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 33,750 in-lb
- Bending stress 32,429 psi against 32,934 psi allowable
- Allowable stress (psi) 32934.1
- Stress ratio 0.98 -- PASS, 2% 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
No published worked example is on file for this calculation. It is checked against a hand-worked derivation of its method and an independent reference test.
Details, formula, and sources
ScopeChecks 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 under 2% to spare once MH16.1's 25% impact load is added, and fails deflection by 4%. ANSI MH16.1 and the manufacturer's capacity at the installed span govern.
Formula or tableTwo equal point loads at the quarter points: M = P L / 4; stress on 0.88 M plus a vertical impact of 25% of one unit load at a quarter point (ANSI MH16.1 2.3, ASD combination 5), not in deflection; 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.
Source and editionANSI 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.
Free accessThe beam relations and the L/180 criterion are public; ANSI MH16.1 itself is a purchased standard.
What governsEstimate. AHJ and licensed professional govern.
API field namesspan_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