Eriksson Culvert follows the seismic analysis procedure outlined in FHWA-NHI-10-034 chapter 13. Below is an example calculation of this analysis, as well as the corresponding Eriksson Culvert file.
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Design Parameters
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Geometric Parameter | Value |
|---|---|
Clear span | 17.667 ft |
Clear Height | 11.667 ft |
Slab thicknesses | 14 in |
Wall thicknesses | 14 in |
Joint Location | 36 in up from center line |
Fill depth | 16 ft |
Haunch dimensions | 15 in depth and width |
Seismic Parameter | Value |
|---|---|
Soil density | 130 pcf |
Poisson’s ratio of soil | 0.5 |
Peak ground acceleration | 0.42 |
Ground shear modulus | 1460 ksf |
Slip interface | full slip |
Estimate the Free-Field Ground Strain
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where 𝜏max is the maximum earthquake induced shear stress,
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For this example,
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Per WSDOT BDM section 8.3.4B, the ground acceleration (PGA) can be reduced according to the depth of fill. The ground motion attenuation is shown in table 1 (below). For a fill of 16', the ratio of ground motion to motion at burried buried structure is 1.0.
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Calculate the Free-Field Relative Displacement
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The flexibility ratio is defined as,
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where w is the total culvert design width and h is the total culvert design height.
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Calculate the Racking Ratio
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The internal forces can be determined through analyzing a 2D frame model with a displacement of 0.273”; though due to the formulation of FEM, it is easier to apply this as an equivalent point load of 98.09 06 kips.
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Eriksson Culvert calculates and stores these internal forces (axial, shear, and moments) at tenth points along all members in the structure for later use in the load combination equations.
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Now the vertical force is calculated as,
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For a rigid foundation model, an equivalent upward force is also applied to the bottom slab.
Eriksson Culvert calculates and stores these internal forces (axial, shear, and moments) at tenth points along all members in the structure for later use in the load combination equations.
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Eriksson Culvert uses the internal forces from both analyses to develop unfactored EQ min/max envelopes for every member in the structure. The considered cases to develop these envelopes are:
Results from the racking analysis
Results from the vertical analysis
Racking + vertical analysis results
Users have the option of determining how ‘(3) Racking + vertical analysis results’ are calculated, by either of the following combinations:
1.0 / 1.0, which includes:
1.0 H + 1.0 V
-1.0 H - 1.0 V
-1.0 H + 1.0 V
1.0 H - 1.0 V
0.3 / 1.0, which includes:
0.3 H + 1.0 V
-0.3 H - 1.0 V
-0.3 H + 1.0 V
0.3 H - 1.0 V
1.0 H + 0.3 V
-1.0 H - 0.3 V
-1.0 H + 0.3 V
1.0 H - 0.3 V
These unfactored forces are then applied in the LRFD extreme event I load combination:
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Results in Eriksson Culvert
The following seismic specific results are found in the Eriksson Culvert text report:
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