Anchorage of longitudinal reinforcement
EUROCODE-2

Anchorage of longitudinal reinforcement

DATA
Type of anchorage (?)

Select the method of anchorage (see Figure 8.1 of EC2)

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Coefficient αct (?)

National choice 3.1.6 (2)P: Coefficient of fatigue strength of the concrete. The recommended value is 1.0. Valid values from 0.5 to 1

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Bar diameter Φ(mm) (?)

Insert the nominal diameter of a reinforcing bar. Valid values from 5 to 40

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Steel strength fyk(MPa) (?)

Insert the characteristic tensile strength of reinforcement fyk. Valid values from 400 to 600

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Ratio (r) σsd/fyd (?)

Ratio of the design stress (at the position from where the anchorage is measured from) and the design yield strength of reinforcement.
Approx. ratio of area of steel required and area of steel provided at this section. Valid values from 0 to 1

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Concrete strength fck(MPa) (?)

Insert the characteristic compressive cylinder strength of concrete fck. Valid values from 20 to 50

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Minimum cover Cd(mm) (?)

Concrete minimum cover
(see Figure 8.3)
Valid values from 10 to 100

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Transverse pressure p(MPa) (?)

Transverse pressure at ultimate limit state along lbd. Valid values from 0 to fck

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Transverse reinforcement not welded
placed between the concrete surface and the anchored bar
Area reinforc. Ast(cm2) (?)

Cross-sectional area of the transverse reinforcement along the design anchorage length lbd. Valid values from Ast,min (1Φ4) and Ast,max (9Φ32).
You can enter the area directly or through the following data:

Núm Φ(mm)
Intro
Type of element (?)

Select the type of structural element

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Form transverse bars (?)

Indicate the form of the transverse bars next to the anchored bar. (According to Figure 8.4: K=0.1 for "Links or U bars" and K=0.05 for "Straight bars")

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RESULT

Design anchorage length lbd (cm)
Bar diameter Φ (mm) Tension Compression
Good bond Poor bond Good bond Poor bond
12 35 50 49 70
Notes (see Figure 8.2 of EC2):
  • Good bond (Good bond conditions): for the reinforcements during concreting form with the horizontal an angle between 45° and 90° or in the case of forming an angle less than 45°, are located in the lower half of the section or at a distance equal or greater than 30 cm of the upper surface of a layer of concrete.
  • Poor bond (Poor bond conditions): for the reinforcements that, during concreting, not found in any of the above cases.


DETAILS OF CALCULATION

Notation and methodology according to clause 8.4 of EC2

Good Bond conditions

1) Tensile bar

lbd (design anchorage length) = 345 mm
lbd = α1 · α2 · α3 · α5 · lb,rqd ≥ lb,min
where:

  • lb,rqd (basic required anchorage length) = 484 mm
    lb,rqd = (Φ / 4) (σsd / fbd)
    with:
    • σsd = r · fyk/γs = 1·500/1.15 = 434.78 MPa
    • fbd (ultimate bond stress) = 2.69 MPa
      fbd = 2.25 · η1 · η2 · fctd
      • η1 = 1, η2 = 1.0
      • fctd = αct·fctk,0.05/γc = 1·1.8/1.5 = 1.2 MPa
      • fctk,0.05 = 0.21· fck(2/3) = 0.21·25(2/3) = 1.8 MPa
  • α1(effect of the form of the bars) = 1
  • α2(effect of concrete minimum cover) = 0.71
    α2 = 1-0.15 (Cd - φ)/ φ = 1-0.15·(35-12)/12 = 0.71
    (≥ 0.7 and ≤ 1.0)
  • α3(effect of transverse reinforcement) = 1
    (It is not considered)
  • α5(effect of the pressure transverse) = 1
    α5 = 1 - 0.04p = 1 – 0.04·0 = 1 (≥ 0.7 and ≤ 1.0)
  • α2 · α3 · α5 = 0.71 (≥ 0.7)
  • lb,min = max(145 ; 120 ; 100) = 145 mm
    lb,min = max{0.3·lb,rqd; 10·φ; 100 mm}

2) Compression bar

lbd (design anchorage length) = 484 mm
lbd = α1 · α2 · α3 · lb,rqd ≥ lb,min
where:

  • lb,rqd (basic required anchorage length) = 484 mm
  • α1 = 1, α2 = 1, α3 = 1
  • lb,min = max(291 ; 120 ; 100) = 291 mm
    lb,min = max{0.6·lb,rqd; 10·φ; 100 mm}
Poor Bond conditions

1) Tensile bar

lbd (design anchorage length) = 493 mm
lbd = α1 · α2 · α3 · α5 · lb,rqd ≥ lb,min
where:

  • lb,rqd (basic required anchorage length) = 692 mm
    lb,rqd = (Φ / 4) (σsd / fbd)
    with:
    • σsd = r · fyk/γs = 1·500/1.15 = 434.78 MPa
    • fbd (ultimate bond stress) = 1.89 MPa
      fbd = 2.25 · η1 · η2 · fctd
      • η1 = 0.7, η2 = 1.0
      • fctd = αct·fctk,0.05/γc = 1·1.8/1.5 = 1.2 MPa
      • fctk,0.05 = 0.21· fck(2/3) = 0.21·25(2/3) = 1.8 MPa
  • α1(effect of the form of the bars) = 1
  • α2(effect of concrete minimum cover) = 0.71
    α2 = 1-0.15 (Cd - φ)/ φ = 1-0.15·(35-12)/12 = 0.71
    (≥ 0.7 and ≤ 1.0)
  • α3(effect of transverse reinforcement) = 1
    (It is not considered)
  • α5(effect of the pressure transverse) = 1
    α5 = 1 - 0.04p = 1 – 0.04·0 = 1 (≥ 0.7 and ≤ 1.0)
  • α2 · α3 · α5 = 0.71 (≥ 0.7)
  • lb,min = max(208 ; 120 ; 100) = 208 mm
    lb,min = max{0.3·lb,rqd; 10·φ; 100 mm}

2) Compression bar

lbd (design anchorage length) = 692 mm
lbd = α1 · α2 · α3 · lb,rqd ≥ lb,min
where:

  • lb,rqd (basic required anchorage length) = 692 mm
  • α1 = 1, α2 = 1, α3 = 1
  • lb,min = max(415 ; 120 ; 100) = 415 mm
    lb,min = max{0.6·lb,rqd; 10·φ; 100 mm}