VM-WB-MECH-069

VM-WB-MECH-069
Barrel Vault Roof Under Self Weight

Overview

Reference:	Cook, R. D. (1981). Concepts and Applications of Finite Element Analysis (2nd ed., pp. 284-287). New York, NY: John Wiley and Sons, Inc.
Solver(s):	Ansys Mechanical
Analysis Type(s):	Static Analysis
Element Type(s):	Shell

Test Case

A cylindrical shell roof of density ρ is subjected to a loading of its own weight. The roof is supported by walls at each end and is free along the sides. Find the x and y displacements at point A and the top and bottom stresses at points A and B. Express stresses in the cylindrical coordinate system. Use a global mesh size of 4 m.

Figure 92: Schematic

Material Properties

Geometric Properties

E = 4.32 x 10⁸ N/m²

ν = 0.3

ρ = 36.7347 kg/m³

t = 0.25 m

r = 25 m

= 50 m

Θ = 40°

g = 9.8 m/s²

Analysis

A one-fourth symmetry model is used. Displacements, UX and UY, and the longitudinal rotation, ROTZ, are constrained at the roof end to model the support wall.

Results Comparison

Results	Target	Mechanical	Error (%)
Directional Deformation Y @ A, m	-0.3019	-0.30908	2.378
Directional Deformation X @ A, m	-0.1593	-0.1627	2.134
Stress_z, Top @ A, Pa	215570	223680	3.762
Stress_z, Bottom @ A, Pa	340700	350100	2.759
Stress_angle, Top @ B, Pa	191230	184290	-3.629
Stress_angle, Bottom @ B, Pa	-218740	-211000	-3.538