International Scientific Journals
of Scientific Technical Union of Mechanical Engineering "Industry 4.0"

A paper recently published explains the differential equations for deflection of beams under bending, including the deflection due to transversal force [1]. The present article contains derivation of the main equations, according to the mentioned approach, for deformations of a simply supported beam that is symmetrically loaded with two forces, also known as four-point bending. These deformations are rotation and deflection of the neutral line due to bending moment and transversal force. For thick beams, deflection due to the transverse force is more than 1% from deflection caused by the bending moment. Special attention was paid to the third-point loading test. The presented model is applicable for calculating deflection due to bending moment and transverse force for both thin and thick beams.

This article explains a mathematically consistent approach for solving the equations of Timoshenko’s beam theory for statically loaded beams. Theoretic sections 3.4 – 3.5 give a good description of the shear deformation and the primary approach for calculating deflections of beams under bending, taking into account both causes for deflection: bending moment and shear force. Values for the shear correction factor are discussed in section 4. This work was started to check the validity of an equation for deflection of a symmetrically loaded short rectangular beam with span/height ratio = 3 under four-point bending with upper-span/span ratio = 1/3. The exact solution is not presented here, but we can confirm that the presented theory, when applied for the mentioned loading scheme, leads to thi s equation using a shear correction factor k = 5/6.

The article discusses optimization of barge hull by decreasing of its mass parameters by changing of thickness of the plates. The fish-feeding barges are usually used in calm water and in this case it is possible to consider only static loads applied on the barge hull.

There are many calculation methods for determining stress and deflections in the thin plates. A lot of them are using uniformly distributed load and constant thickness of the plate. In real conditions, a hydrostatic pressure is applied on the barge hull. In this research, we consider a calculation method of thin plates taking into account variable thickness of the plates and non-uniformly load. In addition, we try to show by experiments and FEM analysis the possibility to use variable thickness of barge hull in building of fish-feeding barges.

The usage of the high-energetic source of the electron beam enables a repeated surface quenching of the chosen areas of an engineering part surface. Different techniques of the electron beam deflections allow the creation of hardened layers of different shapes and above all the thicknesses. The deflection was tested at one point, six points, a line and a field on the material 42CrMo4 (1.7225). The effect of the process speed and defocusing of the electron beam was studied. The electron beam surface quenching resulted in a very fine martensitic microstructure with the hardness over 700 HV0.5. The thickness of the hardened layers depends on the type of deflection and depends directly on the process speed. The maximum observed depth was 1.49 mm. The electron beam defocusing affects the width of the hardened track and can cause an extension of the trace up to 40%. The hardness values continuously decrease from the surface to the material volume.