I have analyzed a structure and find that there are instability messages in the .anl (output) file, as follows :
***WARNING - INSTABILITY AT JOINT 26 DIRECTION = FX PROBABLE CAUSE SINGULAR-ADDING WEAK SPRING K-MATRIX DIAG= 5.3274384E+03 L-MATRIX DIAG= 0.0000000E+00 EQN NO 127***NOTE - VERY WEAK SPRING ADDED FOR STABILITY**NOTE** STAAD DETECTS INSTABILITIES AS EXCESSIVE LOSS OF SIGNIFICANT DIGITSDURING DECOMPOSITION. WHEN A DECOMPOSED DIAGONAL IS LESS THAN THE BUILT-IN REDUCTION FACTOR TIMES THE ORIGINAL STIFFNESS MATRIX DIAGONAL,STAAD PRINTS A SINGULARITY NOTICE. THE BUILT-IN REDUCTION FACTOR IS 1.000E-09THE ABOVE CONDITIONS COULD ALSO BE CAUSED BY VERY STIFF OR VERY WEAK ELEMENTS AS WELL AS TRUE SINGULARITIES.What is the significance of such messages? An instability is a condition where a load applied on the structure is not able to make its way into the supports because no paths exist for the load to flow through, and may result in a lack of equilibrium between the applied load and the support reaction.There is some explanation available in the STAAD.Pro Technical Reference Manual for the typical cause of instabilities. You will find it if you search by "Modeling and Numerical Instability Problems".
Also here is a list of related wikis on the topic:
STAAD.Pro Instability And Zero Stiffness