Materials according to EOTA technical reports¶
EOTATR029 limit state checking¶
Anchor design according to EOTA TR029

materials.eota.EOTA_TR029_limit_state_checking.
AcV2Pernos
(h, c1, s2)¶ Area del cono de anclaje para dos pernos. see figure 5.7 b of EOTA TR029.
Parameters:  c1 – edge distance in direction 1; in case of anchorages close to an edge loaded in shear c 1 is the edge distance in direction of the shear load (see Figure 2.1b and Figure 5.7of EOTA TR029).
 h – Concrete part thickness.
 s2 – Distance between the bolts.

materials.eota.EOTA_TR029_limit_state_checking.
AcV2PernosC2
(h, c1, c2, s2)¶ Area del cono de anclaje para dos pernos junto a un borde libre. see figure 5.7 b y c of EOTA TR029.
Parameters:  c1 – edge distance in direction 1; in case of anchorages close to an edge loaded in shear c 1 is the edge distance in direction of the shear load (see Figure 2.1b and Figure 5.7of EOTA TR029).
 c2 – edge distance in direction 2; direction 2 is perpendicular to direction 1.
 h – Concrete part thickness.
 s2 – Distance between the bolts.

materials.eota.EOTA_TR029_limit_state_checking.
VRkC0Expr58
(d, hEf, fckCube, c1, cracked)¶ Initial value of the characteristic resistance of an anchor placed in cracked or noncracked concrete and loaded perpendicular to the edge according to expression 5.8a of clause 5.2.3.4 (a) of EOTA TR029.
Parameters:  d – anchor diameter.
 hEf – effective anchorage depth.
 fckCube – characteristic concrete compression strength measured on cubes with a side length of 150 mm (value of concrete strength class according to ENV 206) (Pa).
 c1 – edge distance in direction 1; in case of anchorages close to an edge loaded in shear c 1 is the edge distance in direction of the shear load (see Figure 2.1b and Figure 5.7of EOTA TR029).
 cracked – True if placed on cracked concrete:

materials.eota.EOTA_TR029_limit_state_checking.
angleFactor
(alpha_v)¶ Factor that introduces the influence of angle alpha_v between the load applied, V, and the direction perpendicular to the free edge of the concrete member (alpha_v≤ 90°, see Figure 4.7c onf EOTA TR029).
Parameters: alpha_v – angle between the load applied, V, and the direction perpendicular to the free edge of the concrete member

materials.eota.EOTA_TR029_limit_state_checking.
areaAcV0
(h, c1)¶ area of concrete cone of an individual anchor at the lateral concrete surface not affected by edges parallel to the assumed loading direction, member thickness or adjacent anchors, assuming the shape of the fracture area as a half pyramid with a height equal to c1 and a baselength of 1.5 c1 and 3 c1. See figure 5.6 and expression 5.8d of EOTA TR029.
Parameters:  h – Concrete part thickness.
 c1 – edge distance in direction 1; in case of anchorages close to an edge loaded in shear c 1 is the edge distance in direction of the shear load (see Figure 2.1b and Figure 5.7of EOTA TR029).

materials.eota.EOTA_TR029_limit_state_checking.
axialInitialResistanceConeFailure
(k1, fck_cube, hEf)¶ Characteristic resistance of an anchor in case of concrete cone failure according to expression 5.3a in clause 5.2.2.4 a) of EOTA TR029.
Parameters:  k1 – 7.2 for applications in cracked concrete and 10.1 for applications in noncracked concrete.
 fck_cube – characteristic concrete compression strength measured on cubes with a side length of 150 mm (value of concrete strength class according to ENV 206) (Pa).
 hEf – effective anchorage depth (m).

materials.eota.EOTA_TR029_limit_state_checking.
axialInitialResistancePullout
(d, hEf, tauRk)¶ Characteristic resistance in case of combined pull out and concrete cone failure according to expression 5.2a in clause 5.2.2.3 a) of EOTA TR029.
Parameters:  d – Anchor diameter (m).
 hEf – effective anchorage depth (m).
 tauRk – Characteristic bond resistance, depending on the concrete strength class, (must be taken from relevant ETA) (Pa).

materials.eota.EOTA_TR029_limit_state_checking.
axialResistanceSteelFailure
(As, fuk)¶ Characteristic value of anchor bolt strength in tension due to steel collapse according to clause 5.2.2.2 of EOTA TR029.
As: stressed cross section of steel (m2). fuk: characteristic steel ultimate tensile strength (nominal value) (Pa).

materials.eota.EOTA_TR029_limit_state_checking.
getA0cN
(anchorPosition, hEf)¶ Polígono que representa el influence area of an individual anchor according to clause 5.2.2.4 b) (figura 5.4a) of EOTA TR029.
Parameters:  anchorPosition – anchor position.
 hEf – effective anchorage depth (m).

materials.eota.EOTA_TR029_limit_state_checking.
getA0pN
(d, anchorPosition, hEf, tauRkUcr)¶ Polígono que representa el influence area of an individual anchor according to clause 5.2.2.3 b) (figura 5.1) of EOTA TR029.
Parameters:  d – anchor diameter (m).
 anchorPosition – Posición del del perno.
 hEf – effective anchorage depth (m).
 tauRkUcr – Characteristic bond resistance for noncracked concrete (must be taken from relevant ETA) (Pa).

materials.eota.EOTA_TR029_limit_state_checking.
getA0spN
(anchorPosition, CcrSp)¶ Polygon that represents the influence area of an individual anchor according to clause 5.2.2.6 b) of EOTA TR029.
Parameters:  anchorPosition – anchor position.
 CcrSp – edge distance for ensuring the transmission of the characteristic tensile resistance of a single anchor without spacing and edge effects in case of splitting failure (m).

materials.eota.EOTA_TR029_limit_state_checking.
getCcrNp
(d, hEf, tauRkUcr)¶  Halfside of the influence area (critical distance to the edge) of an
 individual anchor according to clause 5.2.2.3 b) (equation 5.2d) of EOTA TR029.
Parameters:  d – anchor diameter (m).
 hEf – effective anchorage depth (m).
 tauRkUcr – Characteristic bond resistance for noncraked concrete (must be taken from relevant ETA) (Pa).

materials.eota.EOTA_TR029_limit_state_checking.
getCcrSpHiltiHY150
(h, hEf)¶  halfside del influence area (critical distance to the edge)
 of an individual anchor according to table 7 of ETA05/0051 (page 19).
param h: thickness of concrete member (m). param hEf: effective anchorage depth (m).

materials.eota.EOTA_TR029_limit_state_checking.
getFactor1N
(C, CcrN)¶ Factor that takes into account the influence of the distance to the edge of the support member in the stress distribution, according to expression 5.2e of clause 5.2.2.3 c).
param C: edge distance. param CcrN: halfside del influence area (critical distance to the edge).

materials.eota.EOTA_TR029_limit_state_checking.
getFactor2cN
(A0cN, AcN)¶ Factor that takes into account the influence of the distance to the edge of the support member according to clause 5.2.2.4.
Parameters:  A0cN – influence area of the anchor (or anchor group).
 AcN – area of the intersection of the anchor influence area and the concrete support contour.

materials.eota.EOTA_TR029_limit_state_checking.
getFactor2pN
(A0pN, ApN)¶ Factor that takes into account the influence of the distance to the edge of the support member according to clause 5.2.2.3 b).
Parameters:  A0pN – influence area of the anchor (or anchor group).
 ApN – Area of the intersection of the anchor influence area and the concrete support contour.

materials.eota.EOTA_TR029_limit_state_checking.
getFactor2spN
(A0spN, AspN)¶  Factor that takes into account the influence of the distance to the edge
 of the support member according to clause 5.2.2.6 b).
Parameters:  A0spN – influence area of the anchor (or anchor group).
 AspN – area of the intersection of the anchor influence area and the concrete support contour.

materials.eota.EOTA_TR029_limit_state_checking.
getFactor3N
(d, spacing, n, hEf, tauRk, fck_cube, cracked)¶ Factor that takes into account the influence of the failure surface for anchor groups according to expression 5.2f of clause 5.2.2.3 d).
param d: anchor diameter (m). param spacing: spacing of the anchor group. param n: number of anchors in a group. param hEf: effective anchorage depth (m). param tauRk: Characteristic bond resistance (must be taken from relevant ETA) (Pa). param fck_cube: characteristic concrete compression strength measured on cubes with a side length of 150 mm (value of concrete strength class according to ENV 206) (Pa). param cracked: true if cracked concrete.

materials.eota.EOTA_TR029_limit_state_checking.
getScrN
(hEf)¶  SideLength del influence area of an individual anchor
according to clause 5.2.2.4 b) (equation 5.3b) del clause 5.2.2.4 b) of EOTA TR029.
param hEf: effective anchorage depth (m).

materials.eota.EOTA_TR029_limit_state_checking.
getScrNp
(d, hEf, tauRkUcr)¶  Spacing for ensuring the transmission of the characteristic resistance
 of a single anchor without spacing and edge effects in case of pullout failure. Is equal to the side of the influence area of an individual anchor (critical distance between anchors) according to clause 5.2.2.3 b) (equation 5.2c) of EOTA TR029.
Parameters:  d – anchor diameter (m).
 hEf – effective anchorage depth (m).
 tauRkUcr – Characteristic bond resistance for noncraked concrete (must be taken from relevant ETA) (Pa).

materials.eota.EOTA_TR029_limit_state_checking.
k1Expr58A
(cracked)¶ Factor that introduces the influence of the concrete cracking in expression 5.8a of EOTA TR029.
Parameters: cracked – True if placed on cracked concrete:

materials.eota.EOTA_TR029_limit_state_checking.
memberThicknessFactor
(h, c1)¶ Factor that introduces the influence of the act that the shear resistance does not decrease proportionally to the member thickness as assumed by the ratio A c,V / A c,V
Parameters:  h – Concrete part thickness.
 c1 – edge distance in direction 1; in case of anchorages close to an edge loaded in shear c 1 is the edge distance in direction of the shear load (see Figure 2.1b and Figure 5.7of EOTA TR029).

materials.eota.EOTA_TR029_limit_state_checking.
psiAlphaVFactor
(alphaV)¶ Factor that takes account of the angle between the applied load and the direction perpendicular to the free edge of the concrete member (must be less than 90 degrees) see figure 4.7c and expression 5.8g on section f) of clause 5.2.3.4 of EOTA TR029.
Parameters: alphaV – angle between the applied load and the direction perpendicular to the free edge of the concrete member.

materials.eota.EOTA_TR029_limit_state_checking.
psiEcVFactor
(ev, c1)¶ Factor that takes account of a group effect when different shear loads are acting on the individual anchors of a group, computed according to expression 5.8h del section f) of clause 5.2.3.4 of EOTA TR029.
param ev: Eccentricity of the shear forces resultant with respect to the group centroid. param c1: edge distance in direction 1; in case of anchorages close to an edge loaded in shear c 1 is the edge distance in direction of the shear load (see Figure 2.1b and Figure 5.7of EOTA TR029).

materials.eota.EOTA_TR029_limit_state_checking.
psiHVFactor
(h, c1)¶ Coefficient that is used to introduce in the calculation the lack of proportionality between the reduction of shear strength and the decrease of the part thickness as is assumed in the quotient Ac,v/Ac,v0. See expression 5.8f of the clause 5.2.3.4 of EOTA TR029.
Parameters:  h – Concrete part thickness.
 c1 – edge distance in direction 1; in case of anchorages close to an edge loaded in shear c 1 is the edge distance in direction of the shear load (see Figure 2.1b and Figure 5.7of EOTA TR029).

materials.eota.EOTA_TR029_limit_state_checking.
psiReVFactor
(descr)¶ Coeficiente que introduce la influencia del tipo de refuerzo empleado en cracked concrete en la expresión 5.8 of EOTA TR029, computed according to section g) of clause 5.2.3.4 of EOTA TR029.
Parameters: descr – Descriptor que puede tomar los valores: 1: anclaje en cracked concrete o no fisurado sin reinforcement de refuerzo en el borde. 2: anclaje en cracked concrete con reinforcement de refuerzo en el borde (diámetro > 12mm). 3: anclaje en cracked concrete con reinforcement de refuerzo en el borde y estribos próximos entre si (separados menos de 10 cm).

materials.eota.EOTA_TR029_limit_state_checking.
psiSVFactor
(c1, c2)¶ Coeficiente que sirve para introducir en el cálculo la perturbación en la distribución de tensiones en el hormigón que produce la presencia de un segundo borde libre próximo al anclaje. Ver expresión 5.8e of clause 5.2.3.4 of EOTA TR029.
Parameters:  c1 – edge distance in direction 1; in case of anchorages close to an edge loaded in shear c 1 is the edge distance in direction of the shear load (see Figure 2.1b and Figure 5.7of EOTA TR029).
 c2 – edge distance in direction 2; direction 2 is perpendicular to direction 1.

materials.eota.EOTA_TR029_limit_state_checking.
shearResistanceConcretePryOut
(NRkp, NRkc, hEf)¶  Shear strength of a bolt by concrete pryout failure
according to expressions 5.7 y 5.7a of clause 5.2.3.3 of EOTA TR029.
param NRkp: Characteristic resistance of combined pullout and concrete cone failure (5.2.2.3 of EOTA TR029). param NRkc: Characteristic resistance in case of concrete cone failure (5.2.2.4 of EOTA TR029). param hEf: effective anchorage depth (m).

materials.eota.EOTA_TR029_limit_state_checking.
shearResistanceGroupWithoutLeverArm
(As, fuk, nr)¶  Shear strength of a bolt group according to clause 5.2.3.2 a) of EOTA TR029.
 As: stressed cross section of steel. fuk: characteristic steel ultimate tensile strength (nominal value). n: number of anchors in a group.

materials.eota.EOTA_TR029_limit_state_checking.
shearResistanceWithoutLeverArm
(As, fuk)¶ Shear strength of a bolt according to clause 5.2.3.2 a) of EOTA TR029.
Parameters:  As – stressed cross section of steel.
 fuk – characteristic steel ultimate tensile strength (nominal value).