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

A truss is a framework of slender members connected at joints.
When all truss members lie in a single two-dimensional plane, it is called a planar truss.
The basic planar truss is a simple truss comprising three members in a triangular arrangement.
It can be expanded by the strategic addition of two members and a joint.
The design and analysis of the truss rely on two simplified assumptions.
Firstly, external loads are applied at joints, and the weight of each member is negligible.
When the weight of a member is significant, half of its magnitude is applied as equally distributed vertical forces at both ends.
Secondly, although members connect with welded, bolted or riveted joints, the joints can be assumed as smooth pins, provided the centerlines of the joining members are concurrent.
These assumptions ensure that truss members act as two-force members experiencing axial compression or tension.
The rigidity and determinacy of a simple truss dictate that the number of members m and the number of joints j are related through an equation.

simple trusses

A truss is a structural framework consisting of slender members connected at joints, designed to support external loads while minimizing material usage and weight. Simple trusses are a type of planar truss where all members lie within a single two-dimensional plane.
The most basic planar truss is a simple truss with three members arranged in a triangular formation. This triangular truss is inherently stable and rigid due to its geometry, making it an ideal starting point for creating more elaborate truss structures. A simple truss can be expanded by strategically adding two members and a joint to the existing framework. This process can be repeated to create a larger truss structure capable of supporting greater loads over longer spans. The configuration of the truss members is critical in determining its overall strength and stability, with common simple truss types including the Pratt, Howe, and Warren trusses.
The design and analysis of simple trusses rely on two key assumptions:
<ol>
	<li>External loads are applied at joints: It is assumed that all external forces act only at the joints of the truss, and the weight of each member is considered negligible. If the weight of a member is significant, half of its magnitude is applied as equally distributed vertical forces at both ends of the member.</li>
	<li>Joints are treated as smooth pins: Although members may be connected using welded, bolted, or riveted joints, the joints can be assumed as smooth pins for analysis purposes. This assumption is valid as long as the centerlines of the joining members are concurrent, ensuring that truss members act as two-force members experiencing axial compression or tension.</li>
</ol>
The rigidity and determinacy of a simple truss dictate the relationship between the number of members (m) and the number of joints (j). For a truss to be statically determinate and stable, m = 2j - 3 must hold. This condition ensures that there are enough members to resist deformation under load while maintaining the stability of the structure. If a truss does not satisfy this equation, it is either indeterminate or unstable, which can lead to structural failure.

A truss is a structural framework consisting of slender members connected at joints, designed to support external loads while minimizing material usage ...

Education

JoVE Core

Mechanical Engineering

Unit 1

Structural Analysis

KEY TERMS AND CONCEPTS

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

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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 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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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

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Simple Trusses and Triangular Frames

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