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Fundamental Period of Vibration (Longitudinal) <br />Per FEMA 460 Appendix A - Development of An Analytical Model for the Displacement Based Seismic <br />Design of Storage Racks in Their Down Aisle Direction <br />(A-7) <br />Where: <br />Wpi = the weight of the ith pallet supported by the storage rack <br />hpi = the elevation of the center of gravity of the ith pallet <br />with respect to the base of the storage rack <br />g = the acceleration of gravity <br />NL = the number of loaded levels <br />kc = the rotational stiffness of the connector <br />kbe = the flexural rotational stiffness of the beam-end <br />kb = the rotational stiffness of the base plate <br />kce = the flexural rotational stiffness of the base upright-end <br />Nc = the number of beam-to-upright connections <br />Nb = the number of base plate connections <br />kbe = <br />6EIb <br />L <br />kce = <br />4EIc <br />H <br />kb = <br />EIc <br />H <br />L = the clear span of the beams <br />H = the clear height of the upright <br />Ib = the moment of inertia about the bending axis of each beam <br />Ic = the moment of inertia of each base upright <br />E = the Young's modulus of the beams <br /># of levels 6 <br />min. # of bays 3 <br />Nc 72 <br />Nb 8 <br />kc 360 kip-in/rad <br />kbe 4005 kip-in/rad <br />kb 327 kip-in/rad <br />kce 1311 kip-in/rad <br />Ib 2.72 in4 <br />L 120 in <br />Ic 3.47 in4 <br />H 312 in <br />E 29500 ksi <br />Level hpi Wpi <br />1 39 in 5 kip <br />2 99 in 5 kip <br />3 159 in 5 kip <br />4 219 in 5 kip <br />5 279 in 5 kip <br />6 340 in 5 kip <br />Calculated T =4.1 <br />Since the calculated T is greater than 1.5, the more conservative value of 1.5 is <br />used in the calculations <br />PROJECT: <br />FOR: <br />ADDRESS: <br />SHEET#: <br />CALCULATED BY: <br />DATE: <br />Behr Process Corp <br />Interlake-Mecalux_Gabr <br />1995 S Standard Av <br />Santa Ana, CA <br />8 <br />kelvira <br />4/11/2024 <br /> TEL:(909)869-0989 <br /> 1130 E. CYPRESS ST, COVINA, CA 91724 <br />PN:20240411_15