Name: beam deflection from loads and supports
Uploaded: 2024-05-23T13:00:01.000Z
Duration: 1 min 15 s
Channel: JoVE

빔 설계에서 중요한 구성 요소는 편향을 식별하고 측정하는 것입니다. 변형에 대한 포괄적인 이해는 불확정 빔을 처리할 때 필요합니다.
두 개의 집중 하중을 전달하는 돌출된 빔을 생각해 보십시오. 지지대에서의 반응은 빔의 자유물체 다이어그램을 분석하여 계산됩니다.
자유물체 다이어그램과 반응 지지대를 사용하여 빔이 어떻게 구부러지는지 설명하는 굽힘 모멘트 다이어그램이 구성됩니다.
굽힘 모멘트 다이어그램은 빔이 양의 굽힘 모멘트로 인해 시작과 특정 지점 사이에서 위쪽으로 곡선을 이루고, 음의 굽힘 모멘트로 인해 해당 지점에서 빔의 끝까지 아래쪽으로 곡선을 그리는 것을 보여줍니다.
곡선의 가장 큰 값 또는 가장 작은 곡률 반경은 굽힘 모멘트가 가장 높은 지지부에서 발생합니다.
빔의 상세한 분석 및 설계를 위해서는 다양한 지점에서 빔의 편향 및 기울기에 대한 정확한 데이터를 확보하는 것이 중요하며, 특히 최대 편향을 이해하는 데 중점을 둡니다.

횡하중을 받는 빔의 변형

특히 돌출된 마디와 다중 집중 하중이 있는 불확실한 빔의 경우 빔 처짐을 이해하는 것은 구조적 무결성과 기능성을 보장하는 데 중요합니다. 이 과정은 빔에 작용하는 힘과 모멘트를 식별하는 데 도움이 되는 정확한 자유 물체 다이어그램을 구성하는 것으로 시작됩니다. 이 다이어그램은 굽힘 모멘트가 빔의 길이에 따라 어떻게 변하여 곡률에 영향을 미치는지 시각화하는 데 매우 중요합니다.

굽힘 모멘트 다이어그램의 통찰력은 빔의 곡률 분석까지 확장됩니다. 빔의 곡률은 빔을 따른 굽힘 모멘트와 상관관계가 있으며 빔의 강성 및 단면과 반비례합니다. 굽힘 모멘트가 높을수록 곡률이 커지며 이는 빔의 편향 프로필을 이해하는 데 필수적입니다.

특히, 과도한 처짐은 구조적 문제나 심지어 파손으로 이어질 수 있으므로 최대 처짐에 중점을 둡니다. 이러한 최대 처짐은 일반적으로 곡률이 가장 큰 곳, 즉 지지대 근처나 하중이 가해지는 지점 바로 아래에서 발생합니다. 빔 설계가 안전 표준을 준수하고 기능적 요구 사항을 충족하는지 확인하려면 이러한 최대 편향을 식별하는 것이 중요합니다. 자유물체 및 굽힘 모멘트 다이어그램을 사용하여 철저한 해석을 수행함으로써 안전하고 특정 하중 조건 및 건축 요구 사항에 적합한 구조를 효과적으로 설계할 수 있습니다.

빔 설계에서 중요한 구성 요소는 편향을 식별하고 측정하는 것입니다. 편향에 대한 포괄적인 이해가 필요합니다 ...

deformation-of-a-beam-under-transverse-loading

Education

교육

JoVE Core

Mechanical Engineering

기계공학

Unit 1

제1단원

Deflection of Beams

보의 처짐

KEY TERMS AND CONCEPTS

주요 용어 및 개념

Deformation of a Beam under Transverse Loading

beam deflection from loads and supports

Beam deflection depends on the loads on a beam and the support conditions at its ends. For indeterminate beams, especially those with overhanging parts and multiple concentrated loads, careful analysis is needed to predict how the beam will bend.

The first step is to draw an accurate free-body diagram. A free-body diagram shows the forces and moments acting on the beam. It helps reveal how the bending moment changes along the beam length.

The bending moment diagram also shows how the beam will curve. Beam curvature is related to the bending moment and is affected by the beam’s stiffness and cross-section. When the bending moment is higher, the curvature is greater, so the deflection profile becomes easier to evaluate.

The main goal is to find the maximum deflection. Too much deflection can cause structural problems or even failure. This largest deflection often appears where curvature is greatest, such as near supports or directly under applied loads. Using free-body and bending moment diagrams helps engineers design beams that stay safe and meet functional requirements under specific loading conditions.

Beam Deflection from Loads and Supports

deformation of a beam under transverse loading

Beam deflection depends on the loads on a beam and the support conditions at its ends. For indeterminate beams, especially those with overhanging parts and multiple concentrated loads, careful analysis is needed to predict how the beam will bend. The first step is to draw an accurate free-body diagram. A free-body diagram shows the forces and moments acting on the beam. It helps reveal how the bending moment changes along the beam length. The bending moment diagram also shows how the beam...

equation of the elastic curve

Beam Deflection and Boundary Conditions

Beam deflection and boundary conditions help describe how a beam bends under load. In structural engineering, the curvature of a plane curve shows how sharply the beam bends. That curvature is found from the curve’s first and second derivatives. A cantilever beam with a point load at its free end is a common example. A diving board works like this type of beam. When slopes are small, the beam’s elastic curve becomes the main shape used in the analysis. The governing equation connects bending...

elastic curve from the load distribution

Beam Deflection Under Distributed Load

Beam deflection under distributed load is a key part of beam analysis in engineering. It helps predict how a beam bends and reacts when a load is spread along its length. Engineers use this relationship to judge whether a structure will stay safe and functional. The analysis starts with the link between load, shear force, and bending moment. These quantities can be written in differential form. When beam flexibility is treated as constant, further differentiation leads to a higher-order...

deflection of a beam

Beam Slope and Deflection by Singularity

Beam slope and deflection can be found with singularity functions when beam loading is hard to write as one simple equation. This method is useful in structural engineering because it helps describe beams under several loads without breaking the problem into many separate cases. Singularity functions are mathematical tools for showing discontinuities in a load, shear force, or bending moment equation. They are especially helpful when a load acts at a single point or over a set interval. In the...

method of superposition

Beam Deflection Under Combined Loads

Beam deflection under combined loads can be found with the method of superposition. This structural engineering method is used to analyze how multiple loads affect a beam. It works by finding the slope and deflection from each load separately, then adding those results together. The method applies only when the beam stays within its elastic limit. In that range, the material deforms in a linearly elastic way. That makes it valid to combine the effects of separate loads without changing the...

moment-area theorems

Beam Deflection Using Moment-Area Rules

The moment-area theorems help describe beam bending in structural engineering. They are often used for building floor supports and other beams under load. The theorems use the elastic curve, which is the shape a beam takes as it deforms. The first theorem links slope change to area on an M/EI diagram. Here, M is the bending moment, E is the modulus of elasticity, and I is the moment of inertia. When M/EI is plotted along the beam length, the area under the curve gives the total rotation...

beams with symmetric loadings

Moment-Area Method for Cantilever Deflection

The moment-area method is used in structural engineering to find the slope and deflection of a beam under load. It is especially useful for a cantilever beam with a concentrated load and a moment at the free end. The analysis begins with a free-body diagram. This diagram helps calculate the reactions at the fixed end. After that, the bending moment diagram is drawn to show how the bending moment changes along the beam. Points where the bending moment is zero are important in this step. Next,...

beams with unsymmetric loadings

Beam Deflection and Level Points

Beam deflection and level points can be found for a supported beam under unsymmetrical loadings using moment-area theorems. This type of analysis helps show how a beam bends when forces are spread unevenly along it. It is an important part of structural engineering because it links load patterns to beam response. The first moment-area theorem is used to find the slope at any point on the beam. It states that the change in slope between two points equals the area under the moment diagram over...

maximum deflection

Locating the Beam’s Highest Deflection

Maximum deflection in a supported beam depends on where the load is placed. With an unsymmetrical load, such as a train moving across a bridge, the beam may bend most at a point that is not the midpoint. Finding that point is important for judging stress and deflection in the structure. The point of maximum deflection is called point O. At point O, the tangent to the deflection curve is horizontal. That means the slope is zero there. To locate point O, the slope at any point X along the beam...

key terms and concepts

Learn how free-body diagrams and bending moment diagrams help predict beam deflection, identify maximum deflection, and check structural safety under load.

Beam Deflection from Loads and Supports | 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

Beam Deflection from Loads and Supports

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