Meriam, Kraige & Bolton — Rigid Bodies: Equivalent Systems of Forces: Problem 3_51

⚡ Mecademy AIENG정역학 · ch3  Problem Statement The lumbar portion of the human spine supports the entire weight of the upper torso and the force load imposed on it. We consider here the disk (shaded red) between the lowest vertebra of the lumbar region () and the uppermost vertebra of the sacrum region. (a) For the case , determine the compressive force and the shear force supported by this disk in terms of the body weight . The weight of the upper torso (above the disk in question) is 68% of the total body weight and acts at . The vertical force which the rectus muscles of the back exert on the upper torso acts as shown in the figure. (b) Repeat for the case when the person holds a weight of magnitude as shown. State any assumptions. Problem 3/51 (a) Compressive and Shear Forces for 1. Formula: First, we determine the muscle force using moment equilibrium about the center of the disk . Let clockwise moments be positive. where , , and . The total vertical reaction is: The compressive force and shear force are the components of relative to the disk inclined at : 2. Substitution: 3. Calculation: L 5 L= 0CS WW u WG 1 F L=W/3 L=0 F O M = ∑ O 0⇒−F⋅d + F W ⋅ u d = u 0 W = u 0.68Wd = F 25 mmd = u 50 mm R R=F+W u CSR θ=41 ∘ C=Rcosθ,S=Rsinθ F= = d F W ⋅d uu 25 (0.68W)⋅50 R=F+0.68W C=Rcos(41) ∘ S=Rsin(41) ∘ Using and : 4. Result: , ● Final Conclusion: For the case without an external load (), the compressive force is and the shear force is . (b) Compressive and Shear Forces for 1. Formu