MODALIDAD DE INVESTIGACIÓN

Eight potential failure mechanisms for hollow-core floors in major earthquakes are identified in Chapter 5. These arise due to the interaction of the precast units with other structural elements. The potential failure mechanisms are;

1. Non-ductile failure of a structure associated with the increase in strength of beams due to interaction with floor slabs containing prestressed precast elements;

2. Loss of support to precast units;

3. Positive moment flexural failure of precast units near the supports; 4. Negative moment flexural failure of precast units near supports; 5. Shear failure near the supports;

6. Incompatible displacements between hollow-core units and other structural elements; 7. Torsion induced in hollow-core units;

8. Loss of shear transfer, or diaphragm action, in a floor.

For each of the failure modes listed above an equivalent ultimate limit-state condition is proposed. Methods of analysis are described to ascertain the displacement or magnitude of a structural action corresponding to each limit-state condition. The relevant value can be used to assess either the corresponding limit as a percentage of New Building Standards (%NBS) (current code requirement). Each potential failure mode will have its own percentage of New Building Standards. These values can be used to assess the need or otherwise to retrofit the structure to achieve an acceptable level of seismic performance.

The background to the different failure modes and proposed assessment criteria are given in Appendix A together with an outline of the relevant research used to develop the criteria. For additional information and appropriate references readers are referred to Appendix A.

6.2 Background

It is only in the last decade and a half that serious questions have been raised about the seismic performance of hollow-core floors. During this period there have been three sub-assembly tests to examine the performance of hollow-core floors in moment resisting frame structuresand two tests to examine the interaction of hollow-core units and walls. In addition there have been a number of tests examining the performance of hollow-core units supported on rigid concrete blocks. Many of the earlier tests on hollow-core floors did not consider the implications of the simultaneous rotation of the precast units on its supports together with displacement associated with elongation. The amount of analytical and experimental work related to hollow-core floors is small compared with that carried out for other structural elements such as columns, beams and walls. While an attempt is made in this chapter to give realistic assessment limits for the different failure modes it must be noted that in many cases there is a lack of relevant experimental and analytical work and hence the criteria cannot be given with the same precision as that implied in current design standards. The number of tests that have been made is in all cases insufficient to enable the variation in strength to be realistically established. Hence it is not possible to accurately establish equivalent values to the lower characteristic strengths, on which structural design standards are based, and hence a certain amount of engineering judgement has been used in setting the proposed criteria. As further research is carried out it should be possible to improve on the limiting design and assessment criteria for hollow-core floors. In this context it should be

noted that concrete strength in hollow-core units is highly variable. Where test cores have been taken it has been found that concrete strengths have varied from 50 to 88MPa. Caution is required in interpreting results of structural tests on hollow-core units where only a few tests have been made and particularly where material strengths have not been recorded. In some situations the strength depends on the tensile strength of concrete. Even when the concrete compression strength has been measured the corresponding tensile strength cannot be reliably predicted, see Section 3.5. Consequently in these cases apparently similar test units can have widely differing ultimate strengths.

NZ Standards base design for the ultimate limit state on strengths calculated using lower characteristic material strengths multiplied by a strength reduction factor. A nominal strength is such that in general 19 out of 20 units will have strengths greater than the nominal value. The use of the strength reduction factor takes the theoretical failure rate (or safety index) to an acceptable value. With hollow-core floors there are insufficient test results to establish a corresponding lower characteristic strength and as noted above in developing design and assessment criteria some judgements have to be made. In evaluating of hollow-core floors for retrofit it is recommended that material strengths and strength reduction factors given in the appropriate materials standard be used where possible. Where displacements or deformations are critical in assessing a collapse mechanism a coefficient, which has a similar function to the strength reduction factor, is required. It is proposed that a deformation factor,φ_df , of 1.25 is used for this purpose. This factor allows for the inherent scatter in deformation predictions. It can be used either to increase the predicted deformation in an assessment or to reduce the maximum permitted design displacement.

6.3 Potential Non-ductile Failure of Building as a Whole

The first step in checking a building is to assess if its design strength, stiffness and the detailing that was used are sufficient to satisfy current NZ Standards. If the building fails to satisfy these it may be necessary to assess what level of earthquake actions the structure can safely sustain. One particular aspect that needs careful consideration is the over-strength of plastic hinges in reinforced concrete beams. Prior to the publication of NZS 3101; 2006 with Amendment 2 the design criteria in a number of situations led to under-estimates of flexural over-strengths of potential plastic regions. In the event of a major earthquake this may result in;

• Columns not being strong enough to ensure that a beam sway mode will develop in preference to a column sway mode;

• Shear reinforcement in the beams not being adequate;

• Plastic deformation of reinforcement or crushing of concrete being initiated outside planned potential plastic regions, where there is inadequate confinement reinforcement, which might result in a premature loss of strength.

In Structural Concrete Standards NZS 3101: 1982 and 1995 the contribution of floor slabs to the flexural strength of beams was under-estimated compared with the provisions in NZS 3101: 2006. To illustrate the changes, which have occurred in the Structural Concrete Standards since 1982, the effective widths of flanges that have been assumed to contribute to negative moment design strength and flexural over-strength strength of beams adjacent to internal columns are shown in Figure 6-1, and described below;

(a) With NZS 3101: 1982 the effective width of a flange on each side of a beam was taken as the distance of 2 times the thickness of the slab on each side of the web. Any reinforcement in this zone was used to calculate both the design strength and over-

strength (clause 6.5.3.2 (e))1_{. Any contribution of prestressed reinforcement in precast}

units to flexural strength of the beam was neglected.

Figure 6-1: Effective flange width in different standards

(b) In NZS 3101: 1995 the effective flange width was taken as the smaller of the distance from the side of the web to a distance equal to 1/4 of the span of the beam, measured from the centreline of the section, or half the distance to the next beam (clause 8.5.3.3). As with the previous edition of this standard the effective width was used for both the design and over-strength calculations.

1 _{Clause numbers refer to Standard being described}

NZS 3101:1995 bf bf NZS 3101 :2006 _{- Nominal} Strength t 2t Flange equal to 2 times the slab thickness on each side.

Prestress in precast units was ignored.

NZS 3101:1982

bf equal to ¼ of beam span

measured from beam centre- line.

Reinforcement in topping counted but no prestress in precast units was ignored.

reinforcement. bf

bf

bf equal to smaller of 8t, h or 1/8th

span of beam with a limit placed on contribution of topping

reinforcement if it is not tied into the beam.

bf

bf

NZS 3101: 2006 _{- Over-strength}

bf equal to smaller of 3h or

proportion of clear span to the next parallel beam.

(c) In NZS3101: 2006 it was recognised that the effective flange width increased as the curvature in the plastic hinge increased. Consequently for the nominal strength, which should be reached close to the point where inelastic deformation is initiated, the width was limited (clause 9.4.1.6.1) to the smaller of;

• one beam depth,

• 8 times the thickness of the slab immediately adjacent to the beam,

• 1/8th _{of the span of the beam,}

• a proportion of the distance to the next parallel beam, which depended on the relative beam depths.

In addition limits were placed on the contribution of flexural reinforcement in the slab to the nominal strength unless this reinforcement was tied into the web of the beam. In cases where the flange reinforcement is not tied into the web separation of the flange from the web may occur by a shear failure at the interface between the section containing the beam shear reinforcement and the slab reinforcement crossing the beam. To limit potential strength loss in the event of separation the contribution to nominal strength of a beam by reinforcement on one side of the web is limited to 10 percent of the total tensile strength. Where there is a flange on both sides the limit is 20 percent (10% on each side). With over-strength conditions high curvatures are sustained in plastic hinges and consequently a greater width of slab contributes to the negative moment strength. This was recognised by increasing the effective flange width on each side of the web from one beam depth to 3 beam depths, deleting the 1/8 of the beam span limit and requiring the contribution of any prestressed reinforcement in the effective flange widths to be included in assessing over-strengths (clause 9.4.1.6.2). The limit on the contribution of flange reinforcement of 10% to the negative moment beam over-strength was not applied as a shear failure at the critical interface may or may not occur.

Where designs have been made on the basis of design rules in Standards prior to the 2006 edition the over-strength of the beams could well be under-estimated compared with values derived from NZS 3101: 2006 including Amendment 2. In these structures the possibility exists that in the event of a major earthquake the enhanced strength of the beams might lead to a non-ductile failure. For example shear or anchorage failures of reinforcement might occur in the beam, or a column sway mechanism might develop instead of the intended ductile beam sway mechanism. Figure 6-2 shows part of a storey shear versus storey drift for a building subjected to inelastic cyclic loading. The figure illustrates how an assessment may be made for the possible development of a column sway mechanism in the storey. To make this assessment the lateral storey shear strengths corresponding to beam and column sway mode mechanisms in the storey can be assessed following the Method B given in NZS 3101: 2006, Appendix D. If the strength of the column sway mode exceeds that of the beam sway mode by a sufficient margin the potential formation of the column sway mode is prevented. In assessing the values of beam and column storey sway shear strengths allowance should be made for redistribution of actions both within a frame and between frames. However, care is required to ensure equilibrium is maintained in this process. The following steps may be followed.

(a) The beam sway storey shear strength corresponding to average material strengths is calculated. This may be based on flexural strengths at the critical sections of the primary plastic hinges being taken as 1.1 times the nominal flexural strength for reinforced concrete sections. The corresponding beam sway storey shear strength is then calculated using these flexural strengths following Method B given in NZS 3101: 2006 (Appendix D, clause D3). This storey shear strength may be assumed to be sustained at a displacement corresponding

to the average elastic limit material strains (curvature) being sustained in the critical sections of the potential plastic regions.

Figure 6-2: Relationship between beam and column storey sway shear strengths

(b) The column storey sway shear strength is calculated on the basis that the nominal flexural strengths are sustained in the critical sections at the top and bottom of the columns in the storey. The column sway storey shear strength is taken as the sum of the shears in the columns multiplied by 0.9. Any change in axial load due to seismic induced actions may be neglected on the basis that a reduction in flexural strength in one column due to reduction in axial load is compensated by an increase the flexural strength associated with an increase in axial load in other columns. Where columns are not confined to meet the minimum requirements for limited ductility further study is required to ensure the necessary curvature can be sustained to develop the nominal flexural strength of all the critical sections. The 0.9 factor is applied to the storey shear sway strength to maintain an adequate margin between the beam sway and column sway shear strengths.

(c) The flexural over-strengths of the primary plastic hinges are calculated assuming the reinforcement has over-strength values of 1.20 and 1.30 times the design yield strength for Grade 300 and Grade 500 reinforcement respectively. These values replace 1.25 and 1.35 in NZS3101:2006 as the strength relates to average reinforcement properties rather than upper characteristic values.

(d) The beam sway storey strength is calculated from the flexural over-strengths of the primary plastic regions determined in step (c) and by following the approach detailed in Method B in

Increase in strength due to increase in effective section and strain hardening