Case 01 — Axial bar under concentrated loads

Open in RodX Download PDF report

This verification case examines the axial displacement of a prismatic steel bar subjected to multiple concentrated axial forces. The results obtained with RodX are verified against analytical solutions and industry-recognized finite element analysis (FEA) software.

Description

A steel bar of diameter 50 mm is subjected to the axial loading shown in the figure. The bar is fixed at point A and loaded by concentrated forces applied at nodes B, C, and D along its length.

Determine:

The axial displacement at point D
The displacement of point B relative to point C

Structural scheme

Axial bar fixed at point A with concentrated axial forces applied at nodes B, C, and D

Geometry, boundary conditions, and load applications used in the verification model.

Model parameters

Parameter	Value
Element type	Beam element
Material	Steel
Young's modulus	2.0 × 10⁸ kN/m²
Diameter	0.05 m
Boundary conditions	Fixed at point A
Loads	Concentrated axial forces

Numerical results

Displacements

Axial displacement distribution along the bar obtained with RodX

Axial Force

Table results from RodX

Table of nodal displacements from RodX showing axial displacement Ux along the bar for elements 1–3 under the default load case

Comparison

Node	Analytical solution	RodX	Midas/Civil
Δx(D)	-0.0891	-0.0891	-0.0891
Δx(B-C)	-0.0764	-0.0764	-0.0764

The numerical results obtained with RodX are in agreement with the analytical solution and reference FEA results.

Reference

Hibbeler, R. C. Mechanics of Materials, 10th Edition (SI Units), Pearson Education, 2017, Example 4.1, p. 147.