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3.4 Classification of stress states……………………………….57
3.5 Plane stress state……………………………………………58
3.5.1 Definition of normal and tangential stresses on an arbitrary
plane…………………………………………………………….59
3.5.2 Finding the position of principal planes and the value of
principal stresses………………………………………………..60
3.5.3 Finding the extreme tangential stresses and the position of
shift planes………………………………………………………63
3.6 Components deformations. The concept of deformed state of
the point…………………………………………………………65
3.7 Generalized Hooke's law…………………………………...67
3.8 Changing the volume of the body in deformation………….68
3.9 Potential energy in a volume stress state…………………..70
3.10 Strength theories…………………………………………..70
Questions for self-assessment……………………………….....75
4 SHEAR. CALCULATIONS FOR CUT AND CRUSHING…76
4.1. The concept of pure shear………………………………….76
4.2 Hooke's law in shear………………………………………..77
4.3 Potential energy of deformation in shear…………………...80
4.4. Condition of strength in shear……………………………..80
4.5 Calculations for cut and crushing…………………………..81
Questions for self-assessment……………………………….....87
5 TORSION……………………………………………………88
5.1 The twisting moment……………………………………….88
5.2 Differential equations of equilibrium………………………89
5.3 Torsional stress of the circular cross-section rod…………..90
5.4 Calculation for strength…………………………………….94
5.5 Deformations and displacements in torsion. Calculation for the
hardness…………………………………………………………95
5.6 Potential energy of deformation……………………………97
5.7 Statically indeterminate problems in torsion……………….99
5.8 Torsion of noncircular cross-section rod…………………...100
5.9 Rational form of cross section……………………………..102
Questions for self-assessment………………………………….103
6 DIRECT CROSS BENDING………………………………...105
6.1 Bending moment and shear force………………………….105
6.2 Differential equations of equilibrium………………………107
6.3 Determination of normal stresses…………………………109
6.4 Determination of tangential stresses……………………….114
6.5 Calculation for the strength under direct cross bending……118
6.6 Beams of rational cross-section……………………………121

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