Design and Analysis
What this domain tests
Design and Analysis covers the process of turning requirements into a verified design: limit states, load combinations, factors of safety, failure modes, and checking that capacity exceeds demand. The exam favors problems where you must choose the governing combination before computing.
Core rules
- Strength design compares factored demand to factored capacity: φR_n ≥ U.
- Serviceability (deflection, vibration, crack width) uses unfactored service loads.
- Common LRFD gravity combination: U = 1.2D + 1.6L.
- Apply load factors to loads and resistance factors to capacity-never both to the same side.
- Use the governing (largest) effect among all applicable combinations, including wind and seismic where required.
Worked example
A simply supported beam spans 6.0 m with D = 20 kN/m and L = 15 kN/m. The design capacity is φM_n = 250 kN·m. Is it adequate? w_u = 1.2(20) + 1.6(15) = 24 + 24 = 48 kN/m. M_u = w_u L²/8 = 48 × 36/8 = 216 kN·m. 216 kN·m < 250 kN·m, so the beam is adequate in flexure for this combination. Reasoning check: service load w = 35 kN/m gives M = 157.5 kN·m; that value is for deflection, not strength. Mixing the two is a common error.
Traps
- Using service loads with factored capacity, or factored loads for deflection.
- Forgetting that self-weight is part of D.
- Using L²/8 for a cantilever or a load not uniformly distributed.
- Stopping after one load combination when another governs.
- Rounding the factored load before computing the moment.