VM-WB-MECH-001

VM-WB-MECH-001
Statically Indeterminate Reaction Force Analysis

Overview

Reference:

Timoshenko, S. (1955). Strength of Materials, Part 1: Elementary Theory and Problems (3rd ed., pp. 22, 26). CBS Publishers and Distributors.

Solver(s):Ansys Mechanical
Analysis Type(s):Linear Static Structural Analysis
Element Type(s):Solid

Test Case

An assembly of three prismatic bars is supported at both end faces and is axially loaded with forces F1 and F2. Force F1 is applied on the face between Parts 2 and 3 and F2 is applied on the face between Parts 1 and 2. Apply advanced mesh control with element size of 0.5".

Find reaction forces in the Y direction at the fixed supports.

Material PropertiesGeometric PropertiesLoading
E = 2.9008e7 psi
ν = 0.3
ρ = 0.28383 lbm/in3
Cross section of all parts = 1" x 1"
Length of Part 1 = 4"
Length of Part 2 = 3"
Length of Part 3 = 3"
Force F1 = -1000 (Y direction)
Force F2 = -500 (Y direction)

Analysis Assumptions and Modeling Notes for Ansys Mechanical

The following figure shows the finite element model in Ansys Mechanical:

Figure 1: Ansys Mechanical Schematic

Ansys Mechanical Schematic

Results Comparison for Ansys Mechanical

ResultsTargetMechanicalError (%)
Y Reaction Force at Top Fixed Support (lbf)900901.140.127
Y Reaction Force at Bottom Fixed Support (lbf)600598.86-0.190