PFC and Plate

How it calculates

The PFC and Plate calculator designs a built-up steel lintel section - a parallel-flange channel (PFC) with a flat plate welded to its underside - under gravity and wind loading, following AS 4100:1998 for member capacity and AS/NZS 1170.0:2002 for load combinations.

Section geometry and composite properties

The combined cross-section consists of the selected PFC and a plate of breadth b_P = flange width + outstand d_H, and user-specified thickness t_P. The calculator derives the following section properties for the combined section:

• Gross area A_g: PFC gross area plus plate area (t_P × b_P)
• Elastic neutral axis (from bottom): area-weighted centroid of PFC and plate, accounting for the plate sitting below the PFC
• Plastic neutral axis: the axis that equalises yield-stress-weighted compression and tension areas; three cases are evaluated depending on whether the PNA falls within the plate, the PFC web, or the PFC flanges
• Second moments of area I_x and I_y: calculated using the parallel axis theorem for each element about the combined centroid
• Elastic section modulus Z_x: I_x divided by the larger of the distances from the neutral axis to the extreme fibres
• Plastic section modulus S_x: first moment of yield-stress-weighted area about the plastic neutral axis
• Minimum yield stress f_y,min: the lesser of the PFC flange, web, and plate yield stresses

Section slenderness and effective section modulus

Section plate slenderness is taken as the maximum of the three element slendernesses - PFC flange, PFC web, and plate outstand - each computed as (b/t)√(f_y/250) per AS 4100:1998 Cl 5.2.2. The effective elastic section modulus Z_ex is then:

• If compact (λ_s ≤ 82): Z_ex = min(1.5 Z_x, S_x) - plastic capacity governs
• If non-compact (82 < λ_s ≤ 115): Z_ex interpolates between Z_x and min(1.5 Z_x, S_x)
• If slender (λ_s > 115): Z_ex = Z_x × 115/λ_s - reduced capacity

Load combinations and design actions

Dead loads G include all distributed dead loads converted from kPa to kN/m using their load widths, plus self-weight of the PFC and plate. Live loads Q include distributed imposed loads, with a minimum equivalent point load at midspan per AS 1170.1 where the more adverse effect governs. Wind uplift W is calculated from site wind class (N1-N4 per AS/NZS 1170.2:2011), net pressure coefficient, and area reduction factor K_a.

The factored design action is assembled from the limit state load combination selected by the user per AS/NZS 1170.0:2002 Cl 4.2.2, covering combinations including strength (1.2G + 1.5Q, 0.9G + 1.0W) and serviceability cases with short-term and long-term imposed action factors.

Moment capacity

The nominal section moment capacity is:

M_s = f_y,min × Z_ex

The reference buckling moment M_0 is computed from the lateral-torsional buckling parameters of the combined open section, with warping constant conservatively set to zero and torsion constant taken as the sum of the PFC and plate torsion constants per AS 4100:1998 Appendix H:

M_0 = √[(π² EI_y / L_e²) × (GJ)]

The slenderness reduction factor αs and moment modification factor αm give the nominal member bending capacity:

M_b = min(αs × αm × M_s, M_s)

The design moment capacity is φ M_b where φ = 0.9 per AS 4100:1998 Table 3.4. The check requires M*_x ≤ φ M_b.

Deflection

Maximum mid-span deflection is computed using double integration for the combined UDL and optional point load. Two serviceability checks are performed:

• Long-term serviceability: dead load plus long-term live load component, checked against the allowable deflection limit
• Short-term serviceability: dead load plus short-term live load component, checked against the allowable deflection limit

Both use I_x and E = 200,000 MPa for the combined section.

Plate checks for eccentric brick load

The plate cantilevering from the heel of the PFC carries the eccentric weight of brickwork acting at the plate outstand. Two checks are performed:

Applied plate stress: computed from the moment-curvature relationship, taking the moment arm as t_P/2 and the relevant section modulus of the plate. The check is against the von Mises yield criterion for pure shear:

σ_E ≤ f_y,P / √3

Total plate deflection: the beam deflection (maximum of long-term and short-term values) plus the cantilever tip deflection of the plate treated as fixed at the PFC heel:

Δ_P = max(Δ_l, Δ_s) + ψ × w_brick × d_H³ / (3 × E × I_plate)

This total deflection is checked against the allowable limit - the governing check for brick cracking in masonry veneer construction.

Reactions

Support reactions are reported as limit-state, dead-load, and live-load components at each end of the span. These values are available for load linking: reactions can be passed directly into supporting column or footing calculations so that changes to the lintel loading propagate automatically downstream.