Name: beam internal force analysis at point a
Uploaded: 2023-09-22T11:49:26.000Z
Duration: 1 min 28 s
Channel: JoVE

考虑一根梁 OC 5千牛，成一定角度倾斜，并在两端有支撑。确定点处的内力载荷 A.
支撑梁的支座会产生反作用力。通过使用关于点 O 的力矩方程并代入数值，可确定点 C 处的反作用力。
梁的重量作用在中心点，可分解为其各个分量。
现在，设想一条通过点 A 的假想直线，将梁分为两部分。接着，绘制未知力最少的梁段的受力分析图。
通过回顾平衡方程并代入水平方向上的力的数值，可确定该截面上的法向力。
负号表示作用在横截面上的法向力的方向相反。
类似地，通过使用平衡方程并代入垂直力的数值，可确定该截面上的剪切力。
最后，利用力矩方程，可以确定点 A 处力矩的大小。

<ol>
	<li>Hibbeler， R.C. （2016） 工程力学:静力学和动力学 新泽西州霍博肯:Pearson Prentice Hall，第 345、355 页。</li>
</ol>

结构构件的内部载荷：求解问题

在结构构件的设计或分析过程中，考虑构件的内部载荷是非常重要的。这些内部载荷包括了法线力、剪力和弯矩。工程师可以通过计算这些内部载荷来确保结构构件可以支持其中的外部力。 为了说明这一点，让我们假设有一个5kN的梁OC，其倾斜角度为 53.13°，并与水平两端产生支撑。以此来确定A点的内部载荷。 <img alt="Equation 1" src="/files/ftp_upload/14299/14299_Figure_1v3.svg" style="text-align: center; height: 250px;"> 为此，我们首先需要计算位于点C处的反作用力。我们可以通过使用关于点O的力矩方程并代入到数值中来进行计算。 <img alt="Equation 1" src="/files/ftp_upload/14299/14299_Equation_1v2.svg" style="text-align: center; height: 13px;"> 这为我们确定点C处水平方向的反力提供了所需要的信息，即为1.87 kN。 接下来，假设梁的重量作用在中心位置，将其分解成各个分量。一旦我们计算出了点C处的反力并将梁的重量分解为其分量，我们就可以继续确定位于点A处的内部载荷。 为了实现这一点，假设通过点A的一条虚拟线能够将梁分为两个部分。然后，绘制处于未知力最少段的受力分析图。通过将平衡方程代入到水平方向上的力值，可以得到位于该部分的法线力为-5.12 kN。负号表示了在假定的方向上，截面上的法线力与所假定的方向是相反的。 类似地，通过使用平衡方程并代入到垂直方向上的力值，我们可以确定截面中的剪力为1.5 kN。最后使用力矩方程，我们可以确定点A处的弯矩的大小为8.94 kN·m。 通过遵循这些步骤，可以确定结构构件点A处的内部载荷。这个问题的解决过程对于确保结构构件能够承受设计要求的力量至关重要。

在设计或分析结构构件时，必须考虑构件内部产生的内力。这些内力……

internal-loadings-in-structural-members-problem-solving

Education

教育

JoVE Core

Mechanical Engineering

机械工程

Unit 1

第一单元

Internal Forces

内力

KEY TERMS AND CONCEPTS

关键术语与概念

Internal Loadings in Structural Members: Problem Solving

beam internal force analysis at point a

Beam internal force analysis shows how normal force, shear force, and bending moment act inside a structural member. These internal loadings help engineers check whether a beam can support the external forces applied to it.

The example uses a beam OC that weighs 5 kN and is inclined at 53.13° with the horizontal. The beam is supported at both ends. The goal is to find the internal loadings at point A.

The first step is to find the reaction force at point C. This is done by taking the moment equation about point O and substituting the known values. From this step, the horizontal reaction force at C is 1.87 kN. The beam’s weight is also treated as acting at the center, and it is resolved into horizontal and vertical components.

Next, an imaginary cut is made through point A. This splits the beam into two sections. A free-body diagram is then drawn for the section with the fewest unknown forces. Using equilibrium equations, the normal force at the cut is found to be -5.12 kN. The negative sign means the force acts opposite to the assumed direction.

The same section is used to find the shear force and bending moment. From the vertical force equation, the shear force is 1.5 kN. From the moment equation, the bending moment at point A is 8.94 kN·m. This step-by-step method shows how internal loadings are determined in a structural member.

Beam Internal Force Analysis at Point A

sign convention

Beam Forces: Tension, Shear, and Bending

Beam analysis depends on the internal forces and moments inside a structure. These include normal force, shear force, and bending moment. Engineers use the method of sections to cut the beam and find these values. A sign convention helps show whether each result is positive or negative. Normal force acts perpendicular to the beam’s cross-section. It can pull the material in tension or push it in compression. Tension is taken as positive, while compression is taken as negative. This makes it...

normal and shear force

Beam Loads and Internal Forces

Beam loads create internal forces inside a structure. Weight, pressure, and other external forces can all act on a beam. These internal forces affect the beam’s stability and strength. Engineers study these forces to find their size and direction. A common approach is the method of sections. In this method, an imaginary cut is made at a chosen point on the beam, and the forces at that section are analyzed. One internal force is the normal force, also called the axial force. It acts...

bending and torsional moments

Forces That Bend and Twist Materials

Bending and torsional moments describe how materials respond to force. These ideas are important in structural engineering because they help explain how beams, rulers, and screws change shape under load. A moment depends on both the size of the force and the distance from the point of interest to the force’s line of action. A bending moment forms when an external force makes a structural element bend. If the element bends upward, the top side is in compression and the bottom side is in tension.

internal loadings in structural members: problem solving

Beam internal force analysis shows how normal force, shear force, and bending moment act inside a structural member. These internal loadings help engineers check whether a beam can support the external forces applied to it. The example uses a beam OC that weighs 5 kN and is inclined at 53.13° with the horizontal. The beam is supported at both ends. The goal is to find the internal loadings at point A. The first step is to find the reaction force at point C. This is done by taking the moment...

beams

Beam Types and Support Conditions

Beams are key parts of structural engineering and construction. They support loads that act at different points along their length. Engineers use beam shape and support conditions to understand how a beam will perform. Beams can be classified by geometry. Straight beams are the most common and have a constant cross-section along their length. Tapered beams change in cross-section from one end to the other, while curved beams have a curved shape. Beam cross-section also matters. Common shapes...

shear diagram

Beam Shear Force Diagram

Beam shear force diagrams show how shear changes along the length of a supported beam. In beam mechanics, they help students track the internal shear force caused by perpendicular loads. The beam AB in this example is supported at both ends, so the first step is to draw a free-body diagram that shows the external forces and internal reactions. The reaction forces at supports A and B are found with equilibrium equations for force and moment. For the beam shown, the vertical reaction at A is 24...

bending moment diagram

Beam Load Analysis with Moment Diagrams

Beam load analysis uses a bending moment diagram to show how bending changes along the length of a beam. This diagram helps engineers and designers check whether a structure can handle applied forces. It is also useful for parts such as shelving arms, which must resist forces and moments from a load. To build the diagram, start by finding the reactive forces and any couple moments on the beam. In some cases, especially when a beam is inclined, these forces must be resolved into components that...

relation between the distributed load and shear

relation-between-the-distributed-load-and-shear

Shear Change Under Distributed Loading

Shear force changes along a beam under a distributed load. In structural analysis, this relationship helps explain how beams respond to loading conditions that also include concentrated loads and a couple moment. To study the link, consider a small beam section that has no concentrated load or couple moment on it. Draw a free-body diagram for that elemental section. It includes the distributed load along the beam, the shear force V(x) on the right-hand side of the cut, and a small added shear...

relation between the shear and bending moment

relation-between-the-shear-and-bending-moment

Shear and Moment Diagrams in Beam Loads

Shear and moment diagrams help show how a beam responds to loads. A beam can carry a distributed load, concentrated loads, and a couple moment. These loads create internal shear forces and bending moments. The beam is examined by isolating a small elemental section and drawing a free-body diagram. For that section to stay in equilibrium, the moment on the right side must be slightly larger than the moment on the left side. The distributed load also has a resultant force that acts at a...

shear and bending moment diagram: problem solving

shear-and-bending-moment-diagram-problem-solving

Beam Load Analysis with Shear Diagrams

Beam load analysis uses shear and bending moment diagrams to track the internal forces in a beam. These diagrams are important when a beam carries concentrated loads and a distributed load. They help show how the beam responds so structures can be designed safely and efficiently. The first step is to draw a free-body diagram of the whole beam. A free-body diagram shows the concentrated loads, the distributed load, and the reaction forces at the supports. Use the equilibrium equations, where...

cable subjected to concentrated loads

Finding Tension in a Loaded Cable

Flexible cables can carry vertical point loads between two fixed supports. The cable is treated as flexible, inextensible, and nearly weightless. Under these conditions, it changes shape to form straight-line segments, and each segment carries a constant tensile force. To analyze the cable, a free-body diagram is drawn for the whole cable. This helps identify the reaction forces at the supports. In many cases, the number of unknown reaction components is greater than the available equilibrium...

cable subjected to a distributed load

Finding Cable Shape Under Distributed Load

Cable shape under a distributed load is found by analyzing the forces along a small piece of the cable. This method is important in suspension bridge design because the main cables must carry changing loads safely. The load causes the tensile force in the cable to change, and it also creates cable deformation. The analysis starts with a free-body diagram of a short cable segment. The diagram shows the distributed load and the change in tensile force across that segment. Equilibrium equations...

cable subjected to its own weight

Cable Sag Under Its Own Weight

Overhead power transmission cables sag under their own weight, and that shape affects how they carry electricity across long distances. To study this behavior, the cable is analyzed with a generalized loading function. This function treats the load along the cable's arc length instead of its projected length, which gives a more accurate picture of the cable's response. The analysis then focuses on a small cable segment. A free-body diagram is drawn to show the forces acting on that segment.

cable: problem solving

Cable Tension Under Uniform Loading

Cable tension under uniform loading is found by analyzing a cable fixed between two supports. The problem starts with the support conditions and the load on the cable. From there, the cable’s shape must be described with an equation that matches the curve formed by the load. The next step is to integrate the shape equation to get the cable’s shape function. This makes it possible to solve for constants in the equation. The boundary condition at the origin gives one constant. The slope, which...

key terms and concepts

Find the internal normal force, shear force, and bending moment at point A of an inclined beam using equilibrium, reaction force, and a free-body diagram.

Beam Internal Force Analysis at Point A | 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

Beam Internal Force Analysis at Point A

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