# Assessment of Simplified Rating Factor Methodology for Shallow Cover Metal Culverts
## Appendix A Example and Comparison
### Refined ODOT Approach
Thus, the actual cover for calculation is: H + R/2 = 13 in/12 + 4.33 ft/2 = 3.25 ft  
Multiple presence factor (AASHTO LRFD 3.6.1.1.2-1): m = 1.2  
Adjust \(m\) based on ADTT (AASHTO LRFD C3.6.1.1.2): 0.9  
After ADTT adjustment: m\({}_{\rm adj}\) = 1.08  
Live load dynamic load allowance at the surface for calculation of surface tire contact area (AASHTO LRFD 3.6.2.2 and Appendix C Proposed Revisions to AASHTO Specifications C3.6.1.2.6) [20]: IM\({}_{\rm surf}\) = 33(1.0 - 0.125D\({}_{\rm E}\))  
D\({}_{\rm E}\) = 0 ft\[\text{IM}_{\text{suf}}=33\%\]  
\[(1+\text{IM}_{\text{suf}})=1.33\]  
The \"second axle\" wheel load for a concrete truck with madj: P\({}_{\text{madj}}=25/2\times 1.08=13.50\) kips  
The surface tire contact area for a concrete truck (AASHTO LRFD C3.6.1.2.5),  
Tire width: W\({}_{\text{T}}=\text{P}_{\text{madj}}/0.8=16.88\) in  
Tire length: L\({}_{\text{T}}=6.4\gamma_{\text{LL}}(1+\text{IM}_{\text{suf}})=11.07\) in  
Distribution of wheel load through earth fill (AASHTO LRFD 3.6.1.2.6), live load patch width at depth of quarter-point H + R/2 when the second axle is over the quarter point: W\({}_{\text{L}}=\text{W}_{\text{T}}+\text{\varphi}_{\text{E}}(\text{H}+\text{R}/2)+0.06 \text{S}=6.14\) ft  
Live load patch length at depth of quarter point H + R/2 when the second axle is over the quarter point: L\({}_{\text{L}}=\text{L}_{\text{T}}+\text{\varphi}_{\text{E}}(\text{H}+\text{R}/2)=4.66\) ft  
The wheel spacing on axle: 6 ft  
The axle spacing: 4 ft  
Live load patch area at depth of quarter point H + R/2 when the second axle is over the quarter point:  
If W\({}_{\text{L}}>6\) ft (overlapping in a single axle), Patch width under a wheel: (W\({}_{\text{L}}+6\) ft)/2  
If W\({}_{\text{L}}\leq 6\) ft (no overlapping in a single axle), Patch width under a wheel: W\({}_{\text{L}}\)  
If L\({}_{\text{L}}>4\) ft (overlapping between adjacent axles), Patch length under a wheel: (L\({}_{\text{L}}+4\) ft)/2  
If L\({}_{\text{L}}\leq 4\) ft (no overlapping between adjacent axles), Patch length under a wheel: L\({}_{\text{L}}\)  
Then, patch area under a wheel: A\({}_{\text{LL}}\) = (W\({}_{\text{L}}+6\) ft)/2 \(\times\) (L\({}_{\text{L}}+4\) ft)/2 = 26.28 ft2 (overlapping in a single axle and between adjacent axles)  
Live load dynamic load allowance at depth of quarter point H + R/2 when the second axle is over the quarter point for calculation of responses: IM = 33(1.0 - 0.125D\({}_{\text{E}}\))  
\[\text{D}_{\text{E}}=\text{H}+\text{R}/2=3.25\text{ ft}\]  
\[\text{IM}=19.6\%\]  
\[(1+\text{IM})=1.196\]  
Pressure at the quarter point due to the second axle over the quarter point plus dynamic load allowance and adjusted multiple presence factor:  
\[\text{\rho}_{(\text{L+IM})\&\text{madj}}=\text{P}_{(\text{L+IM})\&\text{madj }}/\text{A}_{\text{LL}}=13.50\times 1.196/26.28=0.614\text{ ksf}\]  
Pipe wall thrust due to live load plus dynamic load allowance and adjusted multiple presence factor (AASHTO LRFD 12.7.2.2): T\({}_{(\text{L+IM})\&\text{madj}}=[\text{\rho}_{(\text{L+IM})\&\text{madj }}(\text{C}_{\text{L}})\text{F}_{1}]/2\)  
\[\text{C}_{\text{L}}=\text{L}_{\text{L}}=4.66\text{ ft}<\text{S}=16.67\text{ ft}\]  
\[F_{1}=Max\left(\frac{0.75(S)}{L_{L}},\frac{15}{12(S)},1\right)=\left(\frac{0. 75(S)}{L_{L}}\right)=2.68\]  
\[\text{T}_{(\text{L+IM})\&\text{madj}}=(0.614\text{ ksf}\times 4.66\text{ ft}\times 2.68)/2=3.841\text{ k/ ft}\]  
Compare the factored T\({}_{(\text{L+IM})\&\text{madj}}=\gamma_{\text{LL}}\text{T}_{(\text{L+IM})\&\text{madj }}\) in simplified approach with CANDE result: \begin{tabular}{c c} \hline \hline
**Simplified** & **CANDE** \\ \hline
4.99 k/ft & 5.29 k/ft \\ \hline \hline \end{tabular}   
The CANDE value is obtained at the footing of the culvert with the second axle stopped over the quarter point.