Patent GB-692992-A (GB)
Title: Apparatus for the calculation of reticulated or framed structures
IPC: G06G7/68
Filed: 1948-12-31
Abstract: 692,992. Electric analogue calculating systems. ORTEGA, M. G. Dec. 31, 1948 [Jan. 5, 1948], No. 33609/48. Class 37. In apparatus for electrically computing the mechanical stresses of a rigid frame system, each of the members connecting the joints of a given frame is represented by a pair of resistance networks oppositely related to the two ends of the member; each network having a first terminal corresponding to one end of the member, a second terminal corresponding to the opposite end, and a third intermediate terminal; the second and third terminals being held to a constant datum potential and the network components being capable of adjustment to values analogous to the known rigidities and coefficients of transmission of moments of the corresponding frame members so that when a potential of magnitude, referred to the datum, proportionate to an angular deflection of the corresponding end of the appropriate member is applied to the first terminal of a network, the resultant currents through the first and second terminals of the network are respectively proportional to the bending moments arising at the corresponding ends of the member, electrical circuits being provided corresponding to each frame joint for additively combining the currents in all the first and second terminals corresponding to the ends of the individual members meeting at the joint, and for applying a potential (referred to the datum) to the combined first terminals, which may be adjusted to obtain equilibrium between the sum of the currents from the first and second terminals and a current set up in an external circuit to represent the known total fixed end moment of the joint due to the loads acting on the frame. Fig. 1 shows a 3-terminal resistance network having a junction point p, wherein the element op has resistance αo/j and current Io/j, element pn has resistance #o/j and current io/j, and element pm has resistance #o/j and current #o/j, points m and n being connected to a datum potential El (denoted by symbol B) intermediate between the positive (denoted by symbol A) and negative (denoted by symbol C) of a potential source E, while point o is connected to similar points o of associated networks. It is shown mathematically that by Kirchoff's Laws, Vo = Ro/jIo/j Io/j = VoAo/j io/j = #o/jIo/j where Vo = the potential difference between points o and n io/j #o/j = - = the ratio of the currents in Io/j pn and op Ro/j = αo/j + #o/j#o/j/#oj+#o/j = the resistance between o and nm Ao/j = the admittance between o and nm. If αo/j is assumed to be zero so that points o and p are equipotential, the network is shown to represent an electrical circuit analogous to a static member oj of a frame system, anchored at end j and deflected through angle #o at end o (Fig. 3) wherein Mo/j = ko/j#o mo/j = (#o/jMo/j where Mo/j is the moment at end o due to deflection #o mo/j is the corresponding moment at end j ko/j is the rigidity of the member at end o #o/j is the coefficient of transmission of moments from end o to end j and according to the analogy, Io/j represents Mo/j io/j represents mo/j Vo represents #o Ao/j represents ko/j #o/j represents #o/j and the resistance values #o/j, #o/j of the analogy network are given by #o/j = 1/#o/jko/j #o/j = 1/(1-#o/j)ko/j A similar analogy network (Fig. 2) may be developed for the frame member oj when it is anchored at end o, and deflected through an angle #j at end j. Fig. 4 shows a portion of a frame system wherein bars oa, ob, oc are joined at a common point o and are represented by an electrical analogy network wherein each bar is represented by two analogous resistance networks having interconnection terminals o and a, b or c corresponding to the several bar ends, and potentials corresponding respectively to the deflections of each bar at end o and at ends a, b or c. A balancing current Io is adjustably supplied to the electrical junction-point o, and it is shown that, using the foregoing notation, for the first series of networks, Io/a = Ao/A/AoIo Io/b = Ao/b/AoIo Io/c = Ao/o/AoIo where Ao is the total conductance between point o and the point denoted by symbol B, analogously to the statical behaviour of the system as represented by Mo/a = Ko/a/KoMo Mo/b = ko/b/KoMo Mo/c = Ko/o/KoMo in which Ko is the total rigidity at end o and Mo is the total amount due to the deflection #o at end o. For equilibrium at point o, the total moment thereabout must be zero, so that considering the fixed end moments due to the deflections of the bars at ends a, b, and c, Mo/a+Mo/b+Mo/c+ma/o+mb/o+mc/o+Mo=o where Mo is the total fixed-end moment at point o due to the several bars, and by analogy, Io/a+Io/b +Io/c+ia/o+ib/o+ic/o+To=o where To is the current corresponding to the total fixed end moment of the bars converging at point o and ia/o, ib/o, ic/o are the currents in the second series of networks corresponding to the moments at point o due to the deflections at a, band c. The above electrical equality is satisfied by additively combining currents Io, ia/o, ib/o, ic/o, To in an ammeter and adjusting Io for null indication, when the current in any individual element of the analogy network indicates the bending moment in the corresponding bar of the corresponding statical system. Fig. 5 shows an electrical analogue network operable as described to compute a statical frame system at successive points, in which the datum potential E<SP>1</SP> is given the value of half the source potential E and the adjustable current Io is derived from a single slider adjustable to traverse alternatively one or other of a pair of resistances E, F, connected respectively to positive potential E and to the negative so that the available potential is variable from + E/2 to - E/2. The adjustable current To is similarly derived from a slider alternatively adjustable over resistances G, H similarly connected to positive potential E and to the negative line, and the currents Io, To are thus independently adjustable to the requisite positive or negative value giving the required null indication. Fig. 6 shows a section of a complete analogue computing apparatus corresponding to a bar oa for solving a complex frame system, wherein the networks analogous to end o are shown on the left and those analogous to end a on the right. To maintain the datum potential at a fixed E value - and to enable the currents Io and To to 2 be respectively varied both positively and negatively, the variable resistances r, t constituting the three-terminal analogue networks are duplicated by identical resistances r<SP>1</SP>, t<SP>1</SP> as shown; the sliders of rand r<SP>1</SP>; t and t<SP>1</SP> being linearly ganged together. The balancing resistances E, F, G, H are similarly duplicated by balancing resistances El, F<SP>1</SP>, G<SP>1</SP>, H<SP>1</SP> and the corresponding sliders are ganged together; each resistance being oppositely connected by comparison with its duplicate as between the positive pole (denoted by symbol A, Fig. 1) and negative pole (denoted by symbol C, Fig. 1) of the potential source E. The sliders of resistances r, t are connected through change-over switches qA, and the sliders of resistances G<SP>1</SP>, H<SP>1</SP> are connected through make-and-break switches qB<SP>1</SP> to one of a pair of bus-bars denoted by symbol B (Fig. 1), while the sliders of resistances r<SP>1</SP>, t<SP>1</SP> and resistances G, H are connected similarly through switches qA<SP>1</SP> and qB to the other corresponding bus-bar of the pair. The bus-bars are interconnected by an ammeter A and the upper ends of the networks r, t; r<SP>1</SP>, t<SP>1</SP> are connected to the sliders of resistances E, F; El, F<SP>1</SP> so that for any position of the sliders of resistances r, t; rl, t<SP>1</SP>; E, F; G, H; El, F<SP>1</SP>; G<SP>1</SP>, H<SP>1</SP>; the datum potential (denoted by symbol B, Fig. 1) remains constant at E/2. The complementary right and left halves of the system corresponding to ends o, a of the bar oa are alternatively and symmetrically interconnected by cross-connections x joining the outlet terminals PA to inlet terminals PC of each complementary network under control of the change-over switches, qA, qA<SP>1</SP>; qC, qC<SP>1</SP>; which cross-connections are analogous to the mechanical reaction of one joint of the frame on the next point due to the interconnecting bar. Corresponding points of other similar switchable networks representing bars converging at points o, a are interconnected to the circuit, at the junction-points o, o<SP>1</SP>, a, a<SP>1</SP> as shown. With the switching set up as shown, the resistances r, t; rl, t1 (corresponding respectively to analogue elements #o/a and #o/a); are adjusted according to the relations derived above, and the resistances corresponding to the complementary elements #a/o, #a/o are similarly adjusted. Resistances G, H; G<SP>1</SP>, H<SP>1</SP> are adjusted according to the static loading of the corresponding E joint of the frame structure so that p = -, 2T where p is the resistance value in circuit and T is the current strength (positive or negative) representing the fixed end moment at each joint, and the voltage Vo appearing between point o or a of the network and the datum potential source is then analogous to the deflection #o at the appropriate joint of the frame. With switches qA, qB and qC corresponding to the junction point o in position 1 and those corresponding to junction point a in position 2 (as shown), the currents io/a and #o/a (amounting to Io/a) flow in the ammeter A, while current #a/o is diverted from the ammeter circuit and current io/a is connected over the cross-connection x to flow through the ammeter. Similarly with switches qA, qB and qC corresponding to junction o in position 2 and those corresponding to junction a in position 1, currents ia/o and #a/o (amounting to Ia/o) and current io/a flow in the ammeter. For the junction o, corresponding