Vertical Forces: Gravity Load Path, Analysis, and Serviceability
Load path and load types
Start every gravity problem by tracing the path: slab or deck → beams → girders → columns/walls → foundation. Dead load includes self-weight of every element plus superimposed MEP and partitions; live load comes from the occupancy table, reduced only where the code permits. Know the difference between tributary area (area of floor carried by one member, used for load takeoff) and influence area (area that contributes to the effect being studied, often roughly 2× tributary for a column, used for live-load reduction).
Analysis basics
For simple spans, wL²/8 and wL/2 are routine; for continuous members remember that maximum positive moment occurs under pattern loading (live load on alternating spans), not full loading, while maximum negative moment at a support occurs with live load on the adjacent spans. Cantilevers reverse the sign convention and concentrate shear at the backspan support. Two-way slabs shed load along yield lines toward supporting beams; one-way members carry load to the two long edges only.
Traps
- Mixing ASD and LRFD combinations, or applying strength-level wind/seismic factors to service deflections.
- Forgetting member self-weight, or double-counting it.
- Applying live-load reduction without the KLL factor or outside the code's area limits.
- Ignoring unbalanced loading on transfer girders and cantilever backspans.
- Checking deflection with factored rather than service loads.
Worked rule of thumb
Interior column, 30 ft × 30 ft bay, office live load 50 psf. Tributary area 900 ft². With KLL = 4, KLL·AT = 3600 ft², so L = 50(0.25 + 15/√3600) = 50(0.5) = 25 psf, subject to the code's minimum. Always state the minimum before finalizing the reduced value.