Factored Loads and Tributary Width practice problems for the FE Civil exam
Structural design questions on the FE Civil exam usually begin by turning a set of service loads into the single number a member must be designed for. Two steps do that work. The first is the tributary width: a beam or girder carries the load from half the span on each side of it, so a distributed area load in pounds per square foot becomes a line load in pounds per foot by multiplying by that tributary width. Get the tributary width wrong and everything downstream is wrong, and the most common way to get it wrong is to use the full bay spacing instead of half the distance to each adjacent member. The second step is factoring. Load and resistance factor design sizes members for a factored load rather than a service load, and the governing gravity combination is one point two times dead load plus one point six times live load. Dead load gets the smaller factor because its magnitude is well known; live load gets the larger one because it is variable. Check the dead-load-only combination as well, because on a member with very little live load one point four times dead can govern. Two errors decide most of these items: factoring a quantity that was already computed from factored loads, and mixing design philosophies by putting service loads on the demand side of a check that already includes a resistance factor.
Key formulas
Line load from an area load
w = q * b (b = tributary width)
Tributary width for an interior member
b = (s_left + s_right) / 2
Basic gravity combination
U = 1.2*D + 1.6*L
Dead load alone
U = 1.4*D
LRFD design check
phi * R_n >= U, with phi <= 1.0
Common mistakes
Using the full bay spacing as the tributary width instead of half the distance to each adjacent member.
Applying load factors to a moment or stress already calculated from factored loads.
Using service loads on the demand side of an LRFD check that includes a resistance factor.
Assuming 1.2D + 1.6L always governs without checking 1.4D on a dead-load-dominated member.
4 worked practice problems
Commit to an answer before opening the solution. Each problem shows the governing model, every substitution, a unit check, and why each wrong choice is wrong.
Original question written by FE Exam AI Prep from the public FE Civil exam specification. Before release, a solver model re-derived the answer twice from the question alone, without its answer key, and a critic model checked the result. No licensed engineer reviews these questions. It is not an NCEES question and does not come from any NCEES practice exam. FE Exam AI Prep is an independent study tool and is not affiliated with, endorsed by, or sponsored by NCEES.
FE Exam AI Prep is an independent study tool and is not affiliated with, endorsed by, or sponsored by NCEES. All practice questions are original and generated for study purposes based on publicly available exam specifications.