Mechanics of Deformable Solids
 DOI. 10.5281/zenodo.1286007

Subbotnitsky V.

VLADIMIR SUBBOTNITSKY, Candidate of Engineering Sciences, Professor, 
Department of Mechanics and Mathematical Modelling, School of Engineering, e-mail:v2s32@mail.ru
Far Eastern Federal University
8 Sukhanova St., Vladivostok, Russia, 690091 

The analysis of errors when determining shear stress in bending moments

Abstract: In the absence of torque, the tangential stresses in the cross sections of the rod are usually associated with the values of the transverse force and are determined by means of D.I. Zhuravsky’s well-known formula. However, this is not always correct. In beams with variable cross-section and even in those with constant rectangular section loaded with longitudinal load the stresses found by Zhuravsky’s formula can differ significantly from the actual ones. The tangential stresses in cross sections with a discontinuous changes in width are not always determined correctly. The article reveals the causes for wrong solutions. Zhuravsky’s formula as well as the type of its record and the scope of applicability is analysed in it. It considers a common method for determining the tangential stresses from all possible loads in beams with a given cross-section whose dimensions can vary along the axis of the rod. The stresses found by this method coincide with sufficient accuracy with the solutions performed by the methods of the theory of elasticity and the numerical ones in complex cases.
Key words: tangential stresses, transverse force, bending moment.

REFERENCES 
1. Kagan-Rozentsveig L.M. Technical theory of tangential stresses in a bent rod. Herald of civil engineers. 2017(62);3:40–49. 
2. Kagan-Rozentsveig L.M. Refinement of the formula for tangential stresses of the technical theory of bending. Herald of civil engineers. 2014(47);6:84–89. 
3. Mechanical engineering: an encyclopedia of 40 tons. Vol. 1–3. A.V. Alexandrovna. Alfutov, V.V. Astana et al. Dynamics and strength of machines. Theory of mechanisms and machines: in 2 books. M., Mechanical Engineering, 1995, 624 p. 
4. Harlab V.D. To the technical theory of tangential stresses in the case of plane bending of beams. Herald of civil engineers. 2016(54);1:82–88. 
5. Harlab V.D. Development of the elementary theory of tangential stresses in the case of plane bending of beams (I). Herald of civil engineers. 2015(48);1:82–87. 
6. Harlab V.D. Development of the elementary theory of tangential stresses in the case of plane bending of beams (II). Herald of civil engineers. 2015(51);4:74–78. 
7. Harlab V.D. Development of the elementary theory of tangential stresses in the case of plane bending of beams (III). Herald of civil engineers. 2017(64);5:77–82. 
8. Timoshenko S.P. History of strength of materials. New York. McGraw-Hill Book C., 1953, 452 p. 
    
 EDUCATIONAL LITERATURE ANALYZED in this ARTICLE   
9. Alexandrov A.V., Potapov V.D. Strength of materials. Fundamentals of the theory of elasticity and plasticity: a textbook for building specialties of universities. M., Higher School, 2002, 400 p. 
10. Alexandrov A.V., Potapov V.D., Derzhavin B.P. Resistance of materials: in 2 parts. Part 1: a textbook and a workshop for academic baccalaureate: 9th edition M., Yurayt, 2018, 293 p. 
11. Belyaev N. Strength of materials. M., Science, 1965, 856 p. 
12. Birger I.A., Mavlyutov R.R. Resistance of materials: a manual. M., Science, 1986, 560 р. 
13. Vardanyan G.S., Atarov N.M., Gorshkov A.A. Resistance of materials: textbook. M., INFRA-M., 2010. 480 p. (Series Higher Education). 
14. Kiselev V.A. The flat problem of the theory of elasticity, a textbook for high schools. M., Higher School, 1976, 151 p.
15. Filin A.P. Applied mechanics of a solid deformable body: Resistance of materials with elements of the theory of continuous media and structural mechanics. Vol. 2. M., Science, 1978, 616 p.
16. Gere J.M., Timoshenko S.P. Mechanics of materials. 4th ed., Boston, an International Thompson Publishing Co., 1997, 942 p.;