Abstract
The problem of pure bending of an elastic curved beam with a given moment M is considered. It is proved that the values of stresses and strains found in this paper depend on the value of the Poisson's ratio μ. An exact analytical solution to this problem is obtained with the determination of unambiguous expressions for stresses and deformations.
Highlights
It is proved that the values of stresses and strains found in this paper depend on the value
An exact analytical solution to this problem is obtained with the determination of unambiguous expressions
А. Полный расчет на прочность упругой балки при изгибе / А
Summary
Рассмотрим задачу чистого изгиба изотропного упругого бруса под действием сосредоточенного изгибающего момента [1, 3,4,5,6]: ( В случае плоского напряженного состояния закон Гука имеет вид: Будем искать деформации в следующем виде: где и – искомые константы; Подставим напряжения (6) в уравнение равновесия (1): Подставим формулы (7) в уравнение (8): ( )
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