A reinforced concrete cylindrical roof (barrel vault) is subjected to a uniform load. It has a length of 50 feet, a thickness of 0.25 feet, a radius of 25 feet and an 80 degree arc length. A 90 lb/ft2 uniform downward load is to be applied.
Determine the vertical displacement at the center of the free edge i.e. at joint 49 of the model.
Due to symmetry of the structure and loading, a quarter of the cylindrical shell (as shown above) is used as a model. It consists of 6 x 6 mesh of shell elements.
The edge from joint 1 to 7 is simply supported and from 7 to 49 is free.
The boundary conditions along the edges from joint 1 to 43 and 43 to 49 are prescribed for symmetry. Here are the joint restraints specified for preserving symmetry:
The input for the model should be generated using a cylindrical coordinate system.
Reference
- MacNeal, R.H. and Harder, R.C., "A Proposed Standard Set of Problems to Test Finite Element Accuracy," Finite Elements in Analysis and Design 1 (1985), pp.3-20, North-Holland.
- Zienkiewicz, O. C., "The Finite Element Method," McGraw-Hill, 1977.
| Axial Z-Displacement in feet at the Support Joints 1-7 | SAP90 | Theory | LARSA | OPENBRIM | PERCENT DIFFERENCE (LARSA vs. THEORY) | PERCENT DIFFERENCE (OPENBRIM vs. THEORY) |
|---|---|---|---|---|---|---|
Location=0.00(deg) | 0.0000 | 0.0004 | 0.0000 | 0.0000 | - | - |
Location=6.67(deg) | 0.0005 | 0.0009 | 0.0005 | 0.0005 | 80% | 80% |
Location=13.33(deg) | 0.0018 | 0.0020 | 0.0018 | 0.0018 | 11% | 11% |
Location=20.00(deg) | 0.0029 | 0.0030 | 0.0029 | 0.0029 | 3.45% | 3.45% |
Location=26.67(deg) | 0.0024 | 0.0021 | 0.0024 | 0.0024 | 12.5% | 12.5% |
Location=33.33(deg) | -0.0017 | -0.0016 | -0.0017 | -0.0017 | 5.88% | 5.88% |
Location=40.00(deg) | -0.0118 | -0.0120 | -0.0118 | -0.0118 | 1.69% | 1.69% |
Vertical Y-Displacement in feet at the Center Joints 43-49 | SAP90 | Theory | LARSA | OPENBRIM | PERCENT DIFFERENCE LARSA vs. THEORY | PERCENT DIFFERENCE OPENBRIM vs. THEORY |
|---|---|---|---|---|---|---|
Location=0.00(deg) | 0.046 | 0.045 | 0.047 | 0.0463 | 4.26% | 2.81% |
Location=6.67(deg) | 0.031 | 0.027 | 0.031 | 0.0309 | 12.9% | 12.6% |
Location=13.33(deg) | -0.013 | -0.018 | -0.013 | -0.0131 | 38.5% | 37.44% |
Location=20.00(deg) | -0.078 | -0.082 | -0.079 | -0.0786 | 3.8% | 4.3% |
Location=26.67(deg) | -0.155 | -0.155 | -0.157 | -0.1557 | 1.3% | 0.45% |
Location=33.33(deg) | -0.234 | -0.241 | -0.236 | -0.2341 | 2.1% | 2.9% |
Location=40.00(deg) | -0.307 | -0.309 | -0.309 | -0.3072 | 0% | 0.6% |