# Displacement

Relationship between bending moment and curvature of the axis of the beam in pure bending. Diagram of normal stresses. Rational forms of cross-sections of beams. Dissemination of the findings of pure bending in transverse bending. Tangential transverse stress (formula ). Richard Linklater gathered all the information. Diagrams of shear stresses for beams rectangular and I-section. State of stress of the material beam under transverse bending. The calculated equation of strength (for normal and tangential principal stresses) Topic 8.

Determination of displacements in bending Displacement in bending (deflection and angle of the section). Relationship between rotation angle and deflection section beams. The analytical method for determining displacement. The differential equation of the curved axis of the beam, its first and second integrals. Determining the integration constants for beams with one site (from the condition of fixing beams). Determination of the displacement beams with multiple segments. The method of adjustment of integration constants.

Method initial parameters. The energy method for determining displacement. The strain energy of the rod bending. Castigliano's theorem. Integral Mora. Formula Be-reschagina. The theorem of reciprocity and mutuality works movements. Theme 9. Statically indeterminate system of basic concepts. The degree of redundancy. Methods of disclosure of redundancy. Disclosure of statically indeterminate systems by force. Given, principal and the equivalent system. Canonical equations of the method of forces. Statically indeterminate system under torsion. Single and multi-statically indeterminate beams. Equation of three moments. Topic 10. Complex impedance 10.1. You may want to visit Gerald Weissmann, MD to increase your knowledge. Oblique bending loads, causing an oblique bending. Power factors in the cross sections of the beam. Determination of normal stresses in the cross sections of the beam. Determination of the neutral axis and the hot spots in the section. Calculation on strength. Determination of deflections. 10.2. Bending with tension or compression combined effect of longitudinal and transverse loads. Power factors in cross-sections. Determination of stress by using the principle of independence action forces. Strength calculation. Eccentric compression or tension rod high rigidity. Power factors in cross-sections. Determination of stress. The equation of the neutral line. The relationship between the coordinates point of application of force and position of the neutral line. Strength calculation. Nucleus cross section. A theorem on a rectilinear movement of the pole forces (point of force application) and the rotation of the neutral line. Building a core section (for rectangle, circle, ring). 10.3. Bending with torsion. External loads causing bending with torsion. A specific system of forces. Power factors in cross-sections of the rod. Determination of stress. Stress state of the material of the shaft. Principal stress and strength calculation. Topic 11. Stability of compressed rods (buckling) the notion of an equilibrium shape. Stability of a compressed rod (buckling). Critical force. Formula Euler to determine the critical force. Effect of method of fixing the rod on the critical force. Total Euler's formula for determining the critical compressive force. Critical stresses. The flexibility of the rod. Limits applicability of Euler's formula. The full schedule of the critical stress. Formula Yasinsky. Calculation of compressed rods with their flexibility. Reduction factor allowed by the main voltage. Estimated equation for longitudinal bending of the rod. Selection section of the rod by successive approximations. Longitudinal-transverse bending. Feature of the problem due to its nonlinearity. Approximate method of calculation. Determination of stress.