Solution C1-27 (Figure C1.2 condition 7 S.M. Targ 1989)

Solution to problem C1-27 (Figure C1.2 condition 7 S.M. Targ 1989)

There is a rigid frame located in a vertical plane, which is hinged at point A and attached to a weightless rod with hinges at the ends or to a hinged support on rollers at point B (Fig. C1.0 - C1.9, Table C1). A cable is attached to the frame, thrown over a block and carrying 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 conditions No. 1, the frame is subject to a force F2 applied at point D at an angle of 15° to the horizontal axis, and a force F3 applied at point E at an angle of 60° to the horizontal axis, etc.

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

Below are the formulas for calculating bond reactions:

∑Fx = 0: AxBx - Vx = 0

∑Fy = 0: AyBy + Cy - V = 0

∑MA = 0: Cy(a) - Bxh - My = 0

where V is the vertical reaction at point B, Vx is the horizontal reaction at point B, Ay is the vertical reaction at point A, Bx is the horizontal reaction at point A, Cy is the cable tension force, My is the moment of force acting on the frame, h - distance between points A and C.

Substituting the values ​​from the table and taking a = 0.5 m, we get:

Condition #1: ∑Fx = 0: Bx - Vx = -12.5 kN ∑Fy = 0: Ay + 21.65 - V = 0 ∑MA = 0: 12.5(0.5) - Bx(2) - 100 = 0

Condition #2: ∑Fx = 0: Bx + Vx = 0 ∑Fy = 0: Ay + 38.35 - V = 0 ∑MA = 0: -38.35(0.5) - Bx(2) - 100 = 0

Solving systems of equations, we obtain:

Condition #1: Ay ≈ 5.77 kN Bx ≈ 10.21 kN V ≈ 27.42 kN Vx ≈ 12.21 kN

Condition #2: Ay ≈ 12.15 kN Bx ≈ -14.18 kN V ≈ 38.35 kN Vx ≈ 14.18 kN

Thus, the reactions of the connections at points A and B under the action of given loads are:

• Condition #1: Ay ≈ 5.77 kN, Bx ≈ 10.21 kN
• Condition #2: Ay ≈ 12.15 kN, Bx ≈ -14.18 kN

It is important to note that this solution is only an example and can only be used for educational purposes. The actual calculations must be carried out taking into account the specific conditions of the problem and the principles of mechanics.

This digital product is a solution to problem C1-27 from the textbook by S.M. Targa 1989, which is presented in Figure C1.2 condition 7. The solution to this problem allows us to determine the reaction of the connections at points A and B of the rigid frame, which is subject to given loads.

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By purchasing this digital product, you receive a complete and understandable solution to problem C1-27 with a detailed description of the calculation process, as well as a beautifully designed html document that can be used for educational purposes or to expand your knowledge in the field of mechanics.

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Solution C1-27 is a structure consisting of a rigid frame located in a vertical plane and hingedly fixed 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 at point C, 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. For example, in condition No. 1, the frame is subject to a force F2 applied at point D at an angle of 15° to the horizontal axis, and a force F3 applied at point E at an angle of 60° to the horizontal axis, etc.

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

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