Chapter 6 for the assessment of hollow-core floors and for buildings containing these
floors.
A.2Over-strength of Plastic Hinges in Beams
The over-strength of plastic hinges in beams built compositely with precast floor components is an area of active research in 2010. Recommendations for assessing over-strength of beams may be expected to change as research progresses.
Research has shown that strength enhancement of negative moment flexural strengths, due to the presence of pretensioned units in a floor, can be considerably greater than that indicated by over- strength calculations based on editions of the Structural Concrete Standard NZS 3101 published prior to 2008 [SANZ, 2006; Fenwick et al 2005; Fenwick et al 2006; Lau 2007]. It should be noted that, as discussed later in this section, some sources of strength enhancement are not considered in current standards (2010). In carrying out an assessment for retrofit of existing buildings it is important to assess the significance of the potential increase in over-strength of beams on seismic performance. An unanticipated change in the shape of the bending moment, due to increased negative moment strength in a beam, may in the event of a major earthquake result in;
• Increased shear forces in regions not adequately reinforced for this shear force;
• Plastic deformation being induced in regions of the beam which are not detailed for ductility; • Premature crushing of concrete due to the increased flexural compression forces sustained by
a beam;
• A column sway mechanism developing instead of the ductile beam sway mechanism assumed in the design.
Figure A-1 illustrates a situation where the use of pretensioned units in a floor has been found to result in a very significant increase in the over-strength of beams in ductile moment resisting frame buildings. When a plastic hinge forms, elongation occurs. Where precast units span past plastic hinges, such as the plastic hinges marked A in Figure A-1 (c), elongation is partially restrained by the pretensioned units in the floor. A tension force, Tslab, which is resisted by the slab, acts with the tension force in the web and it can result in a considerable increase in the negative moment flexural strength of the plastic hinge that is adjacent to the column, see left hand side of Figure A-1 (a). In addition the increase in the resultant compression force balancing the tension forces in the web and the slab can reduce the ductility of the plastic hinge. The influence of the tension force in the slab on the positive moment strength is small, as the line of action of this force is nearly co-axial with the compression force. The area of concrete available to resist the compression force for the positive moment includes part of the slab adjacent to the beam, see Figure A-1 (b), and consequently the magnitude of the internal lever-arm for the tension force in the bottom of the beam is not significantly reduced.
The Structural Concrete Standard, NZS 3101: 2006 (see clause 9.4.1.6.2) gives details of how the flexural over-strength can be assessed when precast prestressed floor units span past an intermediate column where plastic hinges may form on both sides of the column.
Figure A-2 illustrates a second situation where precast units in a floor can increase the flexural strength. In this case the pretensioned units are supported on transverse beams, which frame into the
columns, and consequently the pretensioned units do not directly confine elongation in the plastic hinges. However, pretensioned units reinforce the floor between the transverse beams, which restricts the opening of flexural cracks that would otherwise extend from the beam into the floor.
Figure A-1: Interaction of floor and beam where precast floor units span passed the beam plastic hinges
Elongation of the plastic hinges results in wide cracks opening along the interface between the transverse beams and the floor slabs, as weak sections exist at locations where the prestressed units terminate. In buildings where the seismic forces are resisted by perimeter frames considerable inelastic deformation, and hence elongation, can be expected to develop. Often the internal frames are designed to resist gravity loads and for this shallower beams with longer spans are adequate. Consequently these frames are more flexible and they resist only a small portion of the seismic forces and they do not undergo significant inelastic deformation, or sustain as much elongation as the perimeter beams. Hence wide cracks can be expected to develop along side the transverse beams adjacent to the perimeter frame but only narrow cracks near the internal frames, see Figure A-2. With this pattern of deformation the floor bays act in a similar manner to deep beams. They are pushed apart at the perimeter frames, as illustrated in Figure A-2, with bending moments and shear forces being induced in the plane of the floor slab in each bay. In a perimeter frame with multiple bays, as shown Figure A-2 (b), the restraining force from this deep beam type action may build up due to the multiple bays.
In a floor, which contains pretensioned units that are supported on a transverse beam close to a plastic hinge, the tension force resisted by the slab, Tslab, is made up of two components. The first of these is the tension force transmitted by reinforcement across the crack that forms at the interface between the transverse beam and floor slab, and the second is the clamping force resisted by the deep beam type action of the bays in the floor slab. Tests have shown that this deep beam type action can in some situations increase the strength to a considerably extent [Lau, 2007; Peng, 2009]. At present there is no published method of assessing the potential strength increase due to deep beam type action of floor
Tslab Tb
2
2
C C
(a) Sectional Elevation 1 - 1
Tb Tslab +ve moment side -ve moment side Height of Tslab (b) Sectional elevation on 2 - 2
(c) Part plan on floor
Area available for compression on +ve moment side
1 1
Tslab
Tension resisted by floor Plastic hinge - type A
slabs containing precast prestressed units and no allowance for this action is included in the Structural Concrete Standard, NZS 3101: 2006 [SANZ, 2006].
Figure A-2: Deep beam action in floor slabs
The magnitude of the tension force resisted by a floor increases with the magnitude of elongation sustained in the plastic hinges. The theoretical flexural strength of a section, based on the measured properties of materials, is typically sustained at a section ductility of the order of 3 to 5. At this level of inelastic deformation typically only the reinforcement within a distance of about beam depth on each side of the web contributes to strength. The peak flexural strength is sustained at a section ductility of an order of magnitude greater than that corresponding to the theoretical strength. With the higher magnitude of inelastic deformation a greater width of floor slab contributes to the flexural strength [Qi and Panatazopoulou, 1991; Fenwick et al, 1995]. For this reason the Concrete Structures Standard, NZS 3101-2006, requires different sections to be used for calculating the design strength