TABLE OF CONTENTS. XXV11 



SUPPLEMENT TO CHAPTER XIII. 



DEMONSTRATION OF ANALYTICAL FORMULA FOR THE 

 CONTINUOUS GIRDER. 



iRT. PAOK 



1. Conditions of equilibrium 243 



2. Equation of elastic line 244 



3. Theorem of three moments 245 



4. Determination of moments Supports all on level 246 



5. Uniform load 248 



6. Formulas for the "Tipper" [Art. 120] 248 



7. Example of two span tipper 249 



8. LITERATURE UPON THE CONTINUOUS GIRDER ... 251 



PAKT III. APPLICATION OF THE GRAPHICAL 

 METHOD TO THE ARCH. 



CHAPTER XIV. 



THE BRACED ARCH. 



157. Different kinds of braced arch 255 



158. Arch hinged at both crown and abutments 255 



159. Hinged at abutments only Continuous at crown 257 



1st. Parabolic arch 258 



2d. Circular arch, Tables for solution of 259 



160. Arch fixed at abutments Continuous at crown 261 



1st. Parabolic arch 262 



2d. Circular arch 264 



162. General method of solution 266 



163. Analytical formulae for horizontal thrust, and vertical reactions. . . . 268 



164. Arches with solid web 270 



165. Strains due to temperature, Formulae for 271 



166. Effects of temperature 273 



SUPPLEMENT TO CHAPTER XIY. 



DEMONSTRATION OF ANALYTICAL FORMULAE FOR THE 

 BRACED ARCH. 



CHAPTER I. 



GENERAL CONSIDERATIONS AND FORMCL/E. 



1. Fundamental equations 275 



2. Displacement of any point 279 



CHAPTER H. 



HINGED ARCH IN GENERAL. 



3. Notation The outer forces in general , 281 



4. Intersection line 283 



5. Parabolic arch Concentrated load 282 



6. Circular arch Concentrated load 284 



7. Integrals used in above discussion 280 



