. Theory of structures and strength of materials. Fig. 28. The rafters react horizontally upon each other at C, andtheir feet are kept in position by the tie-beam AB. Considerthe rafter A C. The resultant of the load upon AC, , W, acts throughthe middle point D. 20 THEORY OF STRUCTURES. Let it meet the horizontal thrust // of BC upon AC m equilibrium, the resultant thrust at A must also actthrough F. The sides of the triangle AFE evidently represent thethree forces. Hence ^ „,AE WAE W ^I/=:lV—- =— —=. = —cot a;Eh 2 DE 2 EF =v AE-^EF EF I (AJiV = ^^/-+4l2r£i = ^ 1 + cot a The thrust R
. Theory of structures and strength of materials. Fig. 28. The rafters react horizontally upon each other at C, andtheir feet are kept in position by the tie-beam AB. Considerthe rafter A C. The resultant of the load upon AC, , W, acts throughthe middle point D. 20 THEORY OF STRUCTURES. Let it meet the horizontal thrust // of BC upon AC m equilibrium, the resultant thrust at A must also actthrough F. The sides of the triangle AFE evidently represent thethree forces. Hence ^ „,AE WAE W ^I/=:lV—- =— —=. = —cot a;Eh 2 DE 2 EF =v AE-^EF EF I (AJiV = ^^/-+4l2r£i = ^ 1 + cot a The thrust R produces a tension H in the tie-beam, and avertical pressure PF upon the , if y is the angle FAE, EF DEtan y = -—- = 2 -—- = 2 tan AE If the rafters AC, BC are unequal, let a^, a„ be their in-clinations to A, B, respectively. Let W^ be the uniformly distributed load upon AC, W^that upon Fig. 29. Let the direction of the mutual thrust P 3I C make anangle ft with the vertical, so that if CO is drawn perpendicular ROOF TRUSSES, 21 to /^C the angle COB = ^ \ the angle ACF= go° — ACO= 90° - (/? - ^,)- Draw AM perpendicular to the direction of P, and considerthe rafter y^C As before, the thrust 7?, at y^, the resultantwe-giit PV^ at the middle point of AC, and the thrust P at Cmeet in the point P. Take moments about A. Then W,AE. But AM = AC s ACM = AC cos {j3 - a,), ^zr ^<^and Ah = — cos 2 W^ cos o-j 2 cos(p — (x^Similarly, by considering the rafter BC, W^ cos a^ W^ cos a,^ P = 2 sin(/? + ^2 — 90°) 2 cos(^ + arj * Hence PTj cos a^ 2 cos(/5 — ^^,) _ p _ ^2 cos «„ 2 cos(^ + «rJ and therefore tan/? = W^ tan o-j — W^ tan ^ar^ The horizontal thrust of each rafter = Psin ft. The vertical thrust upon the support A — W^ — P cos ft. ? The vertical thrust upon the support i? = W^-\- P cos ft. 13. King-post Truss.—The simple triangular trus
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Keywords: ., bookcentury1800, bookdecade1890, bookpublishernewyo, bookyear1896
