Solution C3-51 (Figure C3.5 condition 1 S.M. Targ 1989)

Solution to Problem C3-51 (see Figure C3.5, Condition 1, S.M. Targ, 1989)

There are six weightless rods hinged to each other in two nodes, which are attached at their ends (also hinged) to fixed supports A, B, C and D. The nodes are located at the vertices H, K, L or M of a rectangular parallelepiped. The rods and nodes are not shown in the figures and should be depicted as solving the problem according to the table data.

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

The faces of a parallelepiped parallel to the xy planes 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 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, MC and MD. The figure also shows the angles φ and θ.

This digital product is a solution to problem C3-51, which is described in Figure C3.5 condition 1 from the book by S.M. Targa, published in 1989. This task consists of determining the forces in six weightless rods, hingedly connected to each other and attached to fixed supports.

The design of this product is made in a beautiful html format, which contains all the necessary data to solve the problem. In particular, tables are provided with data on the force applied at each node, as well as the angles formed by this force with the coordinate axes. Also in Figure C3.10 is an example of a drawing for this problem, where nodes and rods are indicated, as well as angles φ and θ.

This digital product will be useful for students and professionals in the field of engineering calculations and mechanics. It will allow you to quickly and efficiently solve problem C3-51 and obtain the necessary results.

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Solution C3-51 is a structure consisting of six weightless rods, hinged to each other in two nodes and attached to fixed supports A, B, C, D. The nodes are located at the vertices H, K, L or M of a rectangular parallelepiped. At the node, which is indicated first in each column of the table, a force P = 200 N is applied; in the second node, a force Q = 100 N is applied. The force P forms angles equal to α1 = 45°, β1 = 60°, γ1 = 60° with the positive directions of the coordinate axes x, y, z, respectively, and the force Q forms angles α2 = 60 °, β2 = 45°, γ2 = 60°.

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. To do this, it is necessary to depict nodes and rods in a drawing that corresponds to the conditions of the problem. Figure C3.10 shows an example of such a drawing for the case when the nodes are located at points L and M, and the rods are LM, LA, LB; MA, MS, MD. The drawing also shows the angles φ and θ.

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