Depth of square or rectangular hollow section
Thickness of square or rectangular hollow section
Capacity factor for strength limit states as per AS 4100:2020 Table 3.4
Moment modification factor for segments fully or partially restrained at both ends
Moment modification factor calculated
$$ \alpha_{m_{cal_{AS4100}}} = {1.0 + 0.35 \cdot \left({ 1 - {\left({ 2 \cdot a }\right) \over l} }\right) ^ 2} $$
Equation taken from AS4100:2020 Table 5.6.1.
Moment modification factor
IF
$ \alpha_{m_{cal_{AS4100}}} $
<
$ 1 $
THEN
$$ \alpha_{m_{AS4100}} = {\alpha_{m_{cal_{AS4100}}}} \:,
$$
OTHERWISE
$$ \alpha_{m_{AS4100}} = {1} $$
Effective section modulus
IF
$ S_{x_{AS4100}} $
<
$ 1.1 * Z_{x_{AS4100}} $
THEN
$$ Z_{e_{AS4100}} = {S_{x_{AS4100}}} \:,
{mm ^ 3}
$$
OTHERWISE
$$ Z_{e_{AS4100}} = {Z_{x_{AS4100}}} \:,
{mm ^ 3}
$$
Section moment capacity
$$ M_{s_{AS4100}} = {f_y \cdot {Z_{e_{AS4100}} \over 10 ^ 3}} $$
The effective length of a segment or sub-segment as per AS 4100:2020 Section 5.6.3
Effective length
$$ l_{e_{AS4100}} = {k_{t_{AS4100}} \cdot k_{l_{AS4100}} \cdot k_{r_{AS4100}} \cdot l_{AS4100}} $$
Outer radius
IF
THEN
$$ R_{o_{RHS}} = {2.5 \cdot t_{RHS}} \:,
{mm}
$$
OTHERWISE
$$ R_{o_{RHS}} = {2 \cdot t_{RHS}} \:,
{mm}
$$
Inner radius
IF
THEN
$$ R_{i_{RHS}} = {1.5 \cdot t_{RHS}} \:,
{mm}
$$
OTHERWISE
$$ R_{i_{RHS}} = {1 \cdot t_{RHS}} \:,
{mm}
$$
Length
$$ h_{RHS} = {2 \cdot \left({ \left({ b_{RHS} - t_{RHS} }\right) + \left({ d_{RHS} - t_{RHS} }\right) }\right) - \left({ R_{o_{RHS}} + R_{i_{RHS}} }\right) \cdot \left({ 4 - \pi }\right)} $$
Area
$$ A_{h_{RHS}} = {\left({ b_{RHS} - t_{RHS} }\right) \cdot \left({ d_{RHS} - t_{RHS} }\right) - \left({ {( R_{o_{RHS}} + R_{i_{RHS}} ) \over 2 }}\right) ^ 2 \cdot \left({ 4 - \pi }\right)} $$
Integration constant
$$ k_{RHS} = {{( 2 \cdot A_{h_{RHS}} \cdot t_{RHS} ) \over h_{RHS}}} $$
Torsional constant
$$ J_{RHS} = {t_{RHS} ^ 3 \cdot {h_{RHS} \over 3} + 2 \cdot k_{RHS} \cdot A_{h_{RHS}}} $$
Reference buckling moment as per AS 4100:2020 Section 5.6.1.1
Reference buckling moment
$$ M_{o_{AS4100}} = {{\sqrt{ \pi ^ 2 \cdot E \cdot {I_{y_{AS4100}} \over l_{e_{AS4100}} ^ 2} \cdot \left({ G \cdot J_{RHS} + \pi ^ 2 \cdot E \cdot {I_{w_{AS4100}} \over l_{e_{AS4100}} ^ 2} }\right) } \over 10 ^ 3}} $$
For RHS Iw = 0 (AS 4100:2020 Section 5.6.1.4)
Slenderness reduction factor
$$ \alpha_{s_{AS4100}} = {0.6 \cdot \left({ \sqrt{ \left({ {M_{s_{AS4100}} \over M_{o_{AS4100}}} }\right) ^ 2 + 3 } - \left({ {M_{s_{AS4100}} \over M_{o_{AS4100}}} }\right) }\right)} $$
Nominal member moment capacity
$$ M_{b_{AS4100}} = {\alpha_{m_{AS4100}} \cdot \alpha_{s_{AS4100}} \cdot M_{s_{AS4100}}} $$
Design bending moment in RHS about the major principal axis analyzed by the elastic method as per AS4100:2020 Section 4.4.2.2
Design bending moment in RHS
$$ M_{x_{AS4100}} = {\phi_{ls_{AS4100}} \cdot M_{b_{AS4100}}} $$