Module 15 · Lesson 15.2
Rafter stability, and why every portal has stays
Near the eaves the purlins restrain the wrong flange. That single fact explains a detail on every portal frame drawing, and it is the one thing about them worth never forgetting.
Why this matters
Look at any portal frame and you will see small members running from the purlins down to the underside of the rafter, near the eaves and nowhere else. They are called stays, they cost almost nothing, and without them the frame would fail at a fraction of its calculated strength. The reason is a single sentence about which flange is in compression — and once you have it, a great deal of what a portal frame looks like stops being arbitrary.
By the end of this lesson you should be able to
- Say which flange is in compression at each point along a rafter
- Explain why the purlins help near the apex and not near the eaves
- Quantify what stays are worth, using Module 8's argument
- Say why a portal's αcr is not a storey-drift calculation
What you should already know
- Lateral-torsional buckling and the effect of restraint (Module 8)
- The collapse mechanisms and the haunch (previous lesson)
- Frame stability and αcr (Module 9)
- Base fixity and its error direction (Module 14)
The purlins are on the wrong side
Purlins sit on top of the rafter. They restrain the top flange.
Near the apex the rafter sags, so the top flange is in compression, and the purlins are restraining exactly the flange that needs it. Everything is as it should be.
Near the eaves the rafter hogs — that is where the big negative moment is, the one the whole frame was designed for. The bottom flange is in compression, and the purlins are on the wrong side of the section entirely.
For the 30 m frame, with 592 kNm hogging at the eaves and 266 kNm sagging at the apex:
| Distance from eaves | Moment | Compression flange | Purlins? |
|---|---|---|---|
| 0% | −592 kNm | inside | no help |
| 20% | −420 kNm | inside | no help |
| 40% | −248 kNm | inside | no help |
| 60% | −77 kNm | inside | no help |
| 80% | +95 kNm | outside | restrained |
| 100% | +266 kNm | outside | restrained |
The moment changes sign at 69% of the way from the eaves to the apex — 10.4 m along a 15.1 m rafter.
Over more than two thirds of the rafter, the compression flange has nothing holding it.
Try it
Which flange, where — and what stays are worth
The bending moment along a portal rafter, from the eaves on the left to the apex on the right. The shaded band is where the INSIDE flange is in compression and the purlins are on the wrong side.
- Contraflexure at
- 69 % along
- Inside flange in compression over
- 10.40 m
- Stays fitted
- 0
- Segment length
- 10.40 m
- Reduction from stays
- 0 %
- Rafter Mc,Rd
- 826 kNm
- LTB slenderness λ̄LT
- 2.032
- Reduction χLT
- 0.242
- Rafter Mb,Rd
- 200 kNm
- Demand at the eaves
- 592 kNm
- Adequate?
- NO
The rafter carries 200 kNm against a demand of 592 — short by a factor of 3.0. The problem is 10.40 m of unrestrained compression flange, not a lack of section: the cross-section resistance is 826 kNm and a strength check would have called this comfortable.
Things worth trying
- Start with no stays. The rafter carries 200 kNm against a demand of 592 — short by a factor of three, while its cross-section resistance is 826 kNm. A strength check would have said it was comfortable.
- Add one stay: 478 kNm. Still not enough. Add a second: 656 kNm, and the frame works. Two small angles.
- Add a third and a fourth and watch the gains fall away — exactly as restraint did in Module 8, and for the same reason.
- Now raise the eaves moment and watch the shaded band grow. A bigger hogging moment leaves more of the rafter with the wrong flange in compression, so it needs more stays AND has more to carry.
- Take the apex moment towards zero. The contraflexure point runs off the end and the ENTIRE rafter has its inside flange in compression — which is what happens under an uplift combination, and it is why wind uplift is a separate stability case.
- Set the eaves moment low and the apex moment high instead. The shaded band shrinks towards nothing and the purlins do the whole job — which is why simply supported roof beams do not need stays.
- Watch where the green dots sit as you add stays: inside the shaded region, not spread along the rafter. Out past the contraflexure point a stay restrains a flange that is in tension and does nothing.
Worked example
Stability of the 30 m rafter
Given
- The frame from the last lesson: eaves moment 592 kNm hogging, apex 266 kNm sagging
- Rafter 533 × 210 × 92 UB in S355, Mc,Rd = 826 kNm
- 6° pitch, so the rafter is 15.08 m from eaves to apex
- Purlins at 1.8 m centres, restraining the top flange only
Find
Whether the rafter is stable, and how many stays it needs.
Assumptions
- The moment varies linearly along the rafter — a simplification, since the real diagram is parabolic, but the sign change sits within a few percent of the same place
- A stay is assumed to provide full torsional restraint at its position
- χLT and its plateau are calibrated and unverified here
Why a portal's stability is not a storey-drift calculation
Module 9 gave αcr for a storey as (H/V)(h/δ), and it is tempting to apply it to a portal. It does not carry across, and the reason is worth understanding.
A portal has two destabilising mechanisms acting at once:
Sway, which the columns and rafter resist in bending. This does behave like a storey, and it can be estimated.
Rafter thrust. A low-pitch rafter is very nearly an arch, and it carries an axial thrust of roughly wL²/8f, where f is the rise. For the 30 m frame at 6° pitch, the rise is 1.58 m and the thrust is 674 kN — a very large axial force in a 533 UB. That is 14% of the rafter's own in-plane Euler load, and it drives both in-plane rafter buckling and snap-through, where the rafters flatten and the frame drops.
The second mechanism has no counterpart in a multi-storey frame at all.
This course's
portalStability()deliberately refuses to return a frame αcr. Combining the two mechanisms needs a calibrated expression that has not been verified here, and the sway estimate alone comes out several times too high — which would say "second-order effects negligible" about a frame that certainly needs them. A plausible-looking αcr for a portal is worse than none at all.
What can be said honestly is the comparison the module is teaching: the rafter thrust is large, it must be checked by a proper method, and nominally fixing the bases doubles the sway component — which is why so many portals have moment-resisting bases, and why that decision belongs to the foundation designer as much as to the frame designer.
Practice
A rafter hogs 592 kNm at the eaves and sags 266 kNm at the apex. What fraction of the way to the apex does the moment change sign?
Practice
The rafter is 15.08 m from eaves to apex. How much of it has the inside flange in compression, in m?
Practice
Two stays are placed within a 10.4 m unrestrained length. What is the resulting segment length, in m?
Practice
A 30 m rafter rises 1.577 m and carries w = 9.45 kN/m. What axial thrust does the arch analogy give, in kN? Take H = wL²/8f.
Check yourself
Why do portal rafters need stays near the eaves but not near the apex?
Summary
- Purlins restrain the TOP flange — right near the apex, wrong near the eaves
- The moment changed sign 69% along the rafter, 10.4 m of a 15.1 m member
- Over all of that the inside flange is in compression with nothing holding it
- Unstayed: χLT = 0.242, Mb,Rd = 200 kNm against a demand of 592
- Two stays gave 656 kNm and made the frame work — two small angles
- The gains saturate exactly as in Module 8: the fifth stay added 10%
- Stays belong INSIDE the hogging region, not spread along the rafter
- A portal's αcr is not a drift calculation: the rafter thrust was 674 kN, 14% of its Euler load
This is educational material. It uses simplified examples to teach principles, and must not be relied on for real design or safety-critical decisions. Module overview and checkpoint