Stress-calculation in frameworks by the method of "systematic relaxation of constraints"—I and II

1―Framed structures, and the principles which govern their design, are familiar to all students of engineering science. Bending and twisting actions impose stresses which range between wide limits, but a straight bar in tension or compression sustains practically the same stress at every point; therefore economy of material can be attained by constructing frameworks from straight numbers, connected at their ends and so arranged that external forces (other than those arising from the weights of the members themselves) are applied only at the joints. In theory we may (for a first approximation) neglect entirely the effects of fixity at the joints, and substitute for the actual framework a "skeleton diagram" in which every member is replaced by a line of thrust or tension. The problem then presented will be soluble by purely statical methods, or it will involve the elastic properties of the members, according as the number of these (m ) is related to the number (j ) of the joints. In a "plane frame" (where the external forces, as well as the lines of thrust or tension, are coplanar) the actions will be statically determinate ifm = 2j - 3.(1)