. Theory of structures and strength of materials. , B, C,. . be W,, W^, VV^, . . , respectively. Drawing the stress diagram in the usual manner, OH rep-resents the horizontal thrust of the frame. The . portions s^s„, s^s.^, ... of the line of loads give adefinite relation between the weights for which the truss willbe stable. The result may be expressed analytically, asfollows: Let cf,, tfj, tr,, . . be the inclinations of AB, BC, CD, . . ,respectively, to the horizontal. Let the horizontal thrust OH = H. Then W//= 1l cot a, 2 w. -^WAco\.a |^+^.+ ^3)cot^3 cot «, = 3 cot <*2 = 5 cot a^ = It
. Theory of structures and strength of materials. , B, C,. . be W,, W^, VV^, . . , respectively. Drawing the stress diagram in the usual manner, OH rep-resents the horizontal thrust of the frame. The . portions s^s„, s^s.^, ... of the line of loads give adefinite relation between the weights for which the truss willbe stable. The result may be expressed analytically, asfollows: Let cf,, tfj, tr,, . . be the inclinations of AB, BC, CD, . . ,respectively, to the horizontal. Let the horizontal thrust OH = H. Then W//= 1l cot a, 2 w. -^WAco\.a |^+^.+ ^3)cot^3 cot «, = 3 cot <*2 = 5 cot a^ = It there are two bars only, viz., AB, BC, on each side of thevertical centre line, the frame will have a double slope, and inthis form is employed to support a Mansard roof. FRAMES LOADED AT THE JOINTS. 7 4. Non-closing Polygons.^Let a number of forces /*,,P^, P^, . . act upon a structure, and let these forces, taken inxirder, be represented in direction and magnitude by the sides of the unclosed figure MNPQ This figure is the unclosed. polygon of forces, and its closing line TM represents in directionand magnitude the resultant of the forces P^, P^, P^, . . For PM is the resultant of P^ and P^, and may replacethem ; QM may replace PM and P^, , /*,, P^, and P^; andso on. Take any point O and join OM, ON, OP, . . Draw a line AB parallel to OM and intersecting the line ofaction of /*, in any point B. Through B draw BC parallel toOA^ and cutting the line of action of P, in C. Similarly, drawCD parallel to OP, BE to OQ, EF to OR, . . The figureABCD ... is called the funicular polygon of the given forceswith respect to the pole O. The position of the pole O is arbi-trary^ and therefore an infinite number of funicular polygonsmay be drawn with diiTerent poles. Also the position of the point B in the line of action of /*,is arbitrary, and hence an infinite number of funicular polygonswith their corresponding sides parallel, , an infinite number•of sifnilar funicular polygons
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Keywords: ., bookcentury1800, bookdecade1890, bookpublishernewyo, bookyear1896
