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130 CHAPTER 5 Design Examples 5.1 Introduction loading is F1; F2 and F3 are horizontal loadings along the transverse (x2-direction or z-direction) and longitudinal Seven detailed design examples are presented in Appendix H. (x3-direction or y-direction) directions of the bridge, respec- The presented examples include (1) Examples 1 through 4 tively. M3 is the moment about the longitudinal direction of FHWA's Geotechnical Engineering Circular No. 6 (GEC6), (x3- or y-axis) due to transverse loading and M2 is the moment Appendix C (Kimmerling, 2002); (b) the foundations of the about the z-axis (transverse direction) due to longitudinal load- central pier and the east abutment of the Billerica, Massa- ing. The load eccentricity across the footing width is eB = M2/F1 chusetts, B-12-025 Bridge; and (c) the foundation of the and across the footing length is eL = M3/F1. The resultant load south abutment of the Marlborough, Massachusetts, N-08-013 inclination is given by 2 F2 + F3 2 F1 . Bridge. The ULS of bridge foundations (bearing capacity) is an- alyzed in the following examples according to the presented 5.3 Examples Summary methodology and the AASHTO design specifications with In Appendix H, the figures present for the different exam- LRFD resistance factors, as given in the current AASHTO (2007) specifications, as well as with the new resistance fac- ples the performance versus footing size, referring to the tors for bearing resistance developed in this research proj- effective footing size. The discussion in Appendix H of the ect. The analysis is based on the conditions that are given in example refers to geometrical size, which includes, for exam- the examples' references, i.e., footing geometry as designed, ple, eccentricity. The limiting eccentricity in all examples was soil conditions, and loading. For design completion, the assumed to be e = B/6. Table 73 provides a summary of major SLS is analyzed as well, using several settlement analysis findings from the design examples referring to the full geo- methods and a range of factors. Summary graphs and tables metrical width. Overall, the use of the new, recommended are provided for the calculations in all examples, and detailed resistance factors for the strength limit states resulted in foun- calculations are shown for two design examples: (1) Exam- dations with varied relations to the actual design, i.e., in five ple 1 from FHWA, in which the footing rests on natural soil cases the designed foundations under the new factors are and the applicable resistance factor depends on the way the smaller, and in two cases the foundations are larger. In most soil parameters are derived and (2) the Central Pier of the cases, the foundations are controlled by limiting eccentricity, B-12-025 Billerica Bridge, in which the footing rests on especially if the contribution of negative eccentricity is not controlled soil. adopted. As in other instances in which designs are compared to each other, the introduction of calibrated factors in RBD 5.2 Loading Conventions methodology provides mixed results in terms of econom- and Notations ics. Overall, no significant change in economics can be The loading conventions and the corresponding notation pointed out; the design improvement and the systematic used in this report are as presented in Figure 120, unless approach are, however, a major improvement to the exist- otherwise stated in the design examples. The vertical-centric ing guidelines.
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131 x2 F1 D M1 M2 F3 F2 M3 L x3 B x1 Figure 120. Loading conventions and notation used. Table 73. Design example details summary. Maximum Eccentricity Design foundation size, B L (ft ft) Example Settlement Foundation and Dominant load to Strength LS Service LS Reference Design in method used soil condition limit state eccentricity footing side (ft) ratio Recommended = 0.45 = 1.0 reference in reference Bridge pier on 50.0 .0 GEC6 - e2/B = 0.23/B 9.75 1 natural soil Service 0.36 9.5 9.5 (Schm78: 19.5 19.5) 16.0 16.0 Hough (1959) Example 1 e3/L = 0.36/L ( = 0.35 to 0.40) deposits (Hough: 16.25 16.25) e2/B = 0.50/B 52.4 (C2 4.5 52.4 Billerica Bridge Pier footing on e3/L = load, = 0.70) Peck et al. 2 Strength 0.50 52.4 (Schm78: 4.3 52.4) 13.1 52.4 Central Pier gravel fill 0.095/52.4 8.9 52.4 (C7 (1974) = 0.0018 (Hough: 2.0 52.4) load, = 0.45) Billerica Bridge Abutment footing e2/B = 2.31/B 15.5 61.65 61.65 (including Peck et al. 3 Strength 2.31 15.5 61.65 12.5 61.7 East Abutment on gravel fill e3/L = n.a. ( = 0.45) Schm78 and Hough) (1974) Integral bridge GEC6 - Limiting e2/B = 1.00/B 6.0 82.0 82.0 (Schm78 and 4 abutment on 1.00 6.0 82.0 9.8 82.0 Hough (1959) Example 2 eccentricity e3/L = n.a. ( = 0.45) Hough: 6.0 82.0*) structural fill Stub seat-type 82.0 GEC6 - Limiting e2/B = 1.39/B 8.35 82.0 5 bridge abutment 1.39 8.35 82.0 (Schm78 and Hough: 10.5 82.0 Hough (1959) Example 3 eccentricity e3/L = n.a. ( = 0.45) on structural fill 8.35 82.0) Full height bridge GEC6 - Limiting e2/B = 3.15/B 18.9 82.0 18.9 82.0 (Schm78 and 6 abutment on 3.15 18.9 82.0 17.1 82.0 Hough (1959) Example 4 eccentricity e3/L = n.a. ( = 0.40) Hough: 18.9 82.0*) natural soil Limiting eccentricity AASHTO Marlborough Single span if not e2/B = 7.38/B 4.0 38.4 (2008) 7 Bridge South abutment footing 7.38 4.0 38.4 4.0 38.4 10.5 38.4 considered e3/L = 0 AASHTO (2008) Eq. Abutment on rock pos/neg 10.6.2.4.4-3 contribution