NM2D2

$N$ - $M$ Interaction Inelastic Section

Reference

Syntax

Option One

Text Only

section NM2D2 (1) (2...9)
# (1) int, unique section tag
# (2) double, EA
# (3) double, EI
# (4) double, yielding axial force
# (5) double, yielding strong axis moment
# (6) double, c
# (7) double, isotropic hardening parameter H
# (8) double, kinematic hardening parameter K
# (9) double, linear density

If the NM2D2 section is defined by using the above command, it is assumed that the $N$ - $M$ interaction surface is defined as follows.

f = 1.15 p^{2} + m_{s}^{2} + 3.67 p^{2} m_{s}^{2} - c

where $p$ and $m_{s}$ are normalised axial force and moment (about strong axis). The surface is suitable for I-sections.

Option Two

One may wish to customise the surface by assigning different weights and orders, it is possible by using the following syntax.

Text Only

section NM2D2 (1) (2...9) [(10 11 12)...]
# (1) int, unique section tag
# (2) double, EA
# (3) double, EI
# (4) double, yielding axial force
# (5) double, yielding strong axis moment
# (6) double, d
# (7) double, isotropic hardening parameter H
# (8) double, kinematic hardening parameter K
# (9) double, linear density
# (10) double, a_i
# (11) double, b_i
# (12) double, c_i

In the above command, parameters (10), (11) and (12) form a triplet and can be appended as many groups as analyst wishes. The surface is assumed to possess the following form,

f = \sum_{i = 1}^{n} a_{i} p^{b_{i}} m_{s}^{c_{i}} - d .

For example, the previous surface $f = 1.15 p^{2} + m_{s}^{2} + 3.67 p^{2} m_{s}^{2} - c$ can be equivalently expressed with the second syntax as follows.

Text Only
1	`section NM2D2 (1) (2...9) 1.15 2. 0. 1. 0. 2. 3.67 2. 2.`

The only validation implemented is the number of triplets. The command takes $3 n$ parameters and interprets them accordingly. Please make sure the definition is correct.

Remarks

The true hardening ratio is defined as

\frac{H + K}{1 + H + K},

given that $H$ and $K$ are hardening ratios based on plastic strain.