Name: finding resultant loads on a beam
Uploaded: 2023-09-22T11:49:22.000Z
Duration: 1 min 29 s
Channel: JoVE

다양한 하중을 받는 길이 L의 빔으로, x축을 따라 포물선 하중 분포와 사다리꼴 하중 분포의 조합입니다.
포물선 하중에서 길이 dx에 대한 힘 dR의 차동 요소를 고려하십시오. 결과 하중은 하중 길이에 걸쳐 차동 요소를 적분하여 얻습니다. 포물선 영역의 중심에 위치하며 중심의 x 좌표는 모멘트 원리를 사용하여 결정됩니다.
사다리꼴 영역은 직사각형과 삼각형 영역으로 나눌 수 있으며, 결과 하중은 중심에서 작용합니다. 이러한 중심은 삼각형의 수직 측면에서 직사각형 길이의 절반과 밑변 길이의 1/3에 위치합니다.
사다리꼴 영역에 대한 결과 하중은 개별 결과 하중을 더하여 얻어지며 모멘트 원리에 의해 결정된 영역의 중심을 통과합니다.
총 분포 하중은 사다리꼴 영역과 포물선 영역의 결과 하중의 합이며, 결합된 영역의 중심을 통과하며 모멘트 원리에 의해 결정됩니다.

<ol>
	<li>맥주, F.P.; 존스턴, ER; 마주렉, D.F; 크롬웰, PJ 및 셀프, BP (2019). 엔지니어를 위한 벡터 역학 \u2012 Statics and Dynamics. 뉴욕 : McGraw-Hill. 쪽 264</li>
	<li>메리암, J.L.; Kraige, L.G. 및 Bolton, J.N. (2020). 엔지니어링 역학 \u2012 정역학. 뉴저지 호보켄: 존 와일리. 쪽 273</li>
	<li>히벨러, R.C. (2016). Engineering Mechanics \u2012 정역학 및 동역학. 뉴저지 호보켄: 피어슨 프렌티스 홀. PP EM-2</li>
</ol>

단일 축을 따라 로드

구조공학에서 다양한 하중을 받는 보를 분석하는 것은 이러한 구조 요소의 거동과 성능을 이해하는 데 매우 중요한 측면입니다. 일반적인 시나리오는 다양한 하중 분포의 조합을 받는 보를 포함합니다.
x축에 따른 포물선 하중과 사다리꼴 하중 분포의 조합인 다양한 하중을 받는 길이의 보 L을 고려해 보겠습니다. 이 경우 이러한 하중 조건에서 보의 반응을 예측하기 위해서는 결과 하중, 위치 및 결합 영역의 중심을 결정하는 것이 필수적입니다.
먼저 포물선 하중분포를 살펴봅니다. 작은 길이 dR에 작용하는 미분요소 dx을 생각해보겠습니다. 포물선 영역의 최종 하중을 결정하기 위해 미분요소 dR은 전체 하중 길이에 걸쳐 적분됩니다. 최종 하중의 위치는 포물선 영역의 중심에 있습니다. 모멘트 원리를 적용하여 중심의 x좌표를 구하는데, 이는 축을 중심으로 한 영역의 첫 번째 모멘트는 면적과 축으로부터의 중심 거리의 곱과 같다는 것입니다.
다음으로 사다리꼴 하중 분포는 두 개의 직사각형 영역과 삼각형 영역으로 나누어 분석됩니다. 이 개별 영역에 대한 결과 하중은 각각의 중심에서 작용합니다. 직사각형 영역의 경우 중심은 직사각형 길이의 절반에 위치합니다. 삼각형 영역의 경우 중심은 삼각형의 수직 변에서 기준 길이의 1/3 떨어져 있습니다.
직사각형 영역과 삼각형 영역에 대한 개별 결과하중을 더하면 전체 사다리꼴 영역에 대한 결과하중을 결정할 수 있습니다. 결과하중의 위치는 사다리꼴 영역의 중심을 지나며, 이는 모멘트 원리를 이용하여 결정할 수도 있습니다.
마찬가지로 포물선 영역과 사다리꼴 영역의 결과 하중을 더하면 보에 작용하는 총 결과 하중이 결정됩니다. 총 결과 하중의 위치는 결합된 영역의 중심을 지나며, 이는 모멘트 원리를 사용하여 추가로 결정할 수 있습니다.

구조 공학에서 다양한 하중을 받는 빔의 분석은 이러한 하중의 동작과 성능을 이해하는 데 중요한 측면입니다.

Education

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JoVE Core

Mechanical Engineering

기계공학

Unit 1

제1단원

Force System Resultants

힘 체계의 합력

KEY TERMS AND CONCEPTS

주요 용어 및 개념

Load along a Single Axis

finding resultant loads on a beam

Structural engineering often requires finding the resultant load on a beam with changing force patterns. Here, a beam of length L carries a varying load made from parabolic and trapezoidal load distributions along the x-axis. The goal is to find the total load, where it acts, and the centroid of the combined area so the beam’s response can be predicted.

The parabolic load is handled first. A small force element, dR, acts over a short distance, dx, and these elements are integrated across the full length of the load. The resultant load for the parabolic area acts at the centroid of that area. The x-coordinate of the centroid is found with the moment principle, which says the first moment of an area about an axis equals the area times the distance to its centroid.

The trapezoidal load is then split into two simpler shapes. One part is rectangular, and the other is triangular. Their resultant loads act at their own centroids. For the rectangle, the centroid lies halfway along its length. For the triangle, the centroid is one-third of the base length from the vertical side.

After those parts are found, their loads are added to get the resultant load of the full trapezoidal area. That load passes through the centroid of the trapezoid, which can also be found with the moment principle. Finally, the resultant loads from the parabolic and trapezoidal areas are combined. Their sum gives the total load on the beam, and its location passes through the centroid of the combined area.

Finding Resultant Loads on a Beam

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key terms and concepts

Learn how parabolic and trapezoidal loads on a beam are broken into simpler areas, then combined to find the resultant force and centroid.

Finding Resultant Loads on a Beam | 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

Finding Resultant Loads on a Beam

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