Name: impact loading on a fixed rod
Uploaded: 2024-05-23T13:00:12.000Z
Duration: 1 min 19 s
Channel: JoVE

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Arizona Science Standards

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Physical Science

HS+Phy.P3

HS+Phy.P3U2.5

Impact Loading

Si consideri un'asta di sezione trasversale uniforme fissata a un'estremità. Quando un altro oggetto in movimento colpisce l'estremità libera dell'asta, l'asta si deforma e al suo interno si sviluppa una sollecitazione. 
Quando l'asta raggiunge la massima sollecitazione, vibra intorno alla posizione media. Lo stress che si è accumulato scompare quando si arriva al riposo. Questi eventi sono noti come carico di impatto.
In questo caso, si presume che il corpo che colpisce trasferisca tutta la sua energia all'asta, il che significa che non si verifica alcuna dissipazione di calore e che il corpo che colpisce non rimbalza sull'asta.
Quindi, l'energia di deformazione corrispondente allo stress massimo è uguale all'energia cinetica del corpo che colpisce.
Nel regime elastico della deformazione, l'energia di deformazione può essere riscritta in termini di sollecitazione massima e modulo di elasticità.
Riorganizzando i termini, si ottiene un'espressione per la massima sollecitazione in termini di velocità del corpo che colpisce.
L'ipotesi qui utilizzata si traduce in una progettazione conservativa per il carico d'impatto, poiché le ipotesi non sono valide nei sistemi reali.

carico d'impatto

Il carico d'impatto si verifica quando un oggetto in movimento urta una struttura stazionaria, come un'asta con un'area di sezione trasversale uniforme fissata ad un'estremità. In queste condizioni, l'asta assorbe l'energia cinetica dell'oggetto colpito, provocandone la deformazione e il conseguente sviluppo di tensioni. Quando l'asta ritorna nella sua posizione originale e raggiunge il massimo stress, l'energia assorbita, inizialmente manifestata come energia cinetica, si trasforma interamente in energia di deformazione.

Nei casi di deformazione elastica, dove il materiale ritorna alla sua forma iniziale senza danni permanenti, l'energia di deformazione accumulata nel punto di massima deformazione è equivalente all'energia cinetica dell'oggetto in movimento. Quest’equivalenza presuppone che nessuna energia venga persa a causa del calore o del rimbalzo, un'idealizzazione che non si trova tipicamente negli ambienti pratici. Da questa relazione si può ricavare la sollecitazione massima subita dall'asta in base alla velocità e alla massa dell'oggetto che colpisce e al modulo di elasticità dell'asta.

<img alt="Equation 1" src="/files/ftp_upload/15686/15686_Equation_1v2.svg" style="height: 40px;">

Le ipotesi formulate in questa analisi portano ad un approccio conservativo alla progettazione ingegneristica, garantendo che le strutture possano resistere a forze impreviste. Questo approccio spesso si traduce in un’ingegneria eccessiva, che incorpora fattori di sicurezza per tenere conto delle perdite di energia e di altre dinamiche non coperte dal modello teorico.

Si consideri un'asta di sezione trasversale uniforme fissata a un'estremità. Quando un altro oggetto in movimento colpisce l'estremità libera dell'asta, l'asta si deforma e lo stress ...

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impact loading on a fixed rod

Impact loading on a fixed rod happens when a moving object strikes a stationary rod that has a uniform cross-sectional area and is fixed at one end. The impact makes the rod deform and begin to develop stress. This setup shows how a sudden hit can store energy in a structure.

As the rod moves back toward its original shape, the stress rises to a maximum. At that point, the energy from the moving object has changed from kinetic energy into strain energy. Kinetic energy is the energy of motion, and strain energy is the energy stored during elastic deformation.

For elastic deformation, the rod returns to its original shape without permanent damage. In that ideal case, the strain energy at maximum deformation is equal to the kinetic energy of the striking object. This relationship assumes that no energy is lost as heat or through rebound, which is rarely true in real situations.

From this energy balance, the maximum stress in the rod can be derived using the mass and velocity of the moving object and the rod’s modulus of elasticity. The result gives engineers a conservative design approach. It can also lead to over-engineering, with safety factors added to account for energy losses and other effects not included in the model.

Impact Loading on a Fixed Rod

strain energy

Load-Deformation and Stored Strain Energy

Strain energy is the energy stored in a material when it deforms under load. It is a key idea in materials science and structural engineering. A loaded rod fixed at one end shows this clearly. When an axial force pulls on the free end, the rod stretches and stress builds inside it. As the axial force increases, the rod elongates more. This creates a direct link between the applied force and the amount of deformation. Engineers can show this relationship with a load-deformation plot. The plot...

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Energy Stored in Loaded Rods

Energy stored in a rod under axial load helps show how a material will respond to stretching and breaking. When the rod elongates, it stores strain energy as potential energy inside the material. Strain energy density is the amount of that energy per unit volume. In the elastic region, stress and strain have a linear relationship that follows Hooke's Law. The strain energy density in this region is found from the area under the stress-strain curve up to the elastic limit. This recoverable...

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Strain Energy in Stressed Materials

Strain energy in stressed materials describes the energy stored when a material deforms under load. It is an important idea in materials science and engineering. For axial loading with a uniform stress distribution, the stress is the internal force divided by the cross-sectional area, and the strain follows from the stress through the modulus of elasticity. When the stress is uniform, the strain energy density can be found from the product of stress and strain. That density is then integrated...

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Shear energy stored in twisted shafts depends on elastic strain energy in a material. This energy is stored when a solid is deformed within its elastic limit. It comes from internal work done against the cohesive forces inside the material. When a material carries shearing stress, it also develops shearing strain. The strain energy density is the energy stored per unit volume. Within the elastic limit, stress is proportional to strain through the modulus of rigidity, so the strain energy...

impact loading

Impact loading on a fixed rod happens when a moving object strikes a stationary rod that has a uniform cross-sectional area and is fixed at one end. The impact makes the rod deform and begin to develop stress. This setup shows how a sudden hit can store energy in a structure. As the rod moves back toward its original shape, the stress rises to a maximum. At that point, the energy from the moving object has changed from kinetic energy into strain energy. Kinetic energy is the energy of motion,...

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Using Strain Energy to Find Deflection

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Beam Deflection from Central Load

Beam deflection from a central load can be found with Castigliano's theorem. The method applies to a simply supported beam with a point load at the center. It links the deflection at the load point to the strain energy stored in the beam. For this beam, the supports share the load equally. Each support carries half of the force. The bending moment at any point along the beam comes from these reactions and is written using the distance from the nearest support. Castigliano's theorem says the...

key terms and concepts

Learn how a moving object striking a fixed rod creates stress, strain energy, and maximum stress in elastic deformation, with a conservative design model.

Impact Loading on a Fixed Rod | JoVE K12

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Impact Loading on a Fixed Rod

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