y - |N xy |
However, if N x > |N xy | (i.e. calculated N xs * > 0) → (*)
N xs * = 0 → (*)
N ys * = N y - |N xy *N xy /N x | → (*)
Similarly, if N y > |N xy | (i.e. calculated N ys * > 0)
N xs * = N x - |N xy *N xy /N y |
N ys * = 0.
If any of thus obtained forces N xs *, N ys * is greater than zero, one should assume the zero value (such forces design a section by reinforcement tension, which is already guaranteed by the tensile forces N xr *, N yr * calculated earlier).
For complex stresses (shells with the activated option of panel design for bending + compression/ tension) with bending moments (M xx , M xy , M yy ) and membrane forces (N xx N xy , N yy ) acting simultaneously, there is no simplified algorithm devised. Since it is often the case that the modeled shells work almost as slabs (with slight membrane forces acting), therefore the possibility to calculate moments M xd *, M yd * according to the method presented still remains and these design moments are superimposed with longitudinal forces N xx , N yy .