This section is from the book "Cyclopedia Of Architecture, Carpentry, And Building", by James C. et al. Also available from Amazon: Cyclopedia Of Architecture, Carpentry And Building.

We shall assume that the lines in Fig. 215 by which we have represented forces F, G, H, and K represent struts which are hinged at their intersections with the forces A, B, and C, which represent loads; and that the two end struts F and K are hinged at two abutments located at y and z. Then all of the struts will be in compression, and the rays of the force diagram will represent, at the same scale as that employed to represent forces or loads A, B, and C, the compression in each of the struts. In the force diagram, draw a line from o, parallel with the line yz. It intersects the load line in the point n. Considering the triangle opn as a force diagram, op represents the force F, while pn and on may represent the direction and amount of two forces which will hold F in equilibrium. Therefore pn would represent the amount and direction of the vertical component of the abutment reaction at y, and on would represent the component in the direction of yz. Similarly we may consider the triangle onq as a force diagram; that nq represents the vertical component R", and that on represents the component in the direction zy. Since on is common to both of these force triangles, they neutralize each other, and the net resultant of the two forces F and K is the two vertical forces R and R") but since the resultant R is the resultant of F and K, we may say that Rr and R" are two vertical forces whose combined effect is the equal and opposite of the force R. Although an indefinite number of combinations of forces could begin and end at the points y and z, and could produce equilibrium with the forces A, B, and C, the forces R' and R" are independent of that particular combination of struts, F, G, H, and K.

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