Name: beam load analysis with moment diagrams
Uploaded: 2025-05-22T09:06:03.000Z
Duration: 1 min 30 s
Channel: JoVE

Rozważmy zwisającą belkę AC pod rozłożonym obciążeniem, podpartą na dwóch połączeniach. Skonstruuj wykres momentu zginającego.
Narysuj wykres swobodnego ciała belki, a za pomocą równań równowagi można obliczyć siły reakcji na każdej podporze.
Zastosuj metodę przekroju do belki.
Następnie rozważ dowolną odległość x w regionie AB. Siła wypadkowa działa w środku przekroju. Korzystając z równania równowagi na wykresie ciała swobodnego i podstawiając wartości, otrzymuje się równanie momentu.
Podobnie rozważmy dowolny punkt w regionie p.n.e. Rysując wykres ciała swobodnego i używając równania równowagi, określa się równanie momentu dla przekroju BC.
Podstawiając wartości położenia w równaniach momentu, obliczane są wartości momentu zginającego.
Wykres momentu zginającego przedstawia graficzne przedstawienie wartości momentu zginającego na całej długości belki.
Przywołując równanie momentu i stosując metodę różniczkowania, uzyskuje się maksima lokalne dla każdego przekroju.
Wykres momentu zginającego uzyskuje się poprzez połączenie tych punktów za pomocą krzywych parabolicznych.

<ol>
	<li>Hibbeler, R.C. (2016). Mechanika inżynierska \u2012 Statyka i dynamika. Hoboken, New Jersey: Pearson Prentice Hall. str. 362.</li>
</ol>

wykres momentu zginającego

Wykres momentu zginającego to graficzna reprezentacja momentów zginających, jakim poddana jest belka na całej jej długości. To niezbędne narzędzie dla inżynierów i projektantów do analizy konstrukcji i zapewnienia ich wytrzymałości na działające siły. Poniżej znajduje się lista kroków do stworzenia wykresu momentu zginającego dla belki.

Określ siły reakcyjne i momenty skręcające: Oblicz wszystkie reakcje podporowe oraz momenty działające na belkę. W pewnych przypadkach, gdy belka jest nachylona pod kątem, te siły są rozkładane na składowe działające prostopadle i równolegle do osi belki.

Podziel belkę i narysuj diagram swobodnego obiektu: Wybierz dowolny przekrój belki, licząc od jej lewego końca. Analizuj różne przekroje na długości belki. Na każdym założonym odstępie podziel belkę i stwórz diagram swobodnego obiektu jednego z segmentów. Upewnij się, że moment zginający (M) jest przedstawiony w jego dodatnim kierunku, zgodnie z przyjętą konwencją znakową.

Oblicz moment zginający: Zastosuj równania równowagi momentów, aby obliczyć moment zginający (M) w wybranym przekroju.

Narysuj wykres momentu: Stwórz wykres momentu (M versus x) na podstawie otrzymanego momentu zginającego wzdłuż długości belki. Jeśli wartości obliczonej funkcji opisującej M są dodatnie, narysuj wartości powyżej osi x. W przeciwnym przypadku, jeśli wartości są ujemne, narysuj je poniżej osi x.

Postępując zgodnie z tymi krokami, można skonstruować dokładne wykresy momentu zginającego i siły tnącej dla dowolnej belki. Wykresy te są kluczowe przy projektowaniu elementów konstrukcyjnych, takich jak belki nośne, które muszą przenosić siły i momenty wywołane obciążeniami.

Wykres momentu zginającego

Wykres momentu zginającego jest graficznym przedstawieniem momentów zginających doświadczanych przez belkę pod obciążeniem na całej długości belki. Jest to niezbędny ...

Education

JoVE Core

Mechanical Engineering

Inżynieria mechaniczna

Unit 1

Jednostka 1

Internal Forces

Siły wewnętrzne

KEY TERMS AND CONCEPTS

Kluczowe terminy i pojęcia

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 act perpendicular and parallel to the beam axis. That gives the values needed for the next step.

Next, section the beam at an arbitrary distance from the left end and draw a free-body diagram for one part of the beam. The chosen distance can be moved to different regions along the beam length. On the cut section, show the bending moment, M, in the positive sense according to the sign convention.

Then apply the moment equilibrium equations to calculate the bending moment about the sectioned end. Use the results to plot the moment diagram, or M versus x, along the beam length. Positive values are drawn above the x-axis, and negative values are drawn below it. Following this method gives accurate shear and bending moment diagrams for beam design.

Beam Load Analysis with Moment Diagrams

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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...

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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...

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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...

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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 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

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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...

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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...

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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...

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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 beam loads by finding reaction forces, sectioning the beam, solving for bending moment, and plotting the moment diagram.

Beam Load Analysis with Moment 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 Moment Diagrams

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