PFC and Angle

How it calculates

The PFC and Angle calculator to AS 4100:1998 analyses a combined section built from a Parallel Flange Channel (PFC) and a steel angle welded or bolted to the PFC. The combined section is common in masonry support and lintel applications where the angle carries the brick course outboard of the PFC web. The calculator evaluates the section for bending, deflection, and the additional torsional stress the brick load places on the angle leg.

Combined section geometry

The first step is assembling the composite cross-section properties from the selected PFC and angle. The calculator retrieves section data - depth, flange width, thickness, area, and second moments of area - from the built-in Australian section database. The angle can be positioned with its vertical leg offset from the bottom of the PFC, and either the longer or shorter leg can be designated as the vertical leg for unequal angles.

From the PFC and angle geometry, the calculator derives:

• Gross area - sum of PFC and angle areas
• Elastic neutral axis - located from the bottom fibre using the first moment of areas of each element
• Second moment of area about the X-axis - combined Ix for the composite section using the parallel axis theorem
• Elastic section modulus - Zex from Ix and the extreme fibre distance
• Plastic section modulus - Sx from the plastic neutral axis depth
• Section plate slenderness - governing slenderness of flange and web plate elements per AS 4100 Table 5.2

Section moment capacity

The nominal section moment capacity Ms is taken as the lesser of the first yield moment (fyZe) and the plastic moment (fySx), where fy is the minimum yield stress across all plate elements of the combined section. The section is assumed to fail as soon as any plate element reaches yield, so the minimum yield stress governs rather than the individual section yield stresses.

Lateral-torsional buckling and member moment capacity

For bending about the major axis, the nominal member moment capacity Mb is derived accounting for lateral-torsional buckling between the points of lateral restraint. The reference buckling moment Mo is calculated from the segment geometry using the effective length Le, which the engineer enters directly based on the bracing conditions.

The slenderness reduction factor is then applied to scale the section moment capacity down to the member moment capacity:

Mb = αs × Ms

where αs is the slenderness reduction factor from AS 4100 Cl 5.6.1, modified by the moment modification factor αm when the bending moment varies along the segment. The calculator evaluates the design bending moment M* at the critical section and checks M* ≤ φMb.

Deflection analysis

Serviceability deflections are computed separately for long-term and short-term load combinations using the flexural rigidity EI of the combined section.

Long-term deflection - calculated from dead loads plus the long-term component of live loads, applying the relevant combination factor.

Short-term deflection - calculated from the short-term design load combination.

Both deflections are compared against the allowable limit, which the engineer sets as a span ratio denominator (for example, L/300). The maximum deflection is located by finding the point of zero shear along the span rather than assuming midspan governs.

Angle stress analysis

The angle carries the brick course as an outboard cantilever from the PFC heel. The calculator models this using three steps.

First, it computes the torque T on the angle due to the distributed brick load acting at the tip of the horizontal leg. The torque arm is half the horizontal leg length.

Second, it converts the torque to a bending stress using the second moment of area of the angle leg per unit length and the moment-curvature stress relationship:

Applied stress = T × (leg length / 2) × 10³ / I_leg

This applied stress is checked against the factored angle yield stress using the von Mises yield criterion:

σE ≤ fy / √3

A separate check evaluates the total deflection at the tip of the angle. This combines the PFC deflection at midspan with the additional cantilever tip deflection of the angle horizontal leg, treated as a fixed cantilever:

Total angle deflection = max(Δ_long, Δ_short) + DL × (leg - offset)³ / (3 × E × I_leg)

Both the stress ratio and the deflection ratio are reported with pass/fail status so the governing limit state is immediately visible.