The Span-to-Depth and Span-to-Weight Ratios for Steel Girders in Short-Medium Span Bridges (SMSB) for Road Bridges
Short medium span steel bridges (12–40 m) rely heavily on efficient girder selection. Two of the most important performance metrics for steel girders are:
- Span-to-depth ratio
- Span-to-weight ratio
These ratios directly influence structural efficiency, fabrication cost, transportation feasibility, and long-term performance. The MTO Manual of Standard Short-Span Steel Bridges provides a rich dataset of girder sizes, weights, and span ranges that allow engineers to derive practical ratios for design optimization.
This article distills those insights into a clear engineering reference.
1. Span Range for Standard Steel Girders
From the manual:
“Spans ranging from 12 to 40 metres in length, tabulated in 2 metre increments.”
This span range covers the majority of municipal and provincial steel bridges in Ontario and aligns with typical North American practice.
2. Span-to-Depth Ratio for Steel Girders
The span-to-depth ratio is a key indicator of structural efficiency. A higher ratio means a shallower girder for the same span, which reduces steel tonnage and improves aesthetics.
Using the girder depths provided in the manual’s tables (W and WWF sections), we derive the following:
2.1 Rolled W‑Sections (No Cover Plates)
These are standard rolled shapes with depths from 610 mm to 1000 mm.
Span (m)
|
Girder
|
Depth (mm)
|
Span/Depth Ratio
|
12
|
W610×91 |
610 |
19.7 |
14
|
W690×125 |
690 |
20.3 |
16
|
W760×147 |
760 |
21.0 |
18
|
W760×147 |
760 |
23.7 |
20
|
W840×176 |
840 |
23.8 |
22
|
W920×201 |
920 |
23.9 |
24
|
W1000×222 |
1000 |
24.0 |
Observations
- W‑sections typically achieve span/depth ratios between 20 and 24.
- Ratios increase with span because deeper rolled sections become available.
- Rolled sections are efficient for spans up to ~24 m.
2.2 Welded WWF Sections (No Cover Plates)
These fabricated girders allow greater flexibility and higher efficiency.
Span (m)
|
Girder
|
Depth (mm)
|
Span/Depth Ratio
|
18
|
WWF700×152 |
700 |
25.7 |
22
|
WWF900×169 |
900 |
24.4 |
26
|
WWF1100×234 |
1100 |
23.6 |
30
|
WWF1200×302 |
1200 |
25.0 |
34
|
WWF1400×358 |
1400 |
24.3 |
40
|
WWF1600×431 |
1600 |
25.0 |
Observations
- WWF girders achieve span/depth ratios between 23 and 26.
- Welded sections outperform rolled sections in efficiency.
- Ideal for spans >24 m where rolled sections are no longer economical.
3. Span-to-Weight Ratio for Steel Girders
Span-to-weight ratio indicates how much span is achieved per unit girder weight. Higher ratios mean more efficient use of steel. Using the girder weights from the manual (e.g., W610×91 → 91 kg/m), we compute:
3.1 Rolled W‑Sections
Span (m)
|
Girder
|
Weight (kg/m)
|
Span/Weight
|
12
|
W610×91 |
91 |
0.132 |
14
|
W690×125 |
125 |
0.112 |
16
|
W760×147 |
147 |
0.109 |
18
|
W760×147 |
147 |
0.122 |
20
|
W840×176 |
176 |
0.114 |
22
|
W920×201 |
201 |
0.109 |
24
|
W1000×222 |
222 |
0.108 |
Observations
- Span/weight ratios for W‑sections cluster around 0.11–0.13.
- Efficiency decreases slightly as girder weight increases.
- Rolled sections are most efficient for shorter spans (12–18 m).
3.2 Welded WWF Sections
Span (m)
|
Girder
|
Weight (kg/m)
|
Span/Weight
|
18
|
WWF700×152 |
152 |
0.118 |
22
|
WWF900×169 |
169 |
0.130 |
26
|
WWF1100×234 |
234 |
0.111 |
30
|
WWF1200×302 |
302 |
0.099 |
34
|
WWF1400×358 |
358 |
0.095 |
40
|
WWF1600×431 |
431 |
0.092 |
Observations
- Span/weight ratios for WWF sections range 0.09–0.13.
- Welded sections are most efficient at mid-range spans (18–22 m).
- Efficiency decreases for very long spans due to heavier plate girders.
4. Engineering Interpretation
Rolled W‑Sections
- Best for short spans (12–20 m).
- Provide higher span-to-weight efficiency in the lower span range.
- Limited by available rolled depths.
Welded WWF Sections
- Best for medium spans (20–40 m).
- Provide higher span-to-depth efficiency due to customizable depth.
- Slightly lower span-to-weight efficiency at long spans due to heavier webs/flanges.
5. Practical Design Guidelines
Span-to-Depth Ratio Targets
- W‑sections: aim for 20–24
- WWF sections: aim for 23–26
Span-to-Weight Ratio Targets
- W‑sections: aim for 0.11–0.13
- WWF sections: aim for 0.10–0.13
General Rule
- Use rolled sections when available and economical.
- Use WWF sections when spans exceed rolled depth limits or when optimizing stiffness.
Conclusion
Span-to-depth and span-to-weight ratios are powerful tools for optimizing steel girder selection in short- and medium-span bridges. The MTO manual provides a clear dataset showing that:
- Rolled W‑sections excel in spans up to ~20 m.
- Welded WWF sections dominate spans from 20–40 m.
- Efficient designs typically fall within span/depth ratios of 20–26 and span/weight ratios of 0.10–0.13.
This article gives engineers a practical reference for selecting steel girders based on structural efficiency and material economy.
