X TABLE OF CONTENTS. 



Page 

 Art. 78. Working Stresses for Cases of Compound 



Stress 117 



" 79. Stresses in Girders 118 



" 80. Beams Stressed beyond the Elastic Limit 121 



Chapter Vll. Deflection of Beams and Girders 127 



Art. 81. Equation of the Elastic Line 127 



" 82. Deflection of a Cantilever Beam for a Load 



at its End 129 



" 83. Deflection of a Beam Supported at its Ends 



and Uniformly Loaded 130 



" 84. Deflection of a Beam Supported at its Ends 



and Carrying a Single Load at Any Point . . 131 

 " 85. Deflection of a Beam Carrying a Number of 



Loads 132 



" 86. Deflection of a Beam or Girder having a Var- 

 iable Cross Section 133 



" 87. Deflection of a Beam Due to Shear 135 



' ' 88. Resilience of Beams 137 



" 89. Points of Contrary Flexure 140 



Chapter VIII. Special Cases of Beams and Girders Loaded 



and Supported in Different Ways 144 



Art. 90. Explanation of Table 144 



" 91. Shear and Moment Diagrams 154 



" 92. Shears and Moments in Cantilever Beams. . . 154 

 " 93. Shears and Moments in a Beam Supported at 



Both Ends 155 



" 94. Combinations of Concentrated and Uniform 



Loads on Cantilever Beams and Beams 



Supported at the Ends 156 



" 95. Bending Moments and Shears for Beams 



having Fixed Ends 157 



' ' 96. Bending Moments and Shears for Continuous 



Beams 158 



1 ' 97. General Equations for Continuous Beams. . . . 160 



" 98. Practical Uses of Continuous Beams 163 



' ' 99. Live Loads on Beams 164 



" 100. Two Concentrated Moving Loads a Fixed 



Distance Apart '. 164 



