Example 8: Cantilever Wingwall Design Loads1 EXAMPLE 8: CANTILEVER WINGWALL DESIGN LOADSProblem StatementExample 8 covers the design of a wingwall cantilevered off a standard CDOT integral abutment.The example illustrates the following items: The 20 ft. length (measured as shown in Figures 1 & 2) used in Example 8 is themaximum length permitted for cantilevered wingwalls per BDM Section The example wingwall is skewed 30 , which is the maximum allowed for an integralabutment per BDM Section 11.3.1. At-rest earth pressure is required for skewed wingwalls per BDM Section Per BDM Section, a portion of the earth pressure acting on the buried part of thewingwall may be neglected, as shown in Figure 1 below. Equations are provided to assistin calculating the resultant wingwall force effects from the trapezoidal shape of earthpressure. Force effects are summarized at the two design sections shown in Figure 2. DesignSection A is the critical design section for the wingwall. Design Section B summarizes theforce-effects transferred to the abutment .Assumptions The backfill is assumed to be sufficiently drained so that hydrostatic pressure does notdevelop. Example 8 assumes that no settlement of the backfill is anticipated. See BDM Section11.3.6.1 for guidance when significant settlement is expected.Figure 1 - Wingwall ElevationFigure 2 - Partial PlanCDOT Bridge Design ManualApril 2021

Example 8: Cantilever Wingwall Design Loads2 GivensWingwall Height, H Wall Thickness, t Live Load Surcharge Height, S End Height, h Wingwall Length, L Abutment Width, A Skew Angle, θ Backfill Unit Weight, γ1 Angle of Internal Friction of Backfill, Φ1 Dead Load Factor, γDC Horizontal Earth Pressure Factor, γEH Live Load Surcharge Factor, γLS Unit Weight of Concrete, γc .750.15ft.ft.ft.ft.ft.ft.degreeskcf (CDOT Class 1)degreesfor at-rest pressureBDM 3.4.1AASHTO 3.4.1AASHTO 3.4.1kcfProvided by Geotechnical Engineer.Figure 3 - Horizontal Load GeometryCDOT Bridge Design ManualApril 2021

Example 8: Cantilever Wingwall Design Loads3 CalculationsEarth PressureEarth pressure moments are calculated about the A and C axes shown in Figure 3.The total thrust, P, due to horizontal earth pressure and live load surcharge, is alsocalculated and located. The following equations are adopted from a Caltrans designaid; the derivations are not provided.At-rest Lateral Earth PressureAASHTOCoefficient, k 01sin ΦEq. 0.441𝑚𝑎𝑥 𝑘 𝛾, 0.057 𝑘𝑐𝑓Effective Fluid Weight, WBDM 0.057 kcfService Limit State:Service Moment, MS AA𝑊𝐿243ℎ 301Service Moment, MS CC𝑊𝐿2𝑆ℎ𝐻12𝑊𝐿𝐻6ℎ2𝑆 𝐻ℎℎ𝐻 ℎ3𝑆kip𝑀𝑃 7.26𝑦𝐻2ℎkft 41.5𝑥̅4𝑆 𝐻kft 188Service Thrust, PS𝐻ft., from back face of abutment𝑀𝑃 4.55ft., from top of wallStrength Limit State:Effective Surcharge height, S'Nominal depth of live load surcharge isincreased to account for the difference inload factors𝛾𝑆𝛾 2.59Ultimate Moment, MU AA𝛾 455CDOT Bridge Design Manualft.𝑊𝐿243ℎ𝐻4𝑆′ 𝐻2ℎkftApril 2021

Example 8: Cantilever Wingwall Design Loads4 Ultimate Moment, MU CC𝛾𝑊𝐿2𝑆′ℎ𝐻12 276Ultimate Thrust, PU𝛾𝑊𝐿𝐻62𝑆′ 𝐻ℎℎ𝐻 ℎ3𝑆′kip𝑀𝑃 7.35𝑦ℎkft 61.9𝑥̅𝐻ft., from back face of abutment𝑀𝑃 4.45ft., from top of wallSelf Weight:Service Wall Weight, V S𝐻𝐿𝑡 𝛾 30.0Ultimate Wall Weight, V U𝛾kip𝑉 37.5Service Moment at Design Section A, MS wall𝑉 kip𝐿2 300Ultimate Moment at Design Section A, MU wall𝑉 375CDOT Bridge Design Manualkft𝐿2kftApril 2021

Example 8: Cantilever Wingwall Design Loads5 Design Section A SummaryPrimary Horizontal ReinforcementMS AAMS AA, per ft. 301𝑀 30.1MU AAMU AA, per ft.kft 𝐻kft/ft 455 kft𝑀 𝐻 45.5kft/ft.These moments are used to design the primary horizontal reinforcement along the inside face ofthe wingwall for a 1 ft. wide section with a depth of t. For example calculations of reinforcedconcrete design, see BDM Design Examples 6 and 11. Per calculations not shown, #8 bars at 6in. spacing are selected as primary reinforcing. All wingwall reinforcement is required to becorrosion resistant, in accordance with BDM Section 5.4.5.Figure 4 - Primary Horizontal ReinforcementTop Horizontal ReinforcementMS wall 300kftMU wall 375kftThese moments are used to design the required top reinforcing bars in the wingwall for a sectionof width t and depth of H. Per calculations not shown, the primary horizontal reinforcing providedabove is sufficient to resist the imposed moment; no additional bars are needed.Figure 5 - Top Horizontal ReinforcementWingwall Reinforcement DetailsSee Figures 11.6-1, 11.6-2, and 11.7-1 of the Bridge Detail Manual for additional wingwallreinforcement details, including development of top and primary horizontal bars into theabutment.CDOT Bridge Design ManualApril 2021

Example 8: Cantilever Wingwall Design Loads6 Design Section B SummaryEarth pressure and dead loads are ultimately transferred to, and must be resisted by, theabutment and its supporting foundation elements. This section resolves earth pressure and selfweight forces into design forces and moments about centroidal axes of the abutment, and atDesign Section B (see Figure 2).The abutment width along the skew, A'𝐴 cos 𝜃 3.46 ft.Figure 6 - Abutment EccentricitiesService Limit State:Tension, Ps 41.5kipShear, Vs 30.0kip𝑒𝐴′2𝑥̅ 8.99𝑒𝐻2ft.𝑦 0.454 ft.My, Service𝑃 𝑒 373Mx, ServiceTz, Service𝑃 𝑒kft 18.8kft𝐿𝐴′𝑉 352CDOT Bridge Design Manual2kftApril 2021

Example 8: Cantilever Wingwall Design Loads7 Strength Limit State:Tension, PuShear, Vu𝑒 61.9 37.5kipkip𝐴′2𝑥̅ 9.08𝑒My, Ultimate𝐻𝑦2 0.548 ft.𝑃 𝑒 562Mx, Ultimate𝑃 𝑒𝑉 440kft 34.0Tz, Ultimateft.kft𝐿𝐴′2kftThe shear, tension, torsion, and bi-axial moments summarized above are concurrent and mustbe resisted by the abutment. Careful detailing is required to provide adequate capacity andsufficient reinforcement development at Design Section B. See Figure 11-13 of the BDM forreinforcement details at the wingwall/abutment interface.ConclusionThis design example shows the primary calculations needed to develop design forces for acantilever wingwall supported by an integral abutment. While all force effects were calculated forcompleteness, it is noted that for this example the following force effects are negligible: selfweight shear at sections A & B, self-weight moment M wall at Section A, and earth pressuremoment Mx at Section B.Other configurations, such as a cantilever wingwall attached to a semi-integral abutment cap,need to resist the same loading as illustrated in this design example. However, in this case, thestructural section available to resist the wingwall forces is reduced because the wingwall issupported only by the abutment cap. It is noted that the aforementioned force effects that aretypically inconsequential for an integral abutment are more critical for this configuration.CDOT Bridge Design ManualApril 2021