Rolled profile with cover plates in bending and axial force to SIA 263
Checks a rolled profile with symmetric welded cover plates under a moment and an axial force, compression or tension, to SIA 263:2013: the reinforced and the unreinforced zones, the member in compression, the length of the plates and the shear of the web. Every step shows its formula and the clause it comes from.
Basic SIA 263:2013
Part of the Basic plan
This module is included in the Basic plan and above, with its calculation note.
About this check
clauses, worked example and questions
Checks a rolled profile with symmetric welded cover plates under a moment and an axial force, compression or tension, to SIA 263:2013: the reinforced and the unreinforced zones, the member in compression, the length of the plates and the shear of the web. Every step shows its formula and the clause it comes from.
What it checks
- Bare profile from h, b, tw, tf and r, fillets included: A and Wy,pl. Reinforced section: Ar = A + 2 · bsem · tsem, Iy,r, the plate force Fsem = fy,sem · bsem · tsem and Mpl + Mpl,sem = fy,k · Wy,pl + Fsem · (h + tsem).
- Class in the reinforced zone and outside it, table 5a.
- Reinforced zone: MEd ≤ MN,Rd, the moment of the plastic stress blocks of profile and plates that carry NEd, about the plastic neutral axis zpl.
- Unreinforced zone: MEd,0 ≤ My,N,Rd = Mpl/γM1 · (1 − n)/(1 − 0.5a), not more than Mpl/γM1, on the bare profile outside l0.
- Flexural buckling about both axes, clause 4.5.1: NK,y,Rd and NK,z,Rd of the bare profile, and Ncr,y = π² · E · Iy/lK,y².
- Stability, bending and compression: NEd/NK,Rd + ω · MEd/((1 − NEd/Ncr) · MRd,r) ≤ 1, with the moment over the resistance of the reinforced section.
- Length of the plates: the weld length at each end bsem + 2Δl = Fsem/fw, Δl = (Fsem/fw − bsem)/2 and lsem = l0 + 2Δl.
- Shear of the web, equation (41): VEd ≤ VR/γM1, with Av by equation (42a), on the profile alone.
What you enter and what you get
You enter fy,k of the profile and fy,sem of the plates from table 1 of your copy of SIA 263, E (clause 2.2), the profile dimensions without the plates, tsem and bsem, and γM1 (clause 4.1.3). You enter NEd with its sense, the largest moment MEd in the reinforced zone, the moment diagram, and MEd,0 outside it. For the member: the length l and the buckling lengths, from the end conditions and intermediate supports or directly. For the plates: l0, and Δl from fw or entered directly. For the shear: τy,k and VEd.
You get the section properties, the class of each zone, the reduced moments, the buckling resistances, the plate length and the utilisation of each check with a pass or fail. With the Basic plan, it prints as an A4 calculation note.
Assumptions and limits
- Symmetric reinforcement only: one plate of the same size on each flange.
- ω = 0.6 + 0.4 · Mmin/Mmax, at least 0.4, for end moments only; 1.0 with a transverse load between the ends or an end not held laterally.
- Compression brings the member check in. Buckling uses the bare profile, the plates stiffening only part of the length, which is conservative.
- Lateral-torsional buckling is taken as prevented by construction measures.
- l0 is read off the moment envelope; no formula gives it. If the unreinforced zone fails, l0 is too short.
- With an axial force the plates still carry at most Fsem: the length and the welds are sized as without it. The weld is not designed.
- Fatigue is not covered, although the end of a welded cover plate is among the worst details a steel beam can have.
Worked example
A rolled profile with h = 114 mm, b = 120 mm, tw = 5 mm, tf = 8 mm and r = 12 mm, with two 100 × 10 mm plates over l0 = 4,300 mm, all in fy,k = 235 N/mm², a member 4.00 m long with two intermediate supports against buckling about z, under NEd = 60 kN in compression, MEd = 40 kN·m with a transverse load, MEd,0 = 22 kNm and VEd = 44.1 kN, with fw = 839 N/mm. These are the module's own results for its worked example, computed when this page was built.
| Input | Value | Ref. |
|---|---|---|
| Characteristic yield strength fy,k | 235 N/mm² | § t.1 |
| Modulus of elasticity E | 210000 N/mm² | § 2.2 |
| Overall depth of the profile, WITHOUT the cover plates h | 114 mm | |
| Flange width b | 120 mm | |
| Web thickness tw | 5 mm | |
| Flange thickness tf | 8 mm | |
| Root radius r | 12 mm | |
| Yield strength of the cover plate fy,sem | 235 N/mm² | § t.1 |
| Plate thickness tsem | 10 mm | |
| Plate width bsem | 100 mm | |
| Resistance factor γM1 | 1.05 | § 4.1.3 |
| The axial force is | Compression | |
| Design axial force NEd | 60 kN | |
| Largest moment in the reinforced zone along the member MEd | 40 kN·m | |
| Moment diagram | Transverse load between the ends — ω = 1,0 | |
| Largest design moment outside the reinforced zone MEd,0 | 22 kNm | |
| Buckling lengths | From the end conditions and intermediate supports | |
| Length of the member l | 4000 mm | |
| Ends, buckling about the strong axis y | Held against sway — both ends pinned | |
| Intermediate supports against buckling about y ny | 0 | |
| Ends, buckling about the weak axis z | Held against sway — both ends pinned | |
| Intermediate supports against buckling about z nz | 2 | |
| Theoretical length of the plates l0 | 4300 mm | |
| Introduction length Δl obtained Δl | From the weld resistance per unit length | |
| Weld resistance per unit length fw | 839 N/mm | |
| Shear check | Considered | |
| Characteristic shear yield strength τy,k | 135 N/mm² | § t.1 |
| Design shear force VEd | 44.1 kN |
| Step | Value | Ref. |
|---|---|---|
| Yield strength of the profile | fy,k = 235 N/mm² | § t.1 |
| Area of the profileFrom h, b, tw, tf and r, fillets included. | A = 2,534 mm² | |
| Plastic section modulus of the profile | Wy,pl = 119,491 mm³ | |
| Area of the reinforced sectionA + 2·bsem·tsem. | Ar = 4,534 mm² | |
| Second moment of area of the reinforced section | Iy,r = 13,765,557 mm⁴ | |
| Force in each plate, fully plastifiedfy,sem·bsem·tsem — also the force the welds introduce. | Fsem = 235.0 kN | |
| Plastic moment of the reinforced section, no axial forcefy,k·Wy,pl + Fsem·(h + tsem). | Mpl + Mpl,sem = 57.22 kN·m | |
| Class in the reinforced zoneFlange outstand c/tf = 5.69 (the plate can only stiffen it); web c/tw = 14.80 with α = 0.845, ψ = -0.781. | – = Class 1 | § t.5a |
| Class outside it | – = Class 1 | § t.5a |
| Step | Value | Ref. |
|---|---|---|
| Plastic neutral axis above the centreWhere the stress blocks of the profile and the plates carry NEd — compression on the side of the axis that carries it. | zpl = -25.5 mm | |
| Reduced plastic moment of the reinforced sectionThe moment of the same stress blocks, /γM1. The plates sit farthest from the axis, so they keep nearly all their contribution while the web takes the axial force. | MN,Rd = 53.77 kN·m | |
| Reinforced zoneMEd ≤ MN,Rd | η = 0.744 · Pass74 % of the capacity used |
| Step | Value | Ref. |
|---|---|---|
| Axial utilisation of the profile | n = 0.1058 | |
| Reduced plastic moment of the profileMpl/γM1·(1 − n)/(1 − 0,5a), a = 0.242, not more than Mpl/γM1. | My,N,Rd = 26.74 kN·m | |
| Unreinforced zoneMEd,0 ≤ My,N,Rd | η = 0.823 · Pass82 % of the capacity used |
| Step | Value | Ref. |
|---|---|---|
| Buckling length, strong axisk·l with k = 1.00 — held against sway — both ends pinned. | lK,y = 4,000 mm | |
| Buckling length, weak axisl/(nz + 1) = 4,000/3: the member buckles between its supports. | lK,z = 1,333 mm | |
| Relative slenderness, strong axis(lK,y/iy)/λE, iy = 48.9 mm, λE = π·√(E/fy,k) = 93.91. | λ̄K,y = 0.8708 | |
| Relative slenderness, weak axis(lK,z/iz)/λE, iz = 30.2 mm. | λ̄K,z = 0.4704 | |
| Buckling resistance, strong axisχK·A·fy,k/γM1, curve b, χK = 0.6799. | NK,y,Rd = 385.5 kN | § 4.5.1 |
| Buckling resistance, weak axisχK·A·fy,k/γM1, curve c, χK = 0.8594. | NK,z,Rd = 487.3 kN | § 4.5.1 |
| Elastic critical load, strong axisπ²·E·Iy/lK,y². It sets the amplification 1/(1 − NEd/Ncr) of the moment. | Ncr,y = 785 kN | |
| Elastic critical load, weak axis | Ncr,z = 2,691 kN |
| Step | Value | Ref. |
|---|---|---|
| Moment factor | ω = 1.0000 | |
| AmplificationWith the stiffness of the bare profile — the plates over part of the length only stiffen it. | 1/(1 − NEd/Ncr,y) = 1.0827 | |
| Axial termThe smaller buckling resistance of the bare profile. | NEd/NK,Rd = 0.1556 | |
| Moment term, amplifiedOver the resistance of the reinforced section, 54.5 kN·m, where the largest moment acts. | ω·MEd/MRd,r = 0.7947 | |
| Stability, bending and compressionNEd/NK,Rd + ω·MEd/((1 − NEd/Ncr)·MRd,r) ≤ 1 | η = 0.950 · Pass95 % of the capacity used |
| Step | Value | Ref. |
|---|---|---|
| Weld length required at each endFsem/fw. | bsem + 2Δl = 280 mm | |
| Introduction length at each endΔl = (Fsem/fw − bsem)/2. | Δl = 90 mm | |
| Total length of each platelsem = l0 + 2Δl. | lsem = 4,480 mm |
| Step | Value | Ref. |
|---|---|---|
| Effective shear area | Av = 846 mm² | § (42a) |
| Shear resistance of the webVEd ≤ VR/γM1 | η = 0.406 · Pass41 % of the capacity used | § (41) |
How this module is verified
Verified clause by clause against SIA 263:2013 and against independent calculations used on real projects, before release.
Questions
Why do the plates lose so little to the axial force?
They sit farthest from the axis, so they keep nearly all their contribution while the web takes the axial force. In the worked example MN,Rd = 53.8 kN·m, against (Mpl + Mpl,sem)/γM1 = 54.5 kN·m without it.
Which stiffness sets the amplification of the moment?
That of the bare profile. In the worked example 1/(1 − NEd/Ncr,y) = 1.083.
Which plan includes this module?
The Basic plan, with its calculation note.
Related
- Rolled steel profile with cover plates in bending
- Rolled I or H section in bending and axial force
- Steel bending and axial force: all sections
- SIA 263: modules and clauses
Norm: SIA 263:2013 · Page updated: 28 October 2026