Three length bases for members of steel space trusses (space grid structures): the distinction between ball-node centre distance (geometrical length), actual member length (net length) and cutting length, the formula parameters and the cutting allowances

Topic Positioning

The three length bases for members of steel space trusses (space grid structures), from "structural geometrical length" to "actual cutting length", covering the parameter make-up of actual pipe lengths in welded-ball and bolted-ball trusses, the cutting allowances (fit-up gaps and weld shrinkage) and the fabrication tolerances.

Core Conclusions

1. The three length bases must be kept apart (not interchangeable)

1. Geometrical length (ball-node centre distance) L: the distance between ball-node centres, computed from the spatial coordinates of the ball nodes given on the space truss shop drawings. The note to JGJ 7-2010 table 5.1.2 states "l is the member's geometrical length (i.e. the distance between node centres)"; because bolted-ball member ends approach pins, the effective length for structural verification takes the geometrical length.
2. Actual member length (net length) l: computed from the centre distance less the occupation of node parts at both ends (DB 51/T 5051-2007 clause 7.3.1, figures 7.3.1-1 and 7.3.1-2).

• Welded-ball truss pipe length: where L is the ball-node centre distance computed from the node coordinates on the drawings; r1 and r2 the outer radii of the welded balls; r the pipe outer radius.
• Bolted-ball truss pipe length: L the ball-node centre distance from the node coordinates; r1 and r2 the bolted-ball diameters; e1 and e2 the hexagonal sleeve end-face diagonal lengths; m1 and m2 the sleeve lengths; h the cover-plate thickness; the Greek delta the cover-plate insert depth into the pipe.

3. Cutting length: the actual pipe length l computed from the drawings, plus the allowances for fit-up gap and weld shrinkage.

2. Cutting allowance values (DB 51/T 5051-2007 clause 7.3.1)

• Steel shall be corrected before cutting; members are preferably cut on machine tools (saw, lathe).
• For welded-ball trusses, to secure full weld penetration the member end keeps a 1-2 mm gap off the ball surface; with a liner tube, 2-6 mm depending on wall thickness; above 4 mm wall the end is bevelled.
• Weld shrinkage: 2-3 mm per butt, 1.5-3 mm with a liner tube. Plate nodes: 2-3 mm shrinkage.
• The allowances shall be verified by procedure trials.

3. Other code positions (all require "pre-adding weld shrinkage")

• JGJ 7-2010 clause 6.2.5: pipe members preferably cut on machine tools. The cutting length shall pre-add weld shrinkage, determinable by trial. The fabrication length tolerance shall be plus/minus 1 mm. Members connected through bolted balls include the cone head or cover plate in their length; members through embedded-hub nodes include the end inserts.
• GB 50755-2012 clause 8.3.7: pipe members of space trusses (girders) are preferably cut on pipe lathes or CNC profiling machines, with machining allowance and weld shrinkage pre-added, the shrinkage determinable by procedure trial; fabrication tolerances per table 8.3.7 (note: r the pipe radius).
• T/CSCS 016-2021 clause 6.8.27: pipes of welded hollow-ball trusses are preferably cut on pipe lathes or CNC profiling machines, the end bevel preferably 30 degrees, with weld shrinkage allowance reserved; tolerances per table 6.8.27 (note: r the member radius, L the member length).

4. Tolerances and sampling

• DB 51/T 5051-2007 table 7.3.1 fabrication tolerances: sample 5% of each member type, not fewer than 5 pieces (note: L the member length, r the cover-plate or cone-head base radius).
• The values in each code's tolerance table must be read from the original tables; GB 50755-2012 table 8.3.7, T/CSCS 016-2021 table 6.8.27 and DB 51/T 5051-2007 table 7.3.1 are three versions of the same position - follow the standard named in the project.

Applicability Boundaries

• The three bases serve different ends: geometrical length for structural design and verification (and from it the effective length l0); actual length for member fabrication; cutting length for sawing. Cutting to geometrical length overshoots through node-part occupation; cutting to actual length alone misses the weld gap and shrinkage.
• Weld shrinkage, gaps and machining allowances are empirical / trial values, to be verified by procedure trials; manual welding, liner tubes and bevels each take different values.
• The full expressions of the welded-ball and bolted-ball actual-length formulas must be read from DB 51/T 5051-2007 figures 7.3.1-1 and 7.3.1-2 and their formulas; table values follow the current valid editions.
• Applies only to fabrication of pipe-member trusses and grids (including spatial girders), not to rolled-section members or non-grid structures.

Further Reading

DB 51/T 5051-2007 Construction Technology Regulation for Steel Structures, clause 7.3.1 (actual member length, cutting allowances, table 7.3.1) and clause 7.4.2 (limit deviations of trial-assembly geometry: for a single-pyramid unit, top-chord length and pyramid height plus/minus 1.5 mm, diagonal plus/minus 2.0 mm, bottom-chord node offset 1.5 mm; for a partial-truss unit, longitudinal and transverse lengths 1/2000 of length and not more than plus/minus 30 mm, bearing centre offset 1/4000 of side and not more than 30 mm, bearing level difference 10 mm); JGJ 7-2010 clause 6.2.5; GB 50755-2012 clause 8.3.7 and table 8.3.7; T/CSCS 016-2021 clause 6.8.27 and table 6.8.27; sleeve, bolt and cone-head / cover-plate dimensions of bolted-ball nodes per GB/T 16939 and JGJ 7-2010 clauses 5.3.6 and 5.3.7.