Name: simple trusses and triangular frames
Uploaded: 2025-05-22T09:06:02.000Z
Duration: 1 min 21 s
Channel: JoVE

K12 Standards

Arizona Science Standards

High School

Physical Science

HS.P3

HS.P3U2.7

Simple Trusses

트러스는 조인트에서 연결된 가느다란 부재의 프레임워크입니다.
모든 트러스 부재가 단일 2차원 평면에 있을 때 이를 평면 트러스라고 합니다.
기본 평면 트러스는 삼각형 배열로 3개의 부재를 포함하는 단순한 트러스입니다.
그것은 두 명의 구성원과 공동의 전략적 추가에 의해 확장될 수 있습니다.
트러스의 설계 및 해석은 두 가지 단순화된 가정에 의존합니다.
첫째, 외부 하중이 조인트에 가해지고 각 부재의 무게는 무시할 수 있습니다.
부재의 무게가 중요할 때, 그 크기의 절반은 양쪽 끝에서 균등하게 분포된 수직 힘으로 적용됩니다.
둘째, 부재가 용접, 볼트 체결 또는 리벳 접합과 연결되더라도 접합 부재의 중심선이 동시에 있는 경우 접합부를 부드러운 핀으로 가정할 수 있습니다.
이러한 가정은 트러스 부재가 축 압축 또는 장력을 경험하는 2하중 부재로 작용하도록 합니다.
단순 트러스의 강성과 결정성은 부재 수 m과 조인트 수 j가 방정식을 통해 관련되어 있음을 나타냅니다.

<ol>
	<li>히벨러, R.C. (2016). Engineering Mechanics \u2012 정역학 및 동역학. 뉴저지 호보켄: Pearson Prentice Hall, pp. 273-275</li>
	<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, pp. 300-302</li>
	<li>메리암, J.L.; Kraige, L.G. 및 Bolton, J.N. (2020). 엔지니어링 역학 \u2012 정역학. 뉴저지 호보켄: 존 와일리, 171-172쪽</li>
</ol>

단순 트러스

트러스는 접합부에 연결된 가느다란 부재로 구성된 구조적 뼈대로서, 재료 사용량과 무게를 최소화하면서 외부 하중을 지지하도록 설계되었습니다. 단순 트러스는 모든 부재가 단일 2차원 평면 내에 위치하는 일종의 평면 트러스입니다.
가장 기본적인 평면 트러스는 세 개의 부재가 삼각형 형태로 배열된 단순한 트러스입니다. 이 삼각형 트러스는 기하학적 특성으로 인해 본질적으로 안정적이고 견고하므로 보다 정교한 트러스 구조를 만들기 위한 이상적인 출발점이 됩니다. 기존 프레임워크에 두 개의 부재와 조인트를 전략적으로 추가하여 간단한 트러스를 확장할 수 있습니다. 이 과정을 반복하여 더 긴 경간에 걸쳐 더 큰 하중을 지탱할 수 있는 더 큰 트러스 구조를 만들 수 있습니다. 트러스 부재의 구성은 프랫(Pratt), 하우(Howe), 워렌(Warren) 트러스를 포함한 일반적인 단순 트러스 유형의 전체적인 강도와 안정성을 결정하는 데 중요합니다.
간단한 트러스의 설계 및 분석은 두 가지 주요 가정에 의존합니다.
<ol>
<li>외부하중은 접합부에 작용: 모든 외력은 트러스의 접합부에만 작용한다고 가정하고, 각 부재의 무게는 무시할 수 있는 것으로 간주합니다. 부재의 무게가 상당할 경우 그 크기의 절반이 부재의 양쪽 끝에 균등하게 분포된 수직력으로 적용됩니다.</li>
<li>접합은 부드러운 핀으로 처리됩니다. 부재는 용접, 볼트 또는 리벳 접합을 사용하여 연결될 수 있지만 해석 목적에서는 접합을 부드러운 핀으로 가정할 수 있습니다. 이 가정은 결합 부재의 중심선이 동시에 존재하는 한 유효하며 트러스 부재가 축 압축 또는 장력을 받는 두 힘 부재로 작용하도록 보장합니다.</li>
</ol>
단순 트러스의 강성과 결정성은 부재 수(m)와 접합부 수(j) 사이의 관계를 나타냅니다. 트러스가 정적으로 확정되고 안정적이려면 m = 2j - 3이 유지되어야 합니다. 이 조건은 구조의 안정성을 유지하면서 하중에 따른 변형에 저항할 수 있는 충분한 부재가 있음을 보장합니다. 트러스가 이 방정식을 만족하지 않으면 불확실하거나 불안정해 구조적 결함이 발생할 수 있습니다.

트러스는 조인트에 연결된 가느다란 부재로 구성된 구조적 프레임워크로, 재료 사용을 최소화하면서 외부 하중을 지지하도록 설계되었습니다.

Education

교육

JoVE Core

Mechanical Engineering

기계공학

Unit 1

제1단원

Structural Analysis

구조 해석

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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 truss systems are built.

A simple truss can grow by adding two members and a new joint to the existing frame. This process can be repeated to make a larger structure that can carry greater loads over longer spans. Common examples of simple truss layouts include the Pratt, Howe, and Warren trusses.

Truss analysis uses two main assumptions. First, external loads are applied at joints, and the weight of each member is usually treated as negligible. If a member’s weight matters, half of that weight is applied as equal vertical forces at both ends of the member.

Second, joints are treated as smooth pins. The real joints may be welded, bolted, or riveted, but the pin model works when the centerlines of the connected members meet at one point. Under this assumption, the members act as two-force members and carry either compression or tension along their length.

The number of members and joints also controls whether a simple truss is stable and statically determinate. For this kind of truss, the relationship m = 2j - 3 must hold, where m is the number of members and j is the number of joints. If a truss does not meet this condition, it may be unstable or indeterminate, which can lead to structural failure.

Simple Trusses and Triangular Frames

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 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...

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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

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,...

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 simple trusses use triangular frames, pin joints, and the m = 2j - 3 rule to stay stable, support loads, and span longer distances.

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Simple Trusses and Triangular Frames

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