Publishing house of the Siberian Federal University, Krasnoyarsk Basic dimensionsĭokshanin SG, Mityaev AE, Troshin SI (2017) Structural machinery mechanics. Vestnik of Nosov Magnitogorsk State Technical University 3(16):98–102 Konev SV, Mikhaylets VF, Fainshtein AS, Teftelev IE (2018) Analysis of the characteristics of the stress state of the flange of the winding device as the annular plate. McGraw-Hill Book-Company, New York, Proceedings of the 6th international conference on industrial engineering (ICIE 2020), Springer Timoshenko SP, Voinovsky-Krieger S (2021) Theory of plates and shells. Timoshenko SP, Goodier J (1959) Theory of elasticity. Murakami Y (2016) Theory of elasticity and stress concentration. Weinberg DV, Weinberg ED (1970) Plate calculations. In: Proceedings of the 6th international conference on industrial engineering (ICIE 2020), Springer Konev SV, Fainshtein AS, Teftelev IE (2021) Calculating the flexure of circular plates with radial stiffening ribs. The effect of the stiffener on the flange flexure when it is arranged within the first (from the side of the inner radius) one-third part of the flange is 2.5–3 times higher than the effect resulting when the stiffener is arranged within the second one-third part of the flange. The analysis of the obtained relationships showed that the addition of one or two stiffening rings resulted in the reduction of spool flange flexure by 29–64%. The obtained findings allowed us to calculate the rigidity of a welding wire spool flange. The approximating function is defined as a beam function for a stepped beam with unit thickness. The calculation was based on the assumption that the middle plane curvature of the ring element was the same as that of the carrier plate, subject to the Kirchhoff hypothesis on normal middle plane element. This fact must be double-checked by calculating the potential strain energy of the stiffening ring more precisely. However, when there is a stiffening ring, the radial stresses existing within the section of the plate will be asymmetric. The flexure of rings with symmetrical cross-sectional shape gives rise to strain fields that are symmetric about the middle plane of the plate. Σ = F b d is larger than one.The authors performed calculation for thin rigid circular plates with stiffening rings by using the Ritz-Timoshenko variational energy method. Both of these forces will induce the same failure stress, whose value depends on the strength of the material.įor a rectangular sample, the resulting stress under an axial force is given by the following formula: If we don't take into account defects of any kind, it is clear that the material will fail under a bending force which is smaller than the corresponding tensile force. Conversely, a homogeneous material with defects only on its surfaces (e.g., due to scratches) might have a higher tensile strength than flexural strength. Therefore, it is common for flexural strengths to be higher than tensile strengths for the same material. However, if the same material was subjected to only tensile forces then all the fibers in the material are at the same stress and failure will initiate when the weakest fiber reaches its limiting tensile stress. When a material is bent only the extreme fibers are at the largest stress so, if those fibers are free from defects, the flexural strength will be controlled by the strength of those intact 'fibers'. In fact, most materials have small or large defects in them which act to concentrate the stresses locally, effectively causing a localized weakness. The flexural strength would be the same as the tensile strength if the material were homogeneous. Most materials generally fail under tensile stress before they fail under compressive stress, so the maximum tensile stress value that can be sustained before the beam or rod fails is its flexural strength. These inner and outer edges of the beam or rod are known as the 'extreme fibers'. At the outside of the bend (convex face) the stress will be at its maximum tensile value. At the edge of the object on the inside of the bend (concave face) the stress will be at its maximum compressive stress value. 1), it experiences a range of stresses across its depth (Fig. When an object is formed of a single material, like a wooden beam or a steel rod, is bent (Fig. 2 - Stress distribution through beam thickness
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