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Analysis and modelling of the seismic behaviour of high ... - Ingegneria

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4. SEISMIC RESPONSE OF PARTIAL-STRENGTH COMPOSITE JOINTS<br />

4.9.1 Pushover vs. incremental dynamic analysis results<br />

Pushover analysis<br />

As said in Chapter 2 Subsection 4, <strong>the</strong> purpose <strong>of</strong> <strong>the</strong> pushover analysis is to<br />

evaluate <strong>the</strong> expected performance <strong>of</strong> a structural system by estimating its strength<br />

<strong>and</strong> deformation dem<strong>and</strong>s in design earthquakes by means <strong>of</strong> a static inelastic<br />

analysis, <strong>and</strong> comparing <strong>the</strong>se dem<strong>and</strong>s to available capacities at <strong>the</strong> performance<br />

levels <strong>of</strong> interest (Krawinkler <strong>and</strong> Seneviratna, 1998). By means <strong>of</strong> <strong>the</strong> numerical<br />

model above described, which implements <strong>the</strong> non-linear <strong>behaviour</strong> <strong>of</strong> <strong>the</strong><br />

structural members <strong>of</strong> <strong>the</strong> prototype structure, <strong>the</strong> NSP analysis based on <strong>the</strong><br />

Capacity Spectrum Method (CSM) <strong>and</strong> on <strong>the</strong> Performance Point Method<br />

proposed in <strong>the</strong> Eurocode 8 (2002) <strong>and</strong> FEMA-273 (1997) were performed. As<br />

explained in Chapter 2, <strong>the</strong> pushover analysis based on <strong>the</strong> CSM obtains <strong>the</strong><br />

performance point in <strong>the</strong> ADRS space (st<strong>and</strong>ard pseudo-acceleration Sa vs.<br />

deformation spectrum Sd). Differently from this, <strong>the</strong> response curve based on <strong>the</strong><br />

EC8 <strong>and</strong> FEMA assumptions is determined by nonlinear static analysis <strong>of</strong> <strong>the</strong><br />

structure subjected to lateral forces with invariant distribution over <strong>the</strong> height but<br />

gradually increasing values until a target value <strong>of</strong> ro<strong>of</strong> displacement is reached<br />

(Target Displacement). The floor displacements, storey drifts, joint rotations, plastic<br />

hinge rotations, etc., computed at <strong>the</strong> target displacement represent <strong>the</strong><br />

earthquake induced dem<strong>and</strong>s on <strong>the</strong> structure. Three distributions <strong>of</strong> lateral forces<br />

are specified in FEMA-273 (1997):<br />

(a) uniform distribution: s *<br />

j = mj (where j = 1, 2, …N is <strong>the</strong> floor number);<br />

(b) equivalent lateral force (ELF) distribution: s *<br />

j = mjh k<br />

j, where hj is <strong>the</strong> height <strong>of</strong><br />

<strong>the</strong> j-th floor above <strong>the</strong> base, <strong>and</strong> <strong>the</strong> exponent k varying linearly from <strong>the</strong> value<br />

1 for fundament period T1 < 0.5 sec <strong>and</strong> <strong>the</strong> value 2 for T1 > 2.5 sec;<br />

(c) SRSS distribution: s * is defined by <strong>the</strong> lateral forces back-calculated from <strong>the</strong><br />

storey shears determined by response spectrum analysis <strong>of</strong> <strong>the</strong> structure,<br />

assumed to be linearly elastic. This last distribution is not present in <strong>the</strong><br />

Eurocode 8 (2002) recommendations.<br />

The lateral force pr<strong>of</strong>iles in static pushover analyses influence <strong>the</strong> structural<br />

response. The first distribution represents <strong>the</strong> lateral forces that are proportional to<br />

<strong>the</strong> vertical distribution <strong>of</strong> <strong>the</strong> mass at various levels. The use <strong>of</strong> <strong>the</strong> uniform load<br />

shape may be justified in <strong>the</strong> light <strong>of</strong> a possible s<strong>of</strong>t storey mechanism <strong>of</strong> irregular<br />

buildings. If this mechanism occurs, <strong>the</strong> response will be controlled by a large drift<br />

in <strong>the</strong> first storey. Therefore, this load distribution may give better predictions <strong>of</strong> <strong>the</strong><br />

overall response. On <strong>the</strong> o<strong>the</strong>r h<strong>and</strong>, <strong>the</strong> code lateral load shape represents <strong>the</strong><br />

forces obtained from <strong>the</strong> predominant mode <strong>of</strong> vibration. The inverted triangular<br />

(code) <strong>and</strong> <strong>the</strong> rectangular (uniform) load shapes also represent <strong>the</strong> extreme cases<br />

151

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