DESARROLLO DEL PROBLEMA

(a) Serviceability Lim it State: This corresponds to the “fully functional” seismic

performance level of Vision 2000. No significant remedial action should be needed for a structure that responds at this limit state. With concrete and masonry structures, no spalling of cover concrete should occur, and though yield of reinforcement should be acceptable at this limit state, residual crack widths should be sufficiently small so that injection grouting is not needed. As suggested by Fig.3.5(b), structural displacements at the serviceability limit state will generally exceed the nominal yield displacement.

For masonry and concrete structures this limit state can be directly related to strain limits in the extreme compression fibres of the concrete or masonry, and in the extreme

Chapter 3. Direct D isplacem ent-B ased D esign: Fundam ental C onsiderations 71

tension reinforcement. With structural steel buildings, the limit state is more likely to be related to non-structural elements, as discussed in the following.

Potential for non-structural damage must also be considered when determining whether or not the serviceability limit state has been exceeded. Ideally, non-structural elements, such as partition walls, and glazing, should be designed so that no damage will occur to them before the structure achieves the strain limits corresponding to the serviceability limit state. Even with brittle partitions this can be achieved, by suitable detailing of the contact between them and the structure, normally involving the use of flexible jointing compounds. However, when the typical construction involves brittle lightweight masonry partitions built hard-up against the structure, significant damage to the partitions is likely at much lower displacement levels than would apply to the structure. For example, reinforced concrete or structural steel building frames are likely to be able to sustain drifts (lateral displacements divided by height) of more than 0 . 0 1 2

before sustaining damage requiring repair. In such cases, the serviceability limit state is unlikely to govern design. A very different conclusion will result if low-strength lightweight masonry infill is placed in the frames, without flexible connection. The infill is likely to reach its limit state at drift levels less than 0.005, and design to avoid non- structural damage in the infill may well govern the structural design. This is considered in more detail in Chapter 5.,

(b) Damage-Control Lim it State: As noted above, this is not directly addressed in the

Vision 2000 document, but is the basis for most current seismic design strategies. At this limit state, a certain amount of repairable damage is acceptable, but the cost should be significantly less than the cost of replacement. Damage to concrete buildings and bridges may include spalling of cover concrete requiring cover replacement, and the formation of wide residual flexural cracks requiring injection grouting to avoid later corrosion. Fracture of transverse or longitudinal reinforcement, or buckling of longitudinal reinforcement should not occur, and the core concrete in plastic hinge regions should not need replacement. With structural steel buildings, flange or shear panel buckling should not occur, and residual drifts, which tend to be larger for structural steel than concrete buildings should not be excessive. With well designed structures, this limit state normally corresponds to displacement ductility factors in the range 3 < //a <6.

Again, non-structural limits must be considered to keep damage to an acceptable level. This is particularly important for buildings, where the contents and services are typically worth three to five times the cost of the structure. It is difficult to avoid excessive damage when the drift levels exceed about 0.025, and hence it is common for building design codes to specify drift limits of 0.02 to 0.025. At these levels, most buildings - particularly frame buildings - will not have reached the structural damage-control limit state. It will be noted that this limitation will not normally apply to non-building structures such as bridges and wharves, and consequently structural limits will govern design to the damage- control limit state for these structures. Effective drift limits for these structures are often in the range 0.03 to 0.045. This limit state is represented in Fig.3.5(b) by the displacement

72 P riestley, Calvi and Kowalsky. D isplacem ent-B ased Seism ic D esign of Structures

(c) Survival Lim it State: It is important that a reserve of capacity exists above that

corresponding to the damage-control limit state, to ensure that during the strongest ground shaking considered feasible for the site, collapse of the structure should not take place. Protection against loss of life is the prime concern here, and must be accorded high priority in the overall seismic design philosophy. Extensive damage may have to be accepted, to the extent that it may not be economically or technically feasible to repair the structure after the earthquake. In Fig.3.5(b) this limit state is represented by the uldmate displacement, Aw.

Although the survival limit state is of critical importance, its determination has received comparatively little attention. Clearly this limit state is exceeded when the structure is no longer able to support its gravity loads, and collapses. This occurs when the gravity-load capacity is reduced below the level of existing gravity loads as a result of (say) total shear failure of a critical column, resulting in progressive collapse. Alternatively, collapse results from a stability failure, when the P-A moments exceed the residual capacity of the structure, as illustrated in Fig.3.6 for a bridge column. If the ultimate displacement capacity assessed from the intersection of the resistance and P-A curves exceeds the maximum expected in the survival-level earthquake, collapse should not occur.

Fig.3.6 P-A Collapse of a Bridge under Transverse ResponseIP4l 3.3.3 Selection of Design Limit State

The discussion in the previous sections indicates that a number of different limit states or performance levels could be considered in design. Generally only one — the damage- control limit state, or at most two (with the serviceability limit state as the second) will be considered, except for exceptional circumstances. Where more than one limit state is considered, the required strength to satisfy each limit will be determined, and the highest chosen for the final design. More information on strain and drift limits corresponding to

Chapter 3. Direct D isplacem ent-B ased D esign: F undam ental C onsiderations 73

different performance levels are included in Section 4.2.5, and in the relevant chapters on different structural systems.

3.4 SINGLE-DEGREE-OF-FREEDOM STRUCTURES