Loads, Load Combinations, and Load Paths (FE Civil)

NCEES FE Civil spec: Structural Engineering, F. Loads, load combinations, and load paths (e.g., dead, live, lateral, influence lines and moving loads, tributary areas). FE Reference Handbook: Civil Engineering chapter, Structural Design section (Loads); Structural Analysis section (Influence Lines).

What the FE Civil Spec Covers

Topic F covers how loads get onto a structure and how they are factored: dead, live, roof, snow, wind and seismic loads; ASCE 7 load combinations for strength design (LRFD) and allowable stress design (ASD); tributary areas and load paths; live load reduction; and influence lines for moving loads. These questions are usually short arithmetic, but they feed every steel and concrete design problem.

Key Concepts

Load path: deck or slab to joists or beams, beams to girders, girders to columns, columns to foundations. Each member carries the load from its tributary area plus whatever the members it supports deliver.
Tributary area for an interior column is the area bounded by lines halfway to the adjacent columns. For a beam, tributary width is half the spacing to each neighboring beam.
Load combinations apply load factors to nominal loads. Every combination must be checked, and the largest effect governs. The wind and seismic combinations with 0.9D check uplift and overturning.
Influence lines show how a reaction, shear or moment at one fixed point changes as a unit load moves across the structure. By the Muller-Breslau principle, the shape matches the deflected shape when the corresponding restraint is released.

Core Formulas

Main ASCE 7 LRFD combinations (nominal loads D, L, Lr, S, R, W, E):

1.4 D

1.2 D + 1.6 L + 0.5 (L_{r} or S or R)

1.2 D + 1.6 (L_{r} or S or R) + (L or 0.5 W)

1.2 D + 1.0 W + L + 0.5 (L_{r} or S or R)

1.2 D + 1.0 E + L + 0.2 S, 0.9 D + 1.0 W, 0.9 D + 1.0 E

The basic ASD combinations start with $D$ , $D + L$ , $D + (L_{r} or S or R)$ and $D + 0.75 L + 0.75 (L_{r} or S or R)$ .

Live load reduction, member supporting one floor (AT in square feet, or use 4.57 in place of 15 with AT in square meters):

L = L_{0} (0.25 + \frac{15}{K _{LL} A _{T}}) \geq 0.50 L_{0}

Influence line ordinate for moment at a section a distance a from the left support of a simple span L (b = L minus a):

IL_{M, m a x} = \frac{ab}{L}, M = P \cdot (ordinate) or w \cdot (area under IL)

Where It Is in the FE Reference Handbook

Search the Civil Engineering chapter, Structural Design section: it lists the nominal loads, the LRFD and ASD combinations from ASCE 7, live load reduction, flat roof snow and wind velocity pressure. Influence lines and moving concentrated load sets are in the Structural Analysis section of the same chapter.

Worked Example: Interior Column Load

An interior column in an office floor has bays of 6 m by 8 m on all sides. Dead load is 4.0 kPa and the unreduced live load is 2.4 kPa. The column supports one floor and $K_{LL} = 4$ . Find the factored axial load with and without live load reduction.

Step 1: Tributary area and nominal loads

A_{T} = 6 \times 8 = 48 m^{2}

D = 4.0 (48) = 192 kN, L_{0} A_{T} = 2.4 (48) = 115.2 kN

Step 2: Load combinations, no reduction

1.4 D = 268.8 kN

1.2 D + 1.6 L = 1.2 (192) + 1.6 (115.2) = 230.4 + 184.3 = 414.7 kN \leftarrow governs

Step 3: Live load reduction

$K_{LL} A_{T} = 192 m^{2} \geq 37.16 m^{2}$ , so reduction is allowed.

\frac{L}{L _{0}} = 0.25 + \frac{4.57}{192} = 0.25 + 0.330 = 0.580 \geq 0.50 ✓

L = 0.580 (115.2) = 66.8 kN

P_{u} = 1.2 (192) + 1.6 (66.8) = 230.4 + 106.9 = 337.3 kN

Live load reduction cuts the factored column load from about 415 kN to about 337 kN. On the exam, read carefully whether the question wants the reduced or unreduced value.

Quick Influence Line Check

A single 50 kN wheel load rolls across a 12 m simple span. What is the largest moment it can cause at a section 3 m from the left support? The moment influence line for that section is a triangle with its peak at the section itself:

ordinate = \frac{ab}{L} = \frac{3 ( 9 )}{12} = 2.25 m

M_{m a x} = P (ordinate) = 50 (2.25) = 112.5 kN \cdot m

The load produces its maximum effect when it sits directly on the section. For a uniform live load, load only the parts of the span where the influence line has the sign you want, and multiply w by that area.

Common Mistakes

Checking only 1.2D + 1.6L and missing 1.4D when dead load dominates.
Using the full bay on each side for an interior column. The tributary area extends only halfway to each neighbor.
Applying the reduction factor to dead load. Only live load is reduced.
Mixing units in the reduction formula: 15 goes with square feet, 4.57 with square meters.
Placing a moving load at midspan by habit. Use the influence line to put the load where the ordinate is largest for the section in question.

Practice Problems

Try these from the free PolyCalc FE Civil problem bank. Each one has a full worked solution.

A column supports nominal loads of dead D = 50 kN, floor live L = 30 kN and roof snow S = 40 kN. There is no wind or seismic load. Using the ASCE 7 strength design (LRFD) combinations, the governing factored axial load is most nearly: See the worked solution or practice the Loads & Codes deck
An interior column supports a floor in a regular grid with bays 6 m by 8 m. The uniform floor load is 5 kPa. The axial load delivered to that column from one floor is most nearly: See the worked solution or practice the Structural Basics deck
An eligible member supports one floor with tributary area AT = 400 ft², KLL = 4 and unreduced live load L₀ = 50 psf. Reduction is permitted. Use L = L₀[0.25 + 15/√(KLL·AT)] with AT in ft², but L must not be less than 0.5L₀. Find the reduced live load. See the worked solution or practice the Loads & Codes deck
At a roof connection the dead-load effect is 18 kN downward and the wind effect is 30 kN upward. Take downward as positive, so D = +18 kN and W = −30 kN. Evaluate the supplied combination U = 0.9D + W (the wind effect is already on the basis this combination requires; no other forces act). What uplift resistance must the connection provide? See the worked solution or practice the Loads & Codes deck
A one-way floor system ends at an edge beam that spans 5 m between its end supports. The next parallel beam is 4 m inward, the slab spans perpendicular to the beams, and there is no overhang beyond the edge beam. The service floor load is 6 kPa. Ignore beam self-weight. What total floor load is delivered to the edge beam over its full span? See the worked solution or practice the Loads & Codes deck
A single 30 kN downward point load can be placed anywhere on a 10 m simply supported beam. There are no other loads. Consider the fixed section 4 m from the left support, with sagging moment positive. Find the greatest bending moment at that section and where the load must be to cause it. See the worked solution or practice the Structural Analysis Methods deck

Related Calculators and Examples

Frequently Asked Questions

Which LRFD load combination usually governs on the FE exam?

For gravity-only problems it is almost always 1.2D + 1.6L + 0.5(Lr or S or R), unless the dead load is very large compared with live load, in which case 1.4D can govern. Always check both. For uplift, check 0.9D + 1.0W.

What is a tributary area?

It is the floor or roof area whose load flows to a given member. For an interior column in a regular grid it is one bay length times one bay width, measured halfway to each neighboring column. For a beam it is the span times the tributary width, halfway to each adjacent beam.

Can live load always be reduced?

No. ASCE 7 allows reduction only when the influence area KLL times AT is at least 400 square feet (37.16 square meters), and generally not for live loads over 100 psf or for assembly occupancies. For one-way slabs, the tributary area used is capped at 1.5 times the slab span squared. The reduced load cannot drop below 50 percent of the unreduced load for members supporting one floor, or 40 percent for two or more floors.

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