I was doing exam question and am confused as to how to determine if the structure is a mechanism or not.
Say that j = number of joints, r = total number of reactions, b = number of bars.
For both (a) and (b) I get 2j-r = b which is a necessary condition for static determinacy.
For (c) I get 2j-r = 6, b = 7 => 2j-r < b which I guess is a condition for static indeterminacy. But this structure by inspection looks unstable.
Same for (c), where I get 2j-r = 6, b = 8 => 2j-r < b which means it is supposed to be statically indeterminate structure but looks very unstable.
What I have been taught is that we have to try to "press" it, i.e. imagine exerting an external force at a certain joint and see if the structure collapses or not. But I get confused when I actually get to do it. Could you please help with this.
Also from the matrix method of solving the linear system I thought 2j-r < b is a necessary and sufficient condition for static indeterminacy.
Say that the linear system for the structure is expressed as E*t + f = 0, where E is the coefficient matrix, t is the tension vector and f is the external force vector.
The size of the matrix E will be 2j-r rows and b columns so if 2j-r < b then there are more variables than equations so I thought it should be a necessary and sufficient condition.
But my lecturer says that the below example shows the case in which 2j-r < b and the structure is still a mechanism, so I was wondering if for this one as well it's only a necessary condition, and if so why that is.