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 2^nd order effects; this requires the value of EA to be sufficiently large to make the 2^nd order effect negligible.

Result	Theoretical formula	Theoretical value	Solver value
a	0	0	0
b	-P	-100	-100
c	-P	-100	-100
d		141.42	141.42
e	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.

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