Name: beam load analysis with shear diagrams
Uploaded: 2025-05-22T09:06:04.000Z
Duration: 1 min 24 s
Channel: JoVE

Rozważmy belkę przenoszącą dwa obciążenia skupione i obciążenie rozłożone. Narysuj wykres momentu ścinającego i zginającego dla belki.
Najpierw narysuj wykres swobodnego ciała belki i za pomocą równania równowagi uzyskuje się siły reakcji.
Następnie podziel belkę na różne sekcje i narysuj schemat swobodnego ciała każdej sekcji. Stosując równanie równowagi dla przekrojów, można wyznaczyć ścinanie dla poszczególnych przekrojów.
Ścinanie pozostaje stałe między obciążeniami skupionymi a siłami reakcji, podczas gdy zmienia się liniowo ze stałym nachyleniem w sekcji obciążenia rozłożonego.
Obszar pod krzywą ścinania między dwoma punktami jest równy zmianie momentu zginającego między tymi samymi dwoma punktami.
Biorąc pod uwagę zerowy moment zginający na końcu belki i przywołując zależność między zmianą momentu zginającego a powierzchnią pod krzywą ścinania, obliczany jest moment zginający w każdym punkcie.
Wykres momentu zginającego jest rysowany poprzez połączenie znanych punktów liniami prostymi dla regionów o stałym ścinaniu i linią paraboliczną dla regionów o ścinaniu liniowym.

<ol>
	<li>Piwo, F.P.; Johnston, E.R.; Mazurek, D.F.; Cromwell, PJ i Jaźń, BP (2019). Mechanika wektorowa dla inżynierów \u2012 Statyka i dynamika. Nowy Jork: McGraw-Hill. Strony 394-395.</li>
</ol>

diagram ścinania i momentu zginającego: rozwiązywanie problemów

Aby analizować belkę wspierającą obciążenie skupione i obciążenie rozłożone, należy narysować diagram ścinania i momentu zginającego. Te diagramy pomagają zrozumieć siły wewnętrzne i momenty działające na belkę, co jest kluczowe dla projektowania bezpiecznych i efektywnych konstrukcji. Postępuj zgodnie z poniższymi krokami, aby tworzyć diagramy ścinania i momentu zginającego:

1. Narysuj diagram ciała swobodnego: Zacznij od narysowania diagramu ciała swobodnego całej belki, włącznie z obciążeniem skupionym, obciążeniem rozłożonym i siłami reakcji na podporach. Przy zastosowaniu równań równowagi (suma sił i momentów równa się zero) można określić siły reakcji na podporach.

2. Podziel belkę na sekcje: Podziel belkę na różne sekcje na podstawie rozkładu obciążenia. Na przykład, można utworzyć oddzielne sekcje dla obszarów między obciążeniami skupionymi, obciążeniem skupionym i siłami reakcji oraz wewnątrz obciążenia rozłożonego. Narysuj diagram ciała swobodnego dla każdej sekcji.

3. Określ siły ścinające: Zastosuj równanie równowagi do diagramów ciał swobodnych poszczególnych sekcji, aby obliczyć siłę ścinającą dla poszczególnych sekcji. Zauważ, że siła ścinająca pozostaje stała między obciążeniem skupionym a siłami reakcji, podczas gdy w sekcji z obciążeniem rozłożonym zmienia się liniowo z równomiernym nachyleniem.

4. Oblicz momenty zginające: Aby znaleźć momenty zginające w różnych punktach belki, przypomnij sobie, że pole pod krzywą ścinającą między dwoma punktami równa się zmianie momentu zginającego między tymi punktami.

5. Narysuj diagram ścinania i momentu zginającego: Na koniec, stwórz diagramy siły ścinającej i momentu zginającego, rysując obliczone wartości.

Diagram ścinania i momentu zginającego: rozwiązywanie problemów

Podczas analizy belki przenoszącej obciążenia skupione i obciążenie rozłożone niezbędne jest narysowanie wykresów momentu ścinającego i zginającego. Te schematy ...

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

Education

JoVE Core

Mechanical Engineering

Inżynieria mechaniczna

Unit 1

Jednostka 1

Internal Forces

Siły wewnętrzne

KEY TERMS AND CONCEPTS

Kluczowe terminy i pojęcia

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 the sum of forces and the sum of moments equal zero, to find the support reactions.

Next, divide the beam into sections based on where the loading changes. Sections may be placed between concentrated loads, between a load and a reaction force, or within the distributed load region. Then draw a free-body diagram for each section so the forces on that part of the beam are clear.

After that, determine the shear force in each section using equilibrium. Shear force stays constant between concentrated loads and reaction forces. In the distributed load section, it changes linearly with a constant slope.

Finally, use the shear curve to find bending moments. The area under the shear curve between two points equals the change in bending moment over that span. Plot the calculated values to create the shear force diagram and the bending moment diagram.

Beam Load Analysis with Shear Diagrams

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

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...

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

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

Learn how to analyze a beam with concentrated and distributed loads by finding support reactions, shear force, and bending moment diagrams.

Beam Load Analysis with Shear Diagrams | 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 Load Analysis with Shear Diagrams

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