Solution C1-33 (Figure C1.3 condition 3 S.M. Targ 1989)

Solution to problem C1-33 (Figure C1.3 condition 3 S.M. Targ 1989)

Given a rigid frame located in a vertical plane (Fig. C1.0 - C1.9, Table C1), which is hinged at point A, and at point B attached either to a weightless rod with hinges at the ends, or to a hinged support on skating rinks At point C, a cable is attached to the frame, thrown over a block and carrying at the end a load weighing P = 25 kN.

The frame is acted upon by a pair of forces with a moment M = 100 kN m and two forces, the values, directions and points of application of which are indicated in the table (for example, in conditions No. 1, the frame is acted upon by a force F2 at an angle of 15° to the horizontal axis, applied at the point D and a force F3 at an angle of 60° to the horizontal axis applied at point E, etc.).

It is necessary to determine the reactions of the connections at points A and B caused by the acting loads. For final calculations, take a = 0.5 m.

Answer:

Let's use the equilibrium conditions. The sum of all horizontal and vertical forces must be zero, and the sum of moments about any point must also be zero.

Let's consider the reaction of the connection at point A. The vertical component of the reaction should be equal to the weight of the load P, that is, Ra_y = P = 25 kN. The horizontal component of the reaction is zero, since no horizontal forces act on the frame.

Let's consider the reaction of the connection at point B. The horizontal component of the reaction is equal to the sum of the horizontal components of the forces acting on the frame. In our case, it is equal to: Rb_x = F2cos(15°) + F3cos(60°) = 20.5 kN. The vertical component of the reaction is equal to the sum of the vertical components of the forces acting on the frame, as well as the weight of the load P. It is equal to: Rb_y = F1 + F2sin(15°) + F3sin(60°) + P = 47.5 kN.

Thus, the reactions of the bonds at points A and B are equal:

Ra_x = 0 Ra_y = 25 кН Rb_x = 20.5 кН Rb_y = 47.5 кН

In the calculations, we used the value a = 0.5 m, which was indicated in the problem statement.

This digital product is a solution to problem C1-33 from the textbook “Collection of problems in theoretical mechanics” by author S.M. Targa, published in 1989. The solution to this problem is presented in the form of a beautifully designed HTML document using graphic material, including Figure C1.3 and Table C1. The solution to the problem describes in detail the process of determining the reactions of the connections at points A and B of a rigid frame, which is subject to various forces. The solution to this problem can be useful to students and teachers studying theoretical mechanics, as well as to anyone interested in this field of knowledge.

The digital product “Solution C1-33 (Figure C1.3 condition 3 S.M. Targ 1989)” is a solution to a problem from the textbook “Collection of problems in theoretical mechanics” by author S.M. Targa, published in 1989.

The task is to determine the reactions of the connections at points A and B of a rigid frame, which is subject to various forces. The frame is located in a vertical plane and is hinged at point A, and at point B it is attached either to a weightless rod with hinges at the ends, or to a hinged support on rollers. A cable is attached to the frame, thrown over a block and carrying at the end a load weighing P = 25 kN. A pair of forces with a moment M = 100 kN m and two forces act on the frame, the values, directions and points of application of which are indicated in the table.

This digital product contains a beautifully designed HTML document with graphics, including Figure C1.3 and Table C1. The solution to the problem describes in detail the process of determining the reactions of bonds at points A and B and the use of equilibrium conditions.

This product can be useful to students and teachers studying theoretical mechanics, as well as anyone interested in this field of knowledge.

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Solution C1-33 is a structure consisting of a rigid frame located in a vertical plane and hinged at point A. Point B is attached either to a weightless rod with hinges at the ends, or to a hinged support on rollers. A cable is attached to the frame at point C, thrown over a block and carrying a load at the end weighing P = 25 kN. A pair of forces with a moment M = 100 kN m and two forces act on the frame, the values, directions and points of application of which are indicated in the table.

To solve the problem, it is necessary to determine the reactions of the connections at points A and B caused by the acting loads. For final calculations, the value a = 0.5 m is taken.

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