Essentials in the theory of framed structures . 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 loadb
Essentials in the theory of framed structures . 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. and ji = the ordinate at the resultant Pi ^2 the ordinate at the resultant Pa- Let the loads be moved any small distance d to the left; insuch a way that no loads pass the points A, C and B. In otherwords Pi and P2 remain constant while the movement takesplace. The bending moment at C for this new position is Mc = P-iiyi. + 322) + Piiyx — yn). The change in the bending moment at C is AMc = Mc — Mc = ^i — Piyn Has the bending moment at C been increased or diminished bythis movement? The answer to this question depends uponwhether Pl>li$P2322- As long as Pi>ii22 Sec. II BRIDGES 13s the bending moment at C is increased by the movement of the loads to the left. From similar triangles and 3n:^::7o:ioo 3;22a::3o:ioo jod , ^od or yn = -— and ^22 = -— 100 100 Hence the bending moment at C will increase as long as 100 100or as long as ]Pi<2)Pi. Let \- Pi = P = total load on the span. If 7^1 < 3-P2 and 3P1 = 3P1 then loPi <3P or Pi<—P. 10 Hence, t
Size: 1505px × 1659px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1900, bookdecade1920, booksubjectstructu, bookyear1922
