Name: load-deformation and stored strain energy
Uploaded: 2025-05-22T09:06:18.000Z
Duration: 1 min 13 s
Channel: JoVE

한쪽 끝에 고정된 막대가 있고 자유 끝에서 축 방향 힘을 받으면 응력이 가해지고 막대가 늘어나는 것을 생각해 보십시오. 
축 방향 힘이 증가하면 연신율이 증가합니다. 축방향 힘 대 연신율의 플롯은 특징적인 하중-변형 플롯을 생성합니다.
막대가 약간 늘어남에 따라 축 방향 힘에 의해 수행되는 작업은 축 방향 힘과 해당 연신율의 곱입니다.
이 작업은 변형 플롯 아래의 면적과 동일하며, 그 너비는 작은 변형과 같습니다.
수행된 총 작업은 연신율 한계 내에서 방정식을 적분하여 계산할 수 있으며 동일한 연신율 한계 내에서 하중-변형 곡선 아래의 면적과 같습니다.
로드에서 수행된 총 작업은 변형 에너지로 알려진 시스템에 입력되는 에너지를 나타냅니다.
탄성 한계 내에서 축 방향 힘은 연신율에 비례합니다. 따라서 변형 에너지는 연신율의 제곱에 비례합니다.

변형 에너지

Strain Energy

변형 에너지는 재료 과학 및 구조 공학 분야의 기본 개념으로, 하중을 받아 변형될 때 재료나 구조에 의해 흡수되는 에너지를 설명합니다.

한쪽 끝이 고정되어 있고 자유 끝에서 축방향 힘을 받는 막대를 생각해 보십시오. 이 축방향 힘은 로드 내부에 응력을 유발하여 로드를 신장시킵니다. 축방향 힘이 증가함에 따라 로드의 신장도 증가하며, 이는 적용된 힘과 그에 따른 변형 사이의 직접적인 관계를 보여줍니다. 이 동작은 하중-변형 플롯으로 그래픽으로 표현될 수 있습니다.

막대를 약간 늘리기 위해 축방향 힘이 수행한 일은 힘과 해당 신장의 곱과 같습니다. 그래픽적으로 이 작업은 주어진 신장에 대한 하중-변형 곡선 아래 영역에 해당합니다. 주어진 신장에 대해 막대에 수행된 총 작업을 계산하려면 신장 한계에 대한 힘 신장 방정식을 적분해야 합니다. 이 총 일은 시스템에 입력된 에너지를 나타내며 변형 에너지로 저장됩니다. 재료의 탄성 한계 내에서 탄성 변형으로 인해 재료에 저장된 변형 에너지 U는 신장률의 제곱에 비례합니다.

<img alt="Equation 1" src="/files/ftp_upload/15682/15682_Equation_1.svg" style="height: 52px;">

변형 에너지의 개념을 통해 엔지니어는 재료나 부품의 에너지 흡수 용량을 정량화할 수 있으며, 이는 영구 변형이나 파손 없이 하중을 견딜 수 있는 능력을 평가하는 데 필수적입니다. 변형 에너지는 충격 흡수 장치, 에너지 저장 장치 설계, 충격력 분석 등 다양한 엔지니어링 응용 분야에서도 중추적인 역할을 합니다.

한쪽 끝에 고정된 막대가 있고 자유 끝에서 축 방향 힘을 받으면 응력이 가해지고 막대가 늘어나는 것을 생각해 보십시오.
로 ...

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교육

JoVE Core

Mechanical Engineering

기계공학

Unit 1

제1단원

Energy Methods

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KEY TERMS AND CONCEPTS

주요 용어 및 개념

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 makes it easier to see how much the rod stretches at each load.

The work done by the axial force over a small elongation is the force multiplied by that elongation. On the graph, this work appears as the area under the load-deformation curve for a given elongation. To find the total work for any elongation, the force-elongation equation is integrated over the elongation limits. That total work is the energy put into the system, and it is stored as strain energy.

Within the elastic limit of the material, the strain energy stored in the rod is proportional to the square of the elongation. This means the stored energy rises as the deformation increases, as long as the material still behaves elastically. Knowing strain energy helps engineers judge how much energy a material or component can absorb before permanent deformation or failure. It is also useful in shock absorbers, energy storage devices, and impact force analysis.

Load-Deformation and Stored Strain Energy

load-deformation-and-stored-strain-energy

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

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

Explore how load creates deformation in a rod, how work becomes stored strain energy, and why this matters in shock absorbers and impact analysis.

Load-Deformation and Stored Strain Energy | 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

Load-Deformation and Stored Strain Energy

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