Name: sizing beams for safe bending loads
Uploaded: 2024-05-23T12:59:46.000Z
Duration: 1 min 23 s
Channel: JoVE

K12 Standards

Texas Essential Knowledge and Skills

High School

Physics

PHYS.2

PHYS.2.D

Design of Prismatic Beams for Bending

Процесс проектирования призматических балок, подверженных изгибу, начинается с определения допустимого напряжения для выбранного материала.
Допустимое напряжение обычно получается из таблицы свойств материалов или проектных спецификаций. В качестве альтернативы она может быть рассчитана путем деления предельной прочности материала на подходящий коэффициент запаса прочности.
Затем строятся диаграммы поперечной силы и изгибающего момента, соответствующие заданным условиям нагружения.
Далее рассчитывается максимальное абсолютное значение изгибающего момента с помощью диаграммы поперечной силы.
Затем рассчитывается минимально допустимый модуль сечения с использованием абсолютного значения изгибающего момента балки и допустимого напряжения.
При проектировании деревянной балки обычно указывается соотношение, характеризующее форму ее поперечного сечения. Неизвестные размеры определяются с помощью соотношения между размерами балки и модулем сечения.
При проектировании стальной прокатной балки обращаются к таблице, содержащей свойства стальной прокатной балки, и учитываются только те сечения балки, у которых модуль сечения больше или равен минимально необходимому модулю сечения.

Расчет призматических балок на изгиб

При проектировании призматических балок, элементов конструкции с равномерным поперечным сечением, основное внимание уделяется обеспечению безопасности и целостности конструкции в условиях нагрузки. Процесс проектирования начинается с определения допустимого напряжения либо по таблицам свойств материала, либо путем деления предельной прочности материала на коэффициент безопасности. Этот коэффициент безопасности важен для учета неопределенностей и варьируется в зависимости от материала — дерева, стали или бетона — каждый из которых имеет уникальные характеристики прочности и напряжения. Его значение будет зависеть от выбранного материала и предполагаемого использования конструкции.

Затем строятся диаграммы силы сдвига и изгибающего момента, чтобы визуализировать распределение нагрузки и определить точки максимального изгибающего напряжения. Эта визуализация является ключом к оптимизации размеров балки, чтобы максимизировать ее безопасность и эффективность.

Наконец, рассчитывается минимальный момент сопротивления сечения, который позволит балке противостоять изгибающему напряжению. Более высокие модули указывают на большее сопротивление. Для деревянных балок проектировщик указывает соотношение формы поперечного сечения, обеспечивающее желаемый модуль упругости. Для стальных балок проектировщик выбирает из уже существующих секций, удостоверившись, что модуль балки превышает расчетный минимум. Такой выбор гарантирует, что балка выдержит изгибающие усилия, сохраняя структурную безопасность и стабильность.

Этот системный подход сочетает в себе соображения безопасности с анализом материалов и нагрузок, гарантируя, что выбранная балка сохраняет целостность и надежность конструкции при ожидаемых нагрузках, что в конечном итоге обеспечивает долгосрочную эксплуатацию конструкции.

Процесс проектирования призматических балок, подверженных изгибу, начинается с определения допустимого напряжения для выбранного материала.
Допустимое напряжение составляет...

Education

JoVE Core

Mechanical Engineering

Машиностроение

Unit 1

Раздел 1

Analysis and Design of Beams for Bending

Анализ и проектирование балок на изгиб

KEY TERMS AND CONCEPTS

ОСНОВНЫЕ ТЕРМИНЫ И ПОНЯТИЯ

sizing beams for safe bending loads

Prismatic beams have a uniform cross-section, and their design focuses on safe bending under load. The goal is to keep stress within a level the material can handle while the structure stays strong and stable.

The first step is to find the allowable stress for the chosen material. Designers can use values from material property tables, or they can divide the material's ultimate strength by a safety factor. This safety factor helps account for uncertainty, and its value depends on the material and the intended use of the structure.

Timber, steel, and concrete each have different strength and stress behavior, so the design method depends on the material. After selecting the material, the designer plots shear force and bending moment diagrams. These diagrams show how the load is distributed and help locate the points where bending stress is highest.

The final step is to calculate the minimum section modulus needed to resist bending stress. A higher section modulus means greater resistance to bending. For timber beams, the designer chooses a cross-section shape ratio that gives the needed modulus. For steel beams, the designer selects a standard section whose modulus is at least as large as the calculated minimum. This process helps the beam carry bending forces safely and maintain structural integrity over time.

Sizing Beams for Safe Bending Loads

design of prismatic beams for bending

Prismatic beams have a uniform cross-section, and their design focuses on safe bending under load. The goal is to keep stress within a level the material can handle while the structure stays strong and stable. The first step is to find the allowable stress for the chosen material. Designers can use values from material property tables, or they can divide the material's ultimate strength by a safety factor. This safety factor helps account for uncertainty, and its value depends on the material...

prismatic beams: problem solving

Timber Beam Design Under Distributed Load

Timber beam design under a distributed load uses the beam’s size and the wood’s properties to keep the structure safe. The beam’s length and width are known at the start. The timber’s grade and species also matter because they affect the allowable stress, which is the highest stress the material can safely handle. The first step is to treat the beam as a free body. A free-body diagram shows the forces and moments acting on the beam. From this, the support reactions can be found by balancing...

singularity functions for shear

Beam Shear Diagrams with Macaulay Brackets

Beam shear diagrams can be written with singularity functions when the load changes suddenly along the beam. In structural analysis, these functions help show discontinuous shear force with one mathematical expression, even when the loading is complex. They make it easier to describe how shear changes from one point to the next. The method starts with a free-body diagram of the beam. Then the beam is cut at specific points to check the shear force in each section. For a beam with width W and...

singularity functions for bending moment

Beam Load Modeling with Singularity Functions

Singularity functions help model beam loads and bending moments when the loading changes along the beam. They make it possible to write the bending moment with one mathematical expression instead of separate equations for each section. In this method, Macaulay’s brackets are often used to show where a load starts or stops. For a simply supported beam AB, the load is uniform from the midpoint M to the right support B. To find the bending moment, the beam is cut at different points. A cut...

key terms and concepts

Learn how prismatic beams are sized for bending by finding allowable stress, using shear and moment diagrams, and choosing the right section modulus.

Sizing Beams for Safe Bending Loads | JoVE K12

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Sizing Beams for Safe Bending Loads

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