Frame geometry and member schedule
Gravity load calculation
Imperial input assumptions
| Parameter | Value |
|---|---|
| Structural calculation units | kip-ft, ksi |
| Bay width | 10 ft |
| Tributary width | 10 ft |
| Dead load area, DL | 100 psf |
| Floor live load area, LL | 50 psf |
| Roof live load area | 0.5LL = 25 psf |
| Beam self-weight | W8x24 = 24 lb/ft |
| Earthquake combination | 1.2D + 0.5L +/- E |
Line-load derivation
wDL,area = 100 psf x 10 ft = 1.000 kip/ft
wDL = 1.000 + 0.024 = 1.024 kip/ft
wLL,floor = 50 psf x 10 ft = 0.500 kip/ft
wLL,roof = 25 psf x 10 ft = 0.250 kip/ft
wfloor = 1.2(1.024) + 0.5(0.500) = 1.479 kip/ft
wroof = 1.2(1.024) + 0.5(0.250) = 1.354 kip/ft
Story weight and final mass conversion
| Quantity | Imperial expression | Final FEM mass |
|---|---|---|
| One 10-ft bay, Levels 1-2 | 1.479 kip/ft x 10 ft = 14.79 kip | 6,707 kg |
| Complete floor, Levels 1-2 | 14.79 kip x 3 bays = 44.37 kip | 20,121 kg |
| One 10-ft bay, roof | 1.354 kip/ft x 10 ft = 13.54 kip | 6,142 kg |
| Complete roof, 3 bays | 13.54 kip x 3 bays = 40.62 kip | 18,426 kg |
Final conversion only: mass [kg] = weight [kip] x 453.59237 kg/kip.
FEM input: M = diag([20121, 20121, 18426]) kg.
Weight reporting: W = M x 9.80665 m/s^2 after the final mass conversion.
FEM idealization
FEM 3 calibration
The saved model is fem_sp_1_org_3.mat with variant inner_column_base_rotation_double_w12x40. The calibrated exterior base rotational stiffness is 1.19410864e7 N·m/rad; the two interior column bases use twice that stiffness.
Rigid floor diaphragms
All nodes at a given floor share one horizontal displacement. Every beam-column and base joint has a rotational degree of freedom. Rotations at different joints remain independent during assembly and are then statically condensed, leaving three lateral generalized coordinates: u₁, u₂, and u₃.
Base rotational springs
Each numerical column base is represented as a translationally restrained hinge with rotational coordinate θb connected to the calibrated spring kθ. The spring supplies moment Mb = kθθb while permitting finite base rotation.
Dynamic model
Use a three-DOF lateral system with the corresponding level mass lumped at each diaphragm. Levels 1–2 use the full floor live load in the stated earthquake combination; the roof uses 0.5 of the floor live load. Weight values are derived only for gravity-load reporting. Use Rayleigh damping fit to modes 1 and 2 at 3%, which gives about 5.19% damping in mode 3, and evaluate both signs of the earthquake action, ±E.