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Section 3: Example Comparison of Inventory, Operating, and Permit Loads

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Typical Continuous I-Beam Bridge

To further demonstrate the differences between the various types of analyses, a typical standard bridge common in Texas is chosen for comparative analysis. This bridge is a three-span continuous I-Beam bridge originally designed in the 1950s and 1960s for use on many of the Farm- and Ranch-to-Market highways. Bridges on these routes were commonly designed to H-15 loads (30,000 lbs) since that load was believed to represent the maximum farm truck. Since that time, many of these routes have been incorporated in more heavily traveled routes. Farm-to-Market (FM) roadways crossing Interstate (IH) or other major highways often have this type of H-15 design. Tractor-trailer trucks with a legal load of 80,000 lbs are now commonly using these bridges. The legal load of these trucks can be 84,000 lbs with use of the Weight Tolerance (2060) Permit7.

Details for the bridge may be found in Standard Ic26h-230 (70-90-70) dated 1965. However, similar bridges before 1965 were also designed to the same H-15 loading. This design loading was in use until about 1975 or 1980. The bridge has a 26-ft roadway between faces of railings and is composed of four 30-inch deep wide-flange rolled beams with relatively short cover plates at the interior supports. The beams are spaced at 7-ft 4-in., and the slab is 6.5-in. thick. An elevation and cross-section of the bridge are shown in Figure 6-1. The design is non-composite, meaning that the slab is assumed to slip longitudinally along the top flanges when loaded. The beams are 36W135 continuous with 10-in. X 0.625-in. X 14-ft cover plates top and bottom at supports.

Typical Continuous I-Beam Bridge Elevation
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Figure 6-1. Typical Continuous I-Beam Bridge Elevation and Cross Section

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Rating Analysis Steps

The steps used in a typical rating analysis for the structure are described below.

Calculate Dead Load. Using the total steel weight given in the plans, subtract calculated weight of beams including cover plates, and check that remainder is about 5 percent of beam weight. This result represents the diaphragms, connections, and other miscellaneous steel. If this number is not about 5 percent, determine the discrepancy. Sometimes the total weight in the plans is in error, but this check usually gives the rater a verification for the estimated dead load. Use the total steel weight, which includes the diaphragms, as a uniform load per linear foot (LF), distributed equally to one of the interior beams. Use the total slab quantity given in the plans calculated as a uniform load per LF also distributed equally to an interior beam. Verify by comparison to the dead load of slab for a typical interior beam using the slab thickness. Add in dead load for any overlay and railings.

Compute Dead Load Moments. Dead load moments need only be calculated at critical locations such as the maximum positive moments for each span and the negative moments at the interior supports. The analysis should use the actual span lengths center-to-center of bearing and not the nominal span lengths. It is preferable to use a computer program, but hand analysis from continuous beam coefficients is also acceptable. The normal sizes of cover plates over supports will "draw" up to about 6 to 12 percent more negative moment and will reduce positive moments when compared to a constant cross section analysis, which is assumed when using continuous beam coefficients or other similar tables or charts. Almost all continuous beam designs in Texas until the advent of computer analysis in the early 1960s used influence coefficients for a constant cross section.

Determine Controlling Live Loading Conditions. Some computer programs do this determination automatically, but there is a risk in using these programs unless the user is familiar with their limitations and assumptions. One popular program is BMCOL518, which is a continuous beam analysis program. It allows any pattern of live load to be moved in increments along the beam, which can have cover plates and any areas of composite section if necessary. Thus, it is particularly suited to the analysis of Superheavy loads. It can also identify the locations where the concentrated load(s) for lane loads must also be placed. Most continuous beams will have the following live load maximum moments:

  • Max positive moment in end and center spans will usually be from an HS-20 live load with 14-ft center-to-center of trailer axles. However, for very long plate girders, the lane loading criteria may sometimes control positive moment.
  • Max negative moment will also usually be from the HS pattern, perhaps with more than 14 feet between the trailer axles if total length of first plus second spans is less than about 70 feet. If the sum of the first two spans is more than about 75 or 80 ft, then the negative moment will be from lane loading of the two adjacent spans with the concentrated loads applied at the critical positions in the two spans.

    The “Texas Bridge Load Rating Program” of 19889 can also be used for analysis. However, the program is limited to simple spans of uniform cross section or the estimate of the equivalent simple span for each span of a continuous beam.

Tabulate the Maximums. Identify the locations for which stresses and ratings are to be calculated. Often the maximum positive moment sum of dead plus live effects will not be at the point of maximum dead load or live load moment. This condition is another reason to use a computer analysis such as BMCOL5110. This program allows the combination of dead and live loads to be investigated at all points along the continuous member with proper consideration of the effects of cover plates and composite regions, if any. The maximum moments in the end spans may not be the same even though they have the same span length, due to the unsymmetrical live load pattern. For the results discussed in the remainder of this section, Program BMCOL51 was used with 69-90-69 ft spans.

Calculate the Moments and Load Ratings. Apply the appropriate load factors for the various ratings to both the dead and live load moments at each member location being investigated. Subtract the dead load effect from the member capacity at yield (if load factor analysis) or from the member capacity at allowable stress (if allowable stress analysis). The remainder is the live load capacity. Ratio the remainder to the calculated live load value at the location, and multiply by the live load ton designation. The result is the member rating at that location. It is best to understand this basic process rather than use a set formula for calculating the load rating.

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Results for I-Beam Bridge

An H-pattern was used for comparison (normally not necessary) with no railing and no overlay as an additional check on the original design using allowable stresses. This design pre-dated the 1965 design shown on the standard plans and obviously was done using an allowable stress of 18 ksi. In 1965 many standard details were changed to specify “H.Y.C.” structural steel11, which is equivalent to ASTM A-36.12 However, the design load was kept the same, and no change was made in the size of the cover plates. An HS loading, using the allowable stress or load factor methods, and Inventory Rating or Operating Rating methods was also made for comparison. The various analyses are summarized in the following table.

Anchor: #i1001127Table 6.1 Comparison of Analyses for Example Bridge

Loading

Analysis Method

First or Third Span

Support

Middle Span

H (1)N

AS – IR

H 20.08

H 14.24 *

H 18.94

H (2)N

AS – IR

H 23.46

H 17.59 *

H 22.28

HS (3)N

AS – IR

HS 15.78

HS 17.60

HS 14.84 *

HS (4)Y

AS – IR

HS 12.65

HS 10.40 *

HS 11.48

HS (5)Y

LF – IR

HS 15.84

HS 17.80

HS 14.97 *

HS (6)Y

LF – OR

HS 26.40

HS 29.67

HS 24.96 *

N = Light railing and no overlay

AS = Allowable stress

OR = Operating rating

Y = T501R railing and 2-in overlay

LF = Load factor

IR = Inventory rating

* = Controlling rating



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Discussion of the Analysis Comparisons

The various analyses summarized in Table 6.1 are discussed in the sequence of the loading number. Current bridge rating analysis usually requires only loadings HS (5) and HS (6). However, if the resulting rating is significantly different than the design load, then solutions similar to loadings H (1) or H (2) may be necessary to determine the reasons for the difference.

  • H (1). Used to verify analysis with an assumed allowable stress of 18 ksi which is appropriate for A7 steel. Also assumed to have no overlay and light railings. Note that the controlling rating of H14.24 is close to H-15. There would be an overstress of 2.5 percent if exactly H-15 loading was used. Designing up to a 5-percent overstress was very common for these structures.
  • H (2). This comparison analysis was made with an allowable stress of 20 ksi, which is appropriate for A36 steel. The remainder of the following comparisons are also with A36 steel.
  • HS (3). This comparison is with an HS truck. Note that the controlling HS14.84 rating implies a total individual rating truck load of 26.7 tons, which compares with the H17.6 rating truck of 17.6 tons.
  • HS (4). This analysis demonstrates the effect of using the actual current in-place modern railing, a T501R retrofit railing in this case, and a 2-in. overlay. This amount of overlay is very common for structures of this age. Note that the controlling rating shifts from the end span to the support due to the added influence of the greater uniform dead load. The reduction in the rating is 30 percent simply due to the added dead load.
  • HS (5). This analysis demonstrates the current IR for the bridge using LF analysis methods. The HS14.97 rating implies a single inventory rating truck load totaling 26.9 tons or two trucks side-by-side totaling 53.9 tons.
  • HS (6). This analysis demonstrates the current OR for the bridge using LF analysis methods. The HS24.96 rating implies a single operating rating truck load totaling 44.9 tons or two trucks side-by-side totaling 89.9 tons. Note that the OR of solution HS (6) is equal to 5/3 x the IR of solution HS (5), which directly reflects the difference in the live load rating factors.

7. Texas Transportation Code, Section 623.011.

8. “A Computer Program to Analyze Beam-Columns under Movable Loads,” Hudson Matlock and Taylor, T.P., Research Report 56-4, Center for Highway Research, University of Texas at Austin, 1968.

9. “Texas Bridge Load Rating Program,” TxDOT, 1988.

10. “A Computer Program to Analyze Beam-Columns under Movable Loads,” Hudson Matlock and Taylor, T.P., Research Report 56-4, Center for Highway Research, The University of Texas at Austin, 1968.

11. Texas Standard Specifications, TxDOT, 1962.

12. “Specification for Carbon Structural Steel A36/A36M -97,” Vol 01.04, ASTM, 1997.

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