r - The Hong Kong Polytechnic University

ξ
( μ − ) 3
eq −ξ0 = C + D 1
4.0
≤ 6. 5
T
T
T
T
eq
y
eq
y
( μ −1) 2 + F( μ 1) 3
−1 = E
−
( μ )
−1 = G + H −1
≤ μ (12b)
μ < 4.0
(13a)
4.0
≤ μ ≤ 6.5
(13b)
Then the displacement capacity equations during post-yield limit should be summarized as follow:
lb
Δ LSi = 5.0efhε
y μLSiT
( Ty,
μ)
(14)
hb
And also the reduction factor to the displacement demand spectrum is substituted in Equation (15).
NUMERICAL ANALYSIS
Yield limit state
η =
0.10
0.05 + ξ
( ) μ LSi
The deterministic analysis stage of DBELA can easily be carried out by simply comparing the capacity and
demand displacement spectra deduced from equations in the yield limit state. An example using DBELA is
provided herein to illustrate the workings of the deterministic method on a building class of beam-sway frames,
and then the accuracy of the assessment result would be checked.
The capacity displacement spectra can be generated from Equation 10, and the parameters are available in Table
1. Twenty artificially seismic waves, of which the acceleration and displacement response spectra are shown in
Figure 4, are selected. And we chose the average displacement spectra of the twenty waves as the demand
displacement curve.
Table 1 Parameter of the RC frames in yield limit state displacement for beam-sway frames
Parameter
Value
Beam length, l b
6.0m
Height of beam section, h b
0.5m
Storey height
3m
Steel yield strain, ε y
0.15%
Mass at top height
50tone
Mass at ordinary-storey 40tone
(15)
Acceleration (cm/s/s)
700
600
500
400
300
200
100
average acc. spectrum
target acc. spectrum
Ta=0.15s
Tb=0.50s
Tc=2.5s
PGA=0.25g
Displacement (cm)
30
25
20
15
10
5
average disp. spectrum
target disp. spectrum
Ta=0.15s
Tb=0.5s
Tc=2.5s
PGA=0.25g
0
0 1 2 3 4 5 6
Period (seconds)
0
0 1 2 3 4 5 6
Period (seconds)
Figure 4 Acceleration and displacement response spectra of 20 artificially waves used in the yield limit state
Comparison of the capacity and demand curves is carried out as shown in Figure 5. Demand curve exceeds the
capacity curve between the period 0.91s and 3.13s, which means that, RC frames with height between 9.1m and
31.3m according to Equation (9) have failed in the yield limit state.
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