A frame of 6m span is carrying a central load of 10kN. Find the forces in structural members by method of section and tabulate the results.
Answers
Explanation:
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Answer: To find the forces in the structural members of the frame, we can use the method of sections. We will make a cut through the frame, dividing it into two parts, and then analyze the forces acting on each part of the frame.
Explanation: Assuming the frame is a simple truss with no horizontal forces or external reactions at the supports, we can analyze the left and right sections of the frame separately.
First, we will consider the left section of the frame. We can make a cut through the frame just to the left of the central support, as shown in the diagram below:
5kN
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V
A ------------ B ------------ C
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10kN
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D
Using the method of sections, we can solve for the forces in the members AB, BC, and BD. To do this, we need to find the external forces acting on the left section of the frame. The only external force is the 5 kN vertical force acting on member AB.
Using the principle of equilibrium, we can write two equations:
- ΣFx = 0 ΣFy = 0
- ΣFx = ABcos(45) - BCcos(30) = 0
- ΣFy = ABsin(45) + BCsin(30) - 5 = 0
Solving these equations simultaneously, we get:
- AB = 7.07 kN BC = 4.08 kN BD = 5.71 kN (from the triangle ABD)
Next, we will consider the right section of the frame. We can make a cut through the frame just to the right of the central support, as shown in the diagram below:
A ------------ B ------------ C
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V
10kN
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D
Using the same method, we can solve for the forces in the members BC, CD, and BD. To do this, we need to find the external forces acting on the right section of the frame. The only external force is the 10 kN vertical force acting on member CD.
Using the principle of equilibrium, we can write two equations:
- ΣFx = 0 ΣFy = 0
- ΣFx = -BCcos(30) - CDcos(45) = 0
- ΣFy = BCsin(30) + CDsin(45) - 10 = 0
Solving these equations simultaneously, we get:
- BC = 5.77 kN CD = 7.81 kN BD = 5.71 kN (from the triangle ABD)
Therefore, the forces in the members of the frame are:
- AB = 7.07 kN BC = 5.77 kN CD = 7.81 kN BD = 5.71 kN
We can tabulate these results as follows:
Member | Force (kN)
-------|----------
AB | 7.07
BC | 5.77
CD | 7.81
BD | 5.71
Learn more about Force here - https://brainly.in/question/23858054
Learn more about External forces here - https://brainly.in/question/27490461
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