Bending stress

Type of material

Member bent about its strong axis (excluding hollow sections)

Rectangular and circular hollow sections, members with an axis of symmetry in the plane of loading bent about the weak axis, and gusset plates in in-plane bending

Plate in out-of-plane bending

Pin in bending

Curvature

Single curvature

Double curvature

Distribution of the bending moment

The bending moment reaches its maximum within the braced length

The bending moment varies linearly within the braced length

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Input

F value

F

Length

L

Modulus of elasticity

E

Section modulus

Z

Second moment of area about the weak axis

I_y

Warping constant

I_w

Shear modulus

G

St. Venant torsion constant

J

Larger end moment

M_1

Smaller end moment

M_2

Result

Elastic limit slenderness ratio

\lambda_e

Plastic limit slenderness ratio

\lambda_p

Correction factor

C

Yield moment

M_y

Torsional buckling moment

M_e

Slenderness ratio of the flexural member

\lambda_b

Critical slenderness ratio

\Lambda

Short-term allowable stress

\sigma_s

Long-term allowable stress

\sigma_l

Notes

Where the Standard writes "stress intensity", this page writes simply "stress".
For a member bent about its strong axis (rectangular hollow sections aside), the equation for the allowable stress on the compression side depends on how $\lambda_b$ compares with $\lambda_p$ and $\lambda_e$ . This tool picks the right one for you.
(M2/M1) is negative for single curvature and positive for double curvature. This tool applies the sign for you.