176 



CONCENTRATED LOADS ON BLOCKS. Art. 109. 



P, or such a non-uniform load that its resultant P will be at a 

 distance e from the axis of the block. If 

 two forces, . each equal to P and acting 

 parallel with its line of action, be assumed 

 to act in opposite directions at a (in the 

 axis of the block), the effect will not be 

 changed. The load P is therefore equiva- 

 lent to a concentric load P and a couple 

 whose moment is Pe. (34). The concentric 

 load produces, on an intermediate section 

 AB, a uniform unit stress as shown by the 

 diagram ABcd; the couple produces a 

 uniformly varying unit stress (diagram 

 ABfg) precisely like that produced upon 

 the section of a beam. (68) (13). The 

 moment of the couple being anti-clockwise 

 the bending stress will be compressive at A 

 and tensile at B ; it is zero at the center of 

 gravity of the cross section. 



Combining the diagrams for the two 

 kinds of stress there results : 



1. Diagram ABli in which the maxi- 

 mum unit tensile stress due to bending is 

 just equal to the unit stress due to the 

 direct compression. 



2. Diagram ABno in which the maxi- 

 mum unit tensile stress due to bending is 

 greater than the unit stress due to direct 

 compression. 



3. Diagram ABkm, in which the maximum unit tensile 

 stress due to bending is less than the unit stress due to direct 

 compression.. 



These values of the maximum unit stress are expressed by 

 the equation P Mv^__ JP_ Pevi ,,~. 



S *A- i '- '- A - nr 



For example, if a load on a stone wall 24 inches thick has 

 an eccentricity of S 1 /^ inches and amounts to 8000 Ibs. per lineal 

 foot, 8000 8000X3^X12 



8 max 12x24" T VX12X24X24X24~ 



=+ 52.1 and + 3.5 Ibs. per sq. inch. 



Fig. 134. 



