Solution to problem 2.4.36 from the collection of Kepe O.E.

Task 2.4.36

It is necessary to determine the intensity q of the distributed load at which the moment in the seal A will be equal to 546 Nm. It is known that the force F is equal to 173 N, the moment of the pair of forces M is equal to 42 N m, and the dimensions AB and CD are equal to 2 m, and BC is equal to 1 m.

To solve the problem, we use the moment equilibrium equation:

ΣM_A = 0

where ΣM_A - the sum of moments about point A.

First, let's find the moment due to force F:

M_F = F * AB = 173 * 2 = 346 Н·м

Here AB is the distance from point A to the line of action of force F.

Then we find the moment from the pair of forces M:

M_M = M = 42 Nm

Now we can write the moment equilibrium equation:

ΣM_A = M_F + M_M + M_q = 0

where M_q - moment from distributed load q.

The distributed load q creates a moment on each section of the beam. Consider section BC 1 m long:

M_q = q * BC * (AB + BC/2) = q * 1 * (2 + 1/2) = 5/2 q Н·м

Now we can write the equation for the moment from a distributed load:

M_q = 5/2 q

And, substituting all the values ​​into the moment equilibrium equation, we get:

546 = 346 + 42 + 5/2 q

Where we find it from:

q = 36 N/m

Thus, the intensity of the distributed load, at which the moment in embedment A is equal to 546 N m, is equal to 36 N/m.

Solution to problem 2.4.36 from the collection of Kepe O..

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Problem 2.4.36 is to determine the intensity q of the distributed load at which the moment in embedment A will be equal to 546 Nm. In the problem, the force F is known equal to 173 N, the moment of the pair of forces M is equal to 42 N m, and the dimensions AB and CD are equal to 2 m, and BC is equal to 1 m.

To solve the problem, the moment equilibrium equation is used, where ΣMA is the sum of moments about point A. First, the moment from the force F is found, then the moment from the pair of forces M, and all values ​​are substituted into the moment equilibrium equation to find the intensity of the distributed load q.

So, by purchasing this digital product, you will receive a detailed description of the solution to problem 2.4.36 from the collection of Kepe O., which will help you understand how to solve this problem in theoretical mechanics. In addition, you can save this product on your computer or smartphone so that you can access it at any time and successfully solve this interesting problem.

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Problem 2.4.36 from the collection of Kepe O.?. requires determining the intensity q of the distributed load at which the moment in the seal A will be equal to 546 N·m. To solve the problem, the following data are known: the force F is equal to 173 N, the moment of the pair of forces M is equal to 42 N m, and the dimensions AB, CD and BC are equal to 2 m, 2 m and 1 m, respectively.

To solve the problem, it is necessary to use equilibrium equations for moments. From the problem conditions it is known that the sum of the moments of forces acting on the embedment A is equal to 546 N m. The sum of the moments of forces is the sum of the moment of the pair of forces and the moment created by the distributed load.

The moment of the pair of forces is equal to M = 42 N m. The distributed load on the segment BC creates a moment of force equal to q * L^2 / 12, where L = BC = 1 m is the length of the segment BC. Thus, the sum of the moments of forces is equal to:

546 N·m = M + q * L^2 / 12

Substituting the known values, we get the equation:

546 N·m = 42 N·m + q * (1 m)^2 / 12

Where can you find the distributed load intensity q:

q = (546 N·m - 42 N·m) * 12 / (1 m)^2 = 36 N/m

Thus, the intensity of the distributed load, at which the moment in embedment A is equal to 546 N m, is 36 N/m.

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