2nd order nonlinear - Tension only cross brace
Problem definition
Calculate the axial forces of the elements a-e shown in the 5x5 pin jointed plane frame shown below. Elements d and e can resist tensile forces only.
Assumptions
All elements are constant and equal EA. A smaller value of EA will increase the influence of second order effects, whereas a larger value will decrease the influence.
Key results
Under the applied loading element e becomes inactive. The theoretical formulas presented below are obtained using basic statics. Note that a positive value indicates tension. These results assume no 2nd order effects; this requires the value of EA to be sufficiently large to make the 2nd order effect negligible.
Result | Theoretical formula | Theoretical value | Solver value | % Error |
---|---|---|---|---|
a | 0 | 0 | 0 | 0 |
b | -P | -100 | -100 | 0 |
c | -P | -100 | -100 | 0 |
d | 141.42 | 141.42 | 0 | |
e | 0 | 0 | 0 | 0 |
Conclusion
An exact match is observed between the values reported by the solver and the values predicted using statics. A 1st order nonlinear analysis can be used, with any section sizes, to confirm this result without second order effects.