DEALING WITH SEISMIC FORCES IN FLOORS OF REAL BUILDINGS: DESIGN ISSUES AND RECOMMENDATIONS.

Transcription

1 DEALING WITH SEISMIC FORCES IN FLOORS OF REAL BUILDINGS: DESIGN ISSUES AND RECOMMENDATIONS. Des K. Bull 1, Richard C. Fenwick 2, Debra Gardiner 3 SUMMARY The paper describes the technical challenges of establishing the forces that are generated by seismic attack, within the floor plates of buildings. These forces are a combination of the inertia effects and forces ( transfer ) generated between the different vertical lateral force resisting sub-structures within a building (frames and walls). During a major earthquake, force paths in the floors of buildings change due to localised plastic deformations in the structure (particularly plastic hinges in beams, Eccentrically Braced Frames (EBFs) and walls). Research in New Zealand, over the last 10 years has indicated the need to consider: - How the localised elastic and particularly plastic deformations, within elements in a structure, can damage the force paths through floor plates. The viable force paths across floors and why these differ significantly from the simple beam analogies used in the past to design floors acting as diaphragms. Recommendations are made to account for localised plasticity; these include a review of the recommendations made 5 years ago and amendments to these recommendations. A simple design-office method of establishing seismic design forces that can be applied to a building to represent the inertia and transfer forces acting on the floors. 1 Professor, University of Canterbury & Technical Director, Holmes Consulting Group Ltd 2 Adjunct Associate Professor (retired), University of Canterbury 3 PhD Postgraduate Student, University of Canterbury

2 INTRODUCTION Significant research over the last 10 years, at the University of Auckland and University of Canterbury, has been undertaken in New Zealand on the performance of floor diaphragms, constructed from precast, prestressed concrete units, topped with reinforced, cast-in-place concrete. This paper focuses on a number of the key findings of the last 10 years and associated recommendations for designers. During a major earthquake, force paths across a floor and throughout a building are altered because regions of the floor plates such as connections to beams, walls and Eccentrically Braced Frames (EBFs) undergo inelastic behaviour. The traditionally held view that floor plates remain fully elastic and hence can be designed as simple elastic members is in error [1,2,3,4]. An example of localised plastic deformations in a structure is the large tears in the connection between floors with precast units and supporting beams. These result from the supporting beams being pushed away from the floor as neighbouring beams, parallel to the floor units, elongate due to the formation of plastic hinges. The elongation action can unseat the floor, rupture the continuity reinforcement from the beam into the topping of the floor or delaminate the concrete topping from the units. Other sources of damage in the floors resulting from lateral movement of a building include: significantly different deformed shapes and relative vertical and horizontal displacements between the floor and the neighbouring beams, or the ductile link in EBFs or the vertical elongation or rocking displacements of walls (individual and at links between walls in close proximity coupled walls ) [3]. AVAILABLE FORCE PATHS ACROSS FLOOR DIAPHRAGMS Loss of connection between floors and supports As discussed in detail in the University of Canterbury (UC) Research Report on assessment of hollowcore floors for seismic performance [5], the presence of pretensioned precast concrete units in the floor structure, effectively forms large panels of floor that are framed by beam and/or wall elements. Any movement in the supporting structure or within the floor (creep, shrinkage and thermal effects) typically results in vertical cracks between the supports and the ends of the precast units at the planes of weakness between the floor and boundary structural elements. During the life of the structure under normal everyday loadings and environment these cracks range in size from 1-5 mm in width. During a major seismic event, these cracks can widen up to 40 mm or more, depending on the structural element configurations. For example, beams that form plastic hinges can push the columns and beams framing in to those columns, away from the adjacent floor, see Figure 1 [5]. A method for estimating the width and length of the cracks at the interface of the floor units and supports, for exterior and interior beams, is detailed in the UC Report on assessment of hollowcore floors [5]. Figure 1(b), indicates that bars may be able to transfer compression or tension forces across the cracks in the immediate vicinity of the columns. In Figure 1(c), columns that are not adequately tied into the floor can be pushed out of the structure by the elongation in plastic hinges in the beams [2]. Restraint can come from either beams framing into the columns (Figure 1(a)) or by bands of reinforcement specifically designed for this task (NZS 3101: 2006, Clause [7]). The lack of adequate restraint over a number of floors can result in the effective length of the columns increasing to the extent that they become susceptible to buckling. Matthews [2] considered two possible modes of displacing or pushing the beams that supported the end of the floors away from the floors. This movement was caused by plastic hinges in the beams. The first mode is shown in Figure 1, with the outward movement of the columns being attributed to lateral distortions of the plastic hinge zones of the adjoining beams. There is a zone between the columns where the floors are largely still connected to the supporting beams. The second mode (Figure 2) shows a crack forming along the entire interface between the floor and supporting beam as the beam is notionally displaced out, in a rigid body type rotation. In 2004, it was concluded that Mode 2 was observed in the Matthews test [2]. However, in recent reviews of the data from that and other tests, at realistic inter-storey drifts in the range of 2.5-3% of the height of a storey, the mode of separation of the beams from the floor plate was similar to that shown in Figure 1. There are zones where the floor plate is still in reasonable contact with the supporting beams: mid zone of the beams, between the plastic hinge zones that occur at the ends of each beam.

3 Figure 1 Influence of potential cracks on the diaphragm action of the floor [5] Beam elongation Loss of support possible over this region Beam elongation Mode 2 (b) Entire beam rotates to allow for beam elongation Figure 2 Cracking along entire length of beams at the floor-to-beam interface due to beam plastic elongation [2] Viable force paths across floor plates Traditional solutions for designing floors acting as diaphragms have been based on simple beam analogies - see Figure 3 [6]. Here the floor is treated as a beam spanning between major frames, which are generally at the ends of the building. The interior secondary frames participate in lateral resistance, as indicted by the shear force diagram (c). The floor inertial forces induce compression forces in the floor in the form of an arch which spans between the perimeter frames or walls providing the major resistance to the lateral forces, see Figure 3(d). The beams spanning perpendicular to the end frames or walls are assumed to act as a tie that completes the equilibrium of the system at Nodes i and j.

4 In 2004, it was concluded that Mode 2 was observed in the Matthews test [2]. However, in recent reviews of the data from that and other tests, at realistic inter-storey drifts in the range of 2.5-3% of the height of a storey, the mode of separation of the beams from the floor plate was Figure 3 Cracking along entire length of beams at the floor-to-beam interface due to beam plastic elongation [6] This form of Tied Arch, actually a Strut & Tie solution, is not adequate for designing floor diaphragms because of the large cracks that form in the floor-to-beam interfaces at the column locations. For this situation, it is not possible for the stress fields or struts to develop at the nodes in Figure 3 (d), as illustrated in Figure 1 (a). Further, the perpendicular frame, in part, is being engaged in the earthquake motion, even with the main direction of force at right angles to this (transverse components or torsion about the vertical axis of the building), or when the earthquake induced displacement are not exactly along the main axis of the building. Therefore some of the strength of the frame in that direction is being used. It is too difficult, and possibly unrealistic, to require designers to determine what capacity is left in the tie frame in order to deal with the tension needed to complete the tied arch. Cl NZS 3101:2006 requires that the shear design of diaphragms is based on the strut & tie method (Appendix A) [7]. In existing buildings, assessment of the tie paths in the floor plates should focus on the ties arriving in the mid regions of beam spans, since the floors will be severely cracked around the column nodes. In Figure 4 [8], the compression field, strut, arrives at the middle of the beam span. The starter bars lap with the topping reinforcement to form the tie. The tie must be anchored to satisfy equilibrium with the rest of the Strut & Tie solution of the whole floor. Designers need to consider the probable performance of the topping reinforcement in terms of providing this tie action, (strength, lapping and localised ductility demands), especially if the reinforcement is formed from cold-drawn wire [2,3,4,5]. NZS 3101:2006 [7] has requirements for the design of new structures. These requirements set a benchmark for assessing existing structures. In NZS 3101:1995, it is recommended that additional reinforcement at column nodes, diagonals, be placed to carry forces in and out of the columns. See Figure 5. There are three major concerns with these recommendations: 1. The cracks between the floors, the beam framing into the columns and the column are so large as to either rupture the bars or delaminate the topping with the risk of fracturing the mesh out at the end of the diagonal bars. 2. The plastically deformed reinforcement and the potential for buckling of the topping off of the units make transfer of compression forces through the diagonal bars very unreliable. 3. There are components of the tension forces in the diagonal bars that add to the strength of the hinges in the beams, for the negative moment cases. See Figure 6. The 1995 NZS 3101 requirements of diagonal bars has been deleted from the 2006 version [7] and column restraint is provided by bands of reinforcement at 90 to the exterior frame or by beams framing in to the intermediate columns.

5 (a) Strut & Tie schematic for forces arriving at mid-section of a beam (Node) (b) Strut & Tie distribute reinforcement as the Node Figure 4 Beam-floor Node mid beam, distributed reinforcement Figure 5 Diagonal reinforcement corner column

6 Tension component Figure 6 Diagonal reinforcement interior column. The use of thin slabs ( mm thick) spanning mm from the precast concrete units to an adjacent beam, wall or EBF link beams is recommended in NZS3101: These slabs, called link slabs, are typically cast on timber plank infills that span between the side of the precast unit and the beam, wall etc, see Figure 7. Research [3,4] has shown that the relatively flexible link slabs can accommodate both the elongation effects of plastic hinges in adjacent beams, and the relative vertical displacement between a beam or wall due to plastic deformation and or rocking type action in walls. The link slabs have been found to sustain many fine cracks instead of wide cracks. This enables the link slab to transmit compression and tension forces from the floor to the surrounding structural elements. Currently, link slabs are required by Cl of NZS 3101:2006 for floor to beam regions, though it is expected that the Standard [7] will be updated to include floor-to-wall and floor-to-ebf connections. It is strongly recommended that this detail be employed wherever there are large distortions expected in the floor next to lateral force resisting structural systems. Timber in-fill 600 mm Figure 7 Timber infill and slab [8]. Recommendations for Determining Seismic forces in Diaphragms The following is an edited summary of Appendix B of Reference 5. Floors and roofs acting as diaphragms should be considered as parts of the primary lateral force resisting system. In terms of the Parts and Components, Cl : NZS [9], diaphragms are NOT to be treated as parts. The manner of determining forces in a diaphragm as being a part was suggested by NZS 4203:1992 and has been revised in NZS [9]. There is an incorrect and commonly held view that transfer diaphragms are only those that occur at podium roofs and the like, and that transfer diaphragms and inertia diaphragms are separate entities. Transfer diaphragm forces are those that result from tying together, the vertical lateral force resisting

7 M Mobobobobstructures (buildings with frames of different stiffness and strengths and buildings with a mixture of systems, e.g. walls and frames). Each and every diaphragm has some degree of transfer function. Inertia and transfer effects are coupled - i.e. inertia causes the building to deform and it is the incompatibility of deformed shapes of each vertical structural system that generates the transfer forces across the diaphragms [8]. NZS [9] gives broad directives on how to determine the forces generated in diaphragms. A quote from the commentary to NZS : For determining the actions in the structure it has been suggested reference 1 (which is reference 8 in this paper) and the references cited therein, that the actions for the structure should be based on capacity design principles. In order to visualise the load paths through the structure, in any design method, it is imperative that equilibrium is maintained across diaphragms, accounting for the interaction of the vertical structure systems via the diaphragms and distribution of the inertia across the floor plates. It is suggested that a pseudo-equivalent Static Analysis (pesa) may be employed, with the floor forces (the inertia of each floor, in effect) factored up by the [overall] building overstrength factor Overall building overstrength factor, ob Building lateral overstrength should account for full plastic mechanism development in the components of the structure, as designed, divided by the demand earthquake event, determined from the Loadings Standard being used). The minimum ob should be in the range of However, depending on how the actual strength is provided to the mechanism ob could be as high as 4.0. Consider when determining ob : The plastic mechanism for the structure needs to be envisaged. This should account from the likelihood of some of the PHZ not forming. For example using the Rv factor in NZS In effect, it is a rudimentary push over analysis. Overall building overstrength factor, ob, can be: E Eor V Vwhere M ob is the overturning moment of resistance at overstrength (this includes the restoring component from gravity). V ob is the lateral shear associated with M ob. M E is the moment demand from an un-amplified Equivalent Static Analysis based on the response spectrum assumed from the Loadings Standard. V E is the base shear associated with M E. The pseudo-equivalent Static Analysis - pesa Using an Equivalent Static Analysis (ESA), the magnitudes and directions of the applied forces at the boundary of the diaphragm are known and are in equilibrium. The coarseness of pesa is somewhat mitigated, if the TIES across the diaphragms are connected correctly into the vertical structures (the nodes of a strut and tie solution). When looking at the both the whole building and individual floors, there are short comings with traditional approaches, which are illustrated in Figure 8 [10]:

8 Diaphragms: Forces F i F i Neither are SATISFACTORY Peak Ground Accn. Equivalent Static Analysis (ESA) Maxima Envelope of Floor Accelerations (Parts & Portions) Figure 8 Equivalent Static Analysis & Maxima Envelope [10] The traditional ESA underestimates the inertia forces at lower levels. The maxima envelope of the Parts and Portions approach (NZS 4203 and ), when incorrectly used as a set of floor forces being applied to the whole building, overestimate the floor inertia and deflection of the building. This in turn overestimates the transfer effects that are driven by lateral displacements of the structure [11,12]. In response to the recommendations of the Commentary of NZS , the pesa was visualised, and is recommended as the approach to determine the forces in diaphragms: Figure 9 Equivalent Static Analysis & Maxima Envelope [12] At the overstrength of the building, the recommended floor forces result in (refer to Figure 9): About the correct deformed shape: Therefore transfer forces are OK. Approximately, the correct amplified inertias in the upper floors. Peak Ground Acceleration (PGA): inertias that are approximately correct in the lower floors; this has little effect on the deformed shape, and hence little effect on transfer forces. The line of action for the floor forces can be taken through the centre of mass of each floor. The NZS requirement of adjusting the application point of the floor force by 0.1 B, where B is the width of the building perpendicular to the line of actions, need not be considered. The Strength Reduction Factor,, is equal to 1, as the actions generated in the building are based on overstrength floor forces.

9 First mode output from a modal analysis can be used in the same way as an equivalent Static Analysis, amplified as above, with: - M E is the moment demand from 1st mode, based on the response spectrum assumed from the Loadings Standard. - V E is the base shear associated with M E. Verification of the pesa was carried out in both a report [11] by Gardiner as part of her Bachelor of Engineering studies and further studies (which are nearing completion) as part of a PhD undertaken by Gardiner, at the University of Canterbury. An Elastic Diaphragm localised damaged can be OK. Diaphragms that respond elastically can be visualised as having virtually no plastic deformation within the body of the diaphragm during seismic action, while possibly accepting permanent deformation (e.g. some plasticity or sliding) at or near the boundaries of the diaphragm. This permanent deformation/plasticity on the diaphragm boundaries can be sustained in the connections and support details for a floor plate and may extend into the diaphragm a nominal distance or by a specifically detailed element to accommodate plasticity (e.g. cast-in-place reinforced concrete infill strip (linking slab) between beams of the frame and precast concrete floor units or nail plates along the edge of a timber diaphragm). In terms of having virtually no plastic deformation within the body of the diaphragm, this means that localised plasticity in the body of the plate may be permitted, providing: - It is transitory, not being relied upon for redistribution of actions nor energy dissipation. - Localised plasticity does not negate the outcomes of the analysis of the structure, based on the assumption of modelling the diaphragm as an elastic element. - Localised plasticity does not compromise the gravity supporting role of the floor plate nor the transfer of forces through the diaphragms. CONCLUSIONS This paper highlights issues with determining the forces across floor plates and how the deformation and damage characteristics of the floor-to-vertical structure connections influences the engineered solutions: The traditional force paths across floors arriving at columns or into walls or to beams of EBFs are rendered ineffective by plastic hinges in beams, plastic rotation of the links in Eccentrically Braced Frames (EBFs) and vertical deformations of walls (individual and at links between walls in close proximity coupled walls ). In reinforced concrete frames, there are zones, in the mid-span region between plastic hinges at the ends of the beams, where shears/forces can be transmitted from the floor to the beams and hence into the frames.. The use of flexible reinforced concrete infill slabs (linking slabs) between the floor units and vertical lateral force resisting systems retains viable force paths across the floor. Columns in reinforced concrete perimeter frames need to be tied in to the building by either beams framing in at an angle (typically 90 to the exterior frame) or by bands of reinforcement in the floor. This requirement, to hold the exterior vertical systems into the structure, is equally applicable to steel moment resisting frames, walls and EBFs. The pseudo-equivalent Static Analysis (pesa), as described in the Commentary to NZS [9], allows a simple means of developing forces in the floors of structures that are in equilibrium and of a justifiable magnitude considering the likely overstrength actions of the building. An adjustment is made to the Equivalent Static force profile in the lowest floors, allowing for the influence of Peak Ground Acceleration (PGA) of these floors.

10 REFERENCES 1. Lau, D., 2007, Influence of precast prestressed flooring on the seismic performance of reinforced concrete perimeter frame buildings, Thesis (PhD-Civil Engineering), University of Auckland. 2. Matthews, J., 2004, Hollow core floor slab performance following a severe earthquake, Thesis (PhD), University of Canterbury. 3. Lindsay, R., 2004, Experiments on the Seismic Performance of Hollow-core Floor Systems in Precast Concrete Buildings, Thesis (ME), Civil Engineering, University of Canterbury. 4. Macpherson, C., 2005, Seismic Performance and Forensic Analysis of Precast Concrete Hollowcore Floor Super-assemblage, Thesis (ME), Civil Engineering, University of Canterbury. 5. Fenwick, R.C., Bull, D.K. and Gardiner, D. Assessment of Hollow-core Floors for Seismic Performance, Research Report , Department of Civil and Natural Resource Engineering, University of Canterbury, New Zealand. 6. Park, R., Paulay, T. and Bull, D., 1997, Seismic Design of Reinforced Concrete Structures, Technical Report No. 20: New Zealand Concrete Society, Wellington, NZS 3101:2006, Concrete Structures, Parts 1 and 2, Standards New Zealand, Wellington, New Zealand. 8. Bull, D.K., Understanding the Complexities of designing Diaphragms in Buildings for Earthquakes, Bulletin of NZ Society for Earthquake Engineering, Vol. 37, No. 2, June NZS1170.5: 2004, Structural Design Actions Part 5: Earthquake actions & Commentary, Standards New Zealand, Wellington, New Zealand. 10. Precast Concrete Design Seminar, Cement & Concrete Association of NZ & Precast NZ, May Gardiner, D.R., 2006, Verification the Pseudo-Static Analysis Method, 3rd Pro Report, Department of Civil and Natural Resource Engineering, University of Canterbury, Gardiner, D.R., Bull, D.K. & Carr, A., Investigation of the Magnitude of Inertial and Transfer Forces in Floor Diaphragms during Seismic Shaking, Proceedings, 14th World Conference on Earthquake Engineering, Beijing, China, 2008.