OS-V: 0730 Scordelis-Lo Roof

MacNeal-Harder Test The Scordelis-Lo Roof is a classical benchmark problem for shell elements. Analytical and experimental investigations were initially performed by Scordelis and Lo.

Figure 1. FE Model of the Beam with Boundary Conditions and Loadcases

Benchmark Model

The roof structure is supported on both ends and loaded by self weight of 90 pounds per square foot, with only one quadrant modeled. Six types of elements are used for this problem. They are tria-shell, quad-shell, and hexa-solid elements, each with 1st and 2nd order. Each element type was benchmarked with different mesh density to check the convergence. As the original study was related to concrete structure, Poisson's ratio is set to zero. The structure is curved and its solution will exhibit membrane and bending behavior. Target solution for the vertical deflection at the midpoint of the free edge is 0.3024.

Linear Static Analysis Results

All results are normalized with the target value.
  Number of Nodes - space per sides
  2 4 6 8 10
QUAD4 1.487 1.082 1.035 1.020 1.013
QUAD8 1.436 1.179 1.139 1.116 1.102
TRI3 1.169 0.753 0.829 0.886 0.920
TRI6 1.326 1.107 1.077 1.063 1.055
HEX8 0.142 0.550 0.868 0.951 1.000
HEX20 1.071 1.052 1.046 1.045 1.043

Figure 2. Convergence check

Model Files

Refer to Access the Model Files to download the required model file(s).

The model files used in this problem include:
  • Roof1.fem
  • Roof2.fem


MacNeal, R.H., and Harder, R.L., A Proposed Standard Set of Problems to Test Finite Element Accuracy, Finite Elements in Analysis and Design, 1 (1985) 3-20.