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CONTENTS

PREFACE…………………………………………………….6
1 BASIC CONCEPTS AND INITIAL STATEMENTS………7
1.1 The science of strength of materials……………………….7
1.2 The real object and computational model………………….9
1.2.1 Model of the material…………………………………….9
1.2.2 Model of the form of a deformable body……………….10
1.2.3 Modeling of support fixing………………………………11
1.2.4 Modeling loadings……………………………………….12
1.3 Deformation at the point…………………………………..15
1.4 Limitations and principles adopted in strength of materials.16
1.4.1 Smallness of deformations (the principle of original
dimensions)…………………………………………………….16
1.4.2 The principle of superposition……………………………16
1.4.3 Saint Venant’s principle…………………………………. 17
1.5 Method of sections…………………………………………18
1.6 The concept of stress……………………………………….20
1.7 The relation between internal force factors and stress……..21
1.8 Model of a deformable rod…………………………………23
Questions for self-assessment……………………………….....24
2 CENTRAL TENSION – COMPRESSION………………….25
2.1 Longitudinal force………………………………………….25
2.2 Differential equations of equilibrium………………………25
2.3 Stresses in cross-sections of the rod………………………..27
2.4 Longitudinal and cross deformations………………………30
2.5 Determination of displacements. Differential equations of
motion…………………………………………………………..33
2.6 Consideration of rod own weight…………………………..35
2.7 Mechanical tests of materials under static tensile and
compression…………………………………………………….36
2.8 Allowable stress. Strength calculation…………………….. 42
2.9 The energy of deformation…………………………………44
2.10 Statically indeterminate system…………………………...46
Questions for self-assessment……………………………….....49
3 THEORY OF STRESS-STRAIN STATE…………………...51
3.1 The concept of the state of stress at a point………………..51
3.2 Determination of stresses at arbitrarily the oriented
platform………………………………………………………...52
3.3 Main areas and Main stresses………………………………54
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