Name: truss force analysis at joints a to e
Uploaded: 2023-09-22T11:49:24.000Z
Duration: 1 min 30 s
Channel: JoVE

Рассмотрим ферменную конструкцию с шарнирами без трения, закрепленными на стене, и роликовой опорой на земле. Если к узлу А приложена сила в 150 Н, то определите силы в каждом элементе фермы.
Силы в каждом стыке могут быть определены с помощью метода стыков.
Во-первых, угол между стержнями AC и AB может быть определен как тан, обратный отношению длины BC и AB.
Во-вторых, нарисуйте диаграмму свободного тела шарнира А и разложите силы на их составляющие. Применяя уравнения равновесия, можно определить неизвестные силы.
Далее, рисуя диаграммы свободного тела суставов B и C и используя уравнения равновесия, можно определить неизвестные силы в суставах B и C.
Наконец, нарисуйте схему свободного тела суставов D и E. Для стержней CD и EF разбейте силы на горизонтальную и вертикальную составляющие. Неизвестные силы в соединениях D и E могут быть определены с помощью уравнений равновесия.

<ol>
	<li>Хиббелер, Р.К. (2016). Инженерная механика \u2012 Статика и динамика. Хобокен, Нью-Джерси: Пирсон Прентис Холл. С. 276-277.</li>
</ol>

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Метод узлов: Решение задачи ii

Рассмотрим ферму с трением между узлами, закрепленной на стене и опоре-ролике. Если на узел A действует сила 150 Н, то с помощью метода узлов можно определить силы в каждом элементе фермы.

<img alt="Figure 1" src="/files/ftp_upload/14283/14283_PT_Fig_1v2.svg" style="text-align: center; height: 350px;" />

Угол между элементами AC и AB может быть найден, взяв обратный тангенс отношения длин BC и AB,, и результат полученный равен 67.38 градусов. Рассматривается силовая диаграмма узла A, и все неизвестные силы разлагаются на составляющие.

Условие равновесия вертикальных сил может быть использовано для определения силы, действующей на элемент CA, которая равна 173.08 Н.

<img alt="Equation 1" src="/files/ftp_upload/14283/14283_PT_Equation_1v2.svg" style="text-align: center; height: 15px;" />

Подобным образом, горизонтальное условие равновесия сил может быть использовано для нахождения силы FAB, которая равна 161.54 Н.

<img alt="Equation 2" src="/files/ftp_upload/14283/14283_PT_Equation_2v2.svg" style="text-align: center; height: 15px;" />

Силовые диаграммы узлов B и C рассматриваются, и условия равновесия вертикальных и горизонтальных сил применяются для расчета неизвестных сил FBD , FCD и and FEC. Полученные значения для FBD , FCD и FEC составляют 161.53 Н, 173.08 Н и 207.70 Н соответственно.

Наконец, рассматриваются силовые диаграммы узлов D и E, и условия равновесия вертикальных и горизонтальных сил применяются. Это дает значения FED и FDF, которые равны 138.46 Н и 265.39 Н соответственно.

Метод узлов: Решение задачи II

Рассмотрим ферменную конструкцию с шарнирами без трения, закрепленными на стене и роликовой опоре. Если к суставу А приложить усилие в 150 Н, то силы в каждом ...

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Method of Joints: Problem Solving II

truss force analysis at joints a to e

Truss force analysis at joints A to E uses the method of joints to find the force in each member. The truss has frictionless joints, a wall support, and a roller support. A 150 N force is applied at joint A, and the member forces are solved from joint to joint.

First, the angle between members AC and AB is found using the inverse tangent of the ratio of BC to AB. This gives an angle of 67.38°. A free-body diagram of joint A is then drawn, and each unknown force is split into vertical and horizontal components.

The vertical force equilibrium equation is used to find the force in member CA, which is 173.08 N. The horizontal force equilibrium equation gives the force in member AB as 161.54 N. Free-body diagrams for joints B and C are then used to continue the calculation.

At joints B and C, the vertical and horizontal equilibrium conditions are applied again. This gives FBD = 161.53 N, FCD = 173.08 N, and FEC = 207.70 N. Free-body diagrams of joints D and E are used last, and the same equilibrium steps give FED = 138.46 N and FDF = 265.39 N.

Truss Force Analysis at Joints A to E

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Truss force analysis at joints A to E uses the method of joints to find the force in each member. The truss has frictionless joints, a wall support, and a roller support. A 150 N force is applied at joint A, and the member forces are solved from joint to joint. First, the angle between members AC and AB is found using the inverse tangent of the ratio of BC to AB. This gives an angle of 67.38°. A free-body diagram of joint A is then drawn, and each unknown force is split into vertical and...

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key terms and concepts

Use the method of joints to solve truss forces at joints A to E. Find member forces from free-body diagrams, angles, and equilibrium equations.

Truss Force Analysis at Joints A to E | 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.

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Truss Force Analysis at Joints A to E

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