Combined stress (tension and bending)

Input

Tensile load

T

Effective sectional area

A_N

Beam length

L

Section modulus (compression side)

Z_c

Section modulus (tension side)

Z_t

Allowable tensile stress

f_t

Allowable bending stress

f_b

Average tensile stress

\sigma_t

Bending moment

M

Bending stress (compression side)

\sigma_{bc}

Bending stress (tension side)

\sigma_{bt}

Combined stress check (compression side)

f_{cc}

Combined stress check (tension side)

f_{tc}

Notes

Based on 6.2 "Tensile force and bending moment" of the AIJ Standard for Allowable Stress Design of Steel Structures (2019): Eq. (6.3) on the tension side and Eq. (6.4) on the compression side.
Enter the effective sectional area, not the gross area. In 6.2 of the same Standard the mean tensile stress is σ_t = T / A_N, where A_N is the Tensile stress area defined in 13.1. Entering the gross area, without deducting bolt holes and the like, errs on the unsafe side.
Work out whichever allowable stresses apply and enter them here. The allowable tensile stress f_t comes from 5.1(1) of the same Standard and the allowable bending stress f_b from 5.1(4).
Take the absolute value of each stress (proviso to 6.2 of the same Standard).
Where the Standard writes "stress intensity", this page writes simply "stress".