A screening check for RC pier columns: slenderness by kL/r, single-curvature moment magnification with EI = EcIg/2.5, and a strain-compatibility P–M interaction diagram with the variable resistance factor of AASHTO 5.5.4.2. Circular columns assume a 12-bar ring; rectangular columns assume steel split equally between the two bending faces.
Bars are placed for real: cover + tie + half-bar sets the ring radius (circular, evenly spaced ring) or the two face rows (rectangular, half the bars per bending face). ρ and the effective bar-spread ratio are computed from that geometry, not assumed.
Magnification uses Cm = 1.0 and φK = 0.75; sustained-load creep refinement (βd) is not applied — treat results as a screen, not a final design.
| Po pure compression (nominal) | – |
| φPn,max cap | – |
| Euler Pe (EI = EcIg/2.5) | – |
| φMn at Pu | – |
| β1 | – |
Treat this as the two-minute sanity check before the real column run. The stiffness assumption EI = EcIg/2.5 is the blunt end of AASHTO’s two options and usually conservative for lightly loaded piers; if δ comes out above roughly 1.4, the column wants either a bigger section or a proper second-order analysis, not a bigger magnifier. Two modelling honesty notes: the circular section here carries a 12-bar ring and the rectangle puts all steel on the two bending faces — a real 4-face cage gives a slightly fatter diagram near pure bending, so this tool errs safe. And remember the interaction check is one axis at a time; bridge piers almost always see biaxial demand from braking plus wind or seismic, so run both directions and combine per 5.6.4.5 before calling it done. Seismic detailing, plastic-hinge confinement and P-Δ at the seismic limit state live entirely outside this screen.