Solution C1-24 (Figure C1.2 condition 4 S.M. Targ 1989)

Solution of problem C1-24 from the textbook by S.M. Targa "Problem book on theoretical mechanics" (1989).

Given a rigid frame located in a vertical plane and hinged at point A, and at point B - 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 at point C. 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 ( for example, in condition No. 1, the frame is subject to a force F2 at an angle of 15° to the horizontal axis, applied at point D and a force F3 at an angle of 60° to the horizontal axis, applied at point E, etc.).

It is required to find the reactions of the connections at points A and B caused by the acting loads. For final calculations, take the distance between points A and B equal to a = 0.5 m.

Answer:

To find bond reactions at points A and B, it is necessary to use equilibrium conditions. First let's look at the vertical balance:

ΣF_y = 0: A_y + B_y - 25 = 0 (1)

Then consider the horizontal equilibrium:

ΣF_x = 0: A_x + B_x = 0 (2)

ΣM_A = 0: B_x * a - 100 = 0 (3)

ΣM_B = 0: -A_y * a + 25 * a - B_y * a = 0 (4)

From equation (2) it follows that A_x = -B_x. From equation (3) we find B_x = 100 / a = 200 kN. Substituting this value into equation (2), we obtain A_x = -200 kN.

From equation (1) we find B_y = 25 - A_y. Substituting this value into equation (4), we find A_y = 12.5 kN. Thus, the reactions of the bonds at points A and B are equal to A_x = -200 kN, A_y = 12.5 kN and B_x = 200 kN, B_y = 12.5 kN, respectively.

Answer: the reactions of the bonds at points A and B are equal to A_x = -200 kN, A_y = 12.5 kN and B_x = 200 kN, B_y = 12.5 kN, respectively.

Solution C1-24 (Figure C1.2 condition 4 S.M. Targ 1989)

Solution of problem C1-24 from the textbook by S.M. Targa "Problem book on theoretical mechanics" (1989).

Given a rigid frame located in a vertical plane and hinged at point A, and at point B - 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 at point C. 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 ( for example, in condition No. 1, the frame is subject to a force F2 at an angle of 15° to the horizontal axis, applied at point D and a force F3 at an angle of 60° to the horizontal axis, applied at point E, etc.).

It is required to find the reactions of the connections at points A and B caused by the acting loads. For final calculations, take the distance between points A and B equal to a = 0.5 m.

Answer:

To find bond reactions at points A and B, it is necessary to use equilibrium conditions. First let's look at the vertical balance:

ΣF_y = 0: A_y + B_y - 25 = 0 (1)

Then consider the horizontal equilibrium:

ΣF_x = 0: A_x + B_x = 0 (2)

ΣM_A = 0: B_x * a - 100 = 0 (3)

ΣM_B = 0: -A_y * a + 25 * a - B_y * a = 0 (4)

From equation (2) it follows that A_x = -B_x. From equation (3) we find B_x = 100 / a = 200 kN. Substituting this value into equation (2), we obtain A_x = -200 kN.

From equation (1) we find B_y = 25 - A_y. Substituting this value into equation (4), we find A_y = 12.5 kN. Thus, the reactions of the bonds at points A and B are equal to A_x = -200 kN, A_y = 12.5 kN and B_x = 200 kN, B_y = 12.5 kN, respectively.

Answer: the reactions of the bonds at points A and B are equal to A_x = -200 kN, A_y = 12.5 kN and B_x = 200 kN, B_y = 12.5 kN, respectively.

This is a digital product in a digital goods store, which is a solution to problem C1-24 from the textbook by S.M. Targa "Problem book on theoretical mechanics" (1989). The problem is given a rigid frame on which loads act, and it is required to find the reactions of the connections at points A and B. The solution is presented in the form of text with a beautiful HTML design, which makes it easy to read and use. The solution steps are described in detail, including calculations and formulas, and the answer to the problem is also given. This digital product will be useful to students and teachers involved in theoretical mechanics, as well as anyone interested in this field of science.

Product description: this is a digital product in a digital goods store, which is a solution to problem C1-24 from the textbook by S.M. Targa "Problem book on theoretical mechanics" (1989). The solution contains a detailed description of the steps to solve the problem, including calculations and formulas, as well as beautiful HTML design for ease of reading. The solution is suitable for students and teachers involved in theoretical mechanics, as well as for anyone interested in this field of science. The task is to determine the reactions of the connections at points A and B of a rigid frame located in a vertical plane and subject to loads. The problem also indicates that at point B the frame is either attached to a weightless rod with hinges at the ends, or to a hinged support on rollers, and that a couple of forces with a moment and two forces act on the frame, the values ​​and points of application of which are indicated in the table. The answer to the problem is also given in the solution.

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Solution C1-24 is a device consisting of a rigid frame located in a vertical plane and hinged at point A. At point B, the frame 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.

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, B, caused by the acting loads. For final calculations, a = 0.5 m should be taken.

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