Rafters and columns as beam-columns

The members of the lesson 1 frame under portal actions to EN 1993-1-1: where the moments are, the sway check α_cr and the imperfections, the buckling lengths in and out of the frame’s plane, purlins and fly braces, uplift, and serviceability, with the STATIX steel member calculator on its Eurocode 3 route.

1. Learning outcomes

After this lesson you can:

read portal frame actions and choose the check sections;
check α_cr and add the sway imperfection to the gravity case;
set in-plane and out-of-plane lengths for a column and a rafter, with purlins, girts and fly braces;
check the rafter under gravity and under uplift with (6.61) and (6.62);
check eaves sway and apex deflection against agreed limits.

2. Before you start

Steel Design 1 (Eurocode) lesson 4 (combined actions, not repeated here) and lesson 1 (the frame and its loads).
The free steel member calculator, set to Eurocode 3 (EN 1993-1-1).
A pocket calculator and about 55 minutes.
The same lesson on the SA code: Steel Design 2, lesson 4 (SANS 10162-1).

3. Portal actions

Portal actions under gravity. The rafter carries a large moment and a small axial force; the column carries the axial force and the eaves moment, which falls to zero at a pinned base. The free steel member calculator checks one section at a time with the actions you bring from a frame analysis; STATIX 3D does that analysis in the model.

Portal actions under uplift. With the light roof lifted by wind (1.0 G + 1.5 W), the moments reverse: along the middle of the rafter the inner (bottom) flange goes into compression, where gravity never put it, and the bases go into tension.

Where to check. The column just below the haunch, the rafter at the haunch tip where the deeper section ends, and the rafter near the apex. Inside the haunch the section is deeper; the haunch and its connection are lesson 4.

4. Sway and imperfections

Sway and α_cr (EN 1993-1-1 5.2.1). A portal is unbraced in its own plane: under a horizontal force it sways, and the vertical loads acting on the sway add moment. For portal frames with shallow roofs, 5.2.1(4)B estimates the elastic critical factor α_cr from the sway δ under the horizontal forces; if α_cr ≥ 10, first-order moments are enough; between 3 and 10 they are amplified (5.2.2(5)); below 3, a second-order analysis is needed.

Imperfections (5.3.2). No frame is built plumb. EN 1993-1-1 represents the out-of-plumb by a sway imperfection φ, applied as equivalent horizontal forces φ N_Ed at the column tops. They may be left out where the horizontal loads are large (H_Ed ≥ 0.15 V_Ed, 5.3.2(4)), as in the wind cases, but not in the gravity case.

α_cr = (H_Ed / V_Ed) (h / δ_H,Ed) (5.2.1(4)B; shallow roofs, small rafter axial force) α_cr ≥ 10: first-order; 3 ≤ α_cr < 10: amplify the sway effects by 1/(1 − 1/α_cr) (5.2.2(5)); < 3: second order φ = φ₀ α_h α_m; equivalent horizontal force at a column top: φ N_Ed (5.3.2(3), (7))

5. Buckling lengths and restraint

Buckling lengths as this course uses them. When the sway effects and the imperfections are in the global analysis (5.2.2(3) b), the members are checked with their own system lengths. Out of plane, the length is the distance between real restraints of the compression flange.

Restraint. Purlins hold the rafter’s top flange at their spacing; fly braces from a purlin (or girt) to the inner flange restrain the bottom flange where they are fitted. Which flange is in compression decides which spacing is the lateral-torsional buckling length.

Which flange is in compression. Under gravity, the inner (bottom) flange is in compression near the eaves and the top flange near the apex; under uplift, the bottom flange along the middle of the rafter. The purlins only ever hold the top flange.

6. The member checks

The member checks are those of Steel Design 1 (Eurocode) lesson 4. For a member of a sway frame Table B.3 takes C_my = C_mz = 0.9; on the steel member calculator, Frame “unbraced” sets this unless you type C_m.

What the steel member calculator’s Eurocode 3 route uses here: the checks of Steel Design 1 (Eurocode) lesson 4, run by the calculator’s steel member engine (6.2.9, 6.3.1, 6.3.2, and 6.3.3 with the Annex B factors), γ_M0 = γ_M1 = 1.0, and Frame “unbraced” giving C_my = C_mz = 0.9 with a note that the moments and lengths must be those of a sway frame. It does not analyse the frame: you bring N, M and V for each section. It also lists flange-induced buckling of the web and the torsional buckling of the member.

7. Serviceability

Serviceability (EN 1993-1-1 7.2). Check the sideways movement of the eaves under wind and the vertical movement of the apex under the roof loads, with characteristic combinations. EN 1993-1-1 leaves the limits to the national annex and the client; agree them with the client and the cladding supplier.

8. In STATIX

The route: analyse the frame (STATIX 3D does it in the model; this lesson gives the actions from a simple elastic analysis), check α_cr and the imperfections, then check each section in the steel member calculator on its Eurocode 3 route with the lengths that match the restraints and Frame set to unbraced.