Geometric Instability
33 The stability of a structure is determined not only by the number of reactions but also by their arrangement.
34 Geometric instability will occur if:
1. All reactions are parallel and a nonparallel load is applied to the structure.
2. All reactions are concurrent, Fig. 12.4.
3. The number of reactions is smaller than the number of equations of equilibrium, that is a mechanism is present in the structure.
35 Mathematically, this can be shown if the determinant of the equations of equilibrium is equal to zero (or the equations are interdependent).
12.2.6 Examples
Example 121: Simply Supported Beam
Determine the reactions of the simply supported beam shown below.
V 
1 \ 
1 
1 \ 
1 
/ 
The beam has 3 reactions, we have 3 equations of static equilibrium, hence it is statically determinate. Ray + Rdy  60 k  (4) k/ft(12) ft =0 12Ray  6Rdy  (60)(6) =0 or through matrix inversion (on your calculator) ay dy ay dy Alternatively we could have used another set of equations: (+^)£Mzd = 0; (Ray)(18)  (60)(12)  (48)(6)= 0 ^ Ray =56 kt Check: 
Responses

Olo Puddifoot8 years ago
 Reply