Chapter 12 — Abutments, Wingwalls, and Retaining Components (15 questions)

Compute the Rankine active earth-pressure coefficient $K_a$ for a level cohesionless backfill with effective friction angle $\varphi' = 32^{\circ}$.

Cantilever wall H = 22 ft, γ = 120 pcf, K_a = 0.307. Compute the total horizontal active thrust per foot of wall $P_a = \tfrac{1}{2} K_a\,\gamma\,H^{2}$ (kip/ft).

The active thrust P_a from Q2 acts at what elevation above the base of the wall (ft)?

For a 20-ft-tall abutment retaining a highway fill, the live-load surcharge per AASHTO §3.11.6.4 is modeled as an equivalent soil height $h_{eq}$ of approximately:

Using h_eq = 3 ft, γ = 120 pcf, K_a = 0.307, and H = 22 ft, compute the total LS thrust$\Delta P_h = K_a\gamma h_{eq}\,H$ in kip/ft.

At Strength I, the abutment above has ΣV = 42 kip/ft (ηγ_p included) at the base and a net horizontal driving force ΣH = 12 kip/ft (P_a + ΔP_h). If δ = φ' = 32°, compute the capacity-to-demand ratio $R_r/H_u$ for sliding.

A 12-ft-wide footing carries ΣV = 45 kip/ft with a resultant moment ΣM = 40 k-ft/ft about the footing centerline. Compute the eccentricity e (ft) and verify against the Strength limit B/3.

For the footing in Q9, compute the equivalent uniform factored bearing pressure $q_u = \Sigma V/(B - 2e)$ in ksf.

An MSE reinforcement layer at depth z = 15 ft has σᵥ = γ z = (0.125)(15) = 1.875 ksf, effective embedment length in the resistant zone Lₑ = 8 ft, pullout resistance factor F* = 0.8, scale-effect α = 1.0, C = 2 (strips, two sides), φ = 0.90. Compute the pullout capacity $\phi\,F^{*}\,\alpha\,\sigma_v\,L_e\,C$ (kip/ft of wall).