Tension in the tie-down chains of a shipping container for hazardous material

摘要

Chains are frequently used to tie the shipping containers of hazardous material to a truck bed. The tie-down system is nonlinear when the container is subjected to a triaxial force during transit. It is nonlinear because chains cannot carry compressive force, and the base of the container may partially lift off from the truck bed. A method was developed to calculate the amount of tension in the chains. This methodology includes three assumptions: (1) No friction exists between the container and the truck bed; (2) The container and the truck bed are rigid; and (3) All chains are properly tightened (i.e., no slacks) during preparation for shipment. The methodology employs an iterative process of a linear tie-down system. This linear system is derived from the nonlinear system with two additional assumptions: (a) All chains can carry compression as well as tension; and (b) There is a point contact between the container and the truck bed. This linear system has a closed-form solution. After the first solution of the linear system is obtained, the unreasonable, or physically impossible, rotational degree of freedom of the container and the chains with compressive force are eliminated in the follow-up iterative calculations using the same linear system. Unreasonable rotation is detected when the results indicate a rotation of the container into the truck bed. Zero rotational value is assigned to this degree of freedom in the follow-up iterations. For chains under compression, the chain length is replaced with a fictitiously large value because a long chain carries essentially no load. This process usually needs only two or three iterations and can easily be carried out in a spread sheet using such programs as Microsoft Excel or LOTUS 123.