Flexural Strength Mn — §I3.4
The nominal flexural strength for compact filled composite sections is calculated using the Plastic Stress Distribution Method (PSDM). The full plastic moment Mp is found by sweeping the plastic neutral axis (PNA) from the center to the bottom of the section, integrating the rectangular stress block contributions from steel (±Fy) and concrete (C2f'c compression only). The maximum moment on the P-M envelope typically occurs near the balanced point, not at zero axial force.
PSDM Interaction Envelope — §I3.4a
Unlike the bilinear H1-1 formula used for pure steel members, compact CFST sections are checked against the full PSDM cross-section interaction envelope. The envelope is derived by sweeping the PNA and recording (P, M) at each position, producing a smooth convex curve with five key characteristic points:
| Point | Axial P | Moment M | Description |
|---|
| A | Pp = FyAs + C2f'cAc | 0 | Pure compression (PNA at bottom) |
| B | 0 | Mp | Pure bending (equal compression/tension areas) |
| C | C2f'cAc | Mp | Balanced point — same M as B but concrete compression only |
| D | PA/2 | Mmax ≈ Mp + extra | Maximum moment point |
| E | 0 | 0 | Origin |
φ-Scaled Design Envelope
For LRFD design, the PSDM envelope is scaled by resistance factors:
- P-axis: φc = 0.75, additionally capped at φcPn (the column buckling capacity) to account for slender columns
- M-axis: φb = 0.90
The cap at φcPn is critical: for a slender column with Pn < Pno, the design P-axis is cut at the lower value, creating a flat horizontal portion at the top of the envelope.
Radial D/C Ratio Check
The demand/capacity ratio is computed as the radial D/C on the φ-scaled PSDM envelope:
- Cast a ray from the origin through the demand point (Mu, Pu)
- Find where the ray intersects the φ-scaled PSDM envelope — this is the capacity point (Mcap, Pcap)
- DCR = |demand| / |capacity| = distance from origin to demand / distance from origin to intersection
If DCR ≤ 1.0, the member is adequate. This approach is more accurate and less conservative than a bilinear H1-1 formula, especially for points near the pure bending or balanced-point region of the envelope.
Biaxial Bending
For rectangular HSS with both Mux and Muy, each axis is checked independently against its own PSDM envelope (x-axis and y-axis envelopes are different for non-square sections). The governing D/C is the maximum of the two:
DCR = max(DCRx, DCRy)
For circular HSS, the cross-section is symmetric about all axes, so only one envelope is needed regardless of the Mu direction.