168 



STRENGTH OF MATERIALS 



through this point ; and hence the moment OC-d = OH- z, where z is 

 the vertical intercept from the equilibrium polygon to the center of 

 moments S. Having determined the moment at any given point, the 

 stresses at this point can be calculated as explained in Article 14!. 



136. Relation of equilibrium polygon to bending moment diagram. 

 In the preceding article it was proved that the moment acting at any 

 point of a structure is equal to the pole distance of the force diagram 

 multiplied by the vertical intercept on the equilibrium polygon t'nmi 

 the center of moments. For a system of vertical loads, however, the 

 pole distance is a constant. Consequently the moment acting n any 

 section is proportional to the vertical intercept on the equilibrium 

 polygon from the center of moments. Therefore, if the equilibrium 

 polygon is drawn to such a scale as to make this factor of ]rnjr- 

 tionality equal to unity, the equilibrium polygon will be identical 

 with the bending moment diagram for the given system of loads. 



Problem 160. Compare the bending moment diagrams and equilibrium polygons 

 for the various cases of loading illustrated in Article 62. 



II. CONCIM T! AND MASONRY ARCHES 



137. Definitions and construction of arches. The following dis- 

 cussion of the arch applies only to that form known as the Barrel 

 arch. Domed and cloistered arches demand a special treat me n t which 



is beyond the scope of 

 this volume. 



The various portions of 

 a simple, or barrel, an-b, 



as shown in projec- 

 tion in Ki^ r . rjr>. bave tin- 

 following special names. 



Soffit: the iniHT or con- 

 oave surface of the arch. 

 Intrados : the eurv.- of in- 



tersection (ACB, Fig. 125) of the soffit, with a vertical plane 

 to the axis, or length, of the arch. 



Extrados: the curve of intersection (DBF, Fig. 125) of a v.-rti.-al p 

 with the outer surface of the arch. 



Crown : the highest part of the arch. 



