Rack Upright Frame Capacity and Unbraced Length
Compares frame load against its rating and shows the Euler buckling load at the entered beam spacing beside the load...
Example
You enter
- Beam spacing / unbraced length (in) 48
- Column moment of inertia (in^4) 0.6
- Effective length factor K (MH16.1: 1.7 unbraced against sidesway, 1.0 braced) 1
- Loaded beam levels 3
- Load per level (lb) 5000
- Rated frame capacity at that spacing (lb) 24000
You get
- Load per column 7,500 lb (frame 15,000 lb)
- Load per frame (lb) 15000
- Against the rated capacity 63% used, 9,000 lb remaining
- Euler load at the entered spacing 74,536 lb
- Euler load with one level removed 18,634 lb at 96 in unbraced
- Removed capacity loss (%) 75
Checked against published worked examples from: Michigan State University (A. Varma, CE 405 Design of Steel Structures).
Details, formula, and sources
ScopeCompares frame load against its rating and shows the Euler buckling load at the entered beam spacing beside the load with one level removed. Doubling the unbraced length quarters the capacity with nothing visible changing. ANSI MH16.1 requires tested capacities, and damage is repaired or replaced rather than derated.
Formula or tableP_cr = pi^2 E I / (K L)^2 with E = 29,000,000 psi over the unbraced length set by the beam spacing; load per column = loaded levels x load per level / 2.
Source and editionANSI MH16.1 Design, Testing and Utilization of Industrial Steel Storage Racks, which requires TESTED capacities for perforated cold-formed columns and requires damaged members be unloaded and repaired or replaced.
Free accessThe Euler relation is public; ANSI MH16.1 itself is a purchased standard.
What governsEstimate. AHJ and licensed professional govern.
API field namesbeam_spacing_in, column_moment_of_inertia_in4, effective_length_factor, loaded_levels, load_per_level_lb, rated_frame_capacity_lb, load_per_column_lb, load_per_frame_lb, utilization_pct, euler_capacity_lb, euler_capacity_level_removed_lb, removed_capacity_loss_pct
- Frame rating stated AT a beam spacing; it is not a property of the frame alonerack manufacturer
- Square law holds only where the column buckles elastically, KL/r above 4.71 sqrt(E/Fy) (about 113 at 50 ksi); a stockier segment is governed by inelastic buckling and loses less than the Euler ratio when a level is removed -- a 60 in segment at KL/r 50 doubled to 100 loses about 42% on the AISC column curve, not 75%AISC 360 E3
- Damage not a derate -- the standard requires unloading and repair or replacement, not a reduction factorANSI MH16.1