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

トラスは、ジョイントで接続された細い部材のフレームワークです。
すべてのトラス部材が 1 つの 2 次元平面にある場合、それは平面トラスと呼ばれます。
基本的な平面トラスは、三角形の配置で3つのメンバーで構成される単純なトラスです。
2人のメンバーとジョイントを戦略的に追加することで拡張できます。
トラスの設計と解析は、2 つの単純化された仮定に依存しています。
まず、ジョイントには外部荷重がかかり、各部材の重量はごくわずかです。
部材の重量が大きい場合、その大きさの半分が両端に均等に分布した垂直方向の力として適用されます。
次に、部材は溶接、ボルト、またはリベット留めのジョイントで接続されますが、接合部材の中心線が同時であれば、ジョイントは滑らかなピンと見なすことができます。
これらの仮定により、トラス部材は、軸方向の圧縮または引張を受ける 2 つの力を持つ部材として機能します。
単純なトラスの剛性と決定性は、メンバーの数 m とジョイントの数 j が方程式を通じて関連していることを示しています。

<ol>
	<li>ヒベラー、RC(2016)。エンジニアリングメカニクス \u2012 静力学と力学。 ニュージャージー州ホーボーケン: Pearson Prentice Hall, pp. 273-275</li>
	<li>ビール、FP;ジョンストン、ER;マズレック、D.F;クロムウェル、PJおよびセルフ、BP(2019)。エンジニアのためのベクトル力学 \u2012 静力学と動力学。ニューヨーク:McGraw-Hill、pp.300-302</li>
	<li>メリアム、J.L.;Kraige、LGおよびBolton、JN(2020)。エンジニアリングメカニクス \u2012 静力学。ニュージャージー州ホーボーケン: John Wiley, pp. 171-172</li>
</ol>

利益相反は宣言されていません。

簡単なトラス

トラスは、節点で接続された細い部材から成る構造フレームであり、外部荷重をサポートしながら材料の使用量と重量を最小限に抑えるために設計されています。シンプルなトラスは、全ての部材が単一の二次元平面内に存在する平面トラスの一種です。

最も基本的な平面トラスは、三つの部材が三角形の形状で配置されたシンプルなトラスです。この三角形トラスは、その幾何学的な形状によって本質的に安定で剛性があります。より複雑なトラス構造を作成するための理想的な出発点となります。シンプルなトラスは、既存のフレームに二つの部材と節点を戦略的に追加することで拡張することができます。このプロセスを繰り返すことで、より大きなトラス構造を作成し、より大きな荷重を長距離にわたってサポートすることができます。トラス部材の配置は、その全体の強度と安定性を決定する上で重要であり、一般的なシンプルなトラスの種類には、プラット、ハウ、ウォーレントラスなどがあります。

シンプルなトラスの設計と解析は、二つの主要な仮定に基づいています：

<ol>
<li>外部荷重は節点に加わる： トラスの外部力は全て節点でのみ働くと仮定されており、各部材の重量は無視されます。部材の重量が有意である場合、その大きさの半分が部材の両端に等分布された鉛直力として適用されます。</li>
<li>節点は滑らかなピンとして扱われる： 部材は溶接、ボルト、リベットで接続されている場合でも、解析の目的上、接点は滑らかなピンとみなすことができます。この仮定は、接合部材の中心線が重なっている場合に有効であり、トラス部材が軸力による圧縮または引張りを経験する二力部材として機能します。</li>
</ol>

シンプルなトラスの剛性と決定性は、部材数（m）と節点数（j）の関係によって決まります。静定で安定なトラスの場合、m = 2j - 3が成り立つ必要があります。この条件は、荷重下で変形に抵抗する十分な数の部材があり、かつ構造の安定性が維持されていることを保証します。この方程式を満たさないトラスは、静定でないか不安定であり、構造の破損を引き起こす可能性があります。

トラスは、ジョイントで接続された細い部材で構成される構造フレームワークであり、材料の使用量を最小限に抑えながら外部荷重を支えるように設計されています...

Education

JoVE Core

Mechanical Engineering

機械工学

Unit 1

ユニット1

Structural Analysis

構造解析

KEY TERMS AND CONCEPTS

主要用語と概念

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...

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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...

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Truss Member Force Calculation by Sections

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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

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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...

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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.

Simple Trusses and Triangular Frames | JoVE K12

JoVE Core 機械工学は、平衡、力、トラス解析、構造力学などの重要なトピックをカバーする簡潔でわかりやすいアニメーション ビデオを提供します。実際のアプリケーションを探索し、科学者主導の実験を通じてこれらのコンセプトが実際に動作しているのを目撃してください。

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Simple Trusses and Triangular Frames

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