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

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5. SEISMIC BEHAVIOUR OF RC COLUMNS EMBEDDING STEEL PROFILES<br />

206<br />

M = V ⋅ d<br />

( 5.43 )<br />

Rd , j, b j, b s<br />

It is assumed that bond failure occurs in <strong>the</strong> outer elements when <strong>the</strong> sum <strong>of</strong> <strong>the</strong><br />

forces is equal to <strong>the</strong> bond strength <strong>of</strong> a set <strong>of</strong> main reinforcing bars.<br />

Tcb + Ttb = Tbf<br />

( 5.44 )<br />

The bond failure strength should be calculated as follows:<br />

T = f ⋅φ ⋅ d<br />

( 5.45 )<br />

bf bd b s<br />

The design value <strong>of</strong> <strong>the</strong> ultimate bond stress fbd for ribbed bars may be taken as:<br />

where:<br />

η1<br />

2<br />

2/ 3<br />

0.7 ⋅0.3 ⋅ fck<br />

fbd = 2.25⋅η1 ⋅η2 ⋅ fctd<br />

= 2.25⋅η1 ⋅η2 ⋅ ( 5.46 )<br />

γ<br />

is a coefficient related to <strong>the</strong> quality <strong>of</strong> <strong>the</strong> bond condition <strong>and</strong> <strong>the</strong><br />

position <strong>of</strong> <strong>the</strong> bar during concreting:<br />

1,0 when good conditions are obtained;<br />

0,7 for all o<strong>the</strong>r cases <strong>and</strong> for bars in structural elements built<br />

with slip-forms, unless it can be shown that good bond<br />

conditions exist;<br />

is a coefficient related to <strong>the</strong> bar diameter φ equal to:<br />

1.0 for φ 32 mm<br />

(132 - φ)/100 for φ > 32 mm<br />

Where not o<strong>the</strong>rwise indicated in Eurocode 8, for frame systems <strong>the</strong> beam-to-<br />

column joints are required to have an increased moment resistance Mjoint,Rd in order<br />

to enhance <strong>the</strong> ductile capacity <strong>of</strong> <strong>the</strong> columns avoiding, in this way, <strong>the</strong> local<br />

formation <strong>of</strong> plastic hinges. Provided that, at <strong>the</strong> design stage, <strong>the</strong> plastic hinge<br />

formation in <strong>the</strong> beams is envisaged, it is necessary in any case to take into<br />

account <strong>the</strong> increase in <strong>the</strong> beam moment values in order to derive <strong>the</strong> design joint<br />

forces. Focusing <strong>the</strong> attention on <strong>the</strong> <strong>behaviour</strong> <strong>of</strong> an internal beam-to-column joint<br />

belonging to a frame free to deform in plane <strong>and</strong> subjected both to gravitational<br />

c

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