III. Recuerdos, miedo y resistencia; después de la fuga de Abarca
3.1. Buscando tranquilidad. Arte Para Sanar a Iguala
3.1.2 Recordar y rememorar. Participantes de Arte Para Sanar a Iguala
K 100 General
101 The distances between the reinforcement bars shall be such as to ensure good bond.
102 Reinforcement in different layers is to be aligned in planes leaving sufficient space to allow for the passage of an internal vibrator.
103 Lap joints shall be made in a way that secures transfer of force from one rebar to another. The reduction of strength of a lap joint due to closely spaced lap joints is to be taken into account where relevant.
104 The lap joints shall be distributed. The maximum number of lap joints occuring at a given cross sectional plane is normally limited by the smaller of:
— 1/2 of the reinforcement area
— one reinforcement layer (the layer with largest reinforce-ment area).
Larger lengths of the lap joint than 80·φ are not to be utilized.
105 Resistance against bond and anchorage failure is to be determined by recognized methods. Both local bond and anchorage bond shall be investigated.
In zones of reduced bond (e.g. where gravitational settling of the concrete may reduce the compaction around the reinforce-ment) the design bond strength is not to be taken higher than
Table J1 Values for force transfer in construction joints Contact
surface
ΣAs > 0.001 As or σc < - 0.4 MPa
Combination 1 Combination 2
τcd μ τcd μ
Smooth 0 0.70 0 0.7
Rough 0 1.50 0.6ftd 0.8
Toothed 0 1.80 1.5 ftd 0.8
70% of the value for good bond zones.
Consideration is to be given to the state of stress in the anchor-age zone. Adequate bond resistance is to be assured by trans-verse reinforcement, stirrups, spirals, hooks or mechanical anchorages.
106 Individual reinforcement bars shall have a development length no less than
lb = 0.25· φ ·σs / fbd + t where:
φ is the diameter of the reinforcement bar
σs is the calculated stress in the reinforcement bar in ulti-mate limit state at the cross section in question fbd is the design bond strength, calculated in accordance
with K116.
t is the specified longitudinal tolerance for the position of the bar end. If such tolerances are not specified on the drawings the value of t shall not be taken less than 3· φ.
107 Required lap length when splicing shall be taken equal to the calculated development length. The lap length shall be not less than the greater of 20· φ and 300 mm.
108 Bundled reinforcement bars shall have a development length no less than
lb = 0.25· φe ·σs /(kn ·fbc + fbs) + t where:
φe = equivalent diameter in term of reinforcement cross section.
fbc and fbs = design bond strengths in accordance with K116 with φ = φc
kn = a factor dependent on the number of bars in the bundle and is taken as:
0.8 for bundle of 2 bars 0.7 for bundle of 3 bars 0.6 for bundle of 4 bars
t = the specified longitudinal tolerance for the position of the bar end, see K106.
The development length shall not be assumed to be effective over a length exceeding 80· φc.
For lapped splices of bundled reinforcement with equivalent diameter larger than 32 mm, the bars shall be lapped individu-ally and staggered at least the development length lb. When ter-minated between supports, the bars shall be terter-minated individually and staggered in the same way. The development length shall be calculated for each individual bar by entering the diameter of the bar in question for φc in the formula.
109 The development length for welded wire fabric shall be no less than
l’b = lb – 0.3· ΣFvn / (γs ·φ ·fbd) where:
ΣFvn /γs = sum of forces Fvn corresponding to shear failure at cross wire welds within the development length
lb = development length in accordance with K106.
l’b shall not be taken as larger than the development length in accordance with K128.
fbd = design bond strength calculated in accordance with K116, see also K106.
For welded wire fabric Fvn = 0.2 ·As ·fsk ≥ 4 kN, where As is the sectional area of the largest wire diameter.
Required lap length is equal to the calculated development length. The lap length shall not be less than the largest of 20·φ and 200 mm.
110 For individual prestressed reinforcement units, the development length for the prestressing force shall be taken as lbp = α·φ + β· σp·φ / fbc
where:
α is a factor given in table K1 β is a factor given in table K1
φ is the nominal diameter of the reinforcement unit σp is the steel stress due to prestressing
fbc is the concrete related portion of the design bond strength in accordance with K1116
The part α · φ in the formula for lbp defines a length where no force transmission is assumed.
111 Post tensioning anchorages shall be designed for the ultimate strength of the tendon. The anchorage unit is to be designed so that transfer of forces to the surrounding concrete is possible without damage to the concrete. Documentation verifying the adequacy of the anchorage unit is to be approved.
112 The design of anchorage zones is to be in accordance with recognized methods. Reinforcement is to be provided, where required, to prevent bursting or splitting.
The design strength of such reinforcement is to be limited to 300 MPa.
113 The release of prestressing force may be assumed to be smooth if one of the following requirements is fulfilled:
— the prestressing force is released gradually from the abut-ments:
— the impact against the end of the concrete structure is damped by a buffer between the end of the concrete struc-ture and the point where the reinforcement is cut
— both concrete and prestressed reinforcement are cut in the same operation by sawing.
114 Development of tensile force caused by external loads shall be calculated in accordance with K106. Within the devel-opment length for prestressed tensile force, fbd ,shall be reduced by the factor (1 - σp/fbc). In this calculation, long-term reduction of σp caused by shrinkage, creep and relaxation shall be considered. The development length for the reduced pre-stressing force shall be assumed to be unchanged, equal to lbp. Table K1 Coefficients to be used when calculating development length for prestressed reinforcement units
Type of reinforcement
Smooth release of prestressing tension
force
Sudden release of prestressed tension
force
α β α β
Plain wire 10 0.20 -
-Indented wire 0 0.17 10 0.21
Strand 0 0.14 5 0.17
Ribbed bar 0 0.07 0 0.08
Figure 12
Prestressed Force introduction length where prestressed force is anchored in bond.
115 Transverse tensile forces in the development zone shall be resisted by reinforcement, unless it is shown that reinforce-ment can be omitted.
116 The design bond strength fbd for ribbed bar, indented bar, indented wire and strand can be taken as
fbd = fbc + fbs ≤ 2·k1·ftd where:
fbc = k1 ·k2 ·ftd (l/3 + 2·c/3·φ) fbs = k3 (Ast / s1·φ) ≤ 1.5 MPa
k1 = a factor depending of the type of reinforcement, given in Table K2
c = the least of the dimensions c1, c2 and (s1 - φ)/2 given in Figure 13
φ = the diameter of the anchored reinforcement
k3 = a factor dependent on the transverse reinforcement and its position as given in Figure 14. The factor k3 is taken as zero for strands.
Ast = the area of transverse reinforcement not utilized for other tensile forces and having a spacing not greater than 12 times the diameter of the anchored reinforce-ment. If the reinforcement is partly utilized, the area shall be proportionally reduced
s1 = the spacing of the transverse reinforcement
k2 = has the value 1.6 if the spacing s between the anchored bars exceeds 9 · φ or (6·c + φ) whichever is the larger, k2 has the value 1.0 if s is less than the larger of 5 φ and (3c + φ). For intermediate values interpolate linearily 117 For plain reinforcement take fbd = k1 ·ftd
Figure 13
Values of concrete cover and bar spacing for calculation of bond strength
a) Distance for anchorage, b) Distance for splices.
Figure 14
Values of k3 for various types of transverse reinforcement for cal-culation of bond strength
118 When calculating development of force in reinforce-ment which during concreting has an angle less than 20° to the horizontal plane, the following reduction of the portion fbc, of the design bond strength fbd according to K116 shall be made:
— if the concreting depth below the reinforcement exceeds 250 mm, the reduction for ribbed bars is 30% and for other types of bars 50%. If the concreting depth is 100 mm or less, no reduction is made. For intermediate values linear interpolation shall be performed.
— if there is a tensile stress perpendicular to the anchored reinforcement larger than 0.5 · ftd in the development zone, the reduction is 20%.
The highest of the reductions given above shall be applied. The reductions shall not be combined.
119 At a simply supported end, the development length determined according to K106 through K115 may be reduced above the support, if the support reaction is applied as direct compression against the tension face. In this case the stirrups shall continue throughout the support region.
When calculating the development length, the value fbc may be σφ
fs
σp
As
As
σsAs
l l
Force caused by external load Prestressing force
bp b
End of
reinforcement unit
C
C2 S
1
Sl l
(Section in way of rebar overlap)
a) b)
Table K2 Values of k1 for various types of Reinforcement
Type of Reinforcement k1
Ribbed bar 1.4
Intented bar and wire 1.2
Strand 1.2
Plain bar 0.9
Plain wire in welded wire fabric and prestressed
rein-forcement 0.5
k = 40 N/mm3 2 k = 20 N/mm3 2 k = 03
increased by 50%, but fbd shall not have a higher value than what corresponds to the maximum value in accordance with K116.
120 Reinforcement that is taken into account at the theoreti-cal support, shall normally be extended at least 100 mm beyond this. The position of the reinforcement shall be given on the drawings, with tolerance limits.
121 If reinforcement in several layers are spliced or anchored in the same section, the capacity shall be limited to the value that can be calculated for the bars in only one layer, using the layer that gives the highest capacity. This provision may be waived if otherwise demonstrated by a more accurate design.
122 Reinforcement can also be anchored with special anchor units such as end plates.
A combination of several anchorage methods may be utilized.
The total anchorage capacity can be calculated as the entire capacity from the anchorage method giving the highest portion and half of the anchorage capacity from each of the remaining anchorage methods. For plain steel, a combination of bond and end anchorage shall not be utilized.
123 For tensile reinforcement of ribbed bar or indented bar with an anchorage hook a concentrated force development along the bent part of the hook may be assumed. A hook shall only be assumed effective if it has transverse reinforcement and is formed in accordance with Q408. If the hook is bent with an angle of 90°, the straight end after the bend shall be at least ten times the diameter of the bent bar. If the angle is 135°, the straight part may be reduced to five times the diameter of the bar.
For bars of steel grade B500A to C (see Q400), the concen-trated force in the bend may be taken as 25% of the capacity of the bar, if the hook has an angle of 90°. If the angle is 135° the force can be taken as 40%.
Anchorage for the remaining portion of the force in the bar shall be calculated by force development along the bar outside the bent part.
Tensile reinforcement of quality B500B or B500C with anchorage hook as described above, may be presumed to be anchored in the bent part of the bar provided the bar is bent with a mandrel of diameter equal to or less than 4·φ and other-wise bent in accordance with Q400.
124 If the development length is not calculated in accord-ance with K106 through K108, the anchorage length of rein-forcement in one layer in normal density concrete may simplified be determined as follows:
a) For ribbed bar, the anchorage length shall be taken as 50·φ for B500A to C. This applies provided the concrete cover is at least φ and the spacing between the anchored bars is at least 8·φ. If the transverse reinforcement is located clos-est to the concrete surface and the concrete cover of the anchored reinforcement is at least 1.5· φ, the spacing shall be at least 5·φ.
b) For plain bars with end hooks, the anchorage length is taken as 40·φ assuming that fsk ≤ 250 MPa.
c) For welded wire fabric, the anchorage length shall be at least so large that
— 3 transverse bars are located in the anchorage zone for welded wire fabric of bars with diameters from 4 to 9
— 4 transverse bars are located in the anchorage zone formm welded wire fabric of bars with diameters from 10 to 12 mm.
In addition, the anchorage length shall be no less than 30·φ for mesh made of indented bars
40·φ for mesh made of plain bars.
The development of the force along the anchorage length may be assumed uniform.
For reinforcement which has a concrete depth below the rein-forcement larger than 150 mm or an angle less than 20° to the horizontal plane, the anchorage length shall be increased by 10 φ for ribbed bars and welded wire fabric of indented bars, and 20·φ for plain bars.
125 The required minimum reinforcement in accordance with Q and R shall be spliced for its full capacity.
126 Along the development length, a transverse reinforce-ment or stirrups shall be provided in accordance with Q303, unless a more accurate assessment is made.