What is a plane truss?

Short Answer:

A plane truss is a type of truss in which all members and joints lie in a single plane, and the loads also act in the same plane. It is a two-dimensional structure that is used to support loads such as roofs, bridges, and towers.

In a plane truss, each member is connected at joints by pins and carries only axial forces (either tension or compression). The geometry of the truss ensures stability and strength while using minimal material, making it an economical and efficient structural system.

Detailed Explanation:

Plane Truss

A plane truss is a framework made up of straight and slender members connected at their ends by frictionless pin joints. The entire structure lies in one geometric plane, and the external loads, reactions, and internal forces also act in that same plane. Since the truss is two-dimensional, it is analyzed using only two equilibrium equations of force—horizontal and vertical components—and one for moments.

The plane truss is one of the simplest and most commonly used truss types in mechanical and structural engineering. It is found in bridges, roofs, towers, and mechanical frames where loads act in one direction, usually vertically or horizontally.

The basic building unit of a plane truss is a triangle, as a triangle is a stable geometric figure that cannot change its shape without altering the length of one of its sides. This triangular arrangement of members makes the truss rigid and prevents deformation.

Construction and Geometry of Plane Truss

A plane truss is made up of several members connected together at joints called nodes. The members are assumed to be pin-connected, which means they can rotate freely at the joints without resisting moments. The load is always applied at these joints, ensuring that each member carries only axial force.

A simple plane truss is built by joining a series of triangular units, starting from a basic triangle and adding new members and joints according to the following stability condition:

where,

  • m = number of members,
  • r = number of reactions,
  • j = number of joints.

If this equation is satisfied, the truss is perfect and stable. If not, it becomes either deficient (unstable) or redundant (over-stable).

Types of Plane Trusses

Plane trusses can be divided into several common forms based on their geometry and application:

  1. Simple Plane Truss:
    Formed by connecting triangles together. It is the most basic type and easy to analyze. Example – a King Post Truss used in small roof structures.
  2. Compound Plane Truss:
    Created by connecting two or more simple trusses together. This type is used when a larger span is required. Example – a Bridge Truss made by combining smaller trusses.
  3. Complex Plane Truss:
    A more complicated type that cannot be formed by simple triangular connections alone. It is used in large structures that require additional members for strength and stiffness.

Common Examples of Plane Trusses

  1. King Post Truss:
    A simple truss with a central vertical member (king post) and two diagonal members. It is used for short roof spans.
  2. Queen Post Truss:
    Contains two vertical members (queen posts) and a horizontal member connecting them. It is used for medium roof spans.
  3. Pratt Truss:
    Diagonals slope toward the center and are in tension. Commonly used in bridges.
  4. Warren Truss:
    Formed by equilateral triangles, providing good load distribution and material efficiency.
  5. Howe Truss:
    Diagonals slope away from the center and are in compression, suitable for longer spans.

These forms are all plane trusses because their geometry and loading lie in a single plane.

Characteristics of a Plane Truss

  1. Two-Dimensional Structure:
    All members and joints lie in a single geometric plane.
  2. Pin-Jointed Members:
    Each member is connected by pin joints that allow rotation but no bending.
  3. Axial Force Only:
    Members carry only axial forces (tension or compression), not bending or shear.
  4. Loads Applied at Joints:
    External loads and reactions act only at the joints.
  5. Stable Geometry:
    Built with triangles to ensure rigidity and prevent shape change under loads.
  6. Efficient Load Transfer:
    Distributes loads evenly among members, providing high strength with less material.

Assumptions Made in Plane Truss Analysis

To simplify analysis, the following assumptions are made:

  1. The truss members are connected by frictionless pin joints.
  2. The loads act only at the joints.
  3. The self-weight of members is negligible compared to external loads.
  4. Each member acts as a two-force member, carrying only axial tension or compression.
  5. The truss is perfectly rigid and stable under applied loads.

These assumptions make it possible to use simple equilibrium equations to determine the forces in each member.

Analysis of Plane Truss

The analysis of a plane truss involves determining the internal forces in its members. The two main methods used are:

  1. Method of Joints:
    Each joint is treated as a free body, and equilibrium equations (ΣFx = 0 and ΣFy = 0) are applied to find unknown forces.
  2. Method of Sections:
    The truss is cut into two parts, and the equations of equilibrium (ΣFx = 0, ΣFy = 0, ΣM = 0) are applied to one part to find forces in specific members.

Both methods rely on static equilibrium principles to determine whether each member is in tension or compression.

Advantages of Plane Truss

  1. Lightweight but Strong:
    Provides high strength while using less material.
  2. Easy to Construct:
    Simple triangular geometry makes fabrication and assembly easy.
  3. Economical Design:
    Reduces cost by efficiently distributing loads among members.
  4. Efficient Load Transfer:
    Effectively transfers loads to supports through axial members.
  5. Versatile Applications:
    Widely used in bridges, roofs, towers, and cranes.

Applications of Plane Truss

  • Bridge Structures: Used in railway and highway bridges for efficient load transfer.
  • Roof Frameworks: Commonly used in industrial sheds, factories, and warehouses.
  • Transmission Towers: Provide rigidity and height stability.
  • Cranes and Lifting Equipment: Used in mechanical frameworks for load-bearing structures.
  • Aircraft and Space Frames: Provide strength with minimum weight.
Conclusion

A plane truss is a two-dimensional framework composed of straight members connected at their ends, all lying in a single plane. The loads and reactions act in the same plane, and each member carries only axial forces — tension or compression. Plane trusses are widely used due to their simplicity, light weight, and high strength. Their design based on triangular geometry ensures rigidity and stability, making them essential in the construction of bridges, roofs, towers, and mechanical structures.