Checks two angles bolted to a column flange and bolted or welded to the beam web, carrying the beam reaction, to SIA 263:2013: two eccentricities in two planes, the bolts, the angles and the beam web. Every step shows its formula and the clause it comes from.
What it checks
- The bolts: one shear plane resists Fv,Rd = 0.6 · fub,k · A/γM2, equation (75), and one bolt in tension Ft,Rd = 0.9 · fub,k · As/γM2, equation (77), with the hole d0 of table 17.
- Eccentricities, each angle taking VEd/2 from the hinge at the face of the column: in the plane of the web, e = gb to the centroid of the web bolts; perpendicular to it, a = gc + tw/2 from the centroid of the column bolts to the axis of the web.
- Web bolts in shear and tension: the worst shear Fv,Ed from the elastic group of one angle under VEd/2 and (VEd/2) · e, and the tension on a top-row bolt from (VEd/2) · a, the group rotating about its bottom row: (Fv,Ed/Fv,Rd)² + (Ft,Ed/Ft,Rd)² ≤ 1, equation (78).
- Column bolts: shear alone at the hinge, VEd/2 per angle, one shear plane, equation (75).
- Bearing, equation (76): 0.85 · (e/d0) · fu,k · d · t/γM2 ≤ 2.4 · fu,k · d · t/γM2, on the beam web under twice the force of one angle, on both legs of an angle and on the column flange. e is the smaller of the end and toe distances; where the pitch p < e + d0/2, p − d0/2 replaces it.
- Net sections in shear, equation (82): one angle, (ha − nr · d0) · ta, and the beam web, Av from equation (42a) less nr · d0 · tw (clause 5.1.4.3).
- Angle in shear and bending at the root of the column leg: lever l = gc − ta, τ = (VEd/2)/(ta · ha) over the whole length, and Mpl,V,Rd = √(fy,k² − 3τ²) · ta · ha²/4/γM1.
- Placing of the holes on each leg and on the column flange: e1, e2 and p1 against the minimum of table 17, with e2 ≥ d0 for the bearing resistance.
What you enter and what you get
You enter fy,k and fu,k from table 1, the five dimensions of the rolled beam, the bolt grade (table 2) and size, whether the shear planes cross the shank or the thread, γM1 and γM2 (clause 4.1.3) and VEd. For the angles: the legs Lb and Lc, ta, ha and the clearance c to the beam end. Then whether the angles are bolted or welded to the web, the rows, pitch, columns and gauge of the web bolts and of the column bolts, and the thickness tf,c and width bc of the column flange.
You get the eccentricities, every force and resistance and the utilisation of each check with a pass or fail. With the Pro plan, it prints as an A4 calculation note.
Assumptions and limits
- The hinge is at the face of the column flange. The angles are bolted to the column in every case.
- The perpendicular moment presses the angles against the column at one end; that contact is not checked.
- The root fillet of the angle is neglected in the lever l.
- The column itself, its flange in bending and its web, is not checked.
Worked example
A rolled beam with h = 270 mm, tw = 6.6 mm, in fy,k = 235 N/mm² and fu,k = 360 N/mm², under VEd = 45 kN, connected by two 90 × 60 × 6 mm angles 120 mm long, bolted to the web and to a 13 mm column flange with two M16 bolts of grade 4.6 at a 50 mm pitch on each leg, gb = 50 mm and gc = 35 mm. These are the module's own results for its worked example, computed when this page was built.
Inputs| Input | Value | Ref. |
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| Characteristic yield strength fy,k | 235 N/mm² | § t.1 |
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| Characteristic tensile strength fu,k | 360 N/mm² | § t.1 |
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| Overall depth h | 270 mm | |
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| Flange width b | 135 mm | |
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| Web thickness tw | 6.6 mm | |
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| Flange thickness tf | 10.2 mm | |
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| Root radius r | 15 mm | |
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| Bolt grade | 4.6 | § t.2 |
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| Bolt size | M16 | § t.17 |
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| The shear planes cross the | Shank — the unthreaded part | |
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| Resistance factor, gross sections γM1 | 1.05 | § 4.1.3 |
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| Resistance factor, bolts, welds and net sections γM2 | 1.25 | § 4.1.3 |
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| Design shear force VEd | 45 kN | |
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| Leg on the beam web Lb | 90 mm | |
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| Leg on the column Lc | 60 mm | |
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| Thickness ta | 6 mm | |
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| Length of the angles ha | 120 mm | |
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| Clearance, column face to the beam end c | 10 mm | |
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| The angles are | Bolted to the beam web | |
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| Rows of web bolts nr | 2 | |
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| Vertical pitch p1 | 50 mm | |
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| Columns of web bolts nc | 1 | |
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| Gauge of the first column from the heel gb | 50 mm | |
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| Rows nr,c | 2 | |
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| Vertical pitch p1,c | 50 mm | |
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| Columns nc,c | 1 | |
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| Gauge of the first column from the heel gc | 35 mm | |
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| Column flange thickness tf,c | 13 mm | |
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| Column flange width bc | 160 mm | |
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Calculation: Common values| Step | Value | Ref. |
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| Bolt | – = M16, grade 4.6, hole d0 = 18 mm | § t.17 |
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| Shear resistance of one plane0,6·fub,k·A/γM2, fub,k = 400 N/mm², A = 201.1 mm². | Fv,Rd = 38.60 kN | § (75) |
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| Shear per angle | VEd/2 = 22.50 kN | |
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| In-plane eccentricitygb: from the face of the column to the centroid of the web bolts. | e = 50.0 mm | |
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| Perpendicular eccentricitya = gc + tw/2: from the centroid of the column bolts to the axis of the beam web. | a = 38.3 mm | |
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| In-plane moment per angle | (VEd/2)·e = 1.125 kN·m | |
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| Perpendicular moment per angleIt presses the angles against the column at one end (contact, not checked) and pulls on the bolts at the other. | (VEd/2)·a = 0.862 kN·m | |
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| Web bolts on each anglenr·nc = 2·1. | n = 2 | |
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Calculation: Check 1 — web bolts, shear and tension| Step | Value | Ref. |
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| Shear on one plane of the worst boltThe elastic group of one angle under VEd/2 and (VEd/2)·e about its centroid. | Fv,Ed = 25.16 kN | |
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| Tension on a top-row bolt(VEd/2)·a·zmax/(nc·Σz²), the group rotating about its bottom row: with two bolts, (VEd/2)·a/p1. | Ft,Ed = 17.23 kN | |
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| Tensile resistance0,9·fub,k·As/γM2. | Ft,Rd = 45.22 kN | § (77) |
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| Web bolts, shear and tension(Fv,Ed/Fv,Rd)² + (Ft,Ed/Ft,Rd)² ≤ 1 | η = 0.570 · Pass57 % of the capacity used | § (78) |
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Calculation: Check 2 — bearing on the beam web| Step | Value | Ref. |
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| End distance usedgb − c, from the beam end. | e = 40.0 mm | § (76) |
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| Bearing resistance per bolt0,85·(e/d0)·fu,k·d·t/γM2 ≤ 2,4·fu,k·d·t/γM2, t = 6.6 mm. | Fb,Rd = 57.45 kN | § (76) |
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| Bearing on the beam web2·Fv,Ed ≤ Fb,Rd | η = 0.876 · Pass88 % of the capacity used | § (76) |
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Calculation: Check 3 — bearing on an angle, web leg| Step | Value | Ref. |
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| End distance usedThe smaller of the end distance 35.0 mm and the toe distance 40.0 mm. | e = 35.0 mm | § (76) |
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| Bearing resistance per bolt0,85·(e/d0)·fu,k·d·t/γM2 ≤ 2,4·fu,k·d·t/γM2, t = 6.0 mm. | Fb,Rd = 45.70 kN | § (76) |
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| Bearing on an angle, web legFb,Ed ≤ Fb,Rd | η = 0.551 · Pass55 % of the capacity used | § (76) |
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Calculation: Check 4 — angle, net section in shear| Step | Value | Ref. |
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| Net shear area of one angle(ha − nr·d0)·ta, along a column of holes. | Av,net = 504 mm² | § (82) |
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| Angle, net section in shearVEd/2 ≤ Veff,Rd | η = 0.298 · Pass30 % of the capacity used | § (82) |
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Calculation: Check 5 — beam web, net section in shear| Step | Value | Ref. |
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| Net shear areaAv − nr·d0·tw, Av by (42a). | Av,net = 1,976 mm² | § 5.1.4.3 |
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| Beam web, net section in shearVEd ≤ Veff,Rd | η = 0.152 · Pass15 % of the capacity used | § (82) |
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Calculation: Check 6 — end distance| Step | Value | Ref. |
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| End distancee1 ≥ 25 mm | η = 0.714 · Pass71 % of the capacity used | § t.17 |
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Calculation: Check 7 — edge distance| Step | Value | Ref. |
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| Edge distancee2 ≥ 20 mm | η = 0.500 · Pass50 % of the capacity used | § t.17 |
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Calculation: Check 8 — pitch in the direction of the force| Step | Value | Ref. |
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| Pitch in the direction of the forcep1 ≥ 40 mm | η = 0.800 · Pass80 % of the capacity used | § t.17 |
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Calculation: Common values| Step | Value | Ref. |
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| Column bolts on each anglenr,c·nc,c = 2·1. | nc = 2 | |
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| Force per column boltVEd/(2·nc): at the hinge, shear alone. | Fv,Ed = 11.25 kN | |
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Calculation: Check 1 — column bolts in shear| Step | Value | Ref. |
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| Column bolts in shearFv,Ed ≤ Fv,Rd | η = 0.291 · Pass29 % of the capacity used | § (75) |
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Calculation: Check 2 — bearing on an angle, column leg| Step | Value | Ref. |
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| End distance usedThe smaller of the end distance 35.0 mm and the toe distance 25.0 mm. | e = 25.0 mm | § (76) |
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| Bearing resistance per bolt0,85·(e/d0)·fu,k·d·t/γM2 ≤ 2,4·fu,k·d·t/γM2, t = 6.0 mm. | Fb,Rd = 32.64 kN | § (76) |
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| Bearing on an angle, column legFb,Ed ≤ Fb,Rd | η = 0.345 · Pass34 % of the capacity used | § (76) |
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Calculation: Check 3 — bearing on the column flange| Step | Value | Ref. |
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| End distance usedAway from any edge of the flange: the cap governs unless the pitch is short. The pitch p = 50 mm is below e + d0/2, so p − d0/2 replaces e. | p − d0/2 = 41.0 mm | § (76) |
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| Bearing resistance per bolt0,85·(e/d0)·fu,k·d·t/γM2 ≤ 2,4·fu,k·d·t/γM2, t = 13.0 mm. | Fb,Rd = 115.98 kN | § (76) |
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| Bearing on the column flangeFb,Ed ≤ Fb,Rd | η = 0.097 · Pass10 % of the capacity used | § (76) |
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Calculation: Check 4 — angle in shear and bending| Step | Value | Ref. |
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| Levergc − ta: from the centroid of the column bolts to the face of the web leg; the root fillet neglected. | l = 29.0 mm | |
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| Shear stress(VEd/2)/(ta·ha). | τ = 31.3 N/mm² | |
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| Reduced plastic moment√(fy,k² − 3τ²)·ta·ha²/4/γM1. | Mpl,V,Rd = 4.704 kN·m | |
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| Angle in shear and bending(VEd/2)·l ≤ Mpl,V,Rd | η = 0.139 · Pass14 % of the capacity used | |
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Calculation: Check 5 — end distance| Step | Value | Ref. |
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| End distancee1 ≥ 25 mm | η = 0.714 · Pass71 % of the capacity used | § t.17 |
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Calculation: Check 6 — edge distance| Step | Value | Ref. |
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| Edge distancee2 ≥ 20 mm | η = 0.800 · Pass80 % of the capacity used | § t.17 |
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Calculation: Check 7 — pitch in the direction of the force| Step | Value | Ref. |
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| Pitch in the direction of the forcep1 ≥ 40 mm | η = 0.800 · Pass80 % of the capacity used | § t.17 |
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Calculation: Check 8 — edge distance| Step | Value | Ref. |
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| Edge distancee2 ≥ 20 mm | η = 0.480 · Pass48 % of the capacity used | § t.17 |
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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 web bolts carry tension in a shear connection?
The column bolts sit off the axis of the web: in the worked example a = 38.3 mm gives (VEd/2) · a = 0.86 kN·m per angle, and the top-row bolt takes Ft,Ed = 17.2 kN. With the shear of 25.2 kN, equation (78) gives η = 0.570.
Is the column checked?
Only the bearing of the bolts on its flange, which is why tf,c is asked for. Its flange in bending and its web are not checked.
Which plan includes this module?
The Pro plan, with its calculation note.
Related
Norm: SIA 263:2013 · Page updated: 8 November 2026