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Ein vollständiger Leitfaden für Kragbalken | Ablenkungen und Momente


Cantilever Beam Definition: Was ist ein Cantilever Beam??

A cantilever beam is a structural element that extends horizontally and is supported on only one end. The unsupported end is known as the cantilever, and it extends beyond the support point. Cantilever beams are often used in construction to support balconies, Dächer, and other overhangs. They can also be used in bridges and other structures to extend the deck out over a waterway or other obstacle.

Cantilever beams are members that are supported from a single side only – typischerweise mit fester Stütze. Um sicherzustellen, dass die Struktur statisch ist, the support must be fixed so that it is able to support all forces and Momente in alle Richtungen. Ein Ausleger wird normalerweise so modelliert, with the left end being the support and the right end being the cantilevered end:

Ein gutes Beispiel für einen Ausleger ist ein Balkon. Ein Balkon wird nur an einem Ende unterstützt, Der Rest des Strahls erstreckt sich über den offenen Raum; es gibt nichts, was es auf der anderen Seite stützt. Other examples would be the end of a continuous beam of a high rise building floor, or the cantilevered girders of a bridge segment.Cantilever Beam Equations.


There are a range of equations for how to calculate cantilever beam forces and deflections. These can be simplified into simple cantilever beam formula, basierend auf folgendem:

Cantilever Beam Deflections

Entnommen aus unserem Strahlablenkungsformel und -gleichung Seite. Cantilever Beam equations can be calculated from the following formula, wo:

  • W = Last
  • L = Mitgliederlänge
  • E = Elastizitätsmodul
  • I = Trägheitsmoment des Strahls
Beispiel für Auslenkung des Auslegers pl Auslegergleichung Durchbiegungsgleichung Punktlast
Beispiel für die Durchbiegung des Auslegers Auslegergleichung Durchbiegungsgleichung verteilte Last
Beispiel für die Auslenkung des Auslegerbalkens für die Punktbelastung des Freikörperdiagramms Auslegergleichung Durchbiegungsgleichung verteilte Last

Cantilever Beam Moments

So how do we calculate the maximum bending moment force of a cantilever beam? You can do this using the same method as shown in our how to calculate bending moment in a beam Artikel. jedoch, there are short hand equations you can use. Zum Beispiel, the equation for the bending moment at any point x along a cantilever beam is given by:

\(M_x = -Px\)


\(M_x \) = bending moment at point x
\(P. \) = load applied at the end of the cantilever
\(x \) = distance from the fixed end (support point) to point of interest along the length of the beam.

For a distributed load, the equation would change to:

\(M_x =∫wx\) over the length (x1 to x2)

wo: w = distributed load x1 and x2 are the limits of integration.

This equation is valid for a simple cantilever beam with a point load or a uniformly distributed load applied at the free end of the beam. It should be considered that cantilevers beam can have complex loading and boundary conditions, such as multiple point loads, varying distributed loads, or even inclined loads, in those cases the above equation might not be valid, and a more complex approach might be required, it’s where the FEA comes in handy.

Cantilever Beam Stress

How to calculate stress in a cantilever beam? Die Kragspannung wird aus der Biegekraft berechnet und ist abhängig vom Balkenquerschnitt. Zum Beispiel, wenn ein Mitglied ziemlich klein ist, Es gibt nicht viel Querschnittsfläche, über die sich die Kraft ausbreiten kann, Der Stress wird also ziemlich hoch sein. Die freitragende Balkenspannung kann entweder in unserem Tutorial ab berechnet werden wie man die Strahlspannung berechnet oder mit SkyCiv Beam Software – Dies zeigt die Spannungen Ihres Trägers.

It’s useful to note that cantilever beams typically result in tension on the upper fibres of the beam. This means that in the case of a concrete cantilever beam, primary tensile reinforcement is typically required along the upper surface. This is in contrast to a conventional concrete beam supported at both ends, where primary tensile reinforcement would typically exist along the bottom surface of the beam.

Cantilever Beam Reaction Forces

Ausleger lenken mehr ab als die meisten anderen Arten von Balken da sie nur von einem Ende unterstützt werden. Dadurch wird die abzutragende Last weniger unterstützt. Cantilever-Balkenablenkung kann auf verschiedene Arten berechnet werden, einschließlich der Verwendung vereinfachter Auslegerbalkengleichungen oder Auslegerbalkenrechner und -software (Weitere Informationen zu beiden finden Sie weiter unten). The equation for the reaction at a fixed support of a cantilever beam is simply given by:

Reaction Force in Y \( = R_y = P\)

Moment Force about Z \( = {F.}_{und} = Px\)


\(F_y \) = reaction force in the Y direction at support A (the fixed support)
\(M_z \) = reaction moment about Z at support A (the fixed support)
\(P. \) = the load applied at the end of the cantilever beam
\(x \) = distance of point load from support

This equation applies when the load is a point load on a cantilever. When the load is distributed, it is the summation of all forces in the horizontal direction that needs to be zero. The equation becomes:

\(∑F_x = 0\)

Where the reaction force would be the algebraic sum of all the horizontal forces acting on the structure. This equation assumes that the support is a fixed support, meaning that it does not have any rotation or translation. If the support has some degrees of freedom, the equation would change and become more complex. It’s important to keep in mind that this equation is just one step in analyzing a structure, in the design process of a real structure, several considerations such as load combinations, safety factors, Das FE-Modell besteht vollständig aus 3D-Timoschenko-Balken-FE mit 6. DOF, etc. will be taken into account before finalizing a design.

Cantilever Beam Design

When designing a cantilever structure, several important factors should be considered:

  1. Ladungen: The cantilever must be able to support the applied loads, including the weight of the structure itself and any additional loads such as wind, Schnee, und seismische Belastungen. The loads should be analyzed and distributed appropriately throughout the structure.
  2. Strength and stiffness: The cantilever must be strong and stiff enough to resist deflection, Knicken, and other types of failure. The properties of the materials used, such as the modulus of elasticity and yield strength, will affect the strength and stiffness of the structure.
  3. Stress concentration: The stress concentration at the fixed end of the cantilever must be taken into account in the design to prevent failure. Stress concentration can be reduced by using larger cross-sections or by using fillets or rounded corners.
  4. Ablenkung: The deflection of the cantilever under load should be analyzed to ensure that it remains within acceptable limits, both for structural safety and also for aesthetic reasons.
  5. Haltbarkeit: The structure should be designed to last for the intended service life with minimal maintenance required. This includes considering factors such as corrosion, ermüden, and the effects of weathering.
  6. Safety factors: Safety factors should be considered and included in the design to ensure that the structure can withstand unexpected loads or other unforeseen circumstances.
  7. Konstruktion methods: The design must take into account the method of construction to be used, whether it be pre-fabricated, vor Ort gegossen, etc. This will affect the type of connections and the overall layout of the structure.
  8. Kosten: Design should consider both initial cost and long-term maintenance costs.
  9. Building codes and regulations: The design must be compliant with the relevant building codes and regulations in the jurisdiction where the structure will be built. Zum Beispiel, if the beam is steel and based in the US, it should comply with the requirements of AISC 360 Design Checks

It’s important to keep in mind that this is not an exhaustive list, and the specific requirements and considerations for a cantilever design may vary depending on the particular structure and its intended use. A structural engineer with expertise in cantilever design would take all of these factors into account and more, to ensure that the design is safe and effective.

Cantilever Beam Software

SkyCiv Strahlanalyse-Software allows users to analyze cantilever beam structures easily and accurately. Sie können eine vereinfachte Analyse Ihres Trägers erhalten, einschließlich Reaktionen, Scherkraft, Biegemoment, Ablenkung, betont, und unbestimmte Strahlen in wenigen Sekunden. Apply any combination of loads and complete a full design as per American, europäisch, australisch, Canadian Standards, um ein paar zu nennen!

Wenn Sie es zuerst versuchen möchten, Kostenloser Online-Strahlrechner ist ein guter Anfang, oder melden Sie sich noch heute kostenlos an!

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