title: ÐÐ·Ð³Ð¸Ð± Ð¶ÐµÑÑÐºÐ¾Ð¹ Ð½Ð°ÑÑÐ½ÑÑÐ¾Ð¹ ÑÑÑÑÐ½Ñ ÑÐ¾ÑÑÐµÐ´Ð¾ÑÐ¾ÑÐµÐ½Ð½Ð¾Ð¹ ÑÐ¸Ð»Ð¾Ð¹
title: Bending of a tensioned beam under the point load
Creators: name: ÐÐµÐ»ÑÐ½Ð¸ÐºÐ¾Ð²Ð°, ÐÐ°ÑÐ°Ð»Ð¸Ñ
name: ÐÑÐ´ÑÑÑÐ¾Ð², ÐÐ²Ð³ÐµÐ½Ð¸Ð¹
name: "Ð¡Ð¾Ð²ÑÐµÐ¼ÐµÐ½Ð½Ð¾Ðµ Ð¼Ð°ÑÐ¸Ð½Ð¾ÑÑÑÐ¾ÐµÐ½Ð¸Ðµ: Ð½Ð°ÑÐºÐ° Ð¸ Ð¾Ð±ÑÐ°Ð·Ð¾Ð²Ð°Ð½Ð¸Ðµ", Ð¼ÐµÐ¶Ð´ÑÐ½Ð°ÑÐ¾Ð´Ð½Ð°Ñ Ð½Ð°ÑÑÐ½Ð°Ñ ÐºÐ¾Ð½ÑÐµÑÐµÐ½ÑÐ¸Ñ (13; 2024; Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³)
Publisher: name: ÐÐÐÐÐ¢ÐÐ¥-ÐÐ ÐÐ¡Ð¡
Year: 2024
Subjects: ÐÐµÑ Ð°Ð½Ð¸ÐºÐ°
ÐÐ°Ð»ÐºÐ¸
ÑÐ°ÑÑÑÐ¶ÐµÐ½Ð¸Ðµ
Ð³ÐµÐ¾Ð¼ÐµÑÑÐ¸ÑÐµÑÐºÐ°Ñ Ð¸ Ð¸Ð·Ð³Ð¸Ð±Ð½Ð°Ñ Ð¶ÐµÑÑÐºÐ¾ÑÑÐ¸
stretching
geometric and bending stiffness

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description: The paper examines analytical solutions to the problem of a tensioned beam under the action of a transverse point load. The nature of the solutions is analyzed depending on the boundary conditions, including fixed and hinged supports. A dimensionless parameter Îº has been identified, the value of Îº allows to decide whether it is necessary to take the bending stiffness of the string into account. A comparison of the obtained solutions with classical solutions for an ideally flexible string is given. The results showed that at large values of Îº, the influence of bending stiffness on the displacement of the wire can be neglected when the load is in the middle of the span. When the load is at supports, the influence of bending stiffness on the solution cannot be neglected. For a rather flexible wire with Îº&gt;&gt;1, the maximal bending moment (and maximal bending stress) occur in the central part of the span and do not depend on the length of the span. The magnitude of the moment is determined, in addition to the magnitude of the load, by the parameter characterizing the ratio of the geometric and bending stiffness of the wire.