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

X ekseni boyunca parabolik ve trapez yük dağılımının bir kombinasyonu olan, değişen bir yüke maruz kalan L uzunluğunda bir kiriş.
Parabolik yükte, dx uzunluğu üzerinde dR kuvvetinin diferansiyel bir elemanını düşünün. Ortaya çıkan yük, diferansiyel elemanın yükleme uzunluğu boyunca entegre edilmesiyle elde edilir. Parabolik alanın merkezinde bulunur ve merkezin x koordinatı moment ilkesi kullanılarak belirlenir.
Trapez alanı, dikdörtgen ve üçgen alanlara bölünebilir ve ortaya çıkan yük merkez bölgelerine etki eder. Bu merkezler, üçgenin dikey tarafından dikdörtgenin uzunluğunun yarısına ve taban uzunluğunun üçte birine yerleştirilir.
Trapez alanı için ortaya çıkan yük, elde edilen tek tek yüklerin eklenmesiyle elde edilir ve moment prensibi ile belirlenen alanın merkezinden geçer.
Toplam dağıtılmış yük, moment prensibi ile belirlenen, birleşik alanın merkezinden geçen trapez ve parabolik alanların ortaya çıkan yüklerinin toplamıdır.

<ol>
	<li>Bira, F.P.; Johnston, E.R.; Mazurek, D.F; Cromwell, P.J. ve Öz, B.P. (2019). Mühendisler için Vektör Mekaniği \u2012 Statik ve Dinamik. New York: McGraw-Tepesi. sayfa 264</li>
	<li>Meriam, J.L.; Kraige, L.G. ve Bolton, J.N. (2020). Mühendislik Mekaniği \u2012 Statik. Hoboken, New Jersey: John Wiley. sayfa 273</li>
	<li>Hibbeler, R.C. (2016). Mühendislik Mekaniği \u2012 Statik ve Dinamik. Hoboken, New Jersey: Pearson Prentice Salonu. pp EM-2</li>
</ol>

tek eksen Üzerinden yük yükleme

Yapı mühendisliğinde, değişken yükler altındaki kirişlerin analizi, bu yapısal elemanların davranışını ve performansını anlamanın önemli bir tarafıdır. Yaygın bir senaryo, farklı yük dağılımlarının bir kombinasyonuna tabi tutulmuş bir kiriş içerir.

X ekseni boyunca değişken bir yüke maruz kalan L uzunluğunda bir kirişi ele alalım. Bu durumda, birleşik alanın sonuç yüklerini, konumlarını ve merkezini belirlemek ve bu yükleme koşulları altında kirişin tepkisini tahmin etmek önemlidir.

Öncelikle, parabolik yük dağılımını inceleyelim. Bir diferansiyel kuvvet dR'un küçük bir uzunluk dx üzerine etki ettiğini düşünelim. Parabolik alan için sonuç yükünü belirlemek için, diferansiyel eleman dR yükünün tam uzunluğu boyunca entegre edilir. Bu sonuç yükünün konumu, parabolik alanın merkezinde bulunur. Moment prensibi, merkezin x-koordinatını bulmak için kullanılır ve bu, bir alanın bir eksen etrafındaki birinci momentinin, alanın ve merkezin eksenden olan uzaklığının çarpımıyla eşit olduğunu belirtir.

Ardından trapezoidal yük dağılımı, bu dağılımı iki dikdörtgen ve üçgen bölgelere bölmek suretiyle analiz edilir. Bu bireysel bölgeler için sonuç yükleri, kendi merkezlerinde etki eder. Dikdörtgen alan için merkez, dikdörtgenin uzunluğunun yarısında yer alır. Üçgen alan için merkez, taban uzunluğunun üçte biri uzaklığında, üçgenin dikey kenarına göre yer alır.

Dikdörtgen ve üçgen bölgelerin bireysel sonuç yükleri toplanarak, trapezoidal alanın toplam sonuç yükü belirlenebilir. Bu sonuç yükünün konumu, trapezoidal alanın merkezi üzerinden geçer ve ayrıca moment prensibi kullanılarak belirlenebilir.

Benzer şekilde, parabolik ve trapezoidal alanların sonuç yükleri toplanarak, kiriş üzerindeki toplam sonuç yükü belirlenebilir. Toplam sonuç yükünün konumu, kombinasyonlu alanın merkezi üzerinden geçer ve moment prensibi kullanılarak daha ileri belirlenebilir.

Tek Eksen Üzerinden Yük Yükleme

Yapı mühendisliğinde, değişen yüklere maruz kalan kirişlerin analizi, bunların davranışını ve performansını anlamanın kritik bir yönüdür ...

Education

JoVE Core

Mechanical Engineering

Makine Mühendisliği

Unit 1

Ünite 1

Force System Resultants

Kuvvet Sistemleri Bileşkesi

KEY TERMS AND CONCEPTS

TEMEL TERİMLER VE KAVRAMLAR

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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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...

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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 Makine Mühendisliği, denge, kuvvetler, kafes kiriş analizi ve yapısal mekanik gibi temel konuları kapsayan kısa, anlaşılması kolay animasyonlu videolar sunar. Gerçek dünyadaki uygulamalarını keşfedin ve bilim insanlarının önderlik ettiği deneylerle bu kavramların uygulanmasına tanık olun.

mechanical engineering

Finding Resultant Loads on a Beam

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