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 2 — LRFD Philosophy, Reliability, and Limit States (15 questions)
20 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.
- Q1
The reliability index β relates to the probability of failure Pf for a normal distribution by:
- Q2
For β = 3.5, estimate Pf (× 10⁻⁴).
×10⁻⁴ - Q3
The φ factor in LRFD accounts for uncertainty in:
- Q4
AASHTO §5.5.4.2 φ for flexure of a tension-controlled reinforced-concrete section (εt ≥ 0.005) is:
- Q5
Extreme Event I load combination uses γLL = ?
- Q6
Simple span L = 90 ft with factored DL wDC = 5.0 klf. Compute Strength I midspan moment (no LL) using γDC = 1.25 (k-ft). The 5.0 klf already includes γ = 1.0.
k-ftStrength I check
- Q7
Load modifier ηD for a non-ductile connection is:
- Q8
Load modifier ηR for a non-redundant member is:
- Q9
Compute η for a bridge with ηD = 1.00, ηR = 1.05 (non-redundant), ηI = 1.05 (critical). Report η.
- - Q10
A composite section has Mn = 8,400 k-ft. φ = 1.00 (flexure, compact composite). Compute φMn (k-ft).
k-ftSteel girder — Strength I
- Q11
The Rackwitz-Fiessler (First-Order Reliability Method) is used in LRFD calibration to:
- Q12
Bias factor λ = mean/nominal. For A992 steel yield, λ ≈ 1.10, coefficient of variation V ≈ 0.06. Compute mean Fy (ksi) for nominal 50 ksi.
ksi - Q13
Service III limit state controls:
- Q14
The AASHTO fatigue truck for Fatigue I has a fixed rear-axle spacing of:
- Q15
Concentrated LL PLL = 40 kip at midspan, L = 50 ft. Include IM = 33 %. Compute midspan Strength I moment contribution from this load (k-ft).
k-ftStrength I with LL
- Q16
For steel main structural members in tension (yielding of gross section), φy equals:
- Q17
Compute the LRFD design tensile capacity of a WT7×24 (Ag = 7.07 in², Ae = 6.36 in², Fy = 50 ksi, Fu = 65 ksi). Report min(φyFyAg, φuFuAe) in kip.
kip - Q18
For a two-span continuous bridge with equal spans of 70 ft, Strength IV (min. LL, high DL/LL) is checked when:
Two-span continuous
- Q19
RC beam: As = 6.00 in², fy = 60 ksi, f'c = 4 ksi, b = 16″, d = 28″. Compute a = Asfy/(0.85 f'c b) (in).
inSingly-reinforced beam
- Q20
Same section: compute φMn = φ As fy (d − a/2) with φ = 0.90 (k-ft). Use a = 6.62″.
k-ftφM_n check
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