Solution C3-40 (Figure C3.4 condition 0 S.M. Targ 1989)

Solution C3-40 (Figure C3.4 condition 0 S.M. Targ 1989)

Six rods, hingedly connected to each other in two nodes and fixed at the other ends also hingedly to fixed supports A, B, C, D, are shown in Figures C3.0 - C3.9 and described in Table C3. In the node indicated first in each column of the table, there is a force P = 200 N, and in the second node - a force Q = 100 N. The force P forms angles α1 = 45°, β1 = 60°, γ1 = 60° with positive coordinate directions axes x, y, z, and force Q - angles α2 = 60°, β2 = 45°, γ2 = 60°. The directions of the x, y, z axes for all figures are shown in Fig. C3.0. The vertices H, K, L or M of a rectangular parallelepiped are also not shown in the figures and must be drawn by the problem solver in accordance with this table.

The faces of a parallelepiped parallel to the xy plane are squares. The diagonals of the other side faces form an angle φ = 60° with the xy plane, and the diagonal of the parallelepiped forms an angle θ = 51° with this plane.

It is necessary to determine the forces in the rods. Figure C3.10 shows an example of how drawing C3.1 should look if the nodes are at points L and M, and the rods are LM, LA, LB; MA, MS, MD. The figure also shows the angles φ and θ.

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Solution C3-40 is a structure consisting of six weightless rods, hinged at their ends to each other in two nodes. One ends of the rods are also hingedly attached to fixed supports A, B, C, D. The nodes are located at the vertices H, K, L or M of a rectangular parallelepiped and should be depicted as solving the problem according to the table data.

In the node indicated first in each column of the table, a force P = 200 N is applied, and in the second node a force Q = 100 N is applied. The forces P and Q form the angles specified in the problem statement with the positive directions of the coordinate axes x, y, z. The directions of the x, y, z axes for all figures are shown in Figure C3.0.

The faces of a parallelepiped parallel to the xy plane are squares. The diagonals of the other side faces form an angle φ = 60° with the xy plane, and the diagonal of the parallelepiped forms an angle θ = 51° with this plane.

It is necessary to determine the forces in the rods. Figure C3.10 shows as an example how drawing SZ.1 should look if, according to the conditions of the problem, the nodes are located at points L and M, and the rods are LM, LA, LB; MA, MS, MD. The angles φ and θ are also shown there.

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