200 GEAPHIO AND ANALYTIC [CHAP. XIL 



We have only to remember that a plus moment at the sup- 

 port gives compression in lower flange and tension in upper, 

 and that a plus shear acts upwards, a minus shear downwards. 

 Also, that for the diagonals, the shear at any apex, multiplied 

 by the secant of the angle with the vertical, gives at once the 

 strain. In the present case the angle is 45 ; therefore the 

 secant is 1.414. 



The shear at any point is equal to the shear just to the right 

 of the left support, minus all the weights, if any between the 

 support and point. Thus, as above, for P x we have for diagonal 

 b c, the shear 36.17 40, or a downward shear of 3.83, since 

 the weight of 40 acts down. This downward shear causes com- 

 pression in b c, since it acts at the top of b c. For a b we have 

 36.17 acting up at the foot of a b, and therefore also causing 

 compression. The diagonals which meet at the weight are 

 always either both tension or both compression, according as. 

 the weight acts at the top or bottom. Right and left from the 

 weight the diagonals alternate in sign. 



The calculation, then, of the strains in any span of a contin- 

 uous girder, as also the diagraming of these strains, is simple 

 and easy, and offers no more real difficulty than the case of a 

 simple truss, provided we know or can find the moments and 

 shearing forces at the supports for the various cases of loading. 

 The method of finding these necessary quantities will form the 

 subject of the next chapter. 



The reader will do well to compare the strains in the above 

 table with those for the same simple girder Similarly loaded 

 Considerable saving of material, so far as indicated by strain, 

 will be found. On the other hand, some of the flanges are sub- 

 jected to both tensile and compressive strains. 



It is to be well noted that a small sinking of one of the sup- 

 ports of a continuous girder may, if the sinking is equal to the 

 deflection, make one span of what before was two. A very 

 slight sinking, then, may cause very great changes in the strains, 

 and hence, in structures of this kind, it is imperative that the 

 foundations must be secure from settling. If this condition ia 



