Elements tested
- B21H
- B22
- B23H
- B31
- B31OS
- B31OSH
- B32H
- B32OS
- B32OSH
- B33H
- PIPE21H
- PIPE22
- PIPE31H
- PIPE32
- ELBOW31
- ELBOW31B
- ELBOW31C
- ELBOW32
Problem description
 The problem consists of a cantilever beam lying along the x-axis. The length of the beam is 75.0, and the model is made up of five elements. For two-dimensional elements, the problem consists of one step in which a transverse load of 25.0 is applied to the end of the beam. For three-dimensional elements this is followed by an additional step in which a moment of 25.0 is applied around the x-axis. Numerous tests with similar geometries and loadings are run to test the available options associated with each of the section definitions. Local coordinate directions are requested in the input files with the open thin-walled slit ring sections (eb3ia3sd.inp, eb3ja3sd.inp, ebo3a3sd.inp) and in two input files using a general beam section (eb32gssd.inp, eb3jgssd.inp).
Material:
Linear elastic, Young's modulus = 3.0 × 106, Poisson's ratio = 0.3.
Section types
Arbitrary (Open and Closed), Box, Channel, Circular, Elbow, General, Hat, Hexagonal, I, L,
Nonlinear General, Pipe, Rectangular, Trapezoidal.
Section forces
All problems are statically determinate, and section forces have been verified to be correct.
Reference solution
- Solid circular sections:
-

9.325 × 10−2, 1.865 × 10−3 (Step 1), 6.466 × 10−5 (Step 2)
- Solid square sections:
-

.8789, 1.758 × 10−2 (Step 1), 7.224 × 10−4 (Step 2)
- Solid thin rectangular sections:
-

.7031, 1.406 × 10−2 (Step 1), 2.440 × 10−4 (Step 2)
Note:
Loadings changed to .0025.
- Closed thin-walled pipe sections:
-

.2712, 5.423 × 10−3 (Step 1), 1.885 × 10−4 (Step 2)
- Closed thin-walled box sections:
-

1.278, 2.556 × 10−2 (Step 1), 7.521 × 10−4 (Step 2)
- Closed thin-walled hexagonal sections:
-

.3489, 6.978 × 10−3 (Step 1), 2.796 × 10−4 (Step 2)
- Open thin-walled I-sections:
-

.8931, 1.786 × 10−2 (Step 1), 7.537 × 10−2 (Step 2)
- Open thin-walled C-sections:
-

.3564, 7.112 × 10−3 (Step 1), .1081 (Step 2)
- Open thin-walled slit ring sections:
-

29.84, .5949 (Step 1), 1.388 (Step 2)
- Open thin-walled L-sections:
-

1.422, 2.857 × 10−2 (Step 1), .6177 (Step 2)
- Open thin-walled T-sections:
-

4.069, 8.138 × 10−2 (Step 1), .1563 (Step 2)
Results and discussion
The results for Step 1 are within 1% of the analytical values. The results for Step 2 are less accurate for . While results for rods and cylinders are exact, other closed sections can have an error of several percent. For open section beams can have errors in excess of 10% unless an open section beam element type is used. Open section beams include warping, which can have a significant effect on .
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