Name: finding zero-force members in trusses
Uploaded: 2025-05-22T09:06:02.000Z
Duration: 1 min 30 s
Channel: JoVE

하중 조건에서 응력을 받지 않는 트러스 부재를 zero-force 부재라고 합니다.
두 개의 비동일선 부재가 있고 외부 하중 또는 지지 반응이 없는 트러스 접합의 경우, 두 부재 모두 하중이 0인 부재여야 합니다.
이 조인트에 대해 자유물체 다이어그램이 그려집니다. 수직 방향을 따르는 힘의 합은 0과 같으며 BA를 따라 힘을 0으로 만듭니다. 수평 방향을 따라 평형 방정식을 사용하면 BC를 따라 힘이 0이 됩니다.
두 개의 동일선 부재를 포함하여 세 개의 부재가 있는 접합의 경우, 세 번째 부재는 이 접합에 외부 하중 또는 지지 반응이 적용되지 않는 한 제로 포스 부재입니다.
다시 말하지만, 자유물체 다이어그램을 그리고 정적 평형 조건을 적용하면 CA를 따르는 힘이 0임을 증명합니다.
롤러와 핀 지지대가 있고 조인트 E에 외부 하중이 있는 트러스를 고려하십시오.
2개의 동일선상 부재를 포함하여 3개의 부재가 있는 조인트가 식별됩니다. 이러한 접합부의 영하중 조건은 FG, EH 및 FD가 영하중 부재임을 의미합니다.
그러나 ED는 외부 부하로 인해 제로 포스 멤버가 될 수 없습니다.

<ol>
	<li>R. C., Hibbeler Engineering Mechanics Statics, Pearson. 282</li>쪽
</ol>

무력부재(zero force member)

트러스는 가늘고 긴 부재들이 접합부로 연결되어 있는 구조물입니다. 트러스는 교량, 지붕, 타워 등의 구조물을 안정화하고 보강하기 위해 건설 및 건축에 널리 사용되고 있습니다. 트러스 부재는 장력과 압축을 통해 하중을 전달하도록 설계되어 있어 트러스가 외력에 견딜 수 있습니다.
트러스 설계에서 중요한 개념 중 하나는 무력부재의 개념입니다. 이는 하중조건에서 응력을 받지 않는 트러스 부재를 의미합니다. 트러스 해석시 특정 부재는 무력을 가질 수 있으며, 이는 구조물의 전체 내하력에 기여하지 않는다는 것을 나타냅니다. 무력부재를 식별하는 것은 트러스 구조물의 설계를 최적화하는 데 필수적입니다.
무력부재가 존재하기 위해서는 두 가지 조건이 존재합니다. 첫째, 2개의 비직선부재만이 트러스 접합부를 형성하고 접합부에 외부하중이나 지지반력이 작용하지 않는 경우, 두 부재 모두 무력부재여야 합니다. 둘째, 3개의 부재가 트러스 접합부를 형성하고 2개가 공선형인 경우, 외력이나 지지반력이 부재를 따라 작용하는 성분이 없는 경우, 세 번째 부재는 무력부재입니다.
<img alt="Figure 1" src="/files/ftp_upload/14284/14284_PT_Fig_1v2.svg" style="text-align: center; height: 350px;" />
롤러와 핀 지지부와 조인트 E에서의 외력 하중을 가진 트러스를 고려해 보겠습니다. 여기서 조인트 H과 G은 2개의 공선부재를 가진 3인조 조인트입니다. 두 번째 조건을 적용하면, EH과 FG은 무력부재입니다. 조인트 F에 무력 조건을 적용하면, DF는 무력부재입니다. 그러나, 외력하중으로 인해, ED는 무력부재가 될 수 없습니다.
제로포스 부재는 트러스 안정성 및 평형 유지, 구조 설계 최적화, 재료 및 건설 비용 절감에 필수적입니다.

트러스는 끝이 관절로 연결된 가느다란 부재로 구성된 프레임워크입니다. 트러스는 엔지니어링 및 건축에서 널리 사용됩니다.

Education

교육

JoVE Core

Mechanical Engineering

기계공학

Unit 1

제1단원

Structural Analysis

구조 해석

KEY TERMS AND CONCEPTS

주요 용어 및 개념

Zero-Force Member

finding zero-force members in trusses

Trusses are frameworks made of slender members that connect at their ends by joints. Engineers and architects use them to stabilize and strengthen structures such as bridges, roofs, and towers. Truss members carry loads through tension and compression so the structure can handle external forces.

A key part of truss analysis is spotting zero-force members. A zero-force member is a truss member that carries no stress under loading conditions. During analysis, some members may show zero force, which means they do not add to the load-bearing capacity of the structure. Finding these members helps improve the design of truss structures.

There are two common conditions for zero-force members. If only two non-collinear members meet at a joint, and no external load or support reaction acts on that joint, both members are zero-force members. If three members meet at a joint and two are collinear, the third member is a zero-force member, as long as no external force or support reaction has a component along that member.

A truss with a roller and pin support and an external load at joint E shows how these rules work. Joints H and G each have three members with two collinear members, so EH and FG are zero-force members. At joint F, the same idea makes DF a zero-force member. ED is not a zero-force member because the external load affects it.

Zero-force members are important for truss stability and equilibrium. They also help optimize structural design. In many cases, identifying them can reduce material use and construction cost.

Finding Zero-Force Members in Trusses

introduction to structures

Structure Types and Force Paths

Structures are systems of interconnected members that support or transfer forces and handle the loads placed on them. Engineers can find the internal forces in a structure by breaking it apart and drawing free-body diagrams for individual members or groups of members. This helps show how structural elements behave and how the whole system stays stable under load. There are three main categories of structures: trusses, frames, and machines. Trusses are stationary structures that stay rigid when...

simple trusses

Simple Trusses and Triangular Frames

Simple trusses are planar trusses built from slender members joined at points in one flat plane. They are designed to carry external loads while using less material and keeping weight low. A truss is a structural framework, and the simple truss is one of its most basic forms. The most basic simple truss uses three members arranged in a triangle. That triangular shape is naturally stable and rigid because of its geometry. It gives students a clear starting point for understanding how larger...

method of joints

Truss Forces Using the Method of Joints

The method of joints is used to find the forces in structural trusses. It relies on equilibrium, which means the forces at a joint must balance. In this model, the truss members are connected by frictionless pins. For a plane truss, the members lie in the same plane. That means each joint has a coplanar and concurrent force system. The analysis begins by identifying and labeling all the joints in the truss. Next, each joint is isolated and shown in a free-body diagram. This diagram includes...

method of joints: problem solving i

Truss Joint Force Analysis by Equilibrium

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...

method of joints: problem solving ii

Truss Force Analysis at Joints A to E

Truss force analysis at joints A to E uses the method of joints to find the force in each member. The truss has frictionless joints, a wall support, and a roller support. A 150 N force is applied at joint A, and the member forces are solved from joint to joint. First, the angle between members AC and AB is found using the inverse tangent of the ratio of BC to AB. This gives an angle of 67.38°. A free-body diagram of joint A is then drawn, and each unknown force is split into vertical and...

zero-force member

Trusses are frameworks made of slender members that connect at their ends by joints. Engineers and architects use them to stabilize and strengthen structures such as bridges, roofs, and towers. Truss members carry loads through tension and compression so the structure can handle external forces. A key part of truss analysis is spotting zero-force members. A zero-force member is a truss member that carries no stress under loading conditions. During analysis, some members may show zero force,...

method of sections

Truss Member Force Analysis by Sections

Truss member force analysis by sections finds the force in selected members of a truss. In this problem, forces F1 and F2 act at joints B and D. The goal is to determine the forces in members EF, DC, and DF. The method uses the idea that a truss in equilibrium also has each of its sections in equilibrium. A free-body diagram of the whole truss is drawn first. The moment equation about joint A is then used to estimate the support reaction at point E. Next, a cut is made along a sectional plane...

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...

method of sections: problem solving ii

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...

space trusses

Space Truss Forces and Stability

A space truss is a three-dimensional truss made from members joined at their ends. It is the 3D version of a planar truss. These frameworks often use ball-and-socket joints, which help the structure stay stable and flexible under load. Space trusses are used in many construction projects because they can adapt to complex forces. Their basic building block is the tetrahedron. A tetrahedron has six members and four triangular faces. Engineers can build larger space trusses by adding one joint...

space trusses: problem solving

3D Truss Force Analysis with Joint Equilibrium

A space truss is a three-dimensional truss structure made of members connected at their ends. It often uses ball-and-socket joints to form a stable and versatile framework. Because it can handle complex loads, this type of structure is used in many construction projects. The example begins with a tripod made from a tetrahedral space truss. A ball-and-socket joint is located at C. The height and the lengths of the horizontal and vertical members are known. A tensile force is applied at joint D.

frames

Frame Analysis in Structural Systems

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

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...

frames: problem solving ii

Hydraulic Hoist Force Analysis

Hydraulic hoist force analysis shows how to find the forces in key members of a simple frame. The load is 1 kN, and the structure is represented with known member dimensions. In this setup, BF and BD act as two-force members. EFG and EDC are multi-force members, so each one is analyzed with a free-body diagram. The first step is to study member EFG. The inclined force in BF is split into vertical and horizontal parts. Then the moment equilibrium condition is applied at joint E. Using this...

machines

Cutting Pliers as a Force-Multiplying Machine

Cutting pliers are a machine that helps transmit force through movable, pin-connected members. In this example, the handles and cutting edges work together to cut wire by turning an input force into a larger output force at the jaws. When equal and opposite forces are applied to the handles, the cutting edges move toward each other. They then apply equal and opposite reaction forces to the wire. These reaction forces are greater than the forces applied to the handles, which is why the wire can...

machines: problem solving i

Toggle Clamp Force Analysis

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...

machines: problem solving ii

Lifting Tong Force Analysis

Lifting tong force analysis shows how forces move through a pin-connected machine. The structure uses movable sections DAF and CBG with member AB linking them together. Because these parts work as connected members, the load can be studied with equilibrium methods. The example starts with a 100 kg load at point E. The load weight is found by multiplying mass by gravity, which gives 981 N. The cable tension acts upward and balances that weight. Since the structure is symmetrical at E, the...

key terms and concepts

Learn how to identify zero-force members in trusses using joint rules, with a worked example that shows how they affect design and cost.

Finding Zero-Force Members in Trusses | 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 Zero-Force Members in Trusses

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