The short answer
- A tapered built-up I-section is three welded plates (two flanges and a web) whose depth varies along the member, so depth sits where the bending moment is high.
- The flange carries most of the bending: prefer wider and thinner until the outstand reaches the compact or semi-compact limit (IS 800 Table 2, AISC 360 Table B4.1).
- The web carries shear and sets the lever arm: go deeper and thinner until shear buckling or web slenderness governs.
- Taper should follow the moment diagram, inside the depth limits your fabricator’s welding line can handle.
Anatomy of a tapered built-up I-section
Strip a pre-engineered building frame down to its parts and almost everything structural is three plates: a top flange, a bottom flange and a web, welded together. What makes the member tapered is that the web is cut on a slope, so the depth at one end differs from the depth at the other.
That simple idea is why PEB frames are economical. A portal frame under gravity load has its largest bending moments at the knees, falling to a smaller value near the ridge. A constant-depth hot-rolled section has to be sized for the peak and carries that depth everywhere. A tapered section can be deep at the haunch and shallow at the ridge, following the moment diagram.
Count the variables: depth at each end, web thickness, and the width and thickness of each flange. That is seven numbers per member before you consider splitting a rafter into segments. They all interact, which is why proportioning them well is both an art and, increasingly, a search problem.
Flanges: width against thickness
In bending, the flanges do most of the work. Their contribution to the section modulus grows with the flange area and with the square of the distance from the neutral axis. For a given area, then, the question is how to shape it.
A wider, thinner flange has the same area as a narrower, thicker one, but it gives a larger minor-axis stiffness, which helps lateral-torsional buckling resistance. Its limit is local buckling of the outstand. Both codes control that with a width-to-thickness ratio:
- IS 800:2007, Table 2: for the outstanding element of a welded compression flange, the limits on b/tf are 8.4ε (plastic), 9.4ε (compact) and 13.6ε (semi-compact), where ε = √(250/fy). Beyond that the flange is slender and its capacity reduces.
- AISC 360, Table B4.1b: for flanges of built-up I-shapes in flexure, the compact limit is λp = 0.38√(E/Fy) and the noncompact limit λr = 0.95√(kcE/FL), with kc depending on the web slenderness.
Note the welded case in IS 800 is stricter than the rolled case, which catches people who carry habits over from hot-rolled design. In practice, many economical PEB flanges sit in the compact or semi-compact band rather than plastic: you give up a little capacity per unit area to get a wider, more stable flange.
When the compression flange should be bigger
Under gravity load the inner flange of the column and the bottom flange of the rafter near the haunch are in compression, and they are often the ones that govern lateral-torsional buckling between flange braces. Under wind uplift the roles swap. Unequal flanges, with the larger one where compression and buckling govern most often, are a legitimate way to save steel. Just make sure the flange braces from the purlins and girts are modelled to match your assumptions.
Web: depth against thickness
The web sets the lever arm between the flanges and carries most of the shear. Going deeper increases bending capacity quickly, because flange force times lever arm is the moment. Going thinner saves a lot of weight, because the web is a large plate in a deep member. The two limits that stop you are:
- Web slenderness in bending. IS 800 Table 2 gives d/tw limits for a web with the neutral axis at mid-depth of 84ε, 105ε and 126ε for plastic, compact and semi-compact, with different values when axial compression shifts the neutral axis. AISC Table B4.1b gives λp = 3.76√(E/Fy) and λr = 5.70√(E/Fy) for webs in flexure.
- Shear buckling. In IS 800, an unstiffened web with d/tw above 67ε must be checked for shear buckling (clause 8.4.2). AISC handles the same thing through the web shear coefficient Cv in Chapter G.
There are also minimum thickness rules for serviceability and handling (IS 800 clause 8.6 limits d/tw for unstiffened webs) and, importantly, the thinnest plate your shop can weld without distortion. Many PEB lines work comfortably with webs from around 4–5 mm upwards, but check with your fabricator rather than assuming.
Why one web thickness everywhere costs you
It is common to see a single web thickness used for a whole frame. That is convenient for ordering plate, but it means the shallow end of the rafter, where shear is low, carries the same web as the deep haunch. Allowing different web thicknesses per member, or per rafter segment, is one of the reliable sources of savings in PEB optimisation.
Taper: following the moment diagram
The taper is what makes these sections special. The ideal taper puts depth where the moment is high and removes it where the moment drops. For a typical gable frame under gravity load that means:
- Columns shallow at the base (where a pinned base has little moment) and deep at the knee;
- Rafters deep at the haunch, tapering towards a shallower section through the middle of the span, sometimes deepening slightly again at the ridge for the ridge connection.
Load combinations complicate this. Wind can reverse moments, and crane loads add concentrated effects at the bracket. The taper that suits gravity alone may not suit the envelope, which is why we check every combination for every candidate rather than optimising for one case.
Checking a tapered member along its length
Because the depth changes, section properties change along the member, and the governing point is not always at an end. Section classification, capacity and stability should be checked at several stations along the member. AISC publishes Design Guide 25, Frame Design Using Web-Tapered Members, which is the standard reference for this in US practice. IS 800:2007 has no separate chapter for web-tapered members, so designers apply the prismatic provisions at stations along the member with care over effective lengths.
Fabrication limits that box you in
An optimal section on paper that the shop cannot build is not optimal. These are the practical constraints we always build into the candidate list:
| Constraint | Why it matters |
|---|---|
| Standard plate thicknesses | Only the thicknesses your mill or stockist supplies are worth considering. |
| Flange width increments | Flange strips are cut in steps (often 25 or 50 mm); odd widths waste plate. |
| Minimum and maximum web depth | The welding line and transport limits set the range of depths you can make. |
| Minimum web thickness | Thin webs distort when welded and are hard to handle. |
| Connection depth | The knee and ridge plates need enough depth for the bolt groups you will detail. |
Building these into the search from the start is far better than optimising freely and then rounding up, which gives back much of the saving.
Putting it together
A sound workflow for a tapered PEB member looks like this:
- Start with a section in the right family: depths from experience, a web thickness you know the shop can weld, flanges in the compact range.
- Analyse the frame with all load combinations so the force envelope is realistic.
- Search flange width, flange thickness, web depths and web thickness together, keeping only candidates inside the slenderness limits and fabrication rules.
- Check every candidate for strength, stability and combined actions under every combination, and keep the lightest that passes.
- Re-analyse with the chosen sections, then check deflection and drift yourself.
Steps 3 and 4 are the ones the PEB Optimization Tool automates for columns and rafters in STAAD.Pro, against IS 800 or AISC 360 (LRFD or ASD). For how the two codes treat these checks differently, see IS 800 vs AISC 360 for PEB frames, and for the modelling side, PEB frame design in STAAD.Pro.
Questions engineers ask
What is a tapered built-up I-section?
It is an I-shaped member made by welding two flange plates to a web plate, where the web is cut so the depth changes along the length. PEB frames use them for columns and rafters so that the section is deep where the bending moment is large (at the knee and haunch) and shallow where it is small.
Why do PEB frames use built-up sections instead of hot-rolled sections?
Built-up sections let each plate be sized independently and let the depth vary along the member. That puts steel only where the forces need it, which is why pre-engineered buildings are typically lighter than equivalent frames made from constant-depth hot-rolled sections.
Which slenderness limits apply to a welded tapered I-section?
Under IS 800:2007, Table 2 gives width-to-thickness limits for welded outstand flanges and for webs, which classify the section as plastic, compact, semi-compact or slender. Under AISC 360, Table B4.1 gives the equivalent limits (lambda-p and lambda-r) for built-up flanges and webs in flexure and compression. Both should be checked at several points along a tapered member, because the web depth changes.
Can the top and bottom flanges be different sizes?
Yes. Unequal flanges are common in PEB frames, for example a wider compression flange where lateral-torsional buckling governs. They complicate the section properties but often save steel.
Does the PEB Optimization Tool handle hot-rolled sections?
No. It works on tapered built-up I-sections for columns and rafters only. Hot-rolled members, purlins, girts and bracing are sized by the engineer as usual.