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

K12 Standards

Arizona Science Standards

High School

Physical Science

HS+Phy.P3

HS+Phy.P3U2.5

Impact Loading

한쪽 끝에 고정된 균일한 단면적의 막대를 고려하십시오. 다른 움직이는 물체가 막대의 자유 끝에 부딪히면 막대가 변형되고 그 안에 응력이 발생합니다. 
막대가 최대 응력에 도달하면 평균 위치 부근에서 진동합니다. 쌓인 스트레스는 휴식이 되면 사라집니다. 이러한 이벤트를 충격 하중이라고 합니다.
여기에서는 타격체가 전체 에너지를 로드로 전달한다고 가정하는데, 이는 방열이 발생하지 않고 타격체가 로드에서 튕겨 나오지 않음을 의미합니다.
따라서 최대 응력에 해당하는 변형 에너지는 타격체의 운동 에너지와 같습니다.
변형의 탄성 영역에서 변형 에너지는 최대 응력과 탄성 계수의 관점에서 다시 쓸 수 있습니다.
항을 재정렬하면, 타격체의 속도에 관한 최대 응력에 대한 표현이 얻어집니다.
여기에 사용된 가정은 실제 시스템에서 유효하지 않기 때문에 충격 하중에 대한 보수적인 설계가 됩니다.

충격 하중

충격 하중은 움직이는 물체가 한쪽 끝이 고정된 균일한 단면적을 가진 막대와 같은 고정 구조물과 충돌할 때 발생합니다. 이러한 조건에서 로드는 충격 물체로부터 운동 에너지를 흡수하여 변형과 그에 따른 응력 발생을 초래합니다. 로드가 원래 위치로 돌아가 최대 응력에 도달하면 처음에는 운동 에너지로 나타나는 흡수된 에너지가 변형 에너지로 완전히 변환됩니다.

재료가 영구적인 손상 없이 초기 형상으로 돌아가는 탄성 변형의 경우, 최대 변형 지점에 축적된 변형 에너지는 움직이는 물체의 운동 에너지와 동일합니다. 이러한 등가성은 열이나 반동으로 인해 에너지가 손실되지 않는다고 가정하며, 이는 실제 환경에서는 일반적으로 찾아볼 수 없는 이상화입니다. 이 관계로부터 타격 물체의 속도와 질량, 막대의 탄성 계수에 따라 막대가 겪는 최대 응력을 도출할 수 있습니다.

<img alt="Equation 1" src="/files/ftp_upload/15686/15686_Equation_1v2.svg" style="height: 40px;">

이 분석에서 만들어진 가정은 구조물이 예상치 못한 힘을 견딜 수 있도록 보장하는 엔지니어링 설계에 대한 보수적인 접근 방식으로 이어집니다. 이러한 접근 방식은 이론적 모델에서 다루지 않는 에너지 손실 및 기타 역학을 설명하기 위해 안전 요소를 통합하여 과도한 엔지니어링을 초래하는 경우가 많습니다.

한쪽 끝에 고정된 균일한 단면적의 막대를 고려하십시오. 다른 움직이는 물체가 막대의 자유 끝에 부딪히면 막대가 변형되고 응력이 ...

Education

교육

JoVE Core

Mechanical Engineering

기계공학

Unit 1

제1단원

Energy Methods

에너지 방법

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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...

strain-energy density

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...

elastic strain energy for normal stresses

elastic-strain-energy-for-normal-stresses

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...

elastic strain energy for shearing stresses

elastic-strain-energy-for-shearing-stresses

Shear Energy Stored in Twisted Shafts

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,...

impact loading on a cantilever beam

Dropped-Weight Bending of a Cantilever Beam

Dropped-weight bending of a cantilever beam shows how impact loading changes a beam’s shape and stress. The beam has a circular cross-section and is fixed at one end. An object is dropped on the free end from a height h, so its potential energy from gravity becomes kinetic energy at impact. After the object hits the beam, the beam bends and develops a bending moment along its length. The bending is not uniform. The fixed end carries the highest strain energy, which is the energy stored in the...

castigliano&#39;s theorem

Using Strain Energy to Find Deflection

Castigliano's theorem uses strain energy to find deflection and rotation in elastic structures. Strain energy is the work done by external loads during elastic deformation. The theorem links that energy to the movement caused by the load. The key idea is simple. The partial derivative of the total strain energy with respect to a specific force gives the displacement at the point where that force acts. The same method also works for a moment, where the derivative gives the rotation at the point...

castigliano&#39;s theorem: problem solving

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

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.

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Impact Loading on a Fixed Rod

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