Name: equivalent resultant loads on beams
Uploaded: 2023-09-22T11:49:23.000Z
Duration: 1 min 21 s
Channel: JoVE

Bir ucunda sabitlenmiş ve dağıtılmış bir yüke maruz kalmış konik bir ışın OB'sini düşünün.
Değişen yükün eşdeğer bileşke kuvvetini belirleyin ve kiriş üzerindeki konumunu bulun.
İlk olarak, dağıtılmış yükü iki üçgen bölgeye bölün.
Daha sonra, sol ve sağ üçgen bölgenin eşdeğer bileşke yükünün büyüklüğü, her üçgenin alanına eşittir.
Ortaya çıkan her yük, üçgenin dikey kenarı AD'den taban uzunluğunun üçte birinde bulunan merkezlerde hareket eder.
Eşdeğer bileşke yükü, her bir üçgen bölgenin ayrı ayrı ortaya çıkan yükünün eklenmesiyle belirlenebilir.
O noktası etrafındaki moment, ortaya çıkan her bir yük nedeniyle hareket eden bireysel momentin eklenmesiyle belirlenebilir.
O noktası etrafındaki eşdeğer bileşke yükün momentinin, eşdeğer bileşke yükün çarpımına ve O noktasına olan mesafeye eşit olduğunu belirten moment ilkesini hatırlayın.
Denklemdeki değerlerin yerine konmasıyla, eşdeğer bileşke yükün yeri belirlenebilir.

<ol>
	<li>Hibbeler, R.C. (2016). Mühendislik Mekaniği \u2012 Statik ve Dinamik. Hoboken, New Jersey: Pearson Prentice Salonu, s. 194-195</li>
</ol>

dağıtılmış yükler: problemlerin Çözümü

Kirişler, farklı yük taşıma kapasitelerine ihtiyaç duyulan mühendislik uygulamalarında yaygın olarak kullanılan yapısal elemanlardır. Dağıtılmış bir yük altındaki bir kirişi analiz etmenin ilk adımı, yükü daha küçük bölgelere ayırarak problemi basitleştirmektir. Bu, her bölgeyi ayrı ayrı ele almayı ve kirişin her bölümünde etkili olan eşdeğer sonuç yükünün büyüklüğünü hesaplamayı sağlar. Her bölge için eşdeğer sonuç yükünün büyüklüğü, ilgili bölgelerin alanının hesaplanmasıyla belirlenebilir, bu alan yükün her bölgede uyguladığı kuvveti temsil eder.

Sonraki adım, her eşdeğer sonuç yükünün kiriş üzerindeki konumunu belirlemektir. Bu, bölgelerin ağırlıklarının düşünülebileceği noktalar olan merkez kuvvetlerini bulmak suretiyle yapılabilir. Bireysel eşdeğer sonuç yükleri, bu merkezlerde etki eder ve kiriş üzerinde belirli noktalarda kuvvetlerini uygular.

Tüm kiriş için eşdeğer sonuç yükü, belirlenen bireysel eşdeğer sonuç yüklerinin büyüklük ve konumlarıyla hesaplanabilir. Bunun için farklı bölgelerin bireysel eşdeğer sonuç yükleri bir araya getirilerek kiriş üzerinde etkili olan toplam eşdeğer sonuç yükü bulunur.

Sonraki adım, bir noktadaki momenti belirlemektir, genellikle kirişin sabit ucu kullanılır. Moment, kiriş üzerinde etkili olan kuvvetin döndürme etkisini ölçer. Sonuçta oluşan moment, her yüke bağlı olarak ortaya çıkan bireysel momentlerin toplanmasıyla belirlenebilir. Her yükün momenti, kuvvetin belirli noktadan olan uzaklığı ile çarpımına eşittir.

<img alt="Equation 1" src="/files/ftp_upload/14280/14280_PT_Equation_1.svg" style="text-align: center; height: 11px;" />

Moment ilkesini hatırlayarak, belirtilen noktadaki eşdeğer sonuç yükünün momenti, eşdeğer sonuç yükü ile o noktadan olan uzaklığın çarpımına eşittir.

<img alt="Equation 2" src="/files/ftp_upload/14280/14280_PT_Equation_2.svg" style="text-align: center; height: 13px;" />

Eşitliği tekrar düzenleyerek ve terimleri yerine koyarak, eşdeğer sonuç yükünün kiriş boyunca olan konumu belirlenebilir.

<img alt="Equation 3" src="/files/ftp_upload/14280/14280_PT_Equation_3.svg" style="text-align: center; height: 35px;" />

Dağıtılmış Yükler: Problemlerin Çözümü

Kirişler, farklı yük taşıma kapasiteleri gerektiren mühendislik uygulamalarında yaygın olarak kullanılan yapı elemanlarıdır. Bir analiz etmenin ilk adımı ...

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

Distributed Loads: Problem Solving

equivalent resultant loads on beams

Equivalent resultant loads on beams can be found by breaking a distributed load into smaller regions. This makes the beam easier to analyze. Each region can then be handled on its own before the results are combined.

The magnitude of the equivalent resultant load for each region comes from the area of that region. In this setting, area represents the force applied by the distributed load over that part of the beam. After finding the force for each region, the position of each resultant load must be located.

The position is found by using the centroid of each region. A centroid is the point where the region’s mass can be treated as concentrated. The individual resultant loads act at these centroids, so each force is placed at a specific point along the beam.

Once the separate forces and locations are known, they are combined to find the equivalent resultant load for the full beam. This is done by adding the individual resultant loads from the different regions. The result gives the overall force acting on the beam.

The next step is to determine the moment about a chosen point, usually the fixed end of the beam. A moment is the turning effect of a force. The total moment comes from adding the moments created by each load, and each moment equals force times distance from the chosen point.

By using the moment principle, the moment of the equivalent resultant load about that point must equal the force multiplied by its distance from the point. Rearranging that relationship makes it possible to find where the single equivalent load acts along the beam. This gives both the size and location of the load that replaces the distributed loading.

Equivalent Resultant Loads on Beams

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distributed loads: problem solving

Equivalent resultant loads on beams can be found by breaking a distributed load into smaller regions. This makes the beam easier to analyze. Each region can then be handled on its own before the results are combined. The magnitude of the equivalent resultant load for each region comes from the area of that region. In this setting, area represents the force applied by the distributed load over that part of the beam. After finding the force for each region, the position of each resultant load...

key terms and concepts

Learn how to replace a distributed load with one equivalent resultant force on a beam by using areas, centroids, and moments to find its location.

Equivalent Resultant Loads on Beams | 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

Equivalent Resultant Loads on Beams

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