Analyses a triangular steel roof truss at the ultimate limit state and verifies every member to SIA 263:2013: axial force alone or with the bending from rigid nodes and loads along the chords, buckling, packing plates and the deflection. Every step shows its formula and the clause it comes from.
What it checks
The truss as a whole
- Geometry: a = l/(2n), the ratio h/l (1/4 to 1/6 for a first sizing) and the inclination α of the first diagonal, economical between 35° and 55°.
- Loads and reactions: γG · G + γQ · Q at the nodes, the self-weight Ga at 78.5 kN/m³, and Av, Ah, Bv.
- Internal forces: the axial force in every member and, with rigid nodes or loads along a chord, its end moments and largest moment.
Each member group (top chord, bottom chord, diagonals, verticals)
- Section class, tables 5a and 5b, in compression. For two angles or channels back to back, Iout = 2 · (I1 + A1 · (s/2 + e)²): the gap counts.
- Buckling curves: c for angles and channels; a for a hot-finished hollow section, c for a cold-formed one.
- Compression: NEd/NK,Rd from λ̄in and λ̄out, and for two angles λ̄TF, since out-of-plane buckling couples with twist. Then NEd/NK,Rd + ω · MEd/(MRd · (1 − NEd/Ncr)) ≤ 1.
- Tension: NRd = A · fy/γM1 on the gross section (clause 4.1.3), then NEd/NRd + MEd/MRd ≤ 1.
- Bending resistance MRd, clause 4.1.3, from the plastic modulus in the plane of the truss, class 1 or 2.
- Packing plates, EN 1993-1-1 6.4.4: sp ≤ 15 · imin of one part, at least two plates per member, where the group has a member in compression.
Deflection: the largest w from the same stiffness analysis against wlim.
What you enter and what you get
You enter fy,k from table 1 of your copy of SIA 263, E and G (clause 2.2), the pattern (Pratt or Howe), the span l, the rise h at the apex, n panels in each half, and pinned or rigid nodes. For the loads: γG, γQ, gtop, qtop, gbot, qbot, at the nodes or along the chord, the self-weight, and up to six nodal forces at chosen nodes. For each group: the section and its dimensions (UPN or UPE flanges for channels), the gap s and spacing sp of a built-up member, the in-plane buckling length and, for the chords, lout. Then γM1 (clause 4.1.3) and the deflection limit.
You get the forces and moments, every member check with its utilisation and a pass or fail, and the deflection. With the Expert plan, it prints as an A4 calculation note.
Assumptions and limits
- With rigid nodes the truss is solved as a plane frame. The axial forces hardly change from the pinned truss; the moments are added in the checks.
- The member axes meet at the nodes. The connections are not designed.
- lout is the out-of-plane buckling length of a compressed chord. Lateral-torsional buckling of a built-up T or ][ chord is not considered: its moments are local, between nodes held out of the plane.
- The in-plane buckling length is the system length, or 0.9 l for a chord and 0.8 l for a web member.
- At bolted joints the net section must also be checked; it is not done here.
Worked example
A Pratt roof truss of 20 m span and 4 m rise, four panels per half, rigid nodes, fy,k = 355 N/mm², gtop = 6 kN/m and qtop = 9 kN/m along the top chord, gbot = 1 kN/m, self-weight and a variable 20 kN at node b4; two angles 120 × 120 × 12 mm on a 12 mm gusset above, two UPN-type channels 140 mm deep below, hot-finished circular hollow sections 88.9 × 5 mm between, lateral supports every 2,500 and 5,000 mm, and l/300 under the variable load. 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 | 355 N/mm² | § t.1 |
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| Modulus of elasticity E | 210000 N/mm² | § 2.2 |
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| Shear modulus G | 81000 N/mm² | § 2.2 |
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| Pattern of the web | Pratt — diagonals in tension, verticals in compression | |
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| Span between the supports l | 20000 mm | |
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| Rise at the apex, between the chord axes h | 4000 mm | |
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| Number of panels in each half n | 4 | |
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| Nodes | Rigid — welded or continuous, the members also bend | |
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| Load factor, permanent actions γG | 1.35 | |
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| Load factor, variable actions γQ | 1.5 | |
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| Distributed loads reach the chords | Along the chord — the chord also bends between the nodes | |
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| Permanent load on the top chord gtop | 6 kN/m | |
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| Variable load on the top chord qtop | 9 kN/m | |
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| Permanent load on the bottom chord gbot | 1 kN/m | |
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| Variable load on the bottom chord qbot | 0 kN/m | |
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| Self-weight of the members | Included — computed from the sections | |
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| Number of nodal forces | 1 | |
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| Force 1 — at node | b4 | |
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| Force 1 — vertical, downwards Fv | 20 kN | |
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| Force 1 — horizontal, to the right Fh | 0 kN | |
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| Force 1 — action | Variable | |
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| Resistance factor γM1 | 1.05 | § 4.1.3 |
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| Deflection | Considered | |
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| Deflection under | Variable load only | |
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| Deflection limit, span divided by | 300 | |
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| Type of section | Two angles back to back | |
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| Leg against the gusset, in the plane of the truss h | 120 mm | |
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| Outstanding leg, across the plane b | 120 mm | |
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| Thickness of the legs t | 12 mm | |
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| Root radius r | 13 mm | |
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| Gap between the two angles, the gusset thickness s | 12 mm | |
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| Spacing of the packing plates sp | 300 mm | |
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| Buckling length in the plane of the truss | System length between the nodes | |
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| Distance between lateral supports of the chord lout | 2500 mm | |
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| Type of section | Two channels back to back | |
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| Depth of the channel, in the plane of the truss h | 140 mm | |
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| Flange width b | 60 mm | |
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| Web thickness tw | 7 mm | |
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| Flange thickness tf | 10 mm | |
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| Root radius r | 10 mm | |
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| Flanges | Tapered at 8 % — UPN | |
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| Gap between the two channels, the gusset thickness s | 12 mm | |
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| Spacing of the packing plates sp | 800 mm | |
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| Buckling length in the plane of the truss | System length between the nodes | |
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| Distance between lateral supports of the chord lout | 5000 mm | |
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| Type of section | Circular hollow section | |
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| Outside diameter D | 88.9 mm | |
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| Wall thickness t | 5 mm | |
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| Manufactured | Hot-finished | |
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| Buckling length in the plane of the truss | System length between the nodes | |
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| Type of section | Circular hollow section | |
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| Outside diameter D | 88.9 mm | |
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| Wall thickness t | 5 mm | |
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| Manufactured | Hot-finished | |
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| Buckling length in the plane of the truss | System length between the nodes | |
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Calculation: Common values| Step | Value | Ref. |
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| Characteristic yield strength | fy,k = 355 N/mm² | § t.1 |
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| Panel lengtha = l/(2n) | a = 2,500.0 mm | |
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| Depth-to-span ratio1 : 5.0. Usual first sizing: 1/4 to 1/6 for a triangular truss. | h/l = 0.2000 | |
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| Inclination of the diagonalsOf the first diagonal. Between 35° and 55° is economical. | α = 38.7 ° | |
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| Nodes and membersm + 3 = 2j: statically determinate — the forces do not depend on the sections. | j · m = 16 nodes · 29 members | |
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| Self-weight of the membersΣ A·l·78,5 kN/m³ over all members — 1.00 kN/m of span. | Ga = 20.02 kN | |
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| Total vertical design loadγG·G + γQ·Q = 1.35·G + 1.50·Q, all nodes. | ΣFd = 516.0 kN | |
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| Reaction at the left support, verticalPin at node b0. | Av = 258.0 kN | |
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| Reaction at the left support, horizontal | Ah = 0.0 kN | |
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| Reaction at the right supportRoller at node b8. | Bv = 258.0 kN | |
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Calculation: Axial forces at the ultimate limit state| Step | Value | Ref. |
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| TC1 — top chord, b0–t1Compression, length 2,693 mm. | NTC1 = -615.1 kN | |
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| TC2 — top chord, t1–t2Compression, length 2,693 mm. | NTC2 = -612.8 kN | |
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| TC3 — top chord, t2–t3Compression, length 2,693 mm. | NTC3 = -537.7 kN | |
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| TC4 — top chord, t3–t4Compression, length 2,693 mm. | NTC4 = -452.5 kN | |
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| TC5 — top chord, t4–t5Compression, length 2,693 mm. | NTC5 = -452.5 kN | |
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| TC6 — top chord, t5–t6Compression, length 2,693 mm. | NTC6 = -537.7 kN | |
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| TC7 — top chord, t6–t7Compression, length 2,693 mm. | NTC7 = -612.8 kN | |
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| TC8 — top chord, t7–b8Compression, length 2,693 mm. | NTC8 = -615.1 kN | |
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| BC1 — bottom chord, b0–b1Tension, length 2,500 mm. | NBC1 = 571.2 kN | |
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| BC2 — bottom chord, b1–b2Tension, length 2,500 mm. | NBC2 = 500.3 kN | |
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| BC3 — bottom chord, b2–b3Tension, length 2,500 mm. | NBC3 = 421.7 kN | |
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| BC4 — bottom chord, b3–b4Tension, length 2,500 mm. | NBC4 = 347.4 kN | |
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| BC5 — bottom chord, b4–b5Tension, length 2,500 mm. | NBC5 = 347.4 kN | |
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| BC6 — bottom chord, b5–b6Tension, length 2,500 mm. | NBC6 = 421.7 kN | |
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| BC7 — bottom chord, b6–b7Tension, length 2,500 mm. | NBC7 = 500.3 kN | |
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| BC8 — bottom chord, b7–b8Tension, length 2,500 mm. | NBC8 = 571.2 kN | |
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| D1 — diagonal, b1–t2Tension, length 3,202 mm. | ND1 = 88.8 kN | |
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| D2 — diagonal, b2–t3Tension, length 3,905 mm. | ND2 = 120.6 kN | |
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| D3 — diagonal, b3–t4Tension, length 4,717 mm. | ND3 = 139.1 kN | |
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| D4 — diagonal, b5–t4Tension, length 4,717 mm. | ND4 = 139.1 kN | |
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| D5 — diagonal, b6–t5Tension, length 3,905 mm. | ND5 = 120.6 kN | |
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| D6 — diagonal, b7–t6Tension, length 3,202 mm. | ND6 = 88.8 kN | |
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| V1 — vertical, b1–t1Compression, length 1,000 mm. | NV1 = -53.4 kN | |
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| V2 — vertical, b2–t2Compression, length 2,000 mm. | NV2 = -85.4 kN | |
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| V3 — vertical, b3–t3Compression, length 3,000 mm. | NV3 = -114.3 kN | |
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| V4 — vertical, b4–t4Tension, length 4,000 mm. | NV4 = 38.8 kN | |
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| V5 — vertical, b5–t5Compression, length 3,000 mm. | NV5 = -114.3 kN | |
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| V6 — vertical, b6–t6Compression, length 2,000 mm. | NV6 = -85.4 kN | |
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| V7 — vertical, b7–t7Compression, length 1,000 mm. | NV7 = -53.4 kN | |
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Calculation: Bending moments at the ultimate limit state| Step | Value | Ref. |
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| TC1 — largest momentAt the ends -6.84 kNm (b0) and -7.74 kNm (t1), sagging positive; largest 10.08 kNm at 1,329 mm from b0. | MTC1 = 10.08 kNm | |
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| TC2 — largest momentAt the ends -6.91 kNm (t1) and -11.74 kNm (t2), sagging positive. | MTC2 = 11.74 kNm | |
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| TC3 — largest momentAt the ends -10.48 kNm (t2) and -9.97 kNm (t3), sagging positive. | MTC3 = 10.48 kNm | |
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| TC4 — largest momentAt the ends -8.55 kNm (t3) and -15.76 kNm (t4), sagging positive. | MTC4 = 15.76 kNm | |
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| TC5 — largest momentAt the ends -15.76 kNm (t4) and -8.55 kNm (t5), sagging positive. | MTC5 = 15.76 kNm | |
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| TC6 — largest momentAt the ends -9.97 kNm (t5) and -10.48 kNm (t6), sagging positive. | MTC6 = 10.48 kNm | |
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| TC7 — largest momentAt the ends -11.74 kNm (t6) and -6.91 kNm (t7), sagging positive. | MTC7 = 11.74 kNm | |
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| TC8 — largest momentAt the ends -7.74 kNm (t7) and -6.84 kNm (b8), sagging positive; largest 10.08 kNm at 1,364 mm from t7. | MTC8 = 10.08 kNm | |
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| BC1 — largest momentAt the ends 6.84 kNm (b0) and 6.46 kNm (b1), sagging positive; largest 8.06 kNm at 1,165 mm from b0. | MBC1 = 8.06 kNm | |
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| BC2 — largest momentAt the ends 6.96 kNm (b1) and -0.13 kNm (b2), sagging positive. | MBC2 = 6.96 kNm | |
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| BC3 — largest momentAt the ends 1.47 kNm (b2) and -0.04 kNm (b3), sagging positive; largest 2.22 kNm at 913 mm from b2. | MBC3 = 2.22 kNm | |
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| BC4 — largest momentAt the ends 1.07 kNm (b3) and -3.96 kNm (b4), sagging positive. | MBC4 = 3.96 kNm | |
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| BC5 — largest momentAt the ends -3.96 kNm (b4) and 1.07 kNm (b5), sagging positive. | MBC5 = 3.96 kNm | |
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| BC6 — largest momentAt the ends -0.04 kNm (b5) and 1.47 kNm (b6), sagging positive; largest 2.22 kNm at 1,587 mm from b5. | MBC6 = 2.22 kNm | |
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| BC7 — largest momentAt the ends -0.13 kNm (b6) and 6.96 kNm (b7), sagging positive. | MBC7 = 6.96 kNm | |
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| BC8 — largest momentAt the ends 6.46 kNm (b7) and 6.84 kNm (b8), sagging positive; largest 8.06 kNm at 1,335 mm from b7. | MBC8 = 8.06 kNm | |
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| D1 — largest momentAt the ends 0.29 kNm (b1) and 0.12 kNm (t2), sagging positive; largest 0.36 kNm at 1,125 mm from b1. | MD1 = 0.36 kNm | |
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| D2 — largest momentAt the ends -0.41 kNm (b2) and 0.45 kNm (t3), sagging positive. | MD2 = 0.45 kNm | |
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| D3 — largest momentAt the ends -0.22 kNm (b3) and -0.11 kNm (t4), sagging positive. | MD3 = 0.22 kNm | |
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| D4 — largest momentAt the ends 0.22 kNm (b5) and 0.11 kNm (t4), sagging positive. | MD4 = 0.22 kNm | |
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| D5 — largest momentAt the ends 0.41 kNm (b6) and -0.45 kNm (t5), sagging positive. | MD5 = 0.45 kNm | |
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| D6 — largest momentAt the ends -0.29 kNm (b7) and -0.12 kNm (t6), sagging positive; largest -0.36 kNm at 1,125 mm from b7. | MD6 = 0.36 kNm | |
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| V1 — largest momentAt the ends -0.79 kNm (b1) and 0.83 kNm (t1), sagging positive. | MV1 = 0.83 kNm | |
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| V2 — largest momentAt the ends -1.19 kNm (b2) and 1.14 kNm (t2), sagging positive. | MV2 = 1.19 kNm | |
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| V3 — largest momentAt the ends -0.89 kNm (b3) and 0.97 kNm (t3), sagging positive. | MV3 = 0.97 kNm | |
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| V4 — largest momentAt the ends 0.00 kNm (b4) and -0.00 kNm (t4), sagging positive. | MV4 = 0.00 kNm | |
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| V5 — largest momentAt the ends 0.89 kNm (b5) and -0.97 kNm (t5), sagging positive. | MV5 = 0.97 kNm | |
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| V6 — largest momentAt the ends 1.19 kNm (b6) and -1.14 kNm (t6), sagging positive. | MV6 = 1.19 kNm | |
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| V7 — largest momentAt the ends 0.79 kNm (b7) and -0.83 kNm (t7), sagging positive. | MV7 = 0.83 kNm | |
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Calculation: Common values| Step | Value | Ref. |
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| Top chord — area | A = 5,545 mm² | |
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| Top chord — second moment of area in the plane | Iin = 7,492,842 mm⁴ | |
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| Top chord — one angle: area, centroid from the gusset faceFrom the dimensions, root fillet included. | A1 · e = 2,772 mm² · 34.2 mm | |
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| Top chord — second moment of area out of the plane, the pair2·(I1 + A1·(s/2 + e)²) with s = 12.0 mm — the gap counts. | Iout = 16,437,759 mm⁴ | |
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| Top chord — radii of gyration | iin · iout = 36.8 · 54.4 mm | |
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| Top chord — shear centre and torsionThe shear centre lies where the outstanding legs meet the plane of the gusset, y0 from the centroid; K = Σ b·t³/3. Buckling out of the plane couples with twist — flexural-torsional buckling. | y0 · K = 28.2 mm · 262,656 mm⁴ | |
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| Top chord — leg against the gusset c/tLimits 7.3 · 8.1 · 11.4 for class 1, 2, 3 in compression. | – = 7.9 | § t.5b |
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| Top chord — outstanding leg c/tLimits 7.3 · 8.1 · 11.4 for class 1, 2, 3 in compression. | – = 7.9 | § t.5b |
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| Top chord — section classIn compression, the least favourable wall. | – = Class 2 | § t.5a |
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| Top chord — buckling curvesAngles: c about both axes. | – = in plane c · out of plane c | |
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| Top chord — buckling length factor in the planeThe system length. | βin = 1.00 | |
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| Top chord — buckling length out of the planeThe distance between lateral supports. | lK,out = 2,500 mm | |
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Calculation: Common values — flexural buckling alone| Step | Value | Ref. |
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| TC1 — flexural buckling aloneλ̄in = 0.959, λ̄out = 0.601, λ̄TF = 0.767 → χ = 0.564; checked with the bending below. | NEd/NK,Rd = 0.581 | |
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| TC2 — flexural buckling aloneλ̄in = 0.959, λ̄out = 0.601, λ̄TF = 0.767 → χ = 0.564; checked with the bending below. | NEd/NK,Rd = 0.579 | |
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| TC3 — flexural buckling aloneλ̄in = 0.959, λ̄out = 0.601, λ̄TF = 0.767 → χ = 0.564; checked with the bending below. | NEd/NK,Rd = 0.508 | |
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| TC4 — flexural buckling aloneλ̄in = 0.959, λ̄out = 0.601, λ̄TF = 0.767 → χ = 0.564; checked with the bending below. | NEd/NK,Rd = 0.428 | |
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| TC5 — flexural buckling aloneλ̄in = 0.959, λ̄out = 0.601, λ̄TF = 0.767 → χ = 0.564; checked with the bending below. | NEd/NK,Rd = 0.428 | |
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| TC6 — flexural buckling aloneλ̄in = 0.959, λ̄out = 0.601, λ̄TF = 0.767 → χ = 0.564; checked with the bending below. | NEd/NK,Rd = 0.508 | |
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| TC7 — flexural buckling aloneλ̄in = 0.959, λ̄out = 0.601, λ̄TF = 0.767 → χ = 0.564; checked with the bending below. | NEd/NK,Rd = 0.579 | |
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| TC8 — flexural buckling aloneλ̄in = 0.959, λ̄out = 0.601, λ̄TF = 0.767 → χ = 0.564; checked with the bending below. | NEd/NK,Rd = 0.581 | |
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Calculation: Check 1 — packing plates of the built-up member| Step | Value | Ref. |
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| Top chord — smallest radius of gyration of one angleAbout the minor principal axis v of the angle. | imin = 23.6 mm | |
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| Top chord — spacing of the packing platessp ≤ 15·imin | η = 0.846 · Pass85 % of the capacity used | EN 1993-1-1 6.4.4 |
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Calculation: Check 2 — axial force with bending| Step | Value | Ref. |
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| Top chord — bending resistance of the sectionPlastic modulus, class 2, in the plane of the truss. | MRd = 53.22 kNm | § 4.1.3 |
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| Top chord — lateral-torsional bucklingThe built-up T section bends about its axis across the gusset; the moments are local, between nodes held out of the plane by the lateral supports, and the out-of-plane stability is that of the buckling check above. | – = Not considered | |
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| TC1 — compression and bendingN/NK,Rd + ωM/(MRd(1 − N/Ncr)) ≤ 1 | η = 0.847 · Pass85 % of the capacity used | |
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| TC2 — compression and bendingN/NK,Rd + ωM/(MRd(1 − N/Ncr)) ≤ 1 | η = 0.837 · Pass84 % of the capacity used | |
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| TC3 — compression and bendingN/NK,Rd + ωM/(MRd(1 − N/Ncr)) ≤ 1 | η = 0.766 · Pass77 % of the capacity used | |
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| TC4 — compression and bendingN/NK,Rd + ωM/(MRd(1 − N/Ncr)) ≤ 1 | η = 0.734 · Pass73 % of the capacity used | |
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| TC5 — compression and bendingN/NK,Rd + ωM/(MRd(1 − N/Ncr)) ≤ 1 | η = 0.734 · Pass73 % of the capacity used | |
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| TC6 — compression and bendingN/NK,Rd + ωM/(MRd(1 − N/Ncr)) ≤ 1 | η = 0.766 · Pass77 % of the capacity used | |
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| TC7 — compression and bendingN/NK,Rd + ωM/(MRd(1 − N/Ncr)) ≤ 1 | η = 0.837 · Pass84 % of the capacity used | |
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| TC8 — compression and bendingN/NK,Rd + ωM/(MRd(1 − N/Ncr)) ≤ 1 | η = 0.847 · Pass85 % of the capacity used | |
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Calculation: Common values| Step | Value | Ref. |
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| Bottom chord — area | A = 4,166 mm² | |
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| Bottom chord — second moment of area in the plane | Iin = 12,423,086 mm⁴ | |
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| Bottom chord — one channel: area, centroid from the gusset faceFrom the dimensions, root fillet included, flanges tapered at 8 %. | A1 · e = 2,083 mm² · 17.9 mm | |
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| Bottom chord — second moment of area out of the plane, the pair2·(I1 + A1·(s/2 + e)²) with s = 12.0 mm — the gap counts. | Iout = 3,696,013 mm⁴ | |
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| Bottom chord — radii of gyration | iin · iout = 54.6 · 29.8 mm | |
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| Bottom chord — flange c/tfLimits 7.3 · 8.1 · 11.4 for class 1, 2, 3 in compression. | – = 4.3 | § t.5b |
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| Bottom chord — web c/twLimits 26.8 · 30.9 · 34.2 for class 1, 2, 3 in compression. | – = 14.3 | § t.5a |
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| Bottom chord — section classIn compression, the least favourable wall. | – = Class 1 | § t.5a |
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| Bottom chord — buckling curvesChannels: c about both axes. | – = in plane c · out of plane c | |
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| Bottom chord — buckling length factor in the planeThe system length. | βin = 1.00 | |
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| Bottom chord — buckling length out of the planeThe distance between lateral supports. | lK,out = 5,000 mm | |
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Calculation: Common values — tension alone| Step | Value | Ref. |
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| Bottom chord — design tension resistanceA·fy/γM1 on the gross section. At bolted joints the NET section must also be checked — not done here. | NRd = 1,408.5 kN | § 4.1.3 |
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| BC1 — tensionChecked with the bending below. | NEd/NRd = 0.406 | |
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| BC2 — tensionChecked with the bending below. | NEd/NRd = 0.355 | |
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| BC3 — tensionChecked with the bending below. | NEd/NRd = 0.299 | |
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| BC4 — tensionChecked with the bending below. | NEd/NRd = 0.247 | |
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| BC5 — tensionChecked with the bending below. | NEd/NRd = 0.247 | |
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| BC6 — tensionChecked with the bending below. | NEd/NRd = 0.299 | |
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| BC7 — tensionChecked with the bending below. | NEd/NRd = 0.355 | |
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| BC8 — tensionChecked with the bending below. | NEd/NRd = 0.406 | |
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| Bottom chord — spacing of the packing platesNo member of the group is in compression: the limit 15·imin = 266 mm of compression members does not apply. | sp = 800 mm | |
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Calculation: Check 1 — axial force with bending| Step | Value | Ref. |
|---|
| Bottom chord — bending resistance of the sectionPlastic modulus, class 1, in the plane of the truss. | MRd = 71.34 kNm | § 4.1.3 |
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| Bottom chord — lateral-torsional bucklingThe built-up ][ section bends about its axis across the gusset; the moments are local, between nodes held out of the plane by the lateral supports, and the out-of-plane stability is that of the buckling check above. | – = Not considered | |
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| BC1 — tension and bendingN/NRd + M/MRd ≤ 1 | η = 0.519 · Pass52 % of the capacity used | |
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| BC2 — tension and bendingN/NRd + M/MRd ≤ 1 | η = 0.453 · Pass45 % of the capacity used | |
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| BC3 — tension and bendingN/NRd + M/MRd ≤ 1 | η = 0.331 · Pass33 % of the capacity used | |
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| BC4 — tension and bendingN/NRd + M/MRd ≤ 1 | η = 0.302 · Pass30 % of the capacity used | |
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| BC5 — tension and bendingN/NRd + M/MRd ≤ 1 | η = 0.302 · Pass30 % of the capacity used | |
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| BC6 — tension and bendingN/NRd + M/MRd ≤ 1 | η = 0.331 · Pass33 % of the capacity used | |
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| BC7 — tension and bendingN/NRd + M/MRd ≤ 1 | η = 0.453 · Pass45 % of the capacity used | |
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| BC8 — tension and bendingN/NRd + M/MRd ≤ 1 | η = 0.519 · Pass52 % of the capacity used | |
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Calculation: Common values| Step | Value | Ref. |
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| Diagonals — area | A = 1,318 mm² | |
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| Diagonals — second moment of area in the plane | Iin = 1,163,739 mm⁴ | |
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| Diagonals — second moment of area out of the plane | Iout = 1,163,739 mm⁴ | |
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| Diagonals — radii of gyration | iin · iout = 29.7 · 29.7 mm | |
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| Diagonals — D/tLimits 33.1 · 46.3 · 59.6 for class 1, 2, 3 in compression. | – = 17.8 | § t.5a |
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| Diagonals — section classIn compression, the least favourable wall. | – = Class 1 | § t.5a |
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| Diagonals — buckling curvesHot-finished hollow section: a. | – = in plane a · out of plane a | |
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| Diagonals — buckling length factor in the planeThe system length. | βin = 1.00 | |
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Calculation: Common values — tension alone| Step | Value | Ref. |
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| Diagonals — design tension resistanceA·fy/γM1 on the gross section. At bolted joints the NET section must also be checked — not done here. | NRd = 445.6 kN | § 4.1.3 |
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| D1 — tensionChecked with the bending below. | NEd/NRd = 0.199 | |
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| D2 — tensionChecked with the bending below. | NEd/NRd = 0.271 | |
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| D3 — tensionChecked with the bending below. | NEd/NRd = 0.312 | |
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| D4 — tensionChecked with the bending below. | NEd/NRd = 0.312 | |
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| D5 — tensionChecked with the bending below. | NEd/NRd = 0.271 | |
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| D6 — tensionChecked with the bending below. | NEd/NRd = 0.199 | |
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Calculation: Check 1 — axial force with bending| Step | Value | Ref. |
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| Diagonals — bending resistance of the sectionPlastic modulus, class 1, in the plane of the truss. | MRd = 11.91 kNm | § 4.1.3 |
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| D1 — tension and bendingN/NRd + M/MRd ≤ 1 | η = 0.229 · Pass23 % of the capacity used | |
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| D2 — tension and bendingN/NRd + M/MRd ≤ 1 | η = 0.308 · Pass31 % of the capacity used | |
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| D3 — tension and bendingN/NRd + M/MRd ≤ 1 | η = 0.330 · Pass33 % of the capacity used | |
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| D4 — tension and bendingN/NRd + M/MRd ≤ 1 | η = 0.330 · Pass33 % of the capacity used | |
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| D5 — tension and bendingN/NRd + M/MRd ≤ 1 | η = 0.308 · Pass31 % of the capacity used | |
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| D6 — tension and bendingN/NRd + M/MRd ≤ 1 | η = 0.229 · Pass23 % of the capacity used | |
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Calculation: Common values| Step | Value | Ref. |
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| Verticals — area | A = 1,318 mm² | |
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| Verticals — second moment of area in the plane | Iin = 1,163,739 mm⁴ | |
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| Verticals — second moment of area out of the plane | Iout = 1,163,739 mm⁴ | |
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| Verticals — radii of gyration | iin · iout = 29.7 · 29.7 mm | |
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| Verticals — D/tLimits 33.1 · 46.3 · 59.6 for class 1, 2, 3 in compression. | – = 17.8 | § t.5a |
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| Verticals — section classIn compression, the least favourable wall. | – = Class 1 | § t.5a |
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| Verticals — buckling curvesHot-finished hollow section: a. | – = in plane a · out of plane a | |
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| Verticals — buckling length factor in the planeThe system length. | βin = 1.00 | |
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Calculation: Common values — tension alone| Step | Value | Ref. |
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| Verticals — design tension resistanceA·fy/γM1 on the gross section. At bolted joints the NET section must also be checked — not done here. | NRd = 445.6 kN | § 4.1.3 |
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| V4 — tensionChecked with the bending below. | NEd/NRd = 0.087 | |
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Calculation: Common values — flexural buckling alone| Step | Value | Ref. |
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| V1 — flexural buckling aloneλ̄in = 0.440, λ̄out = 0.440 → χ = 0.942; checked with the bending below. | NEd/NK,Rd = 0.127 | |
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| V2 — flexural buckling aloneλ̄in = 0.881, λ̄out = 0.881 → χ = 0.746; checked with the bending below. | NEd/NK,Rd = 0.257 | |
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| V3 — flexural buckling aloneλ̄in = 1.321, λ̄out = 1.321 → χ = 0.459; checked with the bending below. | NEd/NK,Rd = 0.559 | |
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| V5 — flexural buckling aloneλ̄in = 1.321, λ̄out = 1.321 → χ = 0.459; checked with the bending below. | NEd/NK,Rd = 0.559 | |
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| V6 — flexural buckling aloneλ̄in = 0.881, λ̄out = 0.881 → χ = 0.746; checked with the bending below. | NEd/NK,Rd = 0.257 | |
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| V7 — flexural buckling aloneλ̄in = 0.440, λ̄out = 0.440 → χ = 0.942; checked with the bending below. | NEd/NK,Rd = 0.127 | |
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Calculation: Check 1 — axial force with bending| Step | Value | Ref. |
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| Verticals — bending resistance of the sectionPlastic modulus, class 1, in the plane of the truss. | MRd = 11.91 kNm | § 4.1.3 |
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| V1 — compression and bendingN/NK,Rd + ωM/(MRd(1 − N/Ncr)) ≤ 1 | η = 0.156 · Pass16 % of the capacity used | |
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| V2 — compression and bendingN/NK,Rd + ωM/(MRd(1 − N/Ncr)) ≤ 1 | η = 0.303 · Pass30 % of the capacity used | |
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| V3 — compression and bendingN/NK,Rd + ωM/(MRd(1 − N/Ncr)) ≤ 1 | η = 0.616 · Pass62 % of the capacity used | |
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| V4 — tension and bendingN/NRd + M/MRd ≤ 1 | η = 0.087 · Pass9 % of the capacity used | |
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| V5 — compression and bendingN/NK,Rd + ωM/(MRd(1 − N/Ncr)) ≤ 1 | η = 0.616 · Pass62 % of the capacity used | |
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| V6 — compression and bendingN/NK,Rd + ωM/(MRd(1 − N/Ncr)) ≤ 1 | η = 0.303 · Pass30 % of the capacity used | |
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| V7 — compression and bendingN/NK,Rd + ωM/(MRd(1 − N/Ncr)) ≤ 1 | η = 0.156 · Pass16 % of the capacity used | |
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Calculation: Check 1 — deflection| Step | Value | Ref. |
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| Largest deflectionAt node t5, under the variable characteristic load — the elongation and shortening of every member, from the same stiffness analysis. | w = 11.84 mm | |
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| Limitl/300 | wlim = 66.67 mm | |
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| Deflectionw ≤ wlim | η = 0.178 · Pass18 % of the capacity used | |
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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 is one vertical in tension?
In the worked example V4, from b4 to the apex, carries 38.8 kN of tension. Each member is checked for the sign of its own force: V4 in tension with bending, the others in compression with bending.
Why does the packing plate limit not apply to the bottom chord?
No member of that group is in compression, so 800 mm passes where 15 · imin = 266 mm would otherwise govern.
Which plan includes this module?
The Expert plan, with its calculation note.
Related
Norm: SIA 263:2013 · Page updated: 29 October 2026