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

Kratownica to szkielet smukłych prętów połączonych na łączeniach.
Gdy wszystkie pręty kratownicy leżą w jednej dwuwymiarowej płaszczyźnie, nazywa się to kratownicą płaską.
Podstawowa kratownica płaska to prosta kratownica składająca się z trzech prętów w układzie trójkątnym.
Można go rozbudować poprzez strategiczne dodanie dwóch członków i stawu.
Projekt i analiza kratownicy opierają się na dwóch uproszczonych założeniach.
Po pierwsze, na połączeniach przykładane są obciążenia zewnętrzne, a ciężar każdego elementu jest znikomy.
Gdy ciężar pręta jest znaczny, połowa jego wielkości jest przykładana jako równomiernie rozłożone siły pionowe na obu końcach.
Po drugie, chociaż pręty łączą się ze złączami spawanymi, śrubowymi lub nitowanymi, połączenia można założyć jako gładkie kołki, pod warunkiem, że linie środkowe prętów łączących są współbieżne.
Założenia te zapewniają, że pręty kratownicy działają jak pręty o dwóch siłach, które ulegają ściskaniu lub rozciąganiu osiowemu.
Sztywność i determinatywność prostej kratownicy dyktują, że liczba prętów m i liczba połączeń j są powiązane za pomocą równania.

<ol>
	<li>Hibbeler, R.C. (2016). Mechanika inżynierska \u2012 Statyka i dynamika. Hoboken, New Jersey: Pearson Prentice Hall, s. 273-275</li>
	<li>Piwo, F.P.; Johnston, E.R.; Mazurek, D.F.; Cromwell, PJ i Self, BP (2019). Mechanika wektorowa dla inżynierów \u2012 Statyka i dynamika. Nowy Jork: McGraw-Hill, s. 300-302</li>
	<li>Meriam, J.L.; Kraige, L.G. i Bolton, J.N. (2020). Mechanika inżynierska \u2012 Statyka. Hoboken, New Jersey: John Wiley, s. 171-172</li>
</ol>

proste dźwigary

Dźwigar to konstrukcja nośna, składająca się z cienkich elementów połączonych w węzłach, zaprojektowana do wspierania obciążeń zewnętrznych przy minimalnym zużyciu materiału i wadze. Proste dźwigary to rodzaj dźwigara planarnego, w którym wszystkie elementy leżą w jednej płaszczyźnie.

Najprostszym dźwigarem planarnym jest prosty dźwigar składający się z trzech elementów ułożonych w trójkątną formację. Ten trójkątny dźwigar jest sam w sobie stabilny i sztywny ze względu na swoją geometrię, co czyni go idealnym punktem wyjścia do tworzenia bardziej skomplikowanych struktur dźwigarowych. Prosty dźwigar może być powiększony poprzez dodanie dwóch elementów i węzła do istniejącej konstrukcji. Ten proces można powtarzać, tworząc większą strukturę dźwigarową zdolną do wspierania większych obciążeń i rozpiętości. Konfiguracja elementów dźwigarowych jest kluczowa dla określenia ich ogólnej wytrzymałości i stabilności, a do najczęściej używanych prostych dźwigarów należą dźwigary Pratta, Howe'a i Warrena.

Projektowanie i analiza prostych dźwigarów opierają się na dwóch kluczowych założeniach:

<ol>
	<li>Obciążenia zewnętrzne są stosowane w węzłach: Zakłada się, że wszystkie zewnętrzne siły działają wyłącznie w węzłach dźwigara, a masa każdego elementu jest pomijalna. Jeśli masa elementu jest znacząca, połowa jego wartości jest stosowana jako równo rozłożone siły pionowe na obu końcach elementu.</li>
	<li>Węzły traktowane są jako gładkie sworznie: Chociaż elementy mogą być połączone spawaniem, śrubowaniem lub nitowaniem, węzły mogą być przyjmowane jako gładkie sworznie w celach analizy. To założenie jest prawdziwe, o ile osie środkowe elementów łączących są współliniowe, co zapewnia, że elementy dźwigara działają jako elementy dwuosiowe, doświadczające ściskania lub rozciągania osiowego.</li>
</ol>

Sztywność i zdeterminowanie prostego dźwigara określają związek między liczbą elementów (m) a liczbą węzłów (j). Aby dźwigar był statycznie zdeterminowany i stabilny, musi spełniać równanie m = 2j - 3. Warunek ten zapewnia, że jest wystarczająca liczba elementów do oporu odkształceniom pod wpływem obciążenia, jednocześnie utrzymując stabilność konstrukcji. Jeśli dźwigar nie spełnia tego równania, jest nieoznaczony lub niestabilny, co może prowadzić do awarii konstrukcji.

Proste dźwigary

Kratownica to rama konstrukcyjna składająca się ze smukłych elementów połączonych na łączeniach, zaprojektowana w celu przenoszenia obciążeń zewnętrznych przy jednoczesnej minimalizacji zużycia materiału ...

Education

JoVE Core

Mechanical Engineering

Inżynieria mechaniczna

Unit 1

Jednostka 1

Structural Analysis

Analiza strukturalna

KEY TERMS AND CONCEPTS

Kluczowe terminy i pojęcia

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...

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

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.

Simple Trusses and Triangular 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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Simple Trusses and Triangular Frames

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