For stable structures, one of the important properties of flexibility and stiffness matrices is that the elements on the main diagonal________________?

For stable structures, one of the important properties of flexibility and stiffness matrices is that the elements on the main diagonal________________?

i) of a stiffness matrix must be positive
ii) of a stiffness matrix must be negative
iii) of a flexibility matrix must be positive
iv) of a flexibility matrix must be negative

The correct answer is
A. (i) and (iii)
B. (ii) and (iii)
C. (i) and (iv)
D. (ii) and (iv)

To generate the j the column of the flexibility matrix________________?

To generate the j the column of the flexibility matrix________________?

A. a unit force is applied at coordinate j and the displacements are calculated at all coordinates
B. a unit displacement is applied at co-ordinate j and the forces are calculated at all coordinates
C. a unit force is applied at coordinate j and the forces are calculated at all coordinates
D. a unit displacement is applied at co-ordinate j and the displacements are calculated at all co-ordinates

If there are m unknown member forces, r unknown reaction components and j number of joints, then the degree of static indeterminacy of a pin-jointed plane frame is given by__________________?

If there are m unknown member forces, r unknown reaction components and j number of joints, then the degree of static indeterminacy of a -jointed plane frame is given by__________________?

A. m + r + 2j
B. m – r + 2j
C. m + r – 2j
D. m + r – 3j