Marshall S White, Jiyoun Yoo, and Joseph R Loferski April 3, 2012 Modeling Compressive Stress Distributions at the Interface Between a Pallet Deck and Distribution Packaging

Components of the unit load portion of consumer and industrial product supply chains Packaging Pallet Material Handling Equipment This research focuses on

Compression stress concentrations at the interface between the pallet deck and distribution packaging Stress concentration Pallet deck Packaging Pallet deck deflection “Non-uniform stress distribution” “Stress concentrations”

The beam on an elastic foundation is an inversion of the actual situation within the unit load Beam Elastic foundation Packaging Pallet section

General Solution for Beam Deflection supported by a deformable elastic foundation k packaging stiffness EI pallet deck stiffness deflection at x=0 slope at x=0 moment at x=0 shear force at x=0 y x 0 L P P General solution for beam deflection y at any point x

Jiyoun Yoo, PhD candidate6 P P Three Levels of pallet connection fixity are modeled PP Free ends PP Semi-rigid (Nailed joint) Fixed ends Same Pivot Point Two equal concentrated forces (p) applied to two pivot points

Free End Model Boundary Conditions ( a) at x 2 = 0; Q 0 = P (b) at x 1 = 0 and x 2 = 0; M(x 1 ) = M(x 2 )= M 0 (c)at x 1 = 0 and x 2 = 0; y(x 1 ) = y(x 2 )= y 0 (d)at x 2 = L 2 ; M=M 0 (e) at x 2 = L 2 ; Q = -P

Semi-Rigid Joint Model Boundary Conditions ( a) at x 2 = 0; Q 0 = P (b) at x 1 = 0 and x 2 = 0; M(x 1 ) = M(x 2 )= M 0 (c)at x 1 = 0 and x 2 = 0; y(x 1 ) = y(x 2 )= y 0 (d)at x 2 = L 2 ; M=M 0 (e) at x 2 = L 2 ; Q = -P M A = F N x d F N = force exerted by nails d = distance between nail and stringer F N = ky k =rotational modulus (lbs. /in.) y = the vertical displacement of the deck at the nail location (in.)

Fixed End Model Boundary Conditions ( a) at x 2 = 0; Q 0 = P (b) at x 1 = 0 and x 2 = 0; M(x 1 ) = M(x 2 )= M 0 (c)at x 1 = 0 and x 2 = 0; y(x 1 ) = y(x 2 )= y 0 (d)at x 2 = L 2 ; M=M 0 (e) at x 2 = L 2 ; Q = -P (f) at x 1 = 0 and x 2 = 0; θ(x 1 ) = θ(x 2 )= θ 0

Model Inputs and Outputs Compressive Stress Distribution Pallet Deck Stiffness (EI) Packaging Stiffness (k) Joint Fixity

Compressive Stress Distribution Models: Free Ends Bottles (k=1345 lbs./in. ) Applied stress (6.5 psi) Empty box (k=854 lbs./in.) Applied stress (6.25 psi) Flour sacks (k=615 lbs./in.) Applied stress (6.82 psi)

Compressive Stress Distribution Models : Semi-Rigid Joint Bottles (k=1345 lbs./in. ) Empty box (k=854 lbs./in.) Flour sacks (k=615 lbs./in.) Applied stress (6.5 psi) Applied stress (6.25 psi) Applied stress (6.82 psi)

Compressive Stress Distribution Models : Fixed Ends Bottles (k=1345 lbs./in. ) Empty box (k=854 lbs./in.) Flour sacks (k=615 lbs./in.) Applied stress (6.5 psi) Applied stress (6.25 psi) Applied stress (6.82 psi)

4.625” Load head Load Applicator Packaging Pressure Sensor Pallet Section I-Beam 0.5” LVDT 1” LVDT 2” LVDT 15.75” 20” Experimental Validation of Model Compression Stress Distribution

Load cell Packaging Pressure sensor Pallet section LVDT Testing setup

Fixed Ends (Epoxy Glued) Top View Semi-rigid joint (nailed) Free Ends Front View Wood Pallet Sections

Corrugated Container with Contents

Measurement of Design Variables Modulus of Elasticity Rotation ModulusPackaging Stiffness Pallet deck stiffness Third point bending test Nailed joint stiffness Moment-rotation curve Vertical Compression stiffness of packaging Load-deflection curve

Input Values for the Beam Models MOE (lbs./in. 2 ) Rotation Modulus (in.-lbs./radian) Packaging stiffness (lbs. /in.) 3/4" 3/8" 3/4"3/8" Bottles in a box Flour sacks Empty box A B A B A B A B A B A B A B A B A B Free end Semi-rigid joint Fixed end

Strain Gage Pressure Sensor Mats Sensel

Pressure Images: Free Ends 5psi 30psi 5psi 30psi BottleEmptyFlour 3/4” 3/8”

Pressure Images: Semi-Rigid Joints 5psi 30psi 5psi 30psi BottleEmptyFlour 3/4” 3/8”

Pressure Images: Fixed Ends 5psi 30psi 5psi 30psi BottleEmptyFlour 3/4” 3/8”

Raw Pressure Data Location (in.) Location (in.) ”8”15.2” 0.8” 8” 15.2” 2-D Pressure Distribution on 5 psi sensor Tabulated Actual Pressure Values 2-D Pressure Distribution on 30 psi sensor

Plot of Raw Pressure Data Location (in.) Average Location (in.) Average

Predicted vs. Measured Results: Free End Bottle 3/4” 3/8” EmptyFlour

Predicted vs. Measured Results: Semi-Rigid Joints Bottle 3/4” 3/8” EmptyFlour

Predicted vs. Measured Results: Fixed Ends 3/8” Bottle 3/4” EmptyFlour

A modification of the principles of an elastic beam supported by an elastic, deformable, foundation can be used to estimate the compression stress distributions between the pallet deck and packaged products. The model inputs are the compression stiffness of the packaged product and the bending stiffness of the pallet deck. The compression stresses at the interface between the pallet deck and packaging are not uniformly distributed. Stress concentrations occur over the pallet stringers or blocks. Average applied compression stress levels of 6 to 7 psi resulted in compression stresses on packaging within a unit load from 0 to 50 psi, for the specimens tested. Maximum compression stresses can be five to ten times greater than the average applied stress. Summary

Summary Stiffer pallet decks and stiffer connections between the pallet deck and stringers or blocks, significantly reduces the maximum compression stress on the packaged product in unit loads. Pallet design can be used to reduce the compression stresses on packaging and reduce packaging cost.