Table lookup and calculation of rebar anchorage lengths: the lab -> la -> laE chain, the five za correction factors, seismic anchorage, and hook/compression boundaries (GB 50010-2010, GB 55008-2021)

Topic Positioning

How the anchorage length of tension reinforcement in concrete structures is determined: the "three quantities, two steps" table/calculation chain from basic anchorage length lab -> anchorage length la -> seismic anchorage length laE, plus the selection of the za and zaE correction factors and boundary rules for hooks and bars in compression. For determining anchorage lengths in structural working-drawing design and in rebar quantity and fabrication checks.

Core Conclusions

1. Relations among the three quantities (GB 50010-2010 Clauses 8.3.1 and 11.1.7)

1. Basic anchorage length: lab = alpha x (fy/ft) x d. fy is the design tensile strength of the reinforcement (fpy for prestressing); ft is the design axial tensile strength of the concrete, taken as for C60 where the concrete grade exceeds C60; d is the bar diameter; alpha is the bar-surface coefficient per Table 8.3.1 (common values: plain round bars 0.16, ribbed bars 0.14). Plain round bars shall have 180-degree hooks at their ends with a straight segment after bending of not less than 3d, but hooks may be omitted when used as compression reinforcement.
2. Anchorage length: la = za x lab, and not less than 200 mm. za for ordinary reinforcement is per Clause 8.3.2; where more than one applies they may be multiplied together, but not below 0.6; for prestressing tendons it may be taken as 1.0. Under no circumstances may the tension anchorage length be less than 0.6 lab and 200 mm. Anchorage of longitudinal tension bars in beam-column joints follows Section 9.3 (II).
3. Seismic anchorage length: laE = zaE x la, where zaE is 1.15 for seismic grades 1 and 2, 1.05 for grade 3, and 1.00 for grade 4. Seismic lap length llE = zl x laE (zl per Clause 8.4.4).

2. The five za correction factors (Clause 8.3.2)

1. Ribbed bars with nominal diameter greater than 25 mm: 1.10;
2. Epoxy-coated ribbed bars: 1.25;
3. Bars liable to disturbance during construction: 1.10;
4. Where the actual provided area of longitudinal reinforcement exceeds the design-calculated area: the ratio of design-calculated to actually provided area — but this item does not apply to members with seismic fortification requirements or directly subject to dynamic loads;
5. Where the cover of the anchored bar is 3d: 0.80; not less than 5d: 0.70; interpolated in between (d = bar diameter).

3. Boundary provisions

• Hooks/mechanical anchorage (Clause 8.3.3): where the ends of longitudinal tension bars use hooks or mechanical anchorage, the anchorage length including the hook or anchorage head (projected length) may be taken as 60% of the basic anchorage length lab, and Clause 8.3.2 corrections shall not be superimposed.
• Bars in compression (GB 55008-2021 Clause 4.4.5): where the compressive strength is fully utilized and anchorage is required, the anchorage length shall not be less than 70% of the tension anchorage length.
• Cover splitting protection (Clause 8.3.1, Item 3): where the cover of the anchored bar is not greater than 5d, transverse reinforcement shall be provided along the anchorage length, with diameter not less than d/4; spacing not greater than 5d in beams, columns, and diagonal braces, not greater than 10d in planar members such as slabs and walls, and in no case greater than 100 mm.
• Seismic splices (Clause 11.1.7): splices of longitudinal load-bearing bars should avoid the stirrup-densified zones at beam and column ends; where they cannot, mechanical or welded connections shall be used; the percentage of spliced area within one splice zone should not exceed 50%.

4. Table-lookup path and worked example First fix the three elements "bar grade + diameter, concrete grade, seismic grade" -> look up the anchorage tables in the flat-planning atlases (16G101-1/22G101-1 series lab/labE, la/laE tables) or compute by formula -> multiply za (product not less than 0.6) -> for seismic multiply zaE -> check la >= 200 mm. Example (HRB400, C30: alpha = 0.14, fy = 360 N/mm2, ft = 1.43 N/mm2): D20: lab approximately 705 mm, la = 705 mm uncorrected, laE approximately 811 mm for seismic grade 1; D28: lab approximately 987 mm, la approximately 1086 mm after multiplying 1.10 (d > 25 mm), laE approximately 1248 mm for seismic grade 1.

Applicable Boundaries

• All three table-lookup preconditions are indispensable: bar grade/diameter, concrete grade, seismic grade.
• The za product shall not be less than 0.6; under no circumstances is la less than 200 mm (nor below the 0.6 lab floor).
• The 0.6 lab hook/mechanical-anchorage allowance and the za corrections must not be superimposed; the provided-area allowance does not apply to members with seismic fortification requirements or directly subject to dynamic loads.
• Where the concrete grade exceeds C60, ft is taken as for C60.
• Version status: GB 50010 Tables 4.1.4 (ft) and 4.2.3 (fy) were superseded by GB 55008-2021 from 2022-04-01 — strength values must be checked against the current effective edition; GB 50010-2010 (2015 edition) has been revised into GB/T 50010-2010 (2024 edition) Standard for Design of Concrete Structures, effective 2024-08-01; the clause texts in this card are from the 2015 edition and must be verified against the new edition in application.
• The worked examples demonstrate normal conditions and do not exhaust the correction combinations (epoxy coating, construction disturbance, prestressing tendons, etc., each take their own factors).

Further Reading

• GB 50010-2010 Code for Design of Concrete Structures (2015 edition), Section 8.3 (8.3.1 basic anchorage formula and surface coefficient table, 8.3.2 corrections, 8.3.3 hook and mechanical anchorage forms and requirements), Section 9.3 (II) (beam-column joint anchorage), Clause 11.1.7 (seismic anchorage and splices).
• GB 55008-2021 General Code for Concrete Structures, Clause 4.4.5 (mandatory anchorage requirement).
• 16G101-1 and 22G101-1 flat-planning atlases for concrete structural working drawings (tables of basic anchorage lengths lab, labE and anchorage lengths la, laE for tension bars).
• DB62/T 3022-2018 Specification for Construction Technology of Reinforcement Works, Clause 10.1.1 (lab table and anchorage-length correction factor table in a local work rule, for comparison).
• Strength tables: design axial tensile strength of concrete ft (GB 50010 Table 4.1.4-2), design tensile strength of reinforcement fy (Table 4.2.3-1).