ÍTEM 7A. INFORMACIÓN CUANTITATIVA Y CUALITATIVA SOBRE RIESGOS DE MERCADO
NOTA 18 – INFORMACIÓN POR SEGMENTOS Y RELACIONADA:
A second study was conducted to determine whether the wind-on-ice limit state is likely to control for LTS structures.
The loads on a horizontal circular tube were considered. The combined loading for maximum wind and dead load was compared to the combined loading for wind on ice, ice weight, and load. The maximum ice thickness and wind speed were selected from ASCE/SEI 7-10. The minimum wind speed was selected from ASCE/SEI 7-10, Figure 3.8-1. By using these extreme values, it was envisioned that the wind-on-ice limit state will control only in extremely rare circumstances.
A spreadsheet was used to compute the distributed load on the horizontal member (see Figure 4-9). The loads acting about different axes (dead load and ice weight acting verti-cally versus wind loads acting horizontally) were combined using vector addition (the square root of the sum of the squares). Note that the level arms and so forth are the same for both load effects so that nominal loading can be consid-ered directly (e.g., a cantilever traffic signal pole).
A parametric study was conducted varying the diameter from 12 in. to 16 in., the thickness from 0.25 in. to 0.50 in., while hold-ing the steel density at 0.490 kcf and the ice density at 0.058 kcf.
With the wind and ice loadings selected to make the wind-on-ice limit state as large as possible, the load for that limit state was varied from 91% to 97.5% of the loading from the extreme wind case. This ratio does not prohibit the wind-on-ice case from controlling (see Table 4-5).
Next, the wind-on-ice speed was increased to determine the speed necessary for the wind-on-ice limit state to control with 1.5 in. of ice. The results of this analysis are presented in Table 4-6.
In order to get the load effect from the wind-on-ice limit state equal to the extreme wind limit state, the speed had to be increased to at least 95 mph, which is more than a 50%
increase from the maximum value from ASCE/SEI coincident wind speeds.
Next, using the maximum (anywhere in the United States) wind-on-ice speed per ASCE/SEI, the ice thickness was increased to determine the thickness required for the wind-on-ice limit state to control. The results of this analysis are presented in Table 4-7.
Finally, two examples were computed; first, a design wind of 110 mph was compared to the load effect of that with an ice load of 1.5 in. The coincident wind to equal to the wind-only load effect was 95 mph to 97.5 mph, which is much larger than the fastest coincident wind in the United States (60 mph).
The second example compares a design wind of 110 mph with the load effect of the maximum coincident wind in the United States (60 mph). To create the same load effect, the ice thickness would be greater than 3 in. (see Table 4-8).
This simple study appears to validate the much more com-plex statistically based analysis.
Conclusion
Two independent analyses indicate that the wind-on-ice load combination may be eliminated from the typical limit-state analysis because it will not control. This is not to sug-gest that wind on icing will not occur and that the LRFD-LTS specifications should ignore or neglect it. Rather, it consid-ers it and does not require the computation because of the research presented herein.
Table 4-2. Possible combination of uniform radial ice thickness and concurrent 3-s gust speeds.
Ice Load Zones
-Table 4-1. 3-s gust speed concurrent with ice load.
Gust speed zones V 50(mph) Cov (mph)
Zone 1 30 0.15 4.5
Figure 4-1.
Figure 4-1. Values of Values of the interactionthe interaction equation at the critical section as a equation at the critical section as a function of wind speed on ice—arm.
function of wind speed on ice—arm.
0.0
Combinatons on arms on arm
1
Figure 4-2. Values of Values of the interactionthe interaction equation at the critical section as a equation at the critical section as a function of wind speed on ice—pole.
function of wind speed on ice—pole.
0.0
Combinatons on poles on pole
1
Figure 4-3. Values of Values of the interactionthe interaction equation at the critical section as a equation at the critical section as a function of ice thickness—arm.
Figure 4-4. Values of Values of the interactionthe interaction equation at the critical section as a equation at the critical section as a function of ice thickness—pole.
Combinatons on poles on pole
80
Figure 4-5. Values of Values of the interactionthe interaction equation at the critical section as a equation at the critical section as a function of wind speed in
function of wind speed in combinatiocombinationn of extreme wind and dead load—arm.
of extreme wind and dead load—arm.
0.0
Figure 4-6. Values of Values of the interactionthe interaction equation at the critical section as a equation at the critical section as a function of wind speed in
function of wind speed in combinaticombinationon of extreme wind and dead load—pole.
of extreme wind and dead load—pole.
0.0
T
Table 4-3. able 4-3. Values of response at the critical section on an arm calculated usingValues of response at the critical section on an arm calculated using interaction equation.
Figure 4-7. Values of Values of the interactionthe interaction equation at the critical section due equation at the critical section due to combination of extreme wind and to combination of extreme wind and dead load versus combination of ice dead load versus combination of ice load, wind on ice, and dead load—arm.
load, wind on ice, and dead load—arm.
0.0
Figure 4-8. Values of Values of the interactionthe interaction equation at the critical section due to equation at the critical section due to combination of extreme wind and dead combination of extreme wind and dead load versus combination of ice load, load versus combination of ice load, wind on ice, and dead load—pole.
wind on ice, and dead load—pole.
0.0
T
Table 4-4. able 4-4. Values of response at the critical section on a pole calculated usingValues of response at the critical section on a pole calculated using interaction equation.
interaction equation.
DL DL + + WLWL DL + WL + IL DL + WL + IL
100
100 mph mph 105 105 mph mph 110 110 mph mph 115 115 mph mph 120 120 mph mph 130 130 mph mph 140 140 mph mph 150 150 mph mph 160 160 mphmph
0.26 0.28 0.31 0.34 0.38 0
0.26 0.28 0.31 0.34 0.38 0.44 .44 0.53 0.53 0.63 0.63 0.750.75
Ice Wind
Ice Wind
0.25”
0.25”
30 mph
30 mph 0.21 0.21 0.21 0.21 0.21 0.21 0.21 0.21 0.21 0.21 0.21 0.21 0.21 0.21 0.21 0.21 0.210.21 40 mph
40 mph 0.21 0.21 0.21 0.21 0.21 0.21 0.21 0.21 0.21 0.21 0.21 0.21 0.21 0.21 0.21 0.21 0.210.21 50 mph
50 mph 0.22 0.22 0.22 0.22 0.22 0.22 0.22 0.22 0.22 0.22 0.22 0.22 0.22 0.22 0.22 0.22 0.220.22 60 mph
60 mph 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.230.23 70 mph
70 mph 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.250.25 80 mph
80 mph 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.270.27
0.50”
0.50”
30 mph
30 mph 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.230.23 40 mph
40 mph 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.24 0.240.24 50 mph
50 mph 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.250.25 60 mph
60 mph 0.26 0.26 0.26 0.26 0.26 0.26 0.26 0.26 0.26 0.26 0.26 0.26 0.26 0.26 0.26 0.26 0.260.26
0.75”
0.75”
30 mph
30 mph 0.26 0.26 0.26 0.26 0.26 0.26 0.26 0.26 0.26 0.26 0.26 0.26 0.26 0.26 0.26 0.26 0.260.26 40 mph
40 mph 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.270.27 50 mph
50 mph 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.270.27
1.00”
1.00”
30 mph
30 mph 0.29 0.29 0.29 0.29 0.29 0.29 0.29 0.29 0.29 0.29 0.29 0.29 0.29 0.29 0.29 0.29 0.290.29 40 mph
40 mph 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.300.30 50 mph
50 mph 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.300.30 60 mph
60 mph 0.31 0.31 0.31 0.31 0.31 0.31 0.31 0.31 0.31 0.31 0.31 0.31 0.31 0.31 0.31 0.31 0.310.31 1.25”
1.25” 30 mph30 mph 0.32 0.32 0.32 0.32 0.32 0.32 0.32 0.32 0.32 0.32 0.32 0.32 0.32 0.32 0.32 0.32 0.320.32 60 mph
60 mph 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.340.34 1.50”
1.50” 40 40 mphmph 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.350.35
(a) (a)
(
(bb)) ((cc))
Figure 4-9.
Figure 4-9. Mast arm loads Mast arm loads with ice and wwith ice and wind.ind.
Table 4-7. Example 1.
Design wind load 110 mph
C D 0.55
Max ice load on ASCE map 1.5 in Coincident wind for equivalent load effect 95 mph to
97.5 mph
Table 4-8. Example 2.
Design wind load 110 mph
C D 0.55
Max coincident wind 60 mph
Ice thickness for equivalent load effect 3.2 in. to 3.4 in.