Name: truss member force analysis by sections
Uploaded: 2025-05-22T09:06:03.000Z
Duration: 1 min 30 s
Channel: JoVE

Рассмотрим произвольную ферменную конструкцию, состоящую из диагональных, вертикальных и горизонтальных элементов, закрепленных на стене.
Метод сечений может быть использован для расчета силы, действующей на стержни CB, GB и GH.
Здесь нагрузки и длины горизонтальных и вертикальных стержней являются известными параметрами.
Разрез выполняется по плоскости, пересекающей стержни CB, GB и GH, и рисуется схема свободного тела правого бокового сечения.
Уравнение мгновенного равновесия относительно точки G дает силу вдоль CB. Положительный знак указывает на напряжение в стержне. 
Теперь FGB может быть выражен с помощью треугольника наклона в BCG, а FGH может быть выражен с помощью треугольника наклона в CEG.
Учитывая суммирование вертикальных и горизонтальных сил, можно записать уравнения равновесия сил.
Подставляется значение FCB. Уравнения равновесия сил решаются одновременно для получения силы вдоль членов GH и GB.
Отрицательный знак FGH указывает на то, что усилие является сжимающим, в то время как положительный знак для FGB указывает на растягивающее усилие.

<ol>
	<li>Р. К., Хиббелер Инженерная механика Статика, Пирсон. стр. 291-293</li>
	<li>Ф.. Бир, Э.Р. Джонстон, Д.Ф. Мазурек,.Д. Корнуэлл, Б.. Селф, Векторная механика для инженеров Статика и динамика Инженерная механика Статика, Mc Graw-Hill Education. С. 217</li>
</ol>

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Метод сечений: решение задачи ii

Рассмотрим произвольную ферму, состоящую из диагональных, вертикальных и горизонтальных элементов, закрепленных на стене. Для расчета сил, действующих на элементы CB, GB и GH, можно использовать метод сечений. Нагрузка и длина горизонтальных и вертикальных элементов являются известными параметрами, как показано на рисунке.

<img alt="Figure 1" src="/files/ftp_upload/14287/14287_PT_Fig_1v2.svg" style="text-align: center; height: 350px;" />

Для начала, выполняется разрез вдоль плоскости, пересекающей элементы CB, GB и GH, и рисуется свободная диаграмма сечения правой стороны.

<img alt="Figure 2" src="/files/ftp_upload/14287/14287_PT_Fig_2v2.svg" style="text-align: center; height: 350px;" />

Затем применяется уравнение моментного равновесия относительно точки G.

<img alt="Equation 1" src="/files/ftp_upload/14287/14287_PT_Equation_1v2.svg" style="text-align: center; height: 13px;" />

Результат дает силу вдоль элемента CB, равную 4 кН, с положительным знаком, указывающим на натяжение элемента.

Теперь FCB можно выразить с использованием треугольника наклона в BCG, а FGH можно выразить с использованием треугольника наклона в CEG. Учитывая сумму вертикальных и горизонтальных сил, уравнения равновесия сил могут быть записаны следующим образом:

<img alt="Equation 2" src="/files/ftp_upload/14287/14287_PT_Equation_2v2.svg" style="text-align: center; height: 15px;" />

<img alt="Equation 3" src="/files/ftp_upload/14287/14287_PT_Equation_3v2.svg" style="text-align: center; height: 13px;" />

Значение FCВ подставляется, и уравнения равновесия сил решаются одновременно. Результатом является сила FGH равная -7.454 кН и сила FGB равная 3.772 кН. Отрицательный знак FGH указывает на сжимающую силу, а положительный знак FGB указывает на растягивающую силу.

Метод сечений: решение задачи II

Рассмотрим произвольную ферменную конструкцию, состоящую из диагональных, вертикальных и горизонтальных элементов, закрепленных на стене. Чтобы рассчитать силу, действующую на стержни ...

Education

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Mechanical Engineering

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Unit 1

Раздел 1

Structural Analysis

Структурный анализ

KEY TERMS AND CONCEPTS

ОСНОВНЫЕ ТЕРМИНЫ И ПОНЯТИЯ

Method of Sections: Problem Solving II

truss member force analysis by sections

Truss member force analysis by sections finds the forces in selected members of a wall-mounted truss. The structure here includes diagonal, vertical, and horizontal members. The known loads and member lengths are used to solve for the forces in CB, GB, and GH.

A cut is made through members CB, GB, and GH. The right side of the truss is then isolated as a free-body diagram. Next, the moment equilibrium equation is taken about point G. This step gives the force in member CB as 4 kN, and the positive sign shows that CB is in tension.

The force in CB is then written with a slope triangle in triangle BCG. The force in GH is written with a slope triangle in triangle CEG. After that, the sums of vertical and horizontal forces are set equal to zero. The equation for CB is substituted, and the remaining equations are solved at the same time.

The final values are FGH = -7.454 kN and FGB = 3.772 kN. The negative sign for GH means the member is in compression. The positive sign for GB means the member is in tension.

Truss Member Force Analysis by Sections

truss-force-analysis-using-method-of-sections

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Truss member force analysis by sections finds the force in selected members of a truss. In this problem, forces F1 and F2 act at joints B and D. The goal is to determine the forces in members EF, DC, and DF. The method uses the idea that a truss in equilibrium also has each of its sections in equilibrium. A free-body diagram of the whole truss is drawn first. The moment equation about joint A is then used to estimate the support reaction at point E. Next, a cut is made along a sectional plane...

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Truss Member Force Calculation by Sections

Truss member forces can be found with the method of sections in a symmetrical roof truss. The structure here includes vertical, diagonal, and horizontal members. Each horizontal member is 4 m long. The vertical members FB and HD are 4 m long, and member GC is 6 m long. The roof truss carries loads at several joints. Joints F, G, and H each have a 2 kN load. Joints A and E each have a 1 kN load. To start the analysis, moment equilibrium is used at point A. The force and distance values are...

method of sections: problem solving ii

Truss member force analysis by sections finds the forces in selected members of a wall-mounted truss. The structure here includes diagonal, vertical, and horizontal members. The known loads and member lengths are used to solve for the forces in CB, GB, and GH. A cut is made through members CB, GB, and GH. The right side of the truss is then isolated as a free-body diagram. Next, the moment equilibrium equation is taken about point G. This step gives the force in member CB as 4 kN, and the...

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frames

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frames: problem solving ii

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machines

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key terms and concepts

Learn how the method of sections isolates a truss cut, uses moment and force balance, and identifies tension or compression in members CB, GB, and GH.

Truss Member Force Analysis by Sections | JoVE K12

JoVE Core Mechanical Engineering offers concise, easy-to-understand animated videos covering key topics such as equilibrium, forces, truss analysis, and structural mechanics. Explore their real-world applications, and witness these concepts in action through scientist-led experiments.

mechanical engineering

Truss Member Force Analysis by Sections

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