CHAPTER VII. 74. Modern Bridge Theory 78 75. The Stresses in Beams 79 76. Vertical and Horizontal Shearing Stresses 80 77. Law of Variation of Stresses of Tension and Compression 82 78. Fundamental Formulæ of Theory of Beams 83 79. Practical Applications 85 80. Deflection 86 81. Bending Moments and Shears with Single Load 87 82. Bending Moments and Shears with any System of Loads 89 83. Bending Moments and Shears with Uniform Loads 92 84. Greatest Shear for Uniform Moving Load 94 85. Bending Moments and Shears for Cantilever Beams 96 86. Greatest Bending Moment with any System of Loading 97 87. Applications to Rolled Beams 99 CHAPTER VIII. 88. The Truss Element or Triangle of Bracing 100 89. Simple Trusses 101 90. The Pratt Truss Type 102 91. The Howe Truss Type 105 92. The Simple Triangular Truss 106 93. Through- and Deck-Bridges 108 94. Multiple Systems of Triangulation 108 95. Influence of Mill and Shop Capacity on Length of Span 109 96. Trusses with Broken or Inclined Chords 109 97. Position of any Moving Load for Greatest Webb Stress 110 98. Application of Criterions for both Chord and Web Stresses 111 99. Influence Lines 112 100. Influence Lines for Moments both for Beams and Trusses 113 101. Influence Lines for Shears both for Beams and Trusses 115 102. Application of Influence-line Method to Trusses 118