VM-WB-MECH-031

VM-WB-MECH-031
Long Bar With Uniform Force and Stress Tool - Plane Stress Model

Overview

Reference:	Any standard Strength of Materials book
Solver(s):	Ansys Mechanical
Analysis Type(s):	Plane Stress Analysis
Element Type(s):	2D Structural Solid

Test Case

A long, rectangular bar assembly is fixed at one of the faces and the opposite face is subjected to a compressive force. To get accurate results, set the advanced mesh control element size to 1 m.

Find the maximum equivalent stress for the whole assembly and safety factor, safety margin, and safety ratio for the first and last part using the maximum equivalent stress theory with Tensile Yield Limit.

Figure 41: Schematic

Material Properties
Material	E (Pa)	ν	Tensile Yield (Pa)
Part 1	1.93e11	0	2.07e8
Part 2	7.1e10	0	2.8e8
Part 3	2e11	0	2.5e8
Part 4	1.1e11	0	2.8e8

Geometric Properties

Part 1: 2 m x 2 m x 3 m

Part 2: 2 m x 2 m x 10 m

Part 3: 2 m x 2 m x 5 m

Part 4: 2 m x 2 m x 2 m

Force = 1e9 N in the negative x-direction

Analysis

Since the loading is uniform and in one plane, the above problem can be analyzed as a plane stress problem. Analysis is done considering thickness of 2 m along z-direction

Figure 42: Plane Stress Model (Analyzing any cross section along Z)

Results Comparison

Results		Target	Mechanical	Error (%)
Maximum Equivalent Stress (Pa)		2.5e8	2.5e8	0.000
Part 1	Safety Factor	0.828	0.828	0.000
	Safety Margin	-0.172	-0.172	0.000
	Safety Ratio	1.207	1.2077	0.058
Part 4	Safety Factor	1.12	1.12	0.000
	Safety Margin	0.12	0.12	0.000
	Safety Ratio	0.892	0.89286	0.096