Erik Luczak, P. Eng.
Edited by Leslie Gordon
Although a structure might be relatively simple, engineers should still consider its weight during design. Consider a simple tripod structure. The frame supports a light fixture weighing 1,500 lb and it has unusually long dimensions, necessary because there are only three possible solid anchoring points available for a secure mount. The builder specified AISI 301 stainless-steel tube because the frame will be subjected to outdoor weather. The intent was to use tubing with a 1-in. OD and 1/32‑in. wall thickness. Allowable yield strength of AISI 301 is 40,000 psi.
Engineers decided as long as the material did not yield, the design would work. They used a design factor of 2 and designed the frame for a load of 3,000 lb. To double-check the design’s feasibility, engineers performed hand calculations, treating the frame as a 3D truss. They only considered axial loads and treated each joint as a ball and socket. The axial stress came from dividing the largest axial load by the tube’s cross-sectional area. To find the maximum vertical deflection of the frame, treating the structure as a 3D truss let engineers use energy-method calculations.
To verify their calculations, engineers built a finite-element (FE) truss model using Grape Software’s 3D Beam/Truss (GBW32 V5.0) design and analysis software. They constructed the truss model using three elements, with each representing one member of the tripod. Truss elements, like the hand calculations, treated each joint as a ball and socket. The truss model assumes there are no moments or torques and only an axial stress. Running the analysis confirmed the hand calculation results. The computed axial stress of 33,040 psi was well below the material yield stress.
The FE model came in handy because it let engineers easily calculate a number of different loading situations. The actual structure is securely fixed to concrete bases and the common joint for the light fixture is welded. Fixed joints and welded connections produce moments and torque in the frame. However, these loads are not present in a 3D truss. The FE model let engineers easily change the elements from truss to beam elements and fix the attachment points for no deflection or rotation.
The software made it simple to divide the original truss elements. Engineers used four beam elements per tube to improve accuracy and study the bending curvature of the frame. Beam elements account for moments and torque and allow modeling the welded connection of the three tubes.
After running the new beam model, engineers found that the axial stresses and deflection compared well to the hand and 3D truss FE calculations. Notably, the beam bending stress only added several hundred pounds per square inch to the axial stress. At this point, it would seem that the design is fine. However, engineers decided they’d better run an analysis which includes the weight of the structure, especially given the long lengths.
Again, the FE model proved useful because engineers didn’t have to change anything in the existing model except add a 1-g load and specify the material density. The analysis revealed large bending stresses of the same magnitude as the axial stress. Adding the two totaled 54,183 psi, well in excess of the yield stress.
Their solution: Change the tube thickness to 1/16-in. (the 1-in. OD cannot change). Running the FEA again confirmed satisfactory stress and deflection levels. In this case, doubling the tubing thickness provided a design that met the criteria.