Meriam, Kraige & Bolton — Analysis of Structures: Problem 6_47

⚡ Mecademy AIENG정역학 · ch6  Problem Statement In wood-frame construction, two shims are frequently used to fill the gap between the framing and the thinner window/door jamb . The members and are shown in cross section in the figure. For the shims shown, determine the minimum necessary coefficient of static friction so that the shims will remain in place. Problem 6/47 (a) Determination of the minimum coefficient of static friction ● Calculation Process 1. Present Final Formula: For a wedge with an angle to be self-locking (remain in place) when squeezed between two surfaces with the same coefficient of static friction , the condition is derived from equilibrium: 2. Substitute Values: Each shim is a wedge with a taper angle of . 3. Partial Operations: Calculate the half-angle: Calculate the tangent: 4. Final Calculation: ● Final Conclusion: The minimum necessary coefficient of static friction for the shims to remain in place is . ✨ Final Answer Summary SDSD 3 ∘ α μ s μ = s tan ( 2 α ) α=3 ∘ μ = s tan ( 2 3 ∘ ) = 2 α = 2 3 ∘ 1.5 ∘ tan(1.5)≈ ∘ 0.0261859 μ ≈ s 0.0262 μ = s 0.0262 (a) Mecademy AI Solution · ENGProblem 6/47 μ = s 0.0262