The paper presents an analytical solution to the differential equation of deflection for a flat cantilever beam loaded with a vertical force and analyzes the possibility of its application for calculating the deflection of specimens used in fatigue strength testing. Integrating the equations leads to the determination of a mathematically precise relationship between the deflection angle and the current independent variable (distance from the origin of the coordinate system). Applying the known solution in cases of large beam deflections leads to significant errors, exceeding 11% of the deflection angle value.To determine the stress values corresponding to the permanent fatigue strength for elastic elements, it is necessary to induce sufficiently large deformations. The mathematical description of such a problem differs from the simplified relationships suitable for analyzing typical engineering structures with high stiffness. An exact solution for the deflection of an elastic beam cannot be presented due to the difficulty of analytically integrating the differential equation, which is why methods leading to approximate solutions are used. [1, 2]Fatigue tests were programmed for bending flat specimens with a cross-section of 2x mm. The length of the specimens was set at 250 mm, including a 30 mm grip section. (…)
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Source: Logistyka Magazine
Calculating deformations of an elastic specimen using an online program – PDF file for download