Dual Cable Support Structures for Wide Intersections Project #C9G79

5th Annual Structures Research Update
August 4, 2015
Dual Cable Support Structures for Wide Intersections
Project #C9G79
FDOT Project Manager Andre Pavlov, PE
Presented by
Hisham Sunna – Ayres Associates
Agenda
• Background
• Observations - Completed Parametric Studies
• ATLAS
– Single Span
• GTSTRUDL
– Single Span
–GTSTRUDL Box Span
• Recap of Observations and Initial Recommendations
• Ongoing Parametric Studies
• GTSTRUDL
– Hanging Box
• ATLAS
– Box (?)
Background
• Systems with the dual cable configuration have been used to limit
deflection and signal head rotation during high winds. However, these
systems are complex to analyze from a design perspective.
• The objective of the contract is to develop a simplified design
approach validated by a rigorous method. The Department has been
using Atlas, a program developed at the University of Florida.
Parametric Studies
• Design Basic Wind Speeds – 110, 130, and 150 MPH
• Wind Angle - 0° to 90° in 30° increments plus 45° angle.
• Wire to Wire Angle (skew) Box and Hanging Box
• Span Lengths – 100 to 240 ft. in 20 ft. increments.
• Number of Signals
…Parametric Studies
• Single Force Coefficient – vary drag coefficient (CD) 0.5 to 0.9
in 0.1 increments with uplift coefficient (CL) kept at 0. The
original ATLAS CD and CL values will also be used in ATLAS.
• Backplates – With/Without.
• Signal Head Material – Aluminum/Polycarbonate.
ATLAS Parametric Study Results
Single Span
Atlas – Solution is combination of two
problems
Figure 1 Pole-cable-light System (Source: ATLAS Manual)
Problem 1 – Cable only
Figure 2 Cable-only Solution (Source: ATLAS Manual)
Problem 2 – Pole Only
Figure 3 Pole-only Solution (Source: ATLAS Manual)
Figure 4 Unstable System (Source: ATLAS Manual)
Single Force Coefficient Study
Legend
Actual Closest Answer (conservative)
Actual Closest Answer (unconservative)
Projected Closest Answer (conservative)
Projected Closest Answer (unconservative)
Cable Tension => SINGLE FORCE COEFFICIENT STUDY
Span
100ft
120ft
140ft
160ft
180ft
200ft
220ft
240ft
5 Signals
Wind Speed
7 Signals
9 Signals
11 Signals
Default
0.5
0.6
0.7
0.8
0.9
0.7 / 0.4
Default
0.5
0.6
0.7
0.8
0.9
0.7 / 0.4
Default
0.5
0.6
0.7
0.8
0.9
0.7 / 0.4
Default
0.5
110mph
5.5
5.3
5.8
6.4
6.9
7.3
7.3
6.5
6.0
6.7
7.3
7.9
8.4
8.5
7.3
6.4
7.2
7.9
8.5
9.1
9.1
130mph
5.5
6.6
7.3
7.9
8.5
9.1
7.9
6.4
7.5
8.3
9.1
9.8
10.5
10.6
8.9
8.1
9.0
9.8
10.6
11.4
11.4
150mph
7.5
8.0
8.8
9.5
10.2
10.9
8.9
7.0
9.1
10.1
11.0
11.9
12.7
12.8
9.9
9.8
10.8
11.9
12.8
13.8
13.8
110mph
5.8
5.6
6.2
6.7
7.3
7.7
7.8
6.8
6.4
7.1
7.8
8.4
9.0
9.0
7.8
7.0
7.8
8.5
9.2
9.9
130mph
7.2
7.0
7.7
8.4
8.9
9.5
6.5
10.0
8.0
8.9
9.7
10.4
11.2
11.3
7.5
8.8
9.7
10.7
11.5
12.4
150mph
9.9
8.5
9.3
10.0
10.8
11.5
9.6
11.8
9.7
10.7
11.7
12.6
13.5
13.7
12.3
10.6
11.8
12.9
13.9
15.0
110mph
6.0
5.8
6.4
7.0
7.5
8.0
8.1
7.0
6.6
7.4
8.0
8.7
9.3
9.4
8.6
7.3
8.1
8.9
9.7
130mph
7.8
7.3
8.0
8.7
9.3
10.0
8.9
8.6
8.4
9.2
10.1
10.9
11.7
11.8
9.2
9.2
10.2
11.2
150mph
7.8
8.8
9.7
10.5
11.3
12.0
9.3
9.1
10.1
11.2
12.2
13.2
14.1
14.4
8.3
11.2
12.4
110mph
6.2
6.0
6.6
7.2
7.7
8.2
8.5
7.2
6.8
7.6
8.3
8.9
9.6
9.7
8.7
7.5
130mph
7.3
7.5
8.3
8.9
9.6
10.2
10.5
8.5
8.6
9.5
10.4
11.2
12.0
12.3
8.4
9.5
150mph
10.2
9.1
10.0
10.8
11.6
12.4
12.8
9.2
10.5
11.6
12.6
13.6
14.5
14.9
10.5
11.6
110mph
6.4
6.1
6.7
7.3
7.9
8.4
8.5
7.8
7.0
7.7
8.5
9.1
9.8
10.0
8.9
130mph
7.5
7.7
8.5
9.2
9.8
10.5
10.1
10.1
8.8
9.8
10.6
11.5
12.3
7.7
150mph
10.3
9.4
10.2
11.1
11.9
12.7
10.8
11.0
10.8
11.9
12.9
13.9
14.8
110mph
6.6
6.2
6.9
7.4
8.0
8.5
8.7
8.0
7.1
7.9
8.6
9.3
130mph
8.4
7.9
8.6
9.3
10.0
10.7
8.9
9.4
9.0
10.0
10.8
150mph
8.4
9.6
10.5
11.3
12.1
12.9
12.6
10.2
11.0
12.1
110mph
6.7
6.3
7.0
7.6
8.1
8.6
8.8
8.1
7.2
130mph
8.5
8.1
8.8
9.5
10.2
10.8
11.2
9.6
150mph
10.4
9.8
10.7
11.5
12.3
13.1
11.4
110mph
7.1
6.4
7.1
7.6
8.2
8.7
8.8
130mph
8.6
8.2
8.9
9.6
10.3
11.0
150mph
10.8
10.0
10.9
11.7
12.5
13.3
0.6
9.9
8.4
7.3
8.2
12.5
8.1
9.2
10.3
15.0
10.7
11.2
12.4
10.4
10.5
8.9
7.8
12.1
13.0
13.2
8.9
13.6
14.7
15.7
16.0
9.1
8.4
9.2
10.0
10.7
10.9
9.7
8.1
10.6
11.6
12.5
13.4
13.7
9.0
10.3
12.9
14.1
15.2
16.3
15.5
11.4
12.5
7.7
8.6
9.4
10.2
11.0
11.2
9.9
11.4
9.8
10.9
11.9
12.8
13.8
14.1
14.6
8.9
11.9
13.2
14.4
15.6
16.7
9.9
10.2
9.0
7.8
8.7
9.6
10.4
11.7
12.5
12.9
11.4
10.0
11.1
12.1
13.2
14.2
15.1
12.8
11.8
12.2
13.5
8.0
8.7
9.4
10.1
10.3
9.2
8.0
9.2
10.1
11.0
11.8
12.7
8.9
11.0
8.8
11.2
12.3
13.4
14.4
15.3
15.9
8.3
7.3
8.1
8.8
9.5
10.2
10.4
10.6
9.7
9.3
10.3
11.1
12.0
12.8
13.1
11.2
11.4
12.5
13.6
14.6
15.5
0.7
13 Signals
0.8
0.9
0.7 / 0.4
Default
0.5
9.0
9.7
10.5
10.4
11.3
12.2
13.1
13.1
13.6
14.8
15.9
15.9
8.7
9.6
10.4
11.2
12.2
9.5
9.8
11.0
12.0
13.0
14.0
14.1
9.4
12.0
13.3
14.6
15.8
17.0
17.2
9.2
12.5
9.0
9.9
10.8
11.6
11.8
10.6
11.4
12.5
13.6
14.6
14.8
9.7
13.9
15.2
16.5
17.7
7.6
9.8
8.3
9.3
10.2
11.1
12.0
12.2
9.5
10.6
11.8
12.9
14.0
15.0
17.4
9.6
12.9
14.4
15.7
17.0
11.2
11.4
10.1
8.5
9.5
10.4
13.1
14.0
14.4
9.8
10.8
12.0
14.7
15.9
17.0
8.0
15.4
13.2
8.9
9.7
10.5
11.3
11.6
10.2
10.1
11.3
12.3
13.3
14.2
10.8
12.5
12.4
13.7
15.0
16.2
17.3
9.3
8.0
9.0
9.8
10.6
11.4
9.1
11.0
10.3
11.4
12.5
13.5
14.4
15.3
10.5
12.6
13.9
15.2
16.4
17.5
15 Signals
0.6
0.7
0.8
0.9
0.7 / 0.4
Default
8.1
9.1
10.0
10.8
11.7
11.7
10.2
11.4
12.5
13.6
14.6
14.7
13.9
15.2
16.5
17.7
17.9
8.5
9.5
10.5
11.4
12.3
12.4
11.2
10.8
12.1
13.3
14.4
15.5
15.7
10.5
13.2
14.7
16.2
17.5
18.8
19.1
10.3
10.9
8.8
9.9
10.9
11.8
11.9
12.2
15.4
10.1
11.2
12.5
13.8
15.0
15.2
18.3
18.7
10.3
13.7
15.3
16.8
17.3
11.3
12.2
12.5
11.0
9.0
10.1
11.1
13.2
14.3
15.4
15.8
10.4
11.5
12.9
14.7
16.1
17.4
18.7
19.3
16.8
14.1
8.6
9.6
10.6
11.5
12.4
12.7
11.2
10.0
11.0
12.3
13.4
11.6
15.6
16.1
9.2
11.3
13.5
15.0
16.4
17.7
19.0
11.8
10.3
8.7
9.7
10.7
11.6
12.5
8.4
10.0
11.2
12.4
13.6
14.7
11.4
15.5
13.7
15.2
16.6
18.0
0.5
17 Signals
0.6
0.7
0.8
0.9
0.7 / 0.4
8.8
9.9
10.9
11.8
12.8
12.8
11.2
12.5
13.7
15.0
16.1
16.2
13.7
15.2
16.7
18.1
19.5
19.7
11.1
8.6
9.7
10.8
11.8
12.8
13.0
15.6
10.2
11.1
12.5
13.8
15.0
16.3
16.6
18.7
19.2
10.5
13.8
15.4
17.0
18.5
19.9
20.4
12.1
13.1
13.4
11.9
9.5
10.6
11.7
12.8
13.8
14.0
14.1
15.3
16.5
16.9
11.3
12.1
13.5
14.9
16.2
17.4
17.8
15.7
17.2
18.7
20.1
20.7
11.4
14.9
16.6
18.2
19.8
21.2
21.8
9.2
10.3
11.3
12.3
13.3
13.7
10.9
11.7
13.1
14.4
15.6
16.8
17.3
18.4
16.9
14.4
16.1
17.6
19.1
20.5
21.2
12.9
11.3
9.3
10.4
11.5
12.5
13.5
13.9
15.8
16.4
11.1
11.9
13.3
14.6
15.9
17.1
17.7
19.3
18.8
17.0
14.7
16.3
17.9
19.4
20.8
21.6
Default
0.5
0.6
0.7
0.8
0.9
0.7 / 0.4
Traffic Signals – 3 Aluminum Heads
Cable Tension vs. Number of Signals
[110 mph wind speed, Default coefficient values]
19.0
17.0
Cable Tension (k)
15.0
100' Span
120' Span
13.0
140' Span
160' Span
11.0
180' Span
200' Span
9.0
220' Span
240' Span
7.0
5.0
5
6
7
8
9
10
Number of Signals
11
12
13
14
15
Traffic Signals – 3 Aluminum Heads
Cable Tension vs. Number of Signals
[130 mph wind speed, Default coefficient values]
19.0
17.0
Cable Tension (k)
15.0
100' Span
120' Span
13.0
140' Span
160' Span
11.0
180' Span
200' Span
9.0
220' Span
240' Span
7.0
5.0
5
6
7
8
9
10
Number of Signals
11
12
13
14
15
Traffic Signals – 3 Aluminum Heads
Cable Tension vs. Number of Signals
[150 mph wind speed, Default coefficient values]
19.0
17.0
Cable Tension (k)
15.0
100' Span
120' Span
13.0
140' Span
160' Span
11.0
180' Span
200' Span
9.0
220' Span
240' Span
7.0
5.0
5
6
7
8
9
10
Number of Signals
11
12
13
14
15
Traffic Signals – 3 Aluminum Heads
Cable tension vs. span length
[110 mph wind speed, default coefficient values ]
18.0
16.0
Cable Tension (k)
14.0
5 signals
12.0
7 signals
9 signals
10.0
11 signals
13 signals
8.0
15 signals
6.0
4.0
100
120
140
160
180
Span Length (ft)
200
220
240
Traffic Signals – 3 Aluminum Heads
Cable tension vs. span length
[130 mph wind speed, default coefficient values ]
18.0
16.0
Cable Tension (k)
14.0
5 signals
12.0
7 signals
9 signals
10.0
11 signals
13 signals
8.0
15 signals
6.0
4.0
100
120
140
160
180
Span Length (ft)
200
220
240
Traffic Signals – 3 Aluminum Heads
Cable Tension vs. Span Length
[150 mph Wind Speed, Default Coefficient Values ]
18.0
16.0
Cable Tension (k)
14.0
5 signals
12.0
7 signals
9 signals
10.0
11 signals
13 signals
8.0
15 signals
6.0
4.0
100
120
140
160
180
Span Length (ft)
200
220
240
Traffic Signals – 3 Polycarbonate Heads
Cable Tension vs. Span Length
[110 mph Wind Speed, Default Coefficient Values ]
18.0
16.0
Cable Tension (k)
14.0
5 signals
12.0
7 signals
9 signals
10.0
11 signals
13 signals
8.0
15 signals
6.0
4.0
100
120
140
160
180
Span Length (ft)
200
220
240
Traffic Signals – 3 Polycarbonate Heads
Cable Tension vs. Span Length
[130 mph Wind Speed, Default Coefficient Values]
18.0
16.0
Cable Tension (k)
14.0
5 signals
12.0
7 signals
9 signals
10.0
11 signals
13 signals
8.0
15 signals
6.0
4.0
100
120
140
160
180
Span Length (ft)
200
220
240
Traffic Signals – 3 Polycarbonate Heads
Cable tension vs. span length
[150 mph wind speed, default coefficient values ]
18.0
16.0
Cable Tension (k)
14.0
5 signals
12.0
7 signals
9 signals
10.0
11 signals
13 signals
8.0
15 signals
6.0
4.0
100
120
140
160
180
Span Length (ft)
200
220
240
Traffic Signals – 5 Aluminum Heads
Cable Tension vs. Span Length
[110 mph Wind Speed, Default Coefficient Values ]
19.0
18.0
17.0
16.0
15.0
Cable Tension (k)
14.0
13.0
5 signals
12.0
7 signals
11.0
9 signals
10.0
11 signals
9.0
13 signals
8.0
7.0
6.0
5.0
4.0
100
120
140
160
180
Span Length (ft)
200
220
240
Traffic Signals – 5 Aluminum Heads
Cable Tension vs. Span Length
[130 mph Wind Speed, Default Coefficient Values ]
19.0
18.0
17.0
16.0
15.0
Cable Tension (k)
14.0
13.0
5 signals
12.0
7 signals
11.0
9 signals
10.0
11 signals
9.0
13 signals
8.0
7.0
6.0
5.0
4.0
100
120
140
160
180
Span Length (ft)
200
220
240
Traffic Signals – 5 Aluminum Heads
Cable Tension vs. Span Length
[150 mph Wind Speed, Default Coefficient Values ]
19.0
18.0
17.0
16.0
15.0
Cable Tension (k)
14.0
13.0
5 signals
12.0
7 signals
11.0
9 signals
10.0
11 signals
9.0
13 signals
8.0
7.0
6.0
5.0
4.0
100
120
140
160
180
Span Length (ft)
200
220
240
Traffic Signals – 5 Polycarbonate Heads
Cable Tension vs. Span Length
[110 mph Wind Speed, Default Coefficient Values ]
18.0
16.0
Cable Tension (k)
14.0
5 signals
12.0
7 signals
9 signals
10.0
11 signals
13 signals
8.0
6.0
4.0
100
120
140
160
180
Span Length (ft)
200
220
240
Traffic Signals – 5 Polycarbonate Heads
Cable Tension vs. Span Length
[130 mph Wind Speed, Default Coefficient Values]
18.0
16.0
Cable Tension (k)
14.0
5 signals
12.0
7 signals
9 signals
10.0
11 signals
13 signals
8.0
6.0
4.0
100
120
140
160
180
Span Length (ft)
200
220
240
Traffic Signals – 5 Polycarbonate Heads
Cable tension vs. span length
[150 mph wind speed, default coefficient values ]
18.0
16.0
Cable Tension (k)
14.0
5 signals
12.0
7 signals
9 signals
10.0
11 signals
13 signals
8.0
6.0
4.0
100
120
140
160
180
Span Length (ft)
200
220
240
Traffic Signals – 3 Aluminum Heads with BP
Number of Signals vs. Cable Tension (110 mph, Default Coefficients, 5" BP)
15.0
14.0
13.0
12.0
Cable Tension (k)
100' Span, 110 mph
11.0
120' Span, 110 mph
10.0
140' Span, 110 mph
9.0
160' Span, 110 mph
180' Span, 110 mph
8.0
200' Span, 110 mph
7.0
220' Span, 110 mph
240' Span, 110 mph
6.0
5.0
4.0
5
7
9
11
13
15
Number of Signals
17
19
21
23
Traffic Signals – 3 Aluminum Heads w/o BP
Number of Signals vs. Cable Tension (110 mph, Default Coefficients, No BP)
15.0
14.0
13.0
12.0
Cable Tension (k)
100' Span, 110 mph
11.0
120' Span, 110 mph
10.0
140' Span, 110 mph
9.0
160' Span, 110 mph
180' Span, 110 mph
8.0
200' Span, 110 mph
7.0
220' Span, 110 mph
240' Span, 110 mph
6.0
5.0
4.0
5
7
9
11
13
15
Number of Signals
17
19
21
23
Traffic Signals – 3 Aluminum Heads with BP
Number of Signals vs. Cable Tension (130 mph, Default Coefficients, 5" BP)
15.0
14.0
13.0
12.0
Cable Tension (k)
100' Span, 130 mph
11.0
120' Span, 130 mph
10.0
140' Span, 130 mph
9.0
160' Span, 130 mph
180' Span, 130 mph
8.0
200' Span, 130 mph
7.0
220' Span, 130 mph
240' Span, 130 mph
6.0
5.0
4.0
5
7
9
11
13
15
Number of Signals
17
19
21
23
Traffic Signals – 3 Aluminum Heads w/o BP
Number of Signals vs. Cable Tension (130 mph, Default Coefficients, No BP)
15.0
14.0
13.0
12.0
Cable Tension (k)
100' Span, 130 mph
11.0
120' Span, 130 mph
10.0
140' Span, 130 mph
9.0
160' Span, 130 mph
180' Span, 130 mph
8.0
200' Span, 130 mph
7.0
220' Span, 130 mph
240' Span, 130 mph
6.0
5.0
4.0
5
7
9
11
13
15
Number of Signals
17
19
21
23
Traffic Signals – 3 Aluminum Heads with BP
Number of Signals vs. Cable Tension (150 mph, Default Coefficients, 5" BP)
18.0
17.0
16.0
15.0
Cable Tension (k)
14.0
100' Span, 150 mph
13.0
120' Span, 150 mph
12.0
140' Span, 150 mph
11.0
160' Span, 150 mph
10.0
180' Span, 150 mph
9.0
200' Span, 150 mph
8.0
220' Span, 150 mph
7.0
240' Span, 150 mph
6.0
5.0
4.0
5
7
9
11
13
15
Number of Signals
17
19
21
23
Traffic Signals – 3 Aluminum Heads w/o BP
Number of Signals vs. Cable Tension (150 mph, Default Coefficients, No BP)
15.0
14.0
13.0
12.0
Cable Tension (k)
100' Span, 150 mph
11.0
120' Span, 150 mph
10.0
140' Span, 150 mph
9.0
160' Span, 150 mph
180' Span, 150 mph
8.0
200' Span, 150 mph
7.0
220' Span, 150 mph
240' Span, 150 mph
6.0
5.0
4.0
5
7
9
11
13
15
Number of Signals
17
19
21
23
GTStrudl Parametric Study Results
Single Span
Traffic Signals – 3 Aluminum Heads
Cable Tension vs. Number of Signals
[110 mph Wind Speed]
19.0
17.0
Cable Tension (k)
15.0
100' Span
120' Span
13.0
140' Span
160' Span
11.0
180' Span
200' Span
9.0
220' Span
240' Span
7.0
5.0
5
7
9
11
# Signals
13
15
Traffic Signals – 3 Aluminum Heads
Cable Tension vs. Number of Signals
[130 mph Wind Speed]
19.0
17.0
15.0
Cable Tension (k)
100' Span
120' Span
13.0
140' Span
160' Span
11.0
180' Span
200' Span
9.0
220' Span
240' Span
7.0
5.0
5
7
9
11
# Signals
13
15
Traffic Signals – 3 Aluminum Heads
Cable Tension vs. Number of Signals
[150 mph Wind Speed]
19.0
17.0
Cable Tension (k)
15.0
100' Span
120' Span
13.0
140' Span
160' Span
11.0
180' Span
200' Span
9.0
220' Span
240' Span
7.0
5.0
5
7
9
11
# Signals
13
15
Traffic Signals – 3 Aluminum Heads
Cable Tension vs. Span Length
[110 mph]
5 signals R² = 0.99
7 signals
9 signals R² = 0.96
19.0
11 signals
17.0
13 signals
15 signals
15.0
Cable Tension (k)
R² = 0.98
13.0
11.0
9.0
7.0
5.0
100
120
140
160
180
Span Length (ft)
200
220
240
R² = 0.97
R² = 0.98
R² = 1.00
Traffic Signals – 3 Aluminum Heads
Cable Tension vs. Span Length
[130 mph]
19.0
5 signals
R² = 0.99
7 signals
R² = 0.98
9 signals
R² = 0.96
11 signals
17.0
13 signals
15 signals
Cable Tension (k)
15.0
13.0
11.0
9.0
7.0
5.0
100
120
140
160
180
Span Length (ft)
200
220
240
R² = 0.97
R² = 0.98
R² = 0.99
Traffic Signals – 3 Aluminum Heads
Cable Tension vs. Span Length
[150 mph]
5 signals
R² = 0.94
7 signals
R² = 0.98
9 signals
19.0
11 signals
17.0
R² = 0.96
R² = 0.96
13 signals
R² = 0.97
15 signals
Cable Tension (k)
15.0
13.0
11.0
9.0
7.0
5.0
100
120
140
160
180
Span Length (ft)
200
220
240
R² = 0.99
Traffic Signals – 3 Polycarbonate Heads
Cable Tension vs. Span Length
[110 mph]
5 signals
R² = 0.99
7 signals
R² = 0.98
9 signals
19.0
11 signals
17.0
13 signals
15 signals
Cable Tension (k)
15.0
13.0
11.0
9.0
7.0
5.0
100
120
140
160
180
Span Length (ft)
200
220
240
R² = 0.96
R² = 0.97
R² = 0.98
R² = 0.99
Traffic Signals – 3 Aluminum Heads
Cable Tension vs. Number of Signals
[110 mph wind speed, Default coefficient values]
19.0
17.0
Cable Tension (k)
15.0
100' Span
120' Span
13.0
140' Span
160' Span
11.0
180' Span
200' Span
9.0
220' Span
240' Span
7.0
5.0
5
6
7
8
9
10
Number of Signals
11
12
13
14
15
Traffic Signals – 3 Polycarbonate Heads
Cable Tension vs. Span Length
[130 mph]
19.0
17.0
Cable Tension (k)
15.0
5 signals
R² = 0.99
7 signals
R² = 0.98
9 signals
R² = 0.96
11 signals
R² = 0.97
13 signals
R² = 0.97
15 signals
13.0
11.0
9.0
7.0
5.0
100
120
140
160
180
Span Length (ft)
200
220
240
R² = 0.99
Traffic Signals – 3 Polycarbonate Heads
5 signals
Cable Tension vs. Span Length
[150 mph]
7 signals
9 signals
19.0
11 signals
R² = 0.94
R² = 0.98
R² = 0.96
R² = 0.96
13 signals
17.0
R² = 0.97
15 signals
R² = 0.99
Cable Tension (k)
15.0
13.0
11.0
9.0
7.0
5.0
100
120
140
160
180
Span Length (ft)
200
220
240
Traffic Signals – 3 Aluminum Heads w/o BP
5 signals
Cable Tension vs. Span Length
[110 mph]
7 signals
9 signals
12.0
11.0
Cable Tension (k)
10.0
8.0
7.0
6.0
5.0
4.0
100
120
140
160
180
Span Length (ft)
200
220
240
R² = 0.99
R² = 0.98
11 signals
R² = 0.98
13 signals
R² = 0.98
15 signals
9.0
R² = 1.00
R² = 1.00
Traffic Signals – 3 Aluminum Heads w/o BP
5 signals
Cable Tension vs. Span Length
[130 mph]
7 signals
9 signals
12.0
11 signals
11.0
R² = 1.00
R² = 0.99
R² = 0.98
R² = 0.98
13 signals
R² = 0.98
10.0
15 signals
Cable Tension (k)
R² = 1.00
9.0
8.0
7.0
6.0
5.0
4.0
100
120
140
160
180
Span Length (ft)
200
220
240
Traffic Signals – 3 Aluminum Heads w/o BP
Cable Tension vs. Span Length
[150 mph]
5 signals
R² = 1.00
7 signals
R² = 0.99
9 signals
12.0
11 signals
11.0
13 signals
R² = 0.98
R² = 0.98
15 signals
10.0
Cable Tension (k)
R² = 0.98
R² = 1.00
9.0
8.0
7.0
6.0
5.0
4.0
100
120
140
160
180
Span Length (ft)
200
220
240
GTStrudl Parametric Study Results
Box Span
Traffic Signals – 3 Aluminum Heads
Concrete Pole CSR Ratio (45 degree Wind Angle / 90 degree Wind Angle)
vs. Number of Signals
[110 mph Wind Speed]
1.26
1.24
Pole CSR Ratio
1.22
100' Span
120' Span
1.20
140' Span
160' Span
1.18
180' Span
200' Span
1.16
220' Span
240' Span
1.14
1.12
3
5
7
9
# Signals
11
13
15
Traffic Signals – 3 Aluminum Heads
Concrete Pole CSR Ratio (45 degree Wind Angle / 90 degree Wind Angle)
vs. Number of Signals
[130 mph Wind Speed]
1.36
1.34
Pole CSR Ratio
1.32
100' Span
1.30
120' Span
1.28
140' Span
1.26
160' Span
180' Span
1.24
200' Span
220' Span
1.22
240' Span
1.20
1.18
3
5
7
9
# Signals
11
13
15
Traffic Signals – 3 Aluminum Heads
Concrete Pole CSR Ratio (45 degree Wind Angle / 90 degree Wind Angle)
vs. Number of Signals
[150 mph Wind Speed]
1.50
1.45
Pole CSR Ratio
100' Span
120' Span
1.40
140' Span
160' Span
1.35
180' Span
200' Span
220' Span
1.30
240' Span
1.25
3
5
7
9
# Signals
11
13
15
Traffic Signals – 3 Aluminum Heads
Concrete Pole CSR Ratio (45 degree Wind Angle / 90 degree Wind Angle)
vs. Span Length
[110 mph]
1.50
1.45
Pole CSR Ratio
1.40
1.35
1.30
3 signals
5 signals
7 signals
9 signals
11 signals
13 signals
15 signals
Linear (3 signals)
Linear (5 signals)
Linear (7 signals)
Linear (9 signals)
Linear (11 signals)
1.25
1.20
1.15
1.10
100
120
140
160
180
Span Length (ft)
200
220
240
R² = 0.99
R² = 0.99
R² = 0.99
R² = 1.00
R² = 1.00
R² = 1.00
R² = 1.00
Traffic Signals – 3 Aluminum Heads
Concrete Pole CSR Ratio (45 degree Wind Angle / 90 degree Wind Angle)
vs. Span Length
[130 mph]
3 signals
5 signals
7 signals
9 signals
11 signals
13 signals
15 signals
Linear (3 signals)
Linear (5 signals)
Linear (7 signals)
Linear (9 signals)
Linear (11 signals)
Linear (13 signals)
1.50
1.45
Pole CSR Ratio
1.40
1.35
1.30
1.25
1.20
1.15
1.10
100
120
140
160
180
Span Length (ft)
200
220
240
R² = 0.99
R² = 1.00
R² = 1.00
R² = 1.00
R² = 1.00
R² = 1.00
R² = 1.00
Traffic Signals – 3 Aluminum Heads
Concrete Pole CSR Ratio (45 degree Wind Angle / 90 degree Wind Angle)
vs. Span Length
[150 mph]
1.65
3 signals
5 signals
7 signals
9 signals
11 signals
13 signals
15 signals
Linear (3 signals)
Linear (5 signals)
Linear (7 signals)
Linear (9 signals)
Linear (11 signals)
1.60
1.55
Pole CSR Ratio
R² = 0.99
1.50
1.45
1.40
1.35
1.30
1.25
100
120
140
160
180
Span Length (ft)
200
220
240
R² = 1.00
R² = 1.00
R² = 0.99
R² = 0.99
R² = 0.99
R² = 0.99
Recap
Single Span Wire Rigorous Analysis
• Traffic Signal Size (3 and 5 head) and Head Material (Aluminum and Polycarbonate) were varied.
A traffic signal without a backplate was also analyzed. Cable Tension was plotted with varying
span length and number of signals.
• GTStrudl Results
• All plots showed similar smooth curves that were mostly linear in nature with a slight tapering of
cable tension as the number of signals or span length were increased.
• Linear trend lines showed R2 values ranging from 0.94 to 1.00 with the majority of the numbers
0.96 and above. This coefficient of determination range indicates a well fit trend line to the data.
• Comparing GTStrudl results between head material shows very little differences in cable tension.
The maximum tension difference was 0.25 kips for the 3 head traffic signal, while the maximum
tension difference was 0.41 kips for the 5 head traffic signal. Both values occurred with the
largest wind speed of 150 mph.
• Comparing GTStrudl results between 3 headed aluminum traffic signals with and without
backplates shows smooth curves that are more logarithmic than linear. Changes in cable tensions
gradually increase as the number of signals and/or the span length increases.
Recap
GTStrudl vs. ATLAS Comparison
1.
Comparing the similar plots of ATLAS to the GTStrudl plots show the greater consistency for
the GTStrudl analyses yet similar curve shapes that were predominately linear with a slight tapering
of cable tension as the number of signals or span length were increased.
2.
Comparing all runs with various span lengths, wind speed, and force coefficients was
difficult due to ATLAS’ propensity to limit the wind speed to a value well below the input speed. By
comparing the runs where the wind speeds were identical between ATLAS and GTStrudl, some
trends were found. a couple
a.
The ATLAS results with the default force coefficients typically provided a lower bound to
the GTStrudl results while the ATLAS results with the constant 0.7/0.4 force coefficients typically
provided the upper bound. This trend was seen in all traffic signal material types and sizes.
b.
Minimum and Maximum % Differences between GTStrudl and ATLAS results for default
force coefficients and 0.7/0.4 force coefficients can be seen below. Note that positive values
indicate GTStrudl results greater than ATLAS while negative values indicate GTStrudl results less
than ATLAS.
Traffic Signal Type
(# Heads, Head Material,
backplate)
3 head, aluminum, backplate
3 head, polycarbonate, backplate
5 head, aluminum, backplate
5 head, polycarbonate, backplate
3 head, aluminum, no backplate
Default
Min. Δ
-3.5%
-2.3%
3.9%
5.6%
-16.1%
Max. Δ
15.3%
14.7%
26.5%
29.6%
8.9%
0.7/0.4
Min. Δ
-30.9%
-30.0%
-23.0%
-22.4%
Max. Δ
-4.9%
-8.2%
5.7%
0.1%
Recap
…GTStrudl vs. ATLAS Comparison
c. Trends for 3 head, aluminum signal with backplate.
• As # signals, span length, and wind speed increases, discrepancy between ATLAS constant coefficient
results and GTS increases.
• As span length and wind speed increases, discrepancy between ATLAS default coefficient results and GTS
increases. As # signals decreases discrepancy increases.
d.
Trends for 3 head, polycarbonate signals with backplate.
e.
Trends for 5 head, aluminum signal with backplate.
• As # signals, span length, and wind speed increases, discrepancy between ATLAS constant coefficient
results and GTS increases.
• As span length and wind speed increases, discrepancy between ATLAS default coefficient results and GTS
increases. As # signals decreases discrepancy increases.
a.
Cable tension increases quicker with ATLAS results than GTS as wind speed increases.
f.
Trends for 5 head, polycarbonate signals with backplate.
g.
Trends for 3 head, aluminum signal without backplate.
• Cable tension increases quicker with ATLAS results than GTS as wind speed increases.
• Cable tension increases quicker with ATLAS than GTS as # signals increases as wind speed and # signals
increases.
• Cable tension increases quicker with GTS than ATLAS as span length increases.
Recap
GTStrudl Box Span Results
• Same Maximum Messenger Cable Tension as Single Span Results
• 0 degree Wind Angle and 90 degree Wind Angle produces same results
• 0 degree / 90 degree Wind Angle controls Cable Design
• Pole Design controls over Cable Design
• 45 degree Wind Angle controls Pole Design
• The larger the skew, the larger the pole moments
• GTStrudl difficult to compare to ATLAS since so few span
configurations ran in ATLAS
• The directly comparable results (Final Wind Speed equal in GTStrudl and
ATLAS) produce a similar cable tension comparison to single span.
Initial Recommendations for potential
Simplified Analysis Procedure
• Determine Maximum Messenger Cable Tension with Charts and Trendline
Equations, See Single Span Charts
• Determine Maximum Pole Moments with Charts and Trend lines developed based
on Pole CSR Ratio (45 degree Wind Angle / 90 degree Wind Angle)
Ongoing Parametric Studies
• GTSTRUDL
Hanging Box
• ATLAS
- Box (?)