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1. Σπίτι
2. Σεμινάρια
3. Μαθήματα Beam
4. Ένας πλήρης οδηγός για την δοκό Cantilever | Εκτροπές και Στιγμές

Ένας πλήρης οδηγός για την δοκό Cantilever | Εκτροπές και Στιγμές

Ορισμός ακτίνων Cantilever: Τι είναι μια ακτίνα Cantilever?

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, χρησιμοποιούνται για τον υπολογισμό της επίδρασης του φορτίου ανέμου που ενεργεί ταυτόχρονα σε συγκεκριμένες επιφάνειες, 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 onlytypically with fixed support. Προκειμένου να διασφαλιστεί ότι η δομή είναι στατική, the support must be fixed so that it is able to support all forces and στιγμές in all directions. Μια δοκός προβόλου συνήθως διαμορφώνεται έτσι, with the left end being the support and the right end being the cantilevered end:

Ένα καλό παράδειγμα δοκού προβόλου είναι ένα μπαλκόνι. Ένα μπαλκόνι υποστηρίζεται μόνο στο ένα άκρο, η υπόλοιπη δέσμη εκτείνεται σε ανοιχτό χώρο; δεν υπάρχει τίποτα που να το υποστηρίζει από την άλλη πλευρά. 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.

Εξισώσεις ακτίνων Cantilever

There are a range of equations for how to calculate cantilever beam forces and deflections. These can be simplified into simple cantilever beam formula, με βάση τα ακόλουθα:

Cantilever Beam Deflections

Λήφθηκε από το δικό μας τύπος και εξίσωση απόκλισης δέσμης σελίδα. Cantilever Beam equations can be calculated from the following formula, όπου:

• W = Φόρτωση
• L = Μήκος μέλους
• E = Συντελεστής Young
• I = η στιγμή της αδράνειας της δέσμης

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 article. Ωστόσο, there are short hand equations you can use. Για παράδειγμα, the equation for the bending moment at any point x along a cantilever beam is given by:

$$M_x = -Px$$

όπου:

$$M_x$$ = bending moment at point x
$$Π$$ = load applied at the end of the cantilever
$$Χ$$ = 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)

όπου: 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.

Πίεση δοκών Cantilever

How to calculate stress in a cantilever beam? Cantilever Stress is calculated from the bending force and is dependent on the beam’s cross-section. Για παράδειγμα, εάν ένα μέλος είναι αρκετά μικρό, δεν υπάρχει μεγάλη περιοχή διατομής για να εξαπλωθεί η δύναμη, έτσι το άγχος θα είναι αρκετά υψηλό. Το άγχος της ακτίνας Cantilever μπορεί να υπολογιστεί είτε από το σεμινάριο μας πώς να υπολογίσετε την ένταση της δέσμης ή χρησιμοποιώντας Λογισμικό SkyCiv Beam – που θα δείξει τις πιέσεις της δέσμης σας.

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

Οι προεξοχές εκτρέπουν περισσότερο από τα περισσότερα τύποι δοκών αφού υποστηρίζονται μόνο από το ένα άκρο. This means there is less support for the load to be transferred. Απόκλιση δοκού προβόλου can be calculated in a few different ways, συμπεριλαμβανομένης της χρήσης απλοποιημένων εξισώσεων ακτίνων προβόλου ή υπολογιστών και λογισμικού δέσμης προβόλου (περισσότερες πληροφορίες για τα δύο είναι παρακάτω). 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 $$= {φά}_{και} = Px$$

όπου:

$$F_y$$ = reaction force in the Y direction at support A (the fixed support)
$$M_z$$ = reaction moment about Z at support A (the fixed support)
$$Π$$ = the load applied at the end of the cantilever beam
$$Χ$$ = 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, ιδιότητες υλικού, και τα λοιπά. will be taken into account before finalizing a design.

Cantilever Beam Design

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

1. Φορτία: The cantilever must be able to support the applied loads, including the weight of the structure itself and any additional loads such as wind, χιόνι, και σεισμικά φορτία. 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, λυγισμός, 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. Εκτροπή: 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. Αντοχή: The structure should be designed to last for the intended service life with minimal maintenance required. This includes considering factors such as corrosion, κούραση, 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. Η SkyCiv έχει συντάξει μια λίστα με συνέδρια και συνέδρια από όλο τον κόσμο που είναι συγκεκριμένα και σχετικά με το ευγενές επάγγελμα του δομικού μηχανικού methods: The design must take into account the method of construction to be used, whether it be pre-fabricated, επί τόπου, και τα λοιπά. This will affect the type of connections and the overall layout of the structure.
8. Κόστος: 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. Για παράδειγμα, if the beam is steel and based in the US, it should comply with the requirements of AISC 360 Έλεγχοι σχεδιασμού

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

Λογισμικό ανάλυσης δέσμης SkyCiv allows users to analyze cantilever beam structures easily and accurately. Μπορείτε να λάβετε μια απλοποιημένη ανάλυση του μέλους δοκού σας, συμπεριλαμβανομένου αντιδράσεις, δύναμη διάτμησης, στιγμή κάμψης, εκτροπή, στρες, και απροσδιόριστα δοκάρια μέσα σε λίγα δευτερόλεπτα. Apply any combination of loads and complete a full design as per American, ευρωπαϊκός, Αυστραλός, Πρότυπα σχεδίασης ξύλου και ψυχρής έλασης – αυτόνομα, για να αναφέρουμε μερικά!

Αν θέλετε να το δοκιμάσετε πρώτα, Δωρεάν ηλεκτρονική αριθμομηχανή δέσμης είναι ένας πολύ καλός τρόπος για να ξεκινήσετε, ή απλά εγγραφείτε δωρεάν σήμερα!

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