DESIGN OF FIXED ENDED AECHES BY THE ELASTIC THEORY 139 



rib which will satisfy the four conditions expressed by equations (13). 

 The pole distance of the true force diagram gives the magnitude of 

 the horizontal arch thrust, the rib closing line gives the line of action 

 of this thrust, and the vertical interscepts between the true frame and 

 the rib are proportional to the bending moments in the rib. These 

 interscepts multiplied by the horizontal thrust give the arch bending 

 moments while the proper components of the rays in the true force 

 diagram give the normal thrusts and the shears at all sections of the 

 rib. The rays of the true force diagram to scale represent the result- 

 ant thrusts at the various sections of the rib. 



Application. 



Concrete- steel structures are becoming all -important to the 

 engineer and before many years of the Twentieth Century have 

 passed, structures of this type will quite generally take the places of 

 those of pure masonry. Monolithic masses of concrete are now used 

 in many ways instead of stone. Retaining walls, bridge piers, cul- 

 verts, small arch bridges, floors, dams and innumerable other engineer- 

 ing things are now made entirely of concrete and mortar. Even 

 ornaments like balusters and mouldings are made of these materials. 

 In fact highway bridges have lately been built in parks and private 

 estates of this country in which the entire ornamented surfaces are of 

 concrete finished with mortar. 



Concrete, like masonry, can withstand great compressive loads 

 but is weak in tension. Where large tensile stresses must be carried 

 concrete, however, can be reinforced and strengthened by embedding 

 in the mass suitable steel work. In such combined structures it is 

 assumed that the concrete masses resist mainly compressive stresses 

 while the steel reduces the tension in the artificial stone to proper 

 low limits or takes the tensile stresses entirely. Where steel work is 

 entirely and securely embedded in concrete it is not acted upon by 

 water and the corrosive agencies of the atmosphere and like wood 

 permanently under water, steel within concrete remains in good con- 

 dition indefinitely. Concrete-steel structures properly designed may 

 therefore be assumed to be as durable as masonry structures, while 



