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Vertical seismic ground motion generates inertial forces in members that span horizontally. These actions need to be considered in design or retrofit of elements that have a low level of ductility. The Loadings Standard for Earthquake Actions, NZS 1170.5, in clause 3.2 specifies that the response spectrum for vertical ground motion should be taken as 70% of the corresponding value for horizontal ground motion.

Hollow-core units, which do not have top strands and are reinforced with mesh in topping concrete, have very limited ductility. The strain causing failure of hard drawn wire mesh is typically in the range of 1 to 2 percent. The performance of ductile mesh is uncertain (see Section 7.3). Though the individual wires may be ductile the spot fusion welding between the wires has limited strength and it is unlikely to be capable of sustaining anchorage of a bar stressed into the strain hardened range. Furthermore any anchorage at a transverse bar induces local bending of the anchored bar. To establish the ductility of ductile mesh tests are required of the mesh buried in concrete in a situation that accurately models its action in topping concrete on precast units. Until such tests have been carried out ductile mesh should be treated as similar to hard wire drawn mesh in terms of its ductility.

Tension stiffening of concrete restricts the yielding of mesh reinforcement to the distance between transverse bars (a distance of 150mm in 665 mesh). A consequence of this is that a peak strain in mesh is much higher than the corresponding average tensile strains in the concrete at the same level as the mesh. Bond between plain wires and topping concrete further reduces the strain levels in the wires away from the crack. The local strain amplification due to tension stiffening reduces the critical strain level predicted in a conventional “plane sections remain plane” analysis to about a quarter of that found in direct tension tests. Consequently standard ultimate strength theory needs to be modified to enable it to be used to predict the negative ultimate flexural strength of these partially prestressed members. Additional information in determining the negative moment flexural strength of hollow-core floors is given in Appendix A.5.2.

In determining an appropriate structural ductility factor for vertical seismic actions in hollow-core flooring units a number of aspects need to be considered;

1. Mesh has very limited ductility and this can result in poor ductile performance of hollow- core with insitu concrete topping when subjected to negative moments;

2. Under downward loading (acceleration in upward direction) any flexural cracks on the topping concrete close and the member behaves in a similar manner to an un-cracked element. However, under upward loading flexural cracks open to allow the reinforcement to resist negative moments. These cracks significantly reduce the stiffness of the member and give the member different stiffnesses with upward and downward displacements. Consequently greater displacements can be expected in the upward direction than in the downward direction. The change in stiffness with direction of loading means the

commonly used equal displacement and equal energy concepts no longer apply and standard design rules based on these concepts can be expected to lead to an under- estimate of critical upward seismic displacements.

3. Whether reinforced with either mesh or conventional reinforcement, the proportion of reinforcement in the insitu concrete topping is generally low. As a consequence the tension force capacity of the reinforcement crossing a primary crack is insufficient to overcome the tensile strength of the concrete and cause secondary cracks to form. Hence yielding of reinforcement is confined to a short length on each side of the primary crack. This may severely limit the ductility of a member.

In view of these points it is recommended that in design or analysis for retrofit of existing floors seismic actions due to vertical ground motion should be based on a structural ductility factor, µ, of 1.25 and a structural performance factor, Sp, of 0.9 where mesh is used anywhere in the topping concrete. It is tentatively suggested that these values be increased, where ductile reinforcement (Grade E) is used in the topping concrete, to give a structural ductility factor of 2 together with a structural performance factor “Sp” factor of 0.8 (this value is based on Structural Concrete Standard, NZS 3101-2006).

3.5.2 Numerical values of vertical seismic actions

The fundamental period of vibration for vertical excitation of flooring units is generally in the range of 0.1 to 0.35 seconds, which is in the peak range of the design acceleration response spectra. Values given in NZS 1170.5: 2004 for modal response should be used in assessments. A fundamental period of less than 0.1 seconds should not be assumed as cracking of insitu concrete and flexibility of support structure including foundations soils are likely to increase the natural period. Only actions corresponding to the first mode of the floor need to be considered.

The standard assumption used in elastic analysis for ground motion is that equivalent static forces, representing dynamic actions, are proportional to the mass and displacement relative to the ground. Consequently for precast units spanning in a horizontal direction the equivalent static forces are not uniformly distributed. They are distributed in proportion to the deflected shape. For hollow-core units supported at each end the deflected shape can be approximated to a parabola. Using this assumption the bending moment, M, and shear, V, at different positions in a span due to vertical seismic actions alone, can be found from Table 3.1 in terms of the vertical seismic force, Fs, acting on the span and the span of the unit, L.

Table 3.1: Distribution of vertical seismic actions along a precast floor unit

x/L 0.0 0.1 0.2 0.3 0.4 0.5

V/Fs 0.5 0.47 0.4 0.28 0.15 0.0

M/Fs L 0.0 0.05 0.09 0.13 0.15 0.16

x = distance from support

The vertical seismic force is given from NZS 1170.5: 2004, by-

W S T C F p v v s = ( ,µ) (Eq. 3-6)

Where W is the gravity weight supported by the unit (dead and long term live load where appropriate) and Tv, is the fundamental period of vibration of the unit. It should be noted that these actions need to be added to forces associated with lateral seismic actions and elongation (see Section 3.4.3). Table 3.2 gives the ratio of vertical seismic force acting on a floor in terms of the dead and seismic live load on the span for the case where R is 1.0 for different cities in New Zealand.

Table 3.2: Vertical seismic force, Fs /W, for main city centres for Tvbetween 0.1 and 0.3s

according to NZS1170.5 assuming R is 1.0 Location

µ Fundamental Period (s) A & B C D & ESite subsoil class

Auckland 1 2 2 2 0-0.35 0.1 0.2 0.3 0.21 0.17 0.15 0.14 0.27 0.21 0.19 0.17 0.27 0.22 0.19 0.17 Wellington 1 2 2 2 0-0.35 0.1 0.2 0.3 0.66 0.52 0.46 0.41 0.82 0.65 0.58 0.51 0.84 0.67 0.59 0.53 Christchurch 1 2 2 2 0-0.35 0.1 0.2 0.3 0.36 0.29 0.25 0.23 0.45 0.35 0.32 0.29 0.46 0.36 0.32 0.29

3.5.3 Combinations of seismic actions

Precast concrete floors subjected to vertical seismic excitation respond in an elastic or near elastic manner. The fundamental period is short. Hence there is an appreciable likelihood that close to peak excitations in both horizontal and vertical actions may occur simultaneously. For simplicity it is recommended that designers assume peak values occur simultaneously and add the seismic actions together. This is a conservative assumption.

Two different situations may arise. In both cases the actions induced at the support or supports should be based on upper characteristic yield strength of reinforcement further amplified to allow for strain hardening.

(a) In the first relative rotation of a precast floor unit to its supporting beam may cause the starter bars to be stressed into the yield, or possibly into the strain hardening range, inducing negative bending moments at one end of the unit and essentially zero moment at the other end support.

(b) Elongation of beams spanning parallel to the precast floor units can apply an axial tension to the starter bars at both support points. Under this situation the unit is subjected to bending moments and axial tension from the starter bars. These moments are smaller than for the case (a) above but the added axial tension induces stress conditions which might be critical in some situations.

In both situations the actions associated with;

• gravity loading, and

• both vertical and horizontal seismic ground motion,

should be added to the actions induced by elongation or otherwise combined in an appropriate manner.