Art. 42 STATICALLY INDETERMINATE CASES. 



40 



such unknown stresses whose lever arms are equal lo some elemen- 

 tary dimension of the structure. Lever arms may sometimes be 

 taken by scale from a proper drawing this should be done in any 

 case as a check when the method becomes partly graphic. A 

 combination of resolution and moment equations is usually the 

 most convenient for many structures. 



42. Statically Indeterminate Cases. In general, the three 

 equations of equilibrium will suffice to determine three unknowns. 

 These may be the magnitudes or directions of three forces, the 

 magnitudes of two and the direction of one, or the directions of 

 two and the magnitude of one. If there are other unknowns the 

 structure is satically indeterminate unless geometrical conditions 

 yield a further relation between unknowns; for example, it is 

 sometimes evident that two unknowns are equal. , 



If the conditions of concurrency or parallelism are imposed 

 upon the forces, only two unknowns can be found as explained in 

 Art. 35. It follows that two stresses may be determined at each 

 joint of a truss. It does not follow, however, that a structure is 

 statically indeterminate, if by proceeding from joint to joint, a 

 joint is found where there are more than two unknown stresses; 

 it depends upon the total number of unknown stresses and the 

 total number of joints. If ,; is the number of joints in a truss, 

 2 j unknowns may be found; if it is supported at its ends, it will 

 require, in general, three equations to determine the reactions. 

 Therefore, if the 



number of members is less than or equal to 2f 3, . (8) 



the truss is sta- 

 tically determi- 

 nate. This is 

 i 1 1 u s trated in 

 the truss of Fig. 

 30. F o r a n y 

 system of loads, 

 the reaction R L 



Fig. 30. having boon 



calculated, stresses 1 and 13 may be found at joint 1; there 

 remain then two unknowns at joint 2 which may likewise be de- 

 termined. The same procedure applies at joint 13 after which 

 there remain three unknowns at joints 12, 3 or 4 and four at 

 joints 14 or 5 but the truss is not statically indeterminate because 



