Essentials in the theory of framed structures . tructed by choosing different points o and / in this or in anyother problem in which the frame has four or more members,and thereby made susceptible to a collapse. Location-direction Drawn Through Given Points.—An infi-nite number of location-direction diagrams may be drawnthrough any given point ^ on a location-direction, by choosing 46 THEORY OF FRAMED STRUCTURES Chap. I different positions for the pole o and beginning the location-direction diagram at p in each instance. An infinite number oflocation-direction diagrams may be drawn through two
Essentials in the theory of framed structures . tructed by choosing different points o and / in this or in anyother problem in which the frame has four or more members,and thereby made susceptible to a collapse. Location-direction Drawn Through Given Points.—An infi-nite number of location-direction diagrams may be drawnthrough any given point ^ on a location-direction, by choosing 46 THEORY OF FRAMED STRUCTURES Chap. I different positions for the pole o and beginning the location-direction diagram at p in each instance. An infinite number oflocation-direction diagrams may be drawn through two points,p on one location-direction and s on another. Call the loca-tion-directions on which the two points p and s are located xyand yz, and draw the location-direction oy connecting p and constructing the magnitude-direction diagram, arrange theorder so that the magnitude-directions xy and yz are the magnitude-direction oy and select any point o on itfor the points/, g and/ (Fig. 21m) may be selected at random. on the location-directions of three forces; and a location-direc-tion diagram drawn through them, provided the points are notin a straight line. Call the location-directions on which /, gand/ are situated, ab, be and cd respectively; and draw the loca-tion-directions ob and oc through/, g and/ as indicated. Beginthe magnitude-direction diagram (Fig. 2iw) so that be willappear between ab and cd. Draw the magnitude-directionsob and oc intersecting at 0, the desired pole. Complete the magnitude-direction diagram in two ways;thus giving two location-direction diagrams through/, g and/. Evidently the points/, g and/ may be connected by location-directions in two other ways; viz., by connecting/ and g, and/ and/; or by connecting/ and/, and g and/. Thus, several Sec. VI EQUILIBRIUM OF COPLANAR FORCES 47 constructions of the location-direction diagram through thethree given points/, g and/ are possible; but the number forany given syste
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