Two identical 3 in. major-diameter power screws (single-threaded) with modified square threads are used to raise and lower a 50-
ton sluice gate of a dam. Quality of construction and maintenance (including lubrication) are good, resulting in an estimated friction coefficient of only 0.1 for the screw. Collar friction can be neglected, as ball thrust bearings are used. Assuming that, because of gate friction, each screw must provide a lifting force of 26 tons, what power is required to drive each screw when the gate is being raised at the rate of 3 ft/min
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Answer:
The principal stresses are σp1 = 27 ksi, σp2 = -37 ksi and the shear stress is zero
Explanation:
The expression for the maximum shear stress is given:
Where
σx = stress in vertical plane = 20 ksi
σy = stress in horizontal plane = -30 ksi
τM = 32 ksi
Replacing:
Solving for τxy:
τxy = ±19.98 ksi
The principal stress is:
Where
σp1 = 20 ksi
σp2 = -30 ksi
(equation 1)
equation 2
Solving both equations:
σp1 = 27 ksi
σp2 = -37 ksi
The shear stress on the vertical plane is zero