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<br />\l"> <br />o <br />If' <br />c.J <br /> <br />o <br /> <br />4 <br /> <br />SLAB ANALOGY EXPERIMENTS <br /> <br />METHODS OF INVESTIGATION <br />SECTION PAGE <br />72 Bending the slab ...................................................................................................... 148 <br />73 Auxiliary functions ....'m_._m_.__..___.___._____.mn.....__.h....____._.m....m_......n.__................ 164 <br />74 Apparatus and operation ......un_n...u..__.........................__n....__............................_.. 164 <br />76 Conclusions ............................................................................................................... 156 <br /> <br />CHAPTER VII-DEVELOPMENT OF EQU.A.TIONS <br /> <br />AIRY'S FUNCTION <br /> <br />76 General derivation ........__....................n....u.....n.__....__.. ...................n...................... 167 <br />77 Airy's function in polar coordinates n.........mn........___........m..._m..............._n... 160 <br /> <br />ANALOGOUS SLABS <br /> <br />78 The slab analogy ...................................................................................................... 161 <br />79 Uniform loading ........................................................................................................ 163 <br />80 Beam loading ............................................................................................................ 165 <br />81 Shear loading ..................m.........................m.......................m................................. 166 <br />82 Weight loading .......................................................................................................... 166 <br />83 Auxiliary function n........__............_.....___...m...m..._____...m...........n.._....._.................. 167 <br /> <br />GEOMETRY OF AIRY'S SURFACE <br /> <br />84 Change of coordinate axes ...._...__......___.........__......m............. ..m._............um......... 169 <br />85 Total force across a 'boundary m.m....'........._...... ........_................ ..................._... 169 <br />86 Moment of forces .__..._,.....__.._......_._,....._.......__.................._......._..._......._..........._........ 170 <br /> <br />DEJVEI..()PMENT OF FOUNDATION EQUATIONS <br /> <br />87 Load at a point ...................................................................................................... 172 <br />88 Distributed load ........................................................................................................ 173 <br />89 Trapezoidal load ........................................................................................................ 174 <br /> <br />DEVELOPMENT OF. AUXILIARY FUNCTIONS <br /> <br />90 Use ot auxiliary function ..._......_h....h................_._................__...........__....._....._....... 176 <br />91 Linear function ........................................................................................................ 176 <br />92 Inclusion of weight .......................................................m........................................ 177 <br />93 Arch function ............................................................................................................ 178 <br />94 Evaluation of constants __....................__...._......._........_._..._...__.............__..........__...... 179 <br />96 Ge'Q.eral arch function ......_.._......__...,................._......h......_...._..._._..._........................ 181 <br />