This lecture notes is addressed to students in the direction of preparation 6.050304 - "Oil and gas engineering". The manual includes lectures on the complex impedattce of one-dimensional body - timber, compressed rod stability, strength rods under dynamic and cyclic at variable loads, calculation of statically undetectable beams, the basis of calculation of the strength of shells and thick-walled cylinders. It is designed to help students with better absorption of the material, a synthesis of the knowledge gained in prior probationary period, and in independent preparation for the exam or classes. У конспекті лекцій розглядаються основні поняття та початкові твердження про опір матеріалів, центральний розтяг стиск стержнів, теорія напружено - деформованого стану, розрахунки на зріз, зім'яття при крученні та прямому поперечному згині. CONTENTS PREFACE 6 1 BASIC CONCEPTS АND INITIАL 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. 53 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 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 crashing 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 6.7 The concept of bending center 122 6.8 Differential equations of the curved axis of a beam 125 6.9 Method of initial parameters 129 6.10 Calculation for hardness 133 6.11 Potential energy of deformation under bending 134 Questions for self-assessment 135 THE LIST OF SOURCES USED 137