Solution C3-27 (Figure C3.2 condition 7 S.M. Targ 1989)

The solution to problem C3-27 (Figure C3.2 condition 7 S.M. Targ 1989) is to determine the forces acting in six weightless rods, hingedly connected at their ends to each other in two nodes and attached at other ends (also hingedly) to fixed supports A, B, C, D (Fig. C3.0 - C3.9, Table C3). The nodes are located at the vertices H, K, L or M of the rectangular parallelepiped, however, they are not shown in the figures and should be depicted solving the problem according to the table data.

In the first node, indicated in each column of the table, a force P = 200 N is applied, forming angles α1 = 45°, β1 = 60°, γ1 = 60° with the positive directions of the coordinate axes x, y, z. At the second node, a force of Q = 100 N is applied, forming angles α2 = 60°, β2 = 45°, γ2 = 60° with the x, y, z axes, respectively. The directions of the x, y, z axes for all figures are shown in Fig. C3.0.

The faces of the parallelepiped, parallel to the xy plane, have the shape of 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.

To determine the forces in the rods, it is necessary to draw a drawing similar to Figure C3.10, provided that the nodes are located at points L and M, and the rods are LM, LA, LB; MA, MS, MD. The figure also shows the angles φ and θ.

This digital product is a solution to problem C3-27 from the textbook by S.M. Targa 1989, which concerns the determination of forces in six weightless rods hinged to each other at two nodes and attached to fixed supports. The solution to the problem is presented in the form of a beautifully designed HTML document, which contains Figure C3.2, condition 7 and a table with data for solving the problem.

This product may be useful to students and teachers of universities and technical schools who study the theory of elasticity and resistance of materials. It will help them better understand the features of calculating forces in complex structures and learn to apply the acquired knowledge in practice.

In addition, thanks to the beautiful html design, this product will be pleasing to the eye and easy to use. The figures and tables in the document clearly and visually demonstrate all the necessary data, which greatly facilitates the process of studying the material.

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Solution C3-27 is a structure consisting of six weightless rods hingedly connected to each other in two nodes. One of the nodes is located at the vertex of the rectangular parallelepiped, and the other at the point indicated in the problem table. The ends of the rods connected to the nodes are also hingedly attached to the fixed supports A, B, C, D.

In the node, which is indicated first in each column of the table, a force P = 200 N is applied to the end of the rod, forming angles α1 = 45°, β1 = 60°, γ1 = 60° with the positive directions of the coordinate axes x, y, z. In the second node, a force Q = 100 N is applied to the end of the rod, forming angles α2 = 60°, β2 = 45°, γ2 = 60° with these axes.

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 required to determine the forces in each of the six rods. The solution drawing must be made in accordance with the requirements specified in the problem table and in Figure C3.10.

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