214 Professors Perry and Ayrion on Structures 



large masonry structures built with common mortar are usually 

 more stable than smaller ones. 



It is quite evident that as a concrete can be obtained which 

 will resist as great a tensile stress as ordinary brick itself, we 

 shall derive great benefit from making all horizontal sections, 

 of a structure which is composed of bricks set in good cement, 

 as great as possible ; that is, we shall find that the most suit- 

 able structure, if of brick or stone, for an earthquake country 

 must be composed of large stones set in good cement with 

 walls as thick as possible near the base, the thickness of wall 

 at every place being roughly proportional to the mass of the 

 building above that place. 



As, however, the resistance to tension of timber is very 

 much superior to that of cement or bricks, and as the mass of 

 a timber building is small, a timber building with sufficiently 

 strong joints must be very much superior to any structure of 

 brick or masonry. And for the same reason a building of 

 wrought iron might be made stronger still, and one of steel 

 strongest of all. 



Ordinary timber houses ought not to be too rigidly fastened 

 to the earth : if the joints of the structure are made, however, 

 very strong, and especially if wrought iron is used as well as 

 wood, and if there is diagonal bracing, then the connexions with 

 the ground may be made more rigid. The stiffness of structures 

 varies so much that we cannot give more definite rules than 

 those contained in this short article ; but it is obvious that our 

 principle of relative vibrations may be easily applied to find 

 the best arrangement in a structure for any given material and 

 with any given foundation. 



Calculations of Times of Vibration of different Buildings. 



Since a square or circular building has usually the same 

 period of vibration in all directions perpendicular to its height, 

 it is not necessary to specify in which direction it is vibrating. 

 Let us consider a prismatic structure of height h well built 

 into the ground and of uniform horizontal section A. Let K 

 be the radius of gyration of the section about an axis through 

 the centre of the building ; then, taking into account bending 

 and shearing stresses, a horizontal force P applied at the centre 

 of gravity of the prism produces a deflection of the centre of 

 gravity equal to 



P ^ P U_ 

 EAK' 2 ' 24 + A ' 2N' 



where E is the modulus of elasticity of the material, and N the 

 modulus of rigidity, which latter is about one third of the former 



