Many design codes require that cross sections have a minimum moment capacity of at least some factor (often 1.2) times the cracking load of the cross section. The cracking load is derived as follows:

f_cr = (M_L + M_B)/S – (P_L + P_B)/A

where

fcr	=	the cracking stress
ML	=	the bending moment due to applied loads at time of cracking
MB	=	the bending moment due to the balance loading (same sign as ML)
S	=	the section modulus for the direction of bending (Z in some communities)
PL	=	the axial compression due to applied loads at time of cracking
PB	=	the axial compression due to the balance loading
A	=	the section area

Solving for M_L results in:

M_L = (f_cr + (P_L + P_B)/A)S - M_B

Assuming that P_L is zero:

M_L = (f_cr + P_B/A)S - M_B

Replacing M_B with M_P + M_H and P_B with P_P + P_H:

M_L = (f_cr + (P_P + P_H)/A)S – (M_P + M_H)

where

MP	=	the "primary" post-tensioning bending moment
MH	=	the hyperstatic post-tensioning bending moment
PP	=	the "primary" post-tensioning axial compression
PH	=	the hyperstatic post-tensioning axial compression (typically negative)

Multiplying by 1.2 to get "1.2 times the cracking load":

1.2 M_L = 1.2 (f_cr + (P_P + P_H)/A) S – 1.2 (M_P + M_H)

To get the design bending moment, we add in the hyperstatic bending moment:

M_D = 1.2 M_L + M_H = 1.2 (f_cr + (P_P + P_H)/A) S – 1.2 (M_P + M_H) + M_H

Simplifying:

M_D = 1.2 (f_cr +(P_P + P_H)/A) S – 1.2 M_P – 0.2 M_H

It is common and usually conservative to assume that P_H is zero:

M_D = 1.2 (f_cr +P_P/A) S – 1.2 M_P – 0.2 M_H

It is common (although not technically correct) to ignore the 0.2 M_H, giving the final design moment equation:

M_D = 1.2 (f_cr + P_P/A) S – 1.2 M_P