TABLE OF CONTENTS. XX111 



ART. PAGE 



48. Properties of the parabola included by the closing line 54 



49. Application of the above principles 54 



50. Most unfavorable position of load system upon a span of given 



length 56 



51. Greatest moment at a given cross-section 59 



CHAPTER VI. 

 MOMENT OF INERTIA OF PARALLEL FORCES. 



52. Application of moment of inertia in proportioning any cross-section. 61 



53. Graphical determination of moment of inertia 62 



54. Signification of the area of the equilibrium polygon 63 



55. Radius of gyration 63 



56. Inertia curves Ellipse and hyperbola of inertia 66 



57. Construction of curve of inertia 69 



58. Example 69 



59. Central curve Central ellipse 71 



60. Centre of action of the statical moments considered as forces 73 



61. Cases where the direction of the conjugate axes of the inertia curve 



can be at once determined 75 



62. Practical applications 76 



1st. The parallelogram 76 



2d Thetriangle 77 



3d. The trapezoid 78 



4:th. The parabolic segment 80 



63. Compound or irregular areas 81 



64. Cases where there is no axis of symmetry 83 



PART II. APPLICATION TO BKIDGES. 

 A. THE SIMPLE GIRDER. 



CHAPTER VII. 



THE SIMPLE GIRDER. 



66. Forces which act upon a bridge 84 



67. Bridge loading 85 



68. Shearing force Moment of rupture, etc 85 



69. Concentrated loads Invariable in position. 87 



70. Concentrated loads Variable in position 88 



71. Position of a given system of loads causing maximum shear. ....... 88 



72. Construction of the maximum shear 89 



73. Maximum moments 90 



74. Construction of maximum moments 91 



75. Absolute maximum of moments 92 



76. Continuous loading 93 



77. Total uniform load 98 



78. Method of loading causing maximum shear 94 



79. Live and dead loads ... 95 



