Capítulo 1. Apuntes feministas sobre maternidad y familia
1.2. Los tópicos de maternidad y familia en contextos de cambios y
Positive moment failure of hollow-core units close to a support was observed in the Matthews’ sub- assembly test of a frame and floor and in tests of single hollow-core units mounted on a rigid concrete blocks [Matthews, 2004; Bull and Matthews, 2003]. In both cases positive moment cracks developed at drift ratios within the elastic range. With the sub-assembly test the positive moment crack was observed at a drift ratio of 0.0025, with collapse occurring at a drift of 0.025. However, in the latter stages of the test the hollow-core units were only supported by dowel action of the strands and if vertical seismic excitation had been present it is anticipated that collapse would have occurred at an earlier stage. With the Bull and Matthews tests the positive moment crack was observed at a drift ratio of 0.005.
Once a positive moment crack has formed adjacent to the support, a weak section is created and any movement of the support, due to beam elongation or any other cause, results in opening up of the crack. Generally if a positive moment crack forms in the hollow-core unit, rather than at the back face
V C
P Development length for strands Tension in web to resist shear “V” A A B B Stresses in section Support missing
under web SECTION B - B
SECTION A - A
Shear in insitu slab centroid
of the unit, it is located at the face of the internal dam in the hollow-core cores, see section 1 in Figure A-17 (a). At this location, which is generally of the order of 75mm from the end of the unit, the prestressed strands are ineffective. The flexural strength depends on the tensile strength of concrete. The strands are ineffective for two reasons. Firstly the section is located within 12.5% of the start of the transfer length and transfer by bond is relatively inefficient for the first few strand diameters. Secondly the pretension strands are located below the webs, which in 300mm deep hollow-core Stresscrete units are approximately 300 mm apart, see Figure A-17 (b). For any compression stress to migrate from the strands to the concrete in the soffit under the cores a distance of the order of 120mm is required (based on 45o dispersion). Hence the concrete in the soffit mid-way between the strands is
not effectively stressed by the minimal prestress transfer that has taken place in the first 75mm of the transfer length. If tensile cracking is initiated in the concrete below the cores the loss in tension force is redistributed to the concrete below the webs. This action over-stresses the remaining tensile concrete zone and bond failure occurs with the strands slipping through the concrete between the crack and the end of the unit.
There are three factors which can indicate the potential for positive moment flexural cracks to form near the face of a supporting beam in an earthquake. The critical section is section 1, as shown in Figure A-17 (a). These three factors are outlined below.
1. The opening up of a wide crack at the back face of the hollow-core unit, section 2 in Figure A- 17 (a), indicates that slippage has occurred between the unit and the support. This indicates that either any bond between the precast unit, mortar pad and concrete in the supporting ledge has been broken, or the frictional resistance has been over-come. In either case the loss of shear transfer between the ledge and precast unit indicates that a positive moment crack will not develop at the critical section (section 1). Cracks often develop at the back face of the unit due to shrinkage and creep of the hollow-core and insitu concrete topping, and/or due to differential thermal stresses between the main beams and floor. However, a narrow crack at the back face of the hollow-core unit does not exclude the possibility of a positive moment failure of the hollow-core unit. Narrow cracks did form in the Matthews’ floor test [Matthews 2004], but failure still occurred due to positive moment flexural cracking near the face of the support. It is assumed a significant crack with width of 0.5mm or more indicates that the unit is sliding on the support and that a positive moment crack will not form at the critical location (section 1).
Figure A-17: Positive moment cracking close to support
2. The use of a mortar pad between hollow-core units and their support beams increases the shear force that can be applied to the soffit of a hollow-core unit. This increases the magnitude of positive moment which may induced at the critical section at the face of the internal dams in the hollow-core units. In both cases where positive moment failures have been observed the hollow-core units were supported on mortar.
Approximately 240mm
Concrete mid way between the strands fails first
(b) Tensile failure of concrete mid way between strands
Potential positive moment cracks
(a) Location of potential positive moment flexural cracks Internal dam in cell to
prevent concrete flowing along the void
3. The higher the strength of the insitu concrete the greater the potential for a positive moment flexural crack to form at the critical section in a major earthquake.
Figure A-18 shows the development of a positive moment flexural crack in a hollow-core unit close to its support. The prestress force in the strands develops over a distance of approximately 50 strand diameters. The longitudinal component of the prestress force is balanced by the longitudinal component of the compression in the concrete. For equilibrium the vertical component of the compression force in the positive moment zone is equal to the shear force. When the width of this crack is small the majority of the shear force is transmitted across the crack by aggregate interlock action, see Figure 18 (b). However, with the opening up of the crack this component of the shear force resistance is greatly reduced or lost entirely, and an alternative load path involving tension in the webs is initiated.
Figure A-18: Positive moment failure of hollow-core units
At the initial stage as the crack widens and shear transfer by aggregate interlock action is reducing the shear transfer by dowel action of the strands is limited due to the flexibility of this mechanism. The near vertical tension stresses in the webs develop to balance the loss in shear transfer by aggregate interlock action, see Figure A-18 (c). When these tensile stresses reach a critical level a crack forms
1 2
1 2
Mortar pad Cjt.
(a) Elevation on hollow-core unit
Longitudinal force through mortar or friction Stresses in insitu concrete if crack
forms at section 2-2 Shear transfer by aggregate interlock 1
Positive moment flexural crack
(b) Positive moment flexural crack forms
(c) Formation of longitudinal crack in hollow-core unit Tension in concrete prior to formation of horizontal crack 1
Dowel action in strands
and it extends in a near horizontal direction, which increases the shear displacement across the near vertical portion of the crack, which allows dowel action of the strands to be mobilised. Continued elongation of the main beams results in a further increase in crack width until failure occurs with the strand pulling out of the concrete. In the Matthews test of a floor slab [Matthews 2004] collapse occurred when the elongation of the plastic hinges in the beams near the support points for the hollow- core units were of the order of 12mm. This implies that the crack widths at the face of the support were of the order of 12 mm. In the individual units tests [Bull and Matthews, 2003], the crack widths and elongation were not directly measured. However, a photographic record together with deflection measurements indicate that collapse occurred when the positive moment flexural crack was of the order of 10 to 15mm in width.
In the tests described above the effect of vertical seismic ground motion was not considered. The rapidly alternating vertical accelerations associated with vertical ground motion, could be expected to result in failure at reduced crack widths.
There is another possible trigger for this form of failure. The 75 mm plug of concrete cast into the ends of the hollow-cores may act as a dowel. If bond between this plug and the hollow-core concrete is poor the plug can only be broken by prying forces acting at the end of the plug and the back face of the hollow-core unit. The theoretical magnitude of these prying forces is sufficient to split the web of a hollow-core unit [Fenwick et al, 2004]. Once the horizontal web crack has formed the failure mechanism follows the mode previously described for positive moment failure.
Breaking out the cells at the end of a hollow-core unit, adequately reinforcing them and filling with insitu concrete prevents the development of a positive moment failure at the critical section. The reinforcement in the cells effectively laps the transfer length of the strands and this increases the positive moment flexural strength. If a positive moment flexural crack does form the reinforcement significantly increases the shear force that can be resisted by dowel action. Finally if this crack did develop the vertical component of the tension force in the bars where it crossed the crack would prevent collapse. However, at this stage the hollow-core unit would have dropped 10 to 20mm off the supporting ledge.