Pallet Rack Beam Load and Deflection
Checks a rack beam pair for bending stress and for the rack industry's L/180 deflection limit under two pallets...
Example
You enter
- Beam clear span (in) 108
- Weight of one pallet (lb) 2500
- Pallets per bay level 2
- Beam moment of inertia (in^4) 2.5
- Beam section modulus (in^3) 1.111
- Steel yield strength (psi) 55000
- Deflection limit denominator (180 = span over 180) 180
You get
- Maximum moment 33750 in-lb
- Bending stress 30378 psi against 32934 psi allowable
- Allowable stress (psi) 32934.1
- Stress ratio 0.92 -- PASS, 8% to spare
- Deflection 0.6222 in against a 0.6000 in limit
- Deflection limit (in) 0.6
- Moment of inertia the limit needs 2.59235
Details, formula, and sources
Checks a rack beam pair for bending stress and for the rack industry's L/180 deflection limit under two pallets at the quarter points, and reports which governs. The worked 108 in beam passes stress with 8% to spare and fails deflection by 4%, which is the ordinary result. ANSI MH16.1 and the manufacturer's capacity at the installed span govern.
Two equal point loads at the quarter points: M = P L / 4; d = P a (3 L^2 - 4 a^2) / (24 E I) with a = L/4 and E = 29,000,000 psi; allowable bending stress = Fy / 1.67; acceptance limit L/180.
ANSI MH16.1 Design, Testing and Utilization of Industrial Steel Storage Racks, the applicable building code, and the rack manufacturer's published beam capacity AT the installed span.
The beam relations and the L/180 criterion are public; ANSI MH16.1 itself is a purchased standard.
Estimate. AHJ and licensed professional govern.
Field names used by the API: span_in, pallet_weight_lb, pallets_per_level, moment_of_inertia_in4, section_modulus_in3, yield_strength_psi, deflection_limit_ratio, moment_in_lb, bending_stress_psi, allowable_stress_psi, stress_ratio, deflection_in, deflection_limit_in, required_moment_of_inertia_in4
- Load pattern two equal pallets delivering point loads at the quarter pointsspec-v1809 idealisation
- Beam end connector not evaluated; its capacity comes from testing and frequently limits the beam firstANSI MH16.1