What is the principle behind the formula for effective section modulus for branch of ASME B31.3-2008 (eq. 21) page 40? Ze=pi*r2^2*Ts?...Because in ASME B31.4 (from other software), it uses the simple formula Z=I/c (properties are all for branch), which sometimes yield lower section modulus (Z), thus creating greater stress (S=M/Z)?....Thanks all fellows...

Cheers

TS is the effective branch wall thickness, lesser of Th and i*Tb.
Tb is thickness of pipe matching branch, Th is the thickness of pipe matching run of tee or header exclusive of reinforcing elements

Using Ze in that form (with Ts the smaller of Th and i*Tb) is a tentative methodology addressing two potential location of failure due to branch moments. It may be at the header wall next to the junction or at the branch pipe next to the junction.
A more detailed explanation is given in Peng's book.
Mr. Peng explains why "the application of equation can be very confusing in actual cases" and proposes an "equivalent stress intensification factor" methodology.

Best regards.