. Theory of structures and strength of materials. veload covers the whole of the girder. The total load due to both dead and live loads z=. [w ^ w)LThe reaction at each abutment due to this total load w -{- w 620 THEORY OF STRUCTURES. Let H be the horizontal thrust at the crown. T tension in the tie. Imagine the girder to be cut by a vertical plane a little onthe right of BD. The portion ABD is kept in equilibrium bythe reaction at A, the weight upon AD, and the forces Uand T. Take moments about B and D. Then and w -\- Zi> Tk = \, r = Hk, w + zvr Let H be the thrust along the chord at any p
. Theory of structures and strength of materials. veload covers the whole of the girder. The total load due to both dead and live loads z=. [w ^ w)LThe reaction at each abutment due to this total load w -{- w 620 THEORY OF STRUCTURES. Let H be the horizontal thrust at the crown. T tension in the tie. Imagine the girder to be cut by a vertical plane a little onthe right of BD. The portion ABD is kept in equilibrium bythe reaction at A, the weight upon AD, and the forces Uand T. Take moments about B and D. Then and w -\- Zi> Tk = \, r = Hk, w + zvr Let H be the thrust along the chord at any point P. Let X be the horizontal distance of P from B. The portion PB is kept in equilibrium by the thrust H atB, the thrust H 2X P, and the weight {w -\- zv)x between Pand B. Hence, H sec i = H = H^{w+ w)V, i being the inclination of the tangent at P to the horizontal,and (tv-^w \i p y the thrust at A = (—^ ^l\~Kp + V Diagonal Stresses due to Live Load.—Assume that the load isconcentrated at the panel points, and let it move from Atowards If the diagonals slope as in Fig, 390, they are all ties, andthe live load produces the greatest stress in any one of them,as QS, when all the panel points from A up to and includingQ are loaded. BOWSTRING TRUSS. 621 Let X, y be the horizontal and vertical co-ordinates, respec-tively, of any point on the parabola with respect to B asorigin The equation of the parabola is y^-j^^ (I) Let the tangent at the apex P meet DB produced in Z,and DC produced in E. Draw the horizontal line PM. From the properties of the parabola, LM = 2BM. Let PM = X and BM = y. From the similar triangles ZJ/Pand LDE, LAI LD 2y k4-y or — MP DE x~ x+QE k — y P — ^x QE = X 2y 8x Also, CE = QE - CE I — 2x l_ \ _ (_^ - 2^) %x QE~ l-\-2x (2) Draw EF perpendicular to QS produced, and imagine thegirder to be cut by a vertical plane a little on the right of PQ. The portion of the girder between PQ and C is kept inequilibrium by the reaction R at C, the thrust in
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Keywords: ., bookcentury1800, bookdecade1890, bookpublishernewyo, bookyear1896
