LAWS OF BONE ARCHITECTURE 191 



If P is the total tensile stress in pounds, 



A is the area of cross section in square inches, 



I is the original length of bar in inches, 



d is the total deformation in inches. * 



then 



E = 



P 



unit stress A PI 



unit deformation d Ad 

 1 



In these units E is expressed in pounds per square inch. The 

 modulus of elasticity is constant with very few exceptions for 

 any given material for stress below its elastic limit, but after 

 passing the elastic limit, it steadily decreases. Working unit 



Fig. 1 a illustrates the action of a compressive force applied in the axis of 

 a given body: Fig. 1 h, the action of a compressive force applied at a slight dis- 

 tance from the axial line and parallel to it: Fig. 1 c, the action of a compressive 

 force applied parallel to the axis of the body but at a distance of one-sixth of 

 the width of the body from the axis, which produces a pressure in the base of the 

 assumed prism varying uniformly from zero on the edge farthest from the line 

 of action of the force to exactly twice the average pressure, at the opposite 

 edge. Fig. 1 d shows the action of a tensile force on a body and figure 1 e illus- 

 trates shearing action in a given body. Paragraphs 9, 10, 11. 



Fig. 2 Parallelogram of forces constructed for the graphic determination 

 of the resultant of two forces acting at the same point, the direction and mag- 

 nitude of both being known. Paragraph 17. 



Fig. 3 Action of levers, explained in paragraph 18. 



Fig. 4 Principle of moments explained in paragraph 18. Figs. 5 a and b 

 Principle of levers applied to levers of any shape, explained in paragraph 20. 



Fig. 5 c Action of a couple, explained in paragraph 31. 



Fig. 6 a Action of vertical shear in a cantilever beam. Paragraphs 24, 25. 



Fig. 6 b Action of vertical shear in a simple beam resting on two supports. 



Figs. 7 a and b A method of constructing graphic diagrams of the vertical 

 shear and of the bending moment for everj' part of a cantilever, and of a simple 

 beam, respectively, carrying a single concentrated load, P. Complete discus- 

 sion in paragraphs 26-32. 



Figs. 8 a and b Indicate the position of vertical loads on a cantilever beam 

 and on a simple beam and show a plane passed through the beams in the line 

 t-t. Explained in paragraphs 29-33. 



