Structural Steel Design / Single-storey buildings and portal frames
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.
Lesson review: expert verification remains open
This lesson has received a full-context editorial review and a check of its technical explanations. Selected arithmetic has been checked separately. This is not independent engineering sign-off.
Corrections checked in this pass
- Zero moment distinguished from physical restraint; positive/reversed/same-sign moment cases handled; presumed stay stations do not prove adequacy; tension-flange restraint can contribute when verified.
Checks needed for project use
- A steel-design reviewer must check the first-generation calculation profiles, second-order analysis assumptions, connection rules and execution references against the applicable standards and amendments.
- Actual bending/axial-force diagram, load reversals, torsional restraint stiffness/strength, segment end conditions and plastic hinge requirements. The library portalStability helper remains an unusable toy analogue, not a validated alpha-cr or actual portal axial-force model.
These are educational models and exercises. Check their assumptions before using the results. The full technical content and every diagram have not yet been independently verified.
Concrete and steel calculations retain their stated first-generation Eurocode teaching basis. Use the standards and amendments specified for your project; do not mix generations without an appropriate design basis.
Read the lesson register and outstanding review notesWhy 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, where required by the loading and restraint design, elsewhere along the frame. 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
A supplied linear moment diagram from eaves to apex. Shading identifies inside-flange compression. Dots illustrate equal restraint spacing, not a verified stay arrangement.
- 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
- Scope
- Illustrative segment comparison; full restraint checks required
On this assumed linear moment diagram the inside flange is in compression over 10.40 m. Purlins on the outside flange do not provide direct inside-flange restraint, but verified tension-flange restraint can contribute. Check both moment signs, axial force and the complete restraint system. Restraint strength, stiffness, connections, bracing anchorage, axial interaction and plastic-hinge requirements are not verified by these dots or the segment comparison.
Things worth trying
- The line shown is an assumed moment diagram, not a solved gravity or uplift envelope.
- Dots divide the inside-compression interval equally for a segment-length comparison; their strength, stiffness and anchorage are not verified.
- Purlins attached to a tension flange can contribute to stability when the relevant conditions are satisfied.
- Check restraint needs for both load directions, tapered regions, axial interaction and plastic hinges. A dot or a green resistance bar does not establish a safe frame.
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
- Use a separate illustrative linear moment diagram from −592 to +266 kNm. Do not claim its sign change approximates a loaded portal within a specified percentage.
- A stay is assumed to provide full torsional restraint at its position
- χLT and its plateau are calibrated and unverified here
Whole-frame stability
A portal requires a global stability assessment that represents its geometry, member axial forces, stiffness and restraints. A storey sway estimate alone may omit significant modes.
The expression wL²/(8f) gives 674 kN for a parabolic three-hinged arch with the supplied load, span and rise. It is not the axial force in this pitched rigid-jointed portal; that force must come from frame analysis. Likewise, fixing a real base does not universally double sway stiffness.
Use an appropriate elastic critical or second-order frame analysis and verify the selected method’s applicability. The lab’s arch and stiffness comparisons are illustrations, not portal stability checks.
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
For a separate parabolic three-hinged arch of span 30 m and rise 1.577 m under a vertical UDL of 9.45 kN/m per horizontal metre, calculate H = wL²/(8f) in kN. This is not a portal-frame thrust calculation.
Check yourself
Under the illustrated gravity loading, why is direct restraint to the inside flange important near the eaves?
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