Name: jib crane reaction forces in frames
Uploaded: 2023-09-22T11:49:25.000Z
Duration: 1 min 24 s
Channel: JoVE

Kasnaktan harici bir yüke sahip bir pergel vinç düşünün.
Vinç elemanlarının boyutları biliniyorsa, kasnakların sürtünmesiz olduğu düşünülürse pim bağlantılarındaki tepki kuvvetleri nelerdir?
Sistem, iki kuvvet elemanı BD ve çok kuvvet elemanı ABC'den oluşan bir çerçeve yapısıdır.
Bir serbest cisim diyagramı göz önüne alındığında ve alt kasnak bölümü için kuvvet denge koşulları uygulanarak kablodaki gerilim elde edilebilir.
C noktası göz önüne alındığında, dikey kablodaki gerilim aşağı doğru yönlendirilirken, yatay kablo için A bağlantısına doğru yönlendirilir.
DB üyesinde, FBD kuvveti bir eğim üçgeni kullanılarak ifade edilebilir.
A eklemindeki moment denge koşulu, BD boyunca kuvveti verir.
Kuvvet denge koşulları uygulanarak, A eklemindeki yatay ve dikey reaksiyon kuvvetleri hesaplanır.
Şimdi, BD elemanı için serbest cisim diyagramı göz önüne alındığında, D'de yatay ve dikey reaksiyon kuvvetlerini elde etmek için D ekleminde kuvvet denge koşulları uygulanabilir.

<ol>
	<li>Hibbeler, R.C. (2016). Mühendislik Mekaniği \u2012 Statik ve Dinamik. Hoboken, New Jersey: Pearson Prentice Salonu. sayfa 305.</li>
	<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 330</li>
	<li>Meriam, J.L., Kraige, L.G. ve Bolton, J.N. (2020). Mühendislik Mekaniği \u2012 Statik. Hoboken, New Jersey: John Wiley. sayfa 200</li>
</ol>

Herhangi bir çıkar çatışması beyan edilmedi.

Çerçeveler: problem Çözme i

Frames: Problem Solving I

Bir kaldıraç vinç, halata asılı bir dış yük ile donatılmıştır. Vinç elemanlarının boyutları şekilde gösterilmektedir. Vinç yapısının sistematik bir analizi, pim eklemlerindeki tepki kuvvetlerini belirlemek için gereklidir ve pülyelerin sürtünmesiz olduğu varsayılır.

<img alt="Figure 1" src="/files/ftp_upload/14291/14291_PT_Fig_1v2.svg" style="text-align: center; height: 350px;" />

Sistem, iki ana yapısal bileşene sahiptir: iki kuvvetli üye BD ve çoklu kuvvetli üye ABC. İki kuvvetli üye BD, sadece uç noktaları B ve D'deki kuvvetlere maruz kalan düz bir elemanı ifade eder ve boyunun boyunca ek kuvvetler yoktur. Bu kuvvetler, büyüklük açısından eşit ancak zıt yönde olduğundan, üye sadece gerilmeye ya da basınca maruz kalır. Öte yandan, çoklu kuvvetli üye ABC, boyunca dağıtılan iki kuvvetten daha fazla kuvvete maruz kalır. Bu kuvvetler, dış yükleri, pim eklemlerindeki reaksiyon kuvvetlerini ve kablonun uyguladığı kuvveti içerebilir. Üye ABC üzerinde birden fazla kuvvet etkisi olduğu için, daha basit iki kuvvetli üye BD'ye kıyasla daha karmaşık bir gerilim dağılımı yaşar.

<img alt="Figure 2" src="/files/ftp_upload/14291/14291_PT_Fig_2v2.svg" style="text-align: center; height: 350px;" />

Alt pulye bölümünü göz önünde bulundurarak, halat gerilimi halatların gerilimini dengeleyerek her bir halatta 10 kN yukarı yönlü bir gerilim oluşturur. Şimdi, üst pulye bölümünü düşünelim, dikey halatın gerilimi aşağı yönlü olup, yatay halat için A noktasına yönlendirilir. Dikey halatın gerilimi de aynı sürekli kablo sistemine aittir ve 10 kN'dir.

DB üyesinde, kuvvet FBD bir eğim üçgeni kullanılarak yatay ve dikey bileşenlerine çözülebilir. A eklemindedeki moment denge koşulu, FBD kuvvetini 50 kN olarak belirler.

Yatay kuvvet denge koşulu A noktasına uygulanabilir.

<img alt="Equation 1" src="/files/ftp_upload/14291/14291_PT_Equation_1v2.svg" style="text-align: center; height: 15px;" />

AB, AC uzunlukları ve C pulye yarıçapının değerlerinin yerine konulmasıyla FBD kuvveti 50 kN olarak bulunur.

Yatay kuvvet denge koşulu, A noktasındaki reaksiyon kuvvetini 40 kN olarak verir.

<img alt="Equation 2" src="/files/ftp_upload/14291/14291_PT_Equation_2v2.svg" style="text-align: center; height: 15px;" />

Benzer şekilde, dikey kuvvet denge koşuluyla A noktasındaki dikey reaksiyon kuvveti -20 kN olarak tahmin edilir.

<img alt="Equation 3" src="/files/ftp_upload/14291/14291_PT_Equation_3v2.svg" style="text-align: center; height: 15px;" />

Kuvvet dengesi koşulları, D noktasındaki yatay ve dikey reaksiyon kuvvetlerini elde etmek için D eklemine uygulanabilir.

<img alt="Equation 4" src="/files/ftp_upload/14291/14291_PT_Equation_4v2.svg" style="text-align: center; height: 15px;" />

<img alt="Equation 5" src="/files/ftp_upload/14291/14291_PT_Equation_5v2.svg" style="text-align: center; height: 15px;" />

Elde edilen sonuçlar, D noktasındaki yatay ve dikey reaksiyon kuvvetlerinin sırasıyla -30 kN ve 40 kN olduğunu göstermektedir.

Çerçeveler: Problem Çözme I

Kasnaktan asılı bir dış yüke sahip bir pergel vinç düşünün. Vinç elemanlarının boyutları şekilde gösterilmiştir. Sistematik bir analiz...

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Structural Analysis

KEY TERMS AND CONCEPTS

jib crane reaction forces in frames

Jib crane reaction forces in frames are found by analyzing the pin joints, the cable tension, and the load carried by the pulley. The structure in this problem has an external load suspended from the pulley, and the member sizes are shown in the figure. Because the pulleys are frictionless, the force balance can be worked out step by step.

The frame has two main parts. Member BD is a two-force member, which means it is a straight part loaded only at its two ends, D and B. Those end forces are equal in size and opposite in direction, so the member is in either tension or compression. Member ABC is a multi-force member, so it carries more than two forces along its length. These forces include the pin reactions, the external load, and the cable force, which makes its stress state more complex.

The lower pulley section shows that the load weight is balanced by the cable tension. That gives an upward tension of 10 kN in each cable. In the upper pulley section, the tension T in the vertical cable points downward, while the horizontal cable tension points toward joint A. The vertical cable tension is also 10 kN because it is part of the same continuous cable system.

To solve member DB, the force FBD is split into horizontal and vertical parts with a slope triangle. A moment balance at joint A gives FBD as 50 kN. The horizontal force balance at A then uses the lengths AB and AC and the pulley radius at C to confirm this value. From that balance, the reaction at A is 40 kN in the horizontal direction, and the vertical reaction at A is -20 kN. The force balance at joint D gives the reaction forces there as -30 kN horizontally and 40 kN vertically.

Jib Crane Reaction Forces in Frames

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The method of joints uses equilibrium to find forces in structural trusses. It treats the truss members as being joined by frictionless pins. For each joint, the forces acting there must balance. That balance makes it possible to solve for the member forces one joint at a time. Here, a truss has 20 N acting at joint C and 10 N acting at joint D. The method of joints is used to find FCB, FDC, FDB, and FAD. The analysis starts with a free-body diagram of joint C. Free-body diagram means drawing...

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method of sections: problem solving i

Truss Member Force Calculation by Sections

Truss member forces can be found with the method of sections in a symmetrical roof truss. The structure here includes vertical, diagonal, and horizontal members. Each horizontal member is 4 m long. The vertical members FB and HD are 4 m long, and member GC is 6 m long. The roof truss carries loads at several joints. Joints F, G, and H each have a 2 kN load. Joints A and E each have a 1 kN load. To start the analysis, moment equilibrium is used at point A. The force and distance values are...

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Truss member force analysis by sections finds the forces in selected members of a wall-mounted truss. The structure here includes diagonal, vertical, and horizontal members. The known loads and member lengths are used to solve for the forces in CB, GB, and GH. A cut is made through members CB, GB, and GH. The right side of the truss is then isolated as a free-body diagram. Next, the moment equilibrium equation is taken about point G. This step gives the force in member CB as 4 kN, and the...

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Frames are important parts of many mechanical and structural systems used every day. They are valued for stability and for their ability to bear heavy loads. A frame is built from two-force members and multi-force members, and the parts are connected with pin joints. Trusses are different because they are made entirely of two-force members. Frames appear in many practical settings. They can support beams and columns in buildings. They are also used in automobile chassis construction. In the...

frames: problem solving i

Jib crane reaction forces in frames are found by analyzing the pin joints, the cable tension, and the load carried by the pulley. The structure in this problem has an external load suspended from the pulley, and the member sizes are shown in the figure. Because the pulleys are frictionless, the force balance can be worked out step by step. The frame has two main parts. Member BD is a two-force member, which means it is a straight part loaded only at its two ends, D and B. Those end forces are...

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A toggle clamp can be analyzed to find its clamping force from a known handle force. In this example, a 200 N force is applied at the handle. The clamp is used in holding and clamping tasks in woodworking, metalworking, and assembly operations. The toggle clamp is a machine structure made of movable, pin-connected multi-force members. These members form a stabilized system that transmits force. Member CD is a two-force member, which means the forces at its ends are equal in magnitude and...

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key terms and concepts

Analyze a jib crane frame with a frictionless pulley, two-force member BD, and multi-force member ABC to find reaction forces at joints A and D.

Jib Crane Reaction Forces in Frames | 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.

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Jib Crane Reaction Forces in Frames

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