Civil Engineering Reference
In-Depth Information
Inspection of Fig. 3.10 shows that derived equations have similar cumulative
probabilities, thus the probability of error for each equation was similar. Table 3.4
provides a range of desired percent errors and their associated probability for each
equation. There is approximately a 50% probability that the |
% error
| of deflec-
tion between all equations and FEM is less than or equal to 10
%
.
Furthermore,
the equations had better than 80% probability to yield a deflection that is within
25% of the value computed using FEM. Each equation has close to a 90% proba-
bility of output yielding less than 30
%
error. More importantly, there is close to a
99% certainty that each equation will produce an output that is less than or equal
to a 50% difference from FEM.
Table 3.4
Confidence in Derived Equations
Probability that error is less than or equal to indicated percentage
P[%error≤X]
Percent Error (%)
X=10% X=15% X=20% X=25% X=30% X=35% X=40% X=45% X=50%
Uniform
0.4576 0.6326 0.7584
0.8448
0.9022
0.9394
0.9630
0.9778 0.9868
Triangle Wind
0.4190 0.5929 0.7233
0.8164
0.8807
0.9238
0.9521
0.9704 0.9819
Hydrostatic
0.5223 0.6856 0.7962
0.8695
0.9172
0.9479
0.9674
0.9798 0.9875
Semi-Elliptical
0.4732 0.6231 0.7314
0.8092
0.8648
0.9044
0.9325
0.9525 0.9666
Uniform+Hydrost.
0.4852 0.6532 0.7711
0.8514
0.9048
0.9397
0.9622
0.9765 0.9855
Uniform +SE
0.4702 0.6282 0.7420
0.8225
0.8788
0.9177
0.9444
0.9626 0.9750
Wind+Hydrost.
0.4639 0.6334 0.7550
0.8393
0.8661
0.9337
0.9582
0.9739 0.9838
Wind + SE
0.4450 0.6028 0.7194
0.8037
0.8637
0.9061
0.9356
0.9561 0.9702
3.5 Effect of Input Parameters on Expression Accuracy
The Weibull statistical analysis gives a general estimate of the absolute error in
the derived equations. Therefore, the effect of various input parameters on the an-
ticipated |
% error
|
is investigated in Fig. 3.11, where |
% error
| for each equation is
plotted against the following parameters:
1.
The building aspect ratio (
H/L
)
2.
Ratio of column inertia to beam inertia (
I
c
/I
b
)
3.
Number of stories per frame (
s
)
4.
Number of bays per frame (
b
)
5.
Location of story from the top,
i
, normalized by number of stories
s
, (
i/s
)
6.
Aspect ratio of each rigidly framed cell (ratio of column length to beam length
(
L
c
/L
b
)
