2nd order nonlinear - Tension only cross brace

Tekla Structural Designer
Tekla Structural Designer

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.


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


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.