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This educational application supplements, but does not replace, the official AASHTO LRFD Bridge Design Specifications, applicable state DOT manuals, project specifications, and professional engineering judgment.

Graded quiz

Chapter 9 — Piers, Columns, and Bent-Cap Design (15 questions)

Chapter 9 — Piers, Columns, and Bent-Cap Design (15 questions)

15 questions · PE-exam format · 70% to pass · attempts save to your progress record when signed in.

Work each item to the requested precision. Use the Show clue button only after an honest attempt — hints reveal the AASHTO section and setup, not the answer.

  1. Q1

    Gross area A_g for D = 42-in pier (in²).

    in²

    Circular pier

    D
  2. Q2

    Steel area for ρ = 2% and A_g = 1385 in² (in²).

    in²
  3. Q3

    Nominal P_n for f′_c = 5, f_y = 60, A_g = 1385, A_st = 27.7 (kip).

    kip
    Pn=0.85fc(AgAst)+fyAstP_n = 0.85\,f'_c\,(A_g - A_{st}) + f_y\,A_{st}
    Pr=0.75(0.80Pn) (tied)P_r = 0.75\,(0.80\,P_n)\ \text{(tied)}
  4. Q4

    Design axial P_r (tied column), from P_n = 7430 kip.

    kip
  5. Q5
    AASHTO caps design axial for a spirally reinforced column at what fraction of P_n?
  6. Q6

    Slenderness kL_u/r for k = 1.2, L_u = 28 ft, r = 12 in (in-consistent).

    -
  7. Q7
    Slenderness threshold above which moment magnification is required (sway column, AASHTO §5.6.4.3):
  8. Q8

    Spiral ρ_s,min: A_g = 1385, A_c = 1075 (core = 37-in), f′_c = 5, f_yh = 60 ksi.

    -
  9. Q9

    Required spiral pitch for #4 bar (A_sp = 0.20 in²), D_core = 37 in, ρ_s = 0.0108 (in).

    in
  10. Q10
    Radius of gyration for a solid circular section of diameter D:
  11. Q11

    Approximate AASHTO barge crush force with DWT = 4000 tons, V = 7 ft/s. Use PB4.112DWTVP_B \approx 4.112\sqrt{DWT}\cdot V.

    kip
    barge towpier
  12. Q12

    Overturning moment about base if barge force acts 10 ft above base and equals 1800 kip (k-ft).

    k-ft
  13. Q13

    Wind base shear on pier: exposed area 500 ft², V = 115 mph. Use P = 0.00256·V² (psf), F = P·A/1000.

    kip
  14. Q14
    Load factor γ_CV for vessel collision at Extreme Event II per AASHTO Table 3.4.1-1:
  15. Q15

    Moment magnifier δ_ns for C_m = 0.85, P_u = 1200 kip, P_c = 9000 kip.

    -
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Bridge Engineering and Design Using AASHTO LRFD

Graduate interactive textbook for civil engineering students. Aligned to AASHTO LRFD Bridge Design Specifications, 10th Edition (2024).

Regional focus

Maryland & Mid-Atlantic — MDOT SHA, VDOT, PennDOT, FHWA.

Educational notice

This educational application supplements, but does not replace, the official AASHTO LRFD Bridge Design Specifications, applicable state DOT manuals, project specifications, and professional engineering judgment.

© 2026 Dr. Steve Efe, Ph.D. All Rights Reserved.

Developed for engineering education. Unauthorized reproduction, distribution, or commercial use is prohibited.

v1.0 · Reference edition · Aligned to AASHTO LRFD, 10th Edition (2024)