Bridges for Service Life Beyond 100 Years: Service Limit State Design (2014) / Chapter Skim
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94 C h a p t e r 5 5.1 Development of Live Load Models for Service Limit States 5.1.1 Introduction The consideration of limit states, both ultimate (strength) and serviceability, requires the knowledge of loads.
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95 • Arkansas (SPS-2) -- Data recorded continuously from January 2008 until December 2008; • Colorado (SPS-2)
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96 • I-81 Northbound and Southbound (Site 9121) -- Data recorded continuously from January 2005 until December 2005; and • Highway 17 Eastbound and Westbound (Site 9631)
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97 regular truck traffic for live load for SLS II. The GVW criteria of 20 kips in Step 3 is a traditional, albeit arbitrary, cutoff used in virtually all previous fatigue studies to reduce the calculation effort by not considering light traffic, which does not contribute significantly to cumulative damage.
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98 Figure 5.4. CDFs of GVW for Indiana, Mississippi, and Ontario.
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99 Table 5.2. WIM Locations and Number of Recorded Vehicles Site No.
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100 Figure 5.6. Legend for all graphs.
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101 Figure 5.7.
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102 Figure 5.8. CDFs of WIM moment and HL-93 moment ratio, span 5 30 ft.
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103 Figure 5.9. CDFs of WIM moment and HL-93 moment ratio, span 5 60 ft.
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104 Figure 5.10. CDFs of WIM moment and HL-93 moment ratio, span 5 90 ft.
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105 Figure 5.11. CDFs of WIM moment and HL-93 moment ratio, span 5 120 ft.
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106 Figure 5.12. CDFs of WIM moment and HL-93 moment ratio, span 5 200 ft.
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107 Truck Moment / HL93 Moment St an da rd N or m al V ar ia bl e Truck Moment / HL93 Moment St an da rd N or m al V ar ia bl e New York 8280 Span 90 ft New York 8382 Span 90 ft Figure 5.15. Data removal from New York Sites 8280 and 8382.
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108 Table 5.3. Removal of Heaviest Vehicles (90-ft Span)
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109 Figure 5.17. Two cases of the simultaneous presence of two trucks with headway distance less than 200 ft.
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110 Figure 5.20. Histogram of trucks one after another (a)
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111 • Generally use a single loaded lane (no multiple loaded lanes)
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112 Table 5.4. Vertical Coordinates for the Mean Maximum Moment Time Period ADTT 250 1,000 2,500 5,000 10,000 1 Day 2.65 3.09 3.35 3.54 3.72 2 Weeks 3.44 3.08 4.02 4.18 4.33 1 Month 3.65 4.00 4.20 4.35 4.50 2 Months 3.82 4.15 4.35 4.50 4.65 6 Months 4.09 4.39 4.59 4.73 4.87 1 Year 4.24 4.55 4.73 4.87 5.01 5 Years 4.59 4.87 5.05 5.18 5.31 50 Years 5.05 5.31 5.47 5.60 5.72 75 Years 5.13 5.38 5.55 5.67 5.78 100 Years 5.18 5.44 5.60 5.72 5.83 from the graph by reading the moment ratio (horizontal axis)
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113 Figure 5.22. Vertical coordinates for different time periods for ADTT 5 1,000 and span 5 120 ft.
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114 Figure 5.23. CDFs of mean maximum moment ratios for ADTT 5 1,000 and span length 5 120 ft.
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115 Figure 5.24. Determination of mean values at 1.5 s.
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116 Table 5.5. Statistical Parameters of Live Load Moments for ADTT 250, l 5 1.5s Time Period Span 30 ft 60 ft 90 ft 120 ft 200 ft 300 ft l µ CV l µ CV l µ CV l µ CV l µ CV l µ CV 1 Day 0.92 0.65 0.28 0.82 0.64 0.23 0.80 0.66 0.17 0.79 0.65 0.15 0.71 0.56 0.18 0.61 0.48 0.18 2 Weeks 1.06 0.80 0.21 1.05 0.80 0.16 1.01 0.80 0.18 1.02 0.80 0.16 0.93 0.73 0.16 0.84 0.67 0.16 1 Month 1.12 0.85 0.21 1.09 0.85 0.19 1.08 0.85 0.18 1.08 0.85 0.17 1.01 0.78 0.19 0.90 0.73 0.16 2 Months 1.14 0.90 0.18 1.15 0.91 0.17 1.14 0.90 0.18 1.14 0.90 0.17 1.05 0.85 0.15 0.95 0.77 0.15 6 Months 1.19 0.95 0.17 1.23 0.96 0.19 1.20 0.97 0.15 1.19 0.98 0.14 1.12 0.91 0.15 1.04 0.85 0.15 1 Year 1.23 1.00 0.15 1.27 0.98 0.19 1.24 1.00 0.16 1.22 1.04 0.12 1.15 0.94 0.15 1.08 0.88 0.15 5 Years 1.31 1.07 0.15 1.35 1.09 0.16 1.31 1.13 0.11 1.31 1.14 0.10 1.25 1.02 0.15 1.18 0.97 0.15 50 Years 1.37 1.17 0.11 1.39 1.16 0.13 1.39 1.25 0.07 1.37 1.19 0.10 1.32 1.06 0.16 1.25 1.02 0.15 75 Years 1.38 1.20 0.10 1.40 1.19 0.12 1.41 1.27 0.07 1.39 1.21 0.10 1.34 1.08 0.16 1.27 1.04 0.15 100 Years 1.39 1.22 0.09 1.43 1.21 0.12 1.42 1.28 0.07 1.41 1.22 0.10 1.35 1.09 0.16 1.29 1.05 0.15 Table 5.6.
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117 Table 5.7. Statistical Parameters of Live Load Moments for ADTT 2,500, l 5 1.5s Time Period Span 30 ft 60 ft 90 ft 120 ft 200 ft 300 ft l µ CV l µ CV l µ CV l µ CV l µ CV l µ CV 1 Day 1.03 0.80 0.19 0.97 0.79 0.18 0.97 0.77 0.17 0.98 0.78 0.17 0.90 0.70 0.19 0.80 0.62 0.19 2 Weeks 1.20 0.93 0.19 1.20 0.96 0.17 1.20 0.96 0.17 1.20 0.97 0.15 1.12 0.92 0.14 1.02 0.84 0.14 1 Month 1.23 0.99 0.16 1.25 0.99 0.17 1.26 1.00 0.17 1.22 1.04 0.12 1.16 0.95 0.15 1.09 0.89 0.15 2 Months 1.28 1.04 0.15 1.31 1.04 0.17 1.29 1.11 0.11 1.27 1.12 0.09 1.21 0.98 0.15 1.12 0.91 0.15 6 Months 1.31 1.07 0.15 1.34 1.07 0.17 1.32 1.15 0.10 1.31 1.14 0.10 1.25 1.01 0.16 1.18 0.95 0.16 1 Year 1.34 1.11 0.14 1.35 1.11 0.14 1.36 1.19 0.09 1.34 1.17 0.09 1.28 1.04 0.15 1.21 0.98 0.15 5 Years 1.36 1.15 0.12 1.39 1.18 0.12 1.39 1.24 0.08 1.38 1.20 0.10 1.33 1.07 0.16 1.26 1.01 0.16 50 Years 1.40 1.25 0.08 1.42 1.22 0.11 1.43 1.29 0.07 1.43 1.23 0.11 1.37 1.11 0.15 1.29 1.05 0.15 75 Years 1.40 1.26 0.07 1.43 1.24 0.10 1.43 1.30 0.07 1.44 1.24 0.10 1.37 1.13 0.14 1.29 1.06 0.14 100 Years 1.40 1.27 0.07 1.44 1.25 0.10 1.44 1.31 0.07 1.44 1.25 0.10 1.39 1.14 0.14 1.32 1.09 0.14 Table 5.8.
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118 Table 5.9. Statistical Parameters of Live Load Moments for ADTT 10,000, l 5 1.5s Time Period Span 30 ft 60 ft 90 ft 120 ft 200 ft 300 ft l µ CV l µ CV l µ CV l µ CV l µ CV l µ CV 1 Day 1.17 0.88 0.22 1.09 0.89 0.16 1.11 0.87 0.18 1.13 0.87 0.20 1.02 0.81 0.17 0.91 0.75 0.17 2 Weeks 1.29 1.02 0.18 1.31 1.04 0.17 1.29 1.11 0.11 1.27 1.12 0.09 1.22 0.98 0.16 1.16 0.93 0.16 1 Month 1.32 1.06 0.16 1.34 1.08 0.16 1.32 1.15 0.10 1.29 1.14 0.09 1.25 1.01 0.16 1.20 0.97 0.16 2 Months 1.35 1.09 0.16 1.35 1.11 0.14 1.35 1.18 0.09 1.32 1.17 0.09 1.28 1.04 0.15 1.23 1.00 0.15 6 Months 1.35 1.12 0.13 1.37 1.14 0.13 1.37 1.20 0.09 1.34 1.19 0.08 1.30 1.06 0.15 1.25 1.02 0.15 1 Year 1.37 1.17 0.11 1.39 1.16 0.13 1.39 1.24 0.08 1.38 1.20 0.10 1.32 1.08 0.15 1.27 1.04 0.15 5 Years 1.39 1.24 0.08 1.41 1.21 0.11 1.42 1.27 0.08 1.42 1.22 0.11 1.37 1.11 0.15 1.30 1.06 0.15 50 Years 1.40 1.28 0.06 1.45 1.24 0.11 1.45 1.30 0.08 1.46 1.25 0.11 1.40 1.14 0.15 1.31 1.07 0.15 75 Years 1.41 1.29 0.06 1.46 1.26 0.10 1.47 1.32 0.08 1.47 1.26 0.11 1.40 1.16 0.14 1.32 1.09 0.14 100 Years 1.42 1.30 0.06 1.47 1.27 0.10 1.49 1.33 0.08 1.48 1.27 0.11 1.42 1.17 0.14 1.33 1.10 0.14 Table 5.10.
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119 Table 5.11. Statistical Parameters of Live Load Reactions for ADTT 1,000, l 5 1.5s Time Period Span 30 ft 60 ft 90 ft 120 ft 200 ft 300 ft µ 1.5s µ CV µ 1.5s µ CV µ 1.5s µ CV µ 1.5s µ CV µ 1.5s µ CV µ 1.5s µ CV 1 Day 1.14 0.94 0.14 0.95 0.80 0.13 0.94 0.80 0.11 0.91 0.79 0.10 0.84 0.70 0.13 0.74 0.62 0.13 2 Weeks 1.31 1.10 0.13 1.17 0.99 0.12 1.19 1.02 0.11 1.19 1.02 0.11 1.09 0.91 0.13 0.97 0.81 0.13 1 Month 1.35 1.15 0.12 1.23 1.03 0.13 1.26 1.08 0.11 1.25 1.07 0.11 1.17 0.97 0.13 1.06 0.88 0.13 2 Months 1.38 1.18 0.11 1.26 1.08 0.11 1.31 1.11 0.12 1.31 1.11 0.12 1.22 1.01 0.14 1.11 0.92 0.14 6 Months 1.42 1.22 0.11 1.29 1.11 0.11 1.38 1.15 0.13 1.37 1.16 0.12 1.28 1.05 0.14 1.18 0.97 0.14 1 Year 1.45 1.25 0.11 1.32 1.14 0.11 1.40 1.19 0.12 1.40 1.19 0.12 1.32 1.09 0.14 1.21 1.00 0.14 5 Years 1.50 1.29 0.11 1.40 1.20 0.11 1.49 1.26 0.12 1.50 1.26 0.13 1.38 1.14 0.14 1.28 1.06 0.14 50 Years 1.56 1.33 0.11 1.46 1.25 0.11 1.56 1.30 0.13 1.57 1.30 0.14 1.47 1.20 0.15 1.35 1.10 0.15 75 Years 1.57 1.34 0.11 1.47 1.26 0.11 1.57 1.31 0.13 1.58 1.31 0.14 1.48 1.21 0.15 1.36 1.11 0.15 100 Years 1.57 1.35 0.11 1.48 1.27 0.11 1.57 1.32 0.13 1.59 1.32 0.14 1.49 1.22 0.15 1.36 1.12 0.15 Table 5.12.
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120 Table 5.13. Statistical Parameters of Live Load Reactions for ADTT 5,000, l 5 1.5s Time Period Span 30 ft 60 ft 90 ft 120 ft 200 ft 300 ft µ 1.5s µ CV µ 1.5s µ CV µ 1.5s µ CV µ 1.5s µ CV µ 1.5s µ CV µ 1.5s µ CV 1 Day 1.25 1.05 0.12 1.09 0.94 0.11 1.14 0.96 0.13 1.12 0.94 0.13 1.02 0.84 0.14 0.90 0.74 0.14 2 Weeks 1.42 1.19 0.13 1.30 1.10 0.12 1.36 1.13 0.13 1.36 1.13 0.13 1.26 1.03 0.15 1.13 0.93 0.15 1 Month 1.46 1.22 0.13 1.34 1.13 0.12 1.39 1.16 0.13 1.40 1.17 0.13 1.30 1.06 0.15 1.18 0.96 0.15 2 Months 1.48 1.24 0.13 1.36 1.15 0.12 1.43 1.20 0.13 1.44 1.20 0.13 1.33 1.09 0.15 1.21 0.99 0.15 6 Months 1.51 1.27 0.13 1.39 1.18 0.12 1.47 1.23 0.13 1.48 1.24 0.13 1.39 1.13 0.15 1.27 1.03 0.15 1 Year 1.54 1.28 0.13 1.41 1.20 0.12 1.50 1.26 0.13 1.51 1.27 0.13 1.41 1.15 0.15 1.29 1.06 0.15 5 Years 1.58 1.32 0.13 1.48 1.25 0.12 1.54 1.30 0.12 1.56 1.30 0.13 1.46 1.19 0.15 1.34 1.09 0.15 50 Years 1.62 1.36 0.13 1.53 1.29 0.12 1.59 1.35 0.12 1.61 1.35 0.13 1.52 1.23 0.15 1.40 1.14 0.15 75 Years 1.63 1.37 0.12 1.54 1.30 0.12 1.60 1.36 0.12 1.62 1.36 0.13 1.53 1.24 0.15 1.41 1.15 0.15 100 Years 1.63 1.38 0.12 1.55 1.31 0.12 1.61 1.37 0.12 1.62 1.37 0.13 1.53 1.25 0.15 1.42 1.15 0.15 Table 5.14.
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121 Table 5.15. Statistical Parameters for Axle Loads, l 5 1.5s Time Period ADTT 250 1,000 2,500 5,000 10,000 l CV (%)
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122 was calculated as an equivalent moment by using the linear damage rule first proposed by Palmgren (1924) and later popularized by Miner (1945)
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123 Figure 5.27. Bending moment time history for a single truck passage on continuous bridges at middle support.
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124 Figure 5.29. Wide-band versus narrow-band history.
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125 Figure 5.30. Rainflow counting diagram.
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126 Table 5.19. Total Number of Load Cycles and Average Number of Load Cycles per Truck Passage for Simply Supported Bridges at the Midspan (continued)
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127 Table 5.21. Total Number of Load Cycles and Average Number of Load Cycles per Truck Passage for Continuous Bridges at 0.4 of the Span Length Site No.
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128 Time St re ss ra ng e, S S3 S2 S1 n1 n2 n3 Figure 5.31. Number of cycles ni for stress range Si.
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129 30 ft. To compare fatigue damage due to design fatigue load and actual fatigue load, it is convenient to remove the resistance part from limit state Equations 5.16, 5.17, and 5.18 [AASHTO LRFD (2012, Equations 6.6.1.2.5-1 and 6.6.1.2.5-2)
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130 Table 5.23. Equivalent Moments for Continuous Bridges at the Middle Support Site No.
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131 To calculate the ratio of fatigue damage caused by the actual fatigue load and design fatigue load, the load factor has to be removed from Equation 5.18. From Equations 5.18 and 5.19, it is possible to calculate the ratio of fatigue damage due to the actual load and fatigue damage due to design load by using Equation 5.20: Boundary of Actual Fatigue Damage eq 3S M S A NR = where Meq = equivalent moment from Miner's Rule; A = resistance constant; and NR = actual number of cycles.
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132 Table 5.27. Fatigue Damage Ratios for Simply Supported Bridges at the Midspan Site No.
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133 Table 5.29. Fatigue Damage Ratios for Continuous Bridges at 0.4 of the Span Length Site No.
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134 Figure 5.35. Moment corresponding to the upper 0.01%, span 5 120 ft.
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135 Table 5.32. Maximum Moment Range for Continuous Bridges at 0.4 of the Span Length Site No.
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136 Figure 5.36. Maximum moment range ratio (Fatigue Limit State I)
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137 Figure 5.37. Maximum moment range ratio (Fatigue Limit State I)
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138 Figure 5.38. Maximum moment range ratio (Fatigue Limit State I)
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139 Figure 5.39. Fatigue damage ratio for proposed change (Fatigue Limit State II)
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140 Figure 5.40. Fatigue damage ratio for proposed change (Fatigue Limit State II)
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141 Figure 5.41. Fatigue damage ratio for proposed change (Fatigue Limit State II)
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142 Table 5.33. Maximum Moment Range Ratio for Fatigue Limit State I Bridge Type Span (ft)
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143 5.5 Development of Overload (Service II) parameters WIM data also forms the basis for estimating how often a given design moment (or shear)
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144 Table 5.35. Number of Times WIM Moments Exceeded Factored HL-93 Loadings (continued)
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