Essentials in the theory of framed structures . the load of i lb. is be-tween C and A, the only forceacting on the right of the section is the right reaction at 5; andthe moment at C equals 15 ft. times the right reaction. As theload moves from A to C, the right reaction increases uniformlyfrom o to I lb.; and 15 ft. times the right reaction increasesuniformly from o to 15 Likewise the ordinate of theline QH, increasing uniformly from zero at Q to 15 at O,represents 15 ft. times the right reaction. Hence, the line QNis the influence line for the bending moment at C, when the lo
Essentials in the theory of framed structures . the load of i lb. is be-tween C and A, the only forceacting on the right of the section is the right reaction at 5; andthe moment at C equals 15 ft. times the right reaction. As theload moves from A to C, the right reaction increases uniformlyfrom o to I lb.; and 15 ft. times the right reaction increasesuniformly from o to 15 Likewise the ordinate of theline QH, increasing uniformly from zero at Q to 15 at O,represents 15 ft. times the right reaction. Hence, the line QNis the influence line for the bending moment at C, when the loadof I lb. is between A and C. These ordinates are also positive,since the moment of the force on the right of the section iscounter-clockwise. Therefore, the line QNO is the influenceline for the bending moment at C; and shows that when asingle load (whether i lb. or 100 lb.) crosses the span from Bto A, the bending moment at C increases uniformly to a maxi-mum as the load arrives at C, and decreases uniformly to zeroas the load arrives at Fig. 98. 134 THEORY OF FRAMED STRUCTURES Chap. IV 87. Criterion for Maxiinum Bending Moment.—Consider aseries of loads so connected that the distances between loads^ are maintained (Fig. 99). As these loads move on the span, the bend-ing moment at C varies. It is de-sired to find the position of theseloads on the span, so that the bend-ing moment at C will be a maxi-mum. The influence line QNO isdrawn in accordance with thepreceding article. The bendingmoment at C, for any given posi-tion of the loads, may be deter-mined by multiplying each loadby its corresponding ordinate in the influence line diagram;and finding the sum of these products. Or, since the influenceline has a constant slope from Q to N, and a constant slope fromN to O; the bending moment at C may be expressed by theequation Mc = Fiji + Piji in which Pi = the sum of the loads between A and CP2 = the sum of the loads between C and B
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Keywords: ., bookcentury1900, bookdecade1920, booksubjectstructu, bookyear1922
