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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 />

boundaries with springs at <strong>the</strong> four corners. These springs simulate <strong>the</strong> resistance<br />

<strong>of</strong> <strong>the</strong> elements surrounding <strong>the</strong> panel zone, in particular <strong>the</strong> bending resistance <strong>of</strong><br />

<strong>the</strong> column flanges.<br />

z eq<br />

d c<br />

Figure 4.12. Ma<strong>the</strong>matical<br />

model for <strong>the</strong> web panel in<br />

shear<br />

If we use <strong>the</strong> ma<strong>the</strong>matical model proposed by Krawinkler, it is possible to<br />

calculate <strong>the</strong> elastic stiffness <strong>of</strong> <strong>the</strong> web panel as follows:<br />

K = G ⋅( H − t ) ⋅ t<br />

( 4.13 )<br />

el el c cf cw<br />

where Gel is <strong>the</strong> elastic shear modulus; Hc is <strong>the</strong> column height; tcf <strong>and</strong> tcw are he<br />

thickness <strong>of</strong> <strong>the</strong> column flange <strong>and</strong> <strong>of</strong> <strong>the</strong> column web, respectively. This equation<br />

is valid until γ < γy: this value is achieved when <strong>the</strong> shear force at general yielding is<br />

equal to:<br />

∗<br />

y, cw<br />

f<br />

Vy = ( Hc − tcf ) ⋅tcw ⋅ ( 4.14 )<br />

3<br />

The f *<br />

y,cw is <strong>the</strong> yield strength <strong>of</strong> <strong>the</strong> column web calculated adopting <strong>the</strong> Henky-<br />

Von Mises yield reduction criterion, when <strong>the</strong> column axial force is not negligible.<br />

The strength <strong>of</strong> <strong>the</strong> column web can be computed by means <strong>of</strong> <strong>the</strong> following<br />

relationship:<br />

y, cw<br />

2<br />

∗<br />

σSd,<br />

col<br />

fy, cw = fy,<br />

cw ⋅ 1−<br />

( 4.15 )<br />

f<br />

K pl<br />

117

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