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CONTENTS

PREFACE……………………………………………………. 5
1 COMBINATION RESISTANCE…………………………… 6
1.1 General concepts………………………………………….. 6
1.2 Oblique bending…………………………………………... 7
1.3 Eccentrical tension – compression………………………… 13
1.4 Bending with torsion……………………………………..... 17
1.4.1 The rod of circular cross-section………………………… 17
1.4.2 The rod of rectangular section…………………………… 19
Questions for self-assessment………………………………..... 20
2 GENERAL METHODS OF DEFLECTION
DETERMINATION…………………………………………… 22
2.1 The work of elastic forces. The potential energy of
deflection of the rod with an arbitrary load…………………..... 22
2.2 Theorems of reciprocal works and reciprocal deflection….. 24
2.3 Kastyliano’s Theorem…………………………………….. 24
2.4 More’s integral…………………………………………….. 26
2.5 Calculation of Mora’s integral by Vereshchagin’s
method………………………………………………………..... 28
Questions for self-assessment………………………………..... 30
3 STATICALLY INDETERMINATE BEAM……………….. 31
3.1 General concepts………………………………………….. 31
3.2 The force method. The canonical equation……………….. 32
3.3 Checking coefficients and free terms of the canonical
equations……………………………………………………….. 34
3.4 Equation of three moments……………………………….. 35
Questions for self-assessment………………………………..... 40
4 CALCULATION OF CURVED BEAMS…………………... 41
4.1 Construction of the internal forces diagrams……………… 41
4.2 Calculation of stresses in cross sections of curved beams.
Conditions strength…………………………………………..... 44
4.3 Calculation of the displacement curves in uneven bars…… 48
Questions for self-assessment………………………………..... 49
5 STABILITY OF COMPRESSED RODS…………………… 50
5.1 Stable and unstable elastic equilibrium of compressed rod.. 51
5.2 Euler’s problem…………………………………………… 52
5.3 Influence of rod fixing on the value of the critical force….. 54

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