Solution C1-77 (Figure C1.7 condition 7 S.M. Targ 1988)

Below is the solution to problem C1-77 (Figure C1.7 condition 7 S.M. Targ 1988).

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 BB1 or to a hinged support on rollers. The rod is attached to the frame and to the fixed support with hinges.

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, a force F1 = 10 N acts on the frame at an angle of 30° to the horizontal axis, applied at point K and force F4 = 40 N at an angle of 60° to the horizontal axis applied at point H, etc.).

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

Answer:

We use equilibrium conditions and a drawing to determine the reactions of the bonds at points A and B.

First, consider the conditions of equilibrium along the X axis. Since the frame is at rest, the sum of all forces along the X axis must be equal to zero:

∑Fx = 0

Also, to prevent the frame from rotating, the sum of the moments of forces must be equal to zero:

∑M = 0

Now let's look at the figure and determine the directions of the bond reactions. By condition, point A is hinged, so the reaction of the connection at point A must be perpendicular to the surface on which it is applied. We assume that the bond reaction at point A is directed upward, and at point B - to the right.

Now we can write down the equilibrium equations. The sum of all forces along the X axis must be zero:

F1cos30° + F2cos45° - F3cos60° - F4cos60° = 0

where F1, F2, F3 and F4 are the values ​​of the forces, the directions and points of application of which are indicated in the table.

The sum of the moments of forces must be equal to zero:

MA - F1sin30°l - F2sin45°l + F3sin60°l + F4sin60°l - VAy * l = 0

MB - VBx * l - 100 = 0

where MA and MB are the moments of forces, VAy and VBx are the vertical and horizontal components of the reactions of the bonds at points A and B, respectively.

Using the equilibrium conditions and directions of bond reactions, we can determine the values ​​of bond reactions at points A and B:

VAy = F1cos30° + F2cos45° - F3cos60° - F4cos60°

VBx = (F1sin30° + F2sin45° - F3sin60° - F4sin60° + 100) / l

MA = (F1sin30° + F2sin45° - F3sin60° - F4sin60°) * l

MB = 100

Thus, the bond reaction at point A is equal to VAy, and at point B - VBx. In this case, the moment of force at point A is equal to MA, and at point B - MB. The values ​​of the bond reactions depend on the values ​​of the forces, directions and points of application of which are indicated in the table. For final calculations we take l = 0.5 m.

Solution C1-77 (Figure C1.7 condition 7 S.M. Targ 1988)

A digital product for students and professionals in the field of mechanics and related disciplines. The solution to problem C1-77, presented in the form of an electronic document with a beautiful html design, will help you quickly and easily understand the problem and find the necessary answers.

The solution provides detailed calculations and explanations based on equilibrium conditions and drawing, which will allow you to easily understand the solution to the problem and obtain the necessary results. The document contains tables with the values ​​of forces, directions and points of application, as well as formulas for determining the reactions of bonds at points A and B.

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Solution C1-77 (Figure C1.7 condition 7 S.M. Targ 1988) is a digital product in html format, which is a solution to the problem of a rigid frame, hinged at point A, and attached at point B either to a weightless rod BB1, or to a hinged support on rollers, which 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.

The solution uses equilibrium conditions and a drawing to determine the reactions of the bonds at points A and B. The document provides detailed calculations and explanations based on the equilibrium conditions and drawing, which help you easily understand the solution to the problem and obtain the necessary results. The document contains tables with the values ​​of forces, directions and points of application, as well as formulas for determining the reactions of bonds at points A and B.

Solution C1-77 (Figure C1.7 condition 7 S.M. Targ 1988) is intended for students and professionals in the field of mechanics and related disciplines. The electronic document is presented in html format, which makes it easy to read and view on any device, including computers, tablets and mobile phones.

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Solution C1-77 is a structure consisting of a rigid frame located in a vertical plane and hingedly fixed at point A. Point B is attached either to the weightless rod BB1 or to the hinged support on the rollers. The rod is attached to the frame and to the fixed support with hinges. 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 this solution, it is necessary to determine the reactions of the connections at points A and B, caused by the given loads. In the final calculations, l = 0.5 m is assumed.

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