Bending tests to estimate the axial force in slender beams with unknown boundary conditions

• Identification of the axial load in beams with unknown boundary conditions is performed.
• In a bending test, only five flexural displacements or curvatures have to be recorded.
• Numerical and experimental tests on tie-rods with different boundary conditions are carried out.

This paper presents a static method for the axial load identification of slender prismatic beams with uncertain length and unknown boundary conditions as is typical of struts and ties of truss structures or tie-rods of arches and vaults. The proposed method requires the knowledge of the beam flexural rigidity only. Flexural displacements or curvatures are measured at five cross sections of the beam subjected to an additional concentred lateral load. Unlike analogous dynamic methods, any set of experimental data may be used in the identification algorithm. The proposed algorithm is verified by means of many numerical and experimental tests on beams having different boundary conditions. Excellent estimates of the axial forces are obtained when the greatest possible distance between sensors is adopted, even if in the presence of high values of the axial forces very accurate displacement measurements are required.