Answer :
The safe dimensions of each screw thread are approximately 19.13 mm in height to withstand the given tensile load and yield stress.
To determine the safe dimensions of each screw thread, we need to consider the yield stress of the C25 annealed steel and the factor of safety.
First, let's calculate the maximum allowable tensile stress in the screws. We'll use the equation:
Allowable stress = Yield stress / Factor of safety
Allowable stress = 360 MPa / 4 = 90 MPa
Next, let's calculate the maximum tensile load that each screw can withstand. We'll assume that the tensile load is evenly distributed between the two screws. Since there are two screws, each screw will carry half of the total load.
Tensile load per screw = Total tensile load / 2
Now, let's calculate the total tensile load. We can do this by using the equation:
Total tensile load = Bearing pressure * Area
Given that the bearing pressure is limited to 1 MPa and the collar has an inside diameter of 55 mm and an outside diameter of 100 mm, we can calculate the area of the collar:
Area = π * (OD^2 - ID^2) / 4
Area = π * (100^2 - 55^2) / 4 = 8779.68 mm²
Total tensile load = 1 MPa * 8779.68 mm² = 8779.68 MPa.mm²
Tensile load per screw = 8779.68 MPa.mm² / 2 = 4389.84 MPa.mm²
Now, let's determine the safe dimensions of each screw thread. We'll use the formula for the tensile stress in the screw threads:
Tensile stress in the screw threads = Tensile load per screw / (Thread height * Mean diameter)
Where the mean diameter is the average of the inside and outside diameters of the collar.
Rearranging the formula, we can solve for the thread height:
Thread height = Tensile load per screw / (Tensile stress in the screw threads * Mean diameter)
Given that the coefficient of friction for both the threads and collar is 0.15, the bearing pressure is limited to 1 MPa, and the screw threads are square-threaded, we can determine the thread height.
Thread height = 4389.84 MPa.mm² / (1 MPa * (100 mm + 55 mm) * 0.15)
Thread height ≈ 19.13 mm
To find the number of threads, we divide the height of the nut engaged with the screw by the thread height:
Number of threads = Height of nut engaged with the screw / Thread height
Since the height of the nut engaged with the screw is not provided in the question, we cannot determine the exact number of threads.
In summary, the safe dimensions of each screw thread are approximately 19.13 mm in height, given the provided information. However, the exact number of threads and the height of the nut engaged with the screw cannot be determined without additional information.
Learn more about Screw threads.
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