. Theory of structures and strength of materials. be the tension in the ;/th vertical due to the deadload. The resultant stress in it when the live load covers AOis vâ â Vâ, and if negative, this is the maximum compressionto which PQ is subjected. If vâ â Vâ is positive, the vertical PQ is never in compression. The maximum tension in a vertical occurs when the live , / load covers the whole of the girder and = ^i ^ + the tension due to the dead load. Aote.âThe same results are obtained when N is odd. 624 THEORY OF STRUCTURES. 13. Bowstring Girder with Isosceles Bracing. Diagonal Stresses due t
. Theory of structures and strength of materials. be the tension in the ;/th vertical due to the deadload. The resultant stress in it when the live load covers AOis vâ â Vâ, and if negative, this is the maximum compressionto which PQ is subjected. If vâ â Vâ is positive, the vertical PQ is never in compression. The maximum tension in a vertical occurs when the live , / load covers the whole of the girder and = ^i ^ + the tension due to the dead load. Aote.âThe same results are obtained when N is odd. 624 THEORY OF STRUCTURES. 13. Bowstring Girder with Isosceles Bracing. Diagonal Stresses due to the Dead Load.âUnder a dead loadthe bow is equilibrated and the tie is subjected to a uniformtensile stress equal in amount to the horizontal thrust at thecrown. The braces merely serve to transmit the load to thebow and are all ties. Let T^, T^ be the tensile stresses in the two diagonalsmeeting at any panel point Q. Let B^, 0^ be the inclinationsof the diagonals to the horizontal. Let W be the panel weight suspended from Fig. 391. The stress in the tie on each side of Q is the same, andtherefore T^, Tâ, and PV Are necessarily in , T, = W cos 6^ cos e^ sin {6, +^ ^^ ^^ = ^^^rnifT+O;) Diagonal Stresses due to the Live Load.â^Let A^ be the num-ber of half ^diweXs. 2/The length of a panel = -tt ; the weight at a panel point ,2/ ;= w â .N Let the load move from A towards C. All the braces in-clined like (9P are ties, and all those inclined like QP dive struts. The live load produces the greatest stress in OP when itcovers the girder between A and O. Denote this stress by Dâ; OG is the nth half-panel. As before, D,EF= R XCE (i) BOWSTRING GIRDER WITH ISOSCELES BRACING. 625 / wnl{ll -f- 2)The load upon AO =^ nw -rrz, and hence R = â17 ~â. ^ N N 2N The ratio of CE to j5/^ is denoted by the same expressionas in the preceding article. Thus, X>. = w I n-\- 2 N â n r + ^K^-^-ix«+or- N n â I ^-- (2) The live load produces the greatest stress in
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