Lifting Horizontal Elastic Beam at Two Points

A uniform slender beam with nonnegligible weight is lifted symmetrically at two points along its length. The elastica theory is used to obtain the nonlinear large deformation equations that are governed by the nondimensional flexibility parameter $K\equiv L(\rho /\mathrm{EI}{)}^{1/3}\text{,}$ where L is the length, ρ is the weight per length, and EI is the flexural rigidity. The beam is rigid when K is zero and becomes progressively limp when K is increased. Solutions are obtained by both perturbations for smaller and numerical integrations for arbitrary K. Forces, moments, deflections, and configurations are determined. The perturbation results, expressed in polynomials of the arc length, are fairly accurate for $K⩽1\text{.}$ Two different sets of optimum lifting locations are considered. One set yields the least maximum moment and another set leads to the least maximum sag. The results are useful in the design of lifting slender materials such as beams, cables and pipelines.