---
type: concept
title: "Bar and Truss Finite Elements"
complexity: intermediate
domain: computational-mechanics
created: 2026-05-29
updated: 2026-05-29
address: c-000064
aliases:
  - bar element
  - truss element
  - plane truss finite element
  - space truss finite element
tags:
  - concept
  - finite-element-method
  - structural-mechanics
  - truss
status: current
related:
  - "[[Direct Stiffness Method]]"
  - "[[Displacement-Based Finite Element Formulation]]"
  - "[[Finite Element Load Vector Assembly]]"
  - "[[Finite Element Modeling and Convergence Checks]]"
sources:
  - "[[A-First-Course-in-the-Finite-Element-Method|A First Course in the Finite Element Method]]"
source_refs:
  - source: "[[A-First-Course-in-the-Finite-Element-Method|A First Course in the Finite Element Method]]"
    raw_path: ".raw/AFirstCourseInTheFiniteElementMethod/"
    raw_files:
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      - "AFirstCourseInTheFiniteElementMethod_070.md"
      - "AFirstCourseInTheFiniteElementMethod_047.md"
      - "AFirstCourseInTheFiniteElementMethod_015.md"
    md_indices:
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    match: "heuristic-heading-keyword"
    confidence: high
---

# Bar and Truss Finite Elements

## Definition

Bar and truss finite elements are one-dimensional structural elements that carry axial force through nodal translational degrees of freedom.

## How They Work

The local bar element assumes an axial displacement field along the element length. The strain is the derivative of that displacement, the stress follows from Hooke's law, and the local stiffness has the familiar axial form proportional to `AE/L`.

For truss analysis, local bar stiffness is transformed into the global coordinate system using direction cosines. Plane truss members use two translational degrees of freedom per node in the global plane, while space truss members extend the same transformation idea to three dimensions. After transformation, each member contributes to the global stiffness matrix through the [[Direct Stiffness Method]].

## Modeling Assumptions

- The member carries axial tension or compression.
- Shear force and bending moment are neglected.
- Transverse displacement effects are ignored within the element formulation.
- Pin-connected truss idealization is appropriate for the structure being modeled.

## Connections

- [[Beam and Frame Finite Elements]] add bending, shear, moments, and rotational degrees of freedom.
- [[Finite Element Load Vector Assembly]] is needed when bars carry distributed or thermal loads.
- [[Direct Time Integration Methods]] extends bar equations by adding mass matrices and time-dependent forcing.

## Sources

- [[A-First-Course-in-the-Finite-Element-Method|A First Course in the Finite Element Method]]