Essentials in the theory of framed structures . y force acting on the left of the sectionis the left reaction i?o, and M2 = aRo. As the load moves fromZe to Lo, Ro increases uniformly from o to i lb., and M2 = aRoincreases uniformly from o to a Likewise the ordinateof the line OK, increasing uniformly from o at L^ to a atLo, represents aRo. Hence, the line ON is the influence linefor M2, when the load of i lb. is between Ls and Z,2. When the load of i lb. is between Lo and Li, the only forceacting on the right of the section is the right reaction R^.When the load is between Li
Essentials in the theory of framed structures . y force acting on the left of the sectionis the left reaction i?o, and M2 = aRo. As the load moves fromZe to Lo, Ro increases uniformly from o to i lb., and M2 = aRoincreases uniformly from o to a Likewise the ordinateof the line OK, increasing uniformly from o at L^ to a atLo, represents aRo. Hence, the line ON is the influence linefor M2, when the load of i lb. is between Ls and Z,2. When the load of i lb. is between Lo and Li, the only forceacting on the right of the section is the right reaction R^.When the load is between Li and L2, there are two forces actingon the right of the section—a floor beam load at L2 and thereaction Ro. Whether the load of i lb. is in the first or second ISO THEORY OF FRAMED STRUCTURES Chap. IV panel, Mi= {I — a)R6. As the load moves from Lo to ig, Reincreases uniformly from o to i lb.; and Mi = {I — a)R6increases uniformly from o to / — a Likewise the ordi-nate to the line QH, increasing uniformly from o at Lo to / — a. Fig. 107. at Ze, represents {I — ajR^. Hence, the Une QN is theinfluence line for M2, when the load of i lb. is between Loand Li. Let Pi represent the load on the segment a and let P representthe total load on the span; then the criterion for a maximumMi, developed as in Article 87, is The stress in UiUi or in L^L^ for either truss, found bydividing Mi by the proper arm, is a maximum when M2 is amaximum. Sec. Ill BRIDGES This criterion is often expressed in the form 151 or Pi a P I I — a and may be stated as follows: A maximum stress in any chordmember of a Pratt or- Parker truss; or of any other truss inwhich the influence line is a triangle (as in Fig. 107), occurswhenever the train is so placed that the average load per foot oneach of the two segments into which the center of momentsdivides the span, equals the average load per foot on the span. If the trusses in Fig. 107 have six equal panels, one-sixth ofthe total load o
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