Meriam, Kraige & Bolton — Analysis of Structures: Problem 6_102

⚡ Mecademy AIENG정역학 · ch6  Problem Statement Shown in the figure is the design of a band-type oil-filter wrench. If the coefficient of friction between the band and the fixed filter is 0.25, determine the minimum value of which ensures that the wrench will not slip on the filter, regardless of the magnitude of the force . Neglect the mass of the wrench and assume that the effect of the small part is equivalent to that of a band wrap which begins at the three-o’clock position and runs clockwise. Problem 6/102 (a) Determination of the minimum value of 1. Formula: Handle equilibrium about pin : Moment arm of strap at about : Torque equilibrium of the wrench system about filter center : Belt friction condition for no slipping: 2. Substitution: Given values: Horizontal distance to pin : Horizontal distance to pin : Moment arm : 3. Calculation: 1. Handle Moment Equation: 2. System Torque Equation: h P A h AM =∑ A 0⟹T ⋅ B d−P⋅(b+ h)=0 BAd=r r+a+b b O(T − B T )r= A P(r+a+b+h) ≤ T A T B e μ β s r=45 mm,a=7 mm,b=26 mm,μ = s 0.25 Ax = A 45+7=52 mm Bx = B 52+26=78 mm dd=45⋅ = 78 26 45⋅ = 3 1 15 mm 15T = B P(26+h)⟹T = B 15 P(26+h) (T − B T )⋅ A 45=P(45+7+26+h)=P(78+h) 3. Solve for : 4. Tension Ratio: 5. Wrap Angle : The strap is tangent to the filter from pin at . The angle of the tangent point from the horizontal is: Since the wrap begins at 3 o'clock () and runs clockwise to the exit point, the wrap angle is: 6. Slipping Limit: Setting the required ratio equal to the friction limit: 4.