Name: energy stored in loaded rods
Uploaded: 2024-05-23T13:00:11.000Z
Duration: 1 min 20 s
Channel: JoVE

축 방향 하중은 막대를 늘리고 그 안에 변형 에너지를 저장하게 합니다. 막대의 변형 에너지 밀도는 단위 부피당 에너지입니다.
여기서, 면적에 대한 축 방향 힘의 비율은 응력이고, 막대의 원래 길이에 대한 연신율의 비율은 생성 된 변형입니다.
탄성 영역 내에서 변형 에너지 밀도는 탄성 계수로 표현될 수 있습니다.
응력-변형률 곡선은 탄성 영역에서 선형 관계를 나타내며, 이는 변형 에너지 밀도가 Hooke의 법칙을 따른다는 것을 의미합니다. 여기서 응력을 제거하면 변형률이 0이 됩니다. 이 에너지 밀도 영역을 탄력성 계수(modulus of resilience)라고 합니다.
플라스틱 영역에서는 응력을 제거한 후에도 일부 영구적인 변형이 남아 있습니다. 따라서 변형 에너지 밀도의 일부만 회수되고 나머지 에너지 밀도는 물체를 열의 형태로 변형시키는 데 사용됩니다. 
곡선 아래의 총 면적을 인성 계수라고 하며 막대를 파열하는 데 필요한 총 에너지 밀도를 나타냅니다.

변형 에너지 밀도

Strain-Energy Density

축방향 하중을 받는 재료의 변형 에너지 밀도를 이해하는 것은 기계적 거동과 내구성을 평가하는 데 중요합니다. 막대가 이러한 하중을 받으면 변형 에너지라고 알려진 에너지를 재료 내의 위치 에너지로 늘려 저장합니다. 이 에너지는 단위 부피당 에너지로 측정됩니다.

재료의 탄성 영역에서 응력과 변형 사이의 관계는 선형이며 훅의 법칙을 따릅니다. 이 영역의 변형 에너지 밀도는 응력-변형 곡선 아래 영역에서 탄성 한계까지 계산됩니다. 이렇게 저장된 에너지는 회복 가능하며 탄성 계수라고 하며, 이는 재료가 얼마나 많은 에너지를 흡수하고 하역 시 원래 모양으로 돌아갈 수 있는지를 나타냅니다.

탄성 한계를 넘어서면 재료는 소성적으로 거동하여 영구적으로 변형됩니다. 이 소성 영역에서는 하역 시 저장된 에너지의 일부만 복구 가능합니다. 나머지는 열로 손실되거나 영구 변형에 사용됩니다. 재료가 파열되기 전에 흡수할 수 있는 총 에너지는 인성 계수로 측정됩니다.

<img alt="Equation 1" src="/files/ftp_upload/15683/15683_Equation_1v2.svg" style="height: 44px;">

이 값은 높은 내충격성 또는 연성을 요구하는 응용 분야에 매우 중요하며, 특정 응용 분야에 대한 재료 선택과 기계적 하중을 견딜 수 있는 구조 설계에 도움이 됩니다.

축 방향 하중은 막대를 늘리고 그 안에 변형 에너지를 저장하게 합니다. 막대의 변형 에너지 밀도는 단위 부피당 에너지입니다.
여기서 비율은 ...

Education

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JoVE Core

Mechanical Engineering

기계공학

Unit 1

제1단원

Energy Methods

에너지 방법

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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 energy is called the modulus of resilience. It shows how much energy a material can absorb and still return to its original shape when the load is removed.

After the elastic limit, the material enters the plastic region. In this stage, the material deforms permanently, so only part of the stored energy comes back during unloading. The rest is lost as heat or used in permanent deformation. The total energy a material can absorb before rupture is called the modulus of toughness. This value is important when choosing materials for impact resistance and ductility, and for designing structures that must handle mechanical loads.

Energy Stored in Loaded Rods

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 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

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 axial load, strain energy density, modulus of resilience, and modulus of toughness describe how materials store and release energy.

Energy Stored in Loaded Rods | 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

Energy Stored in Loaded Rods

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