Meriam, Kraige & Bolton — Distributed Forces: Centroids and Centers of Gravity: Problem 5_123

⚡ Mecademy AIENG정역학 · ch5  Problem Statement The angle strut is welded to the end of the I-beam and supports the vertical force. Determine the bending moment at and the distance to the left of at which the bending moment is zero. Also construct the moment diagram for the beam. Problem 5/123 (a) Bending moment at 1. Formula: First, calculate the reaction forces by considering the equilibrium of the entire beam. The applied vertical force at the end of the strut is equivalent to a downward force and a counter-clockwise moment at point , where . 2. Substitution: Equivalent moment at : Moment equilibrium about : Force equilibrium: 3. Calculation: (Upward) (Downward) Internal bending moment at (from the left side): 4. Result: ● Final Conclusion: The bending moment at is . The negative sign indicates a hogging moment (tension in the top fibers of the beam). C1.6-kN BxC B P=1.6 kN PM = C P⋅d Cd=200 mm M = ∑ A 0, F = ∑ y 0 CM = C 1.6 kN×0.2 m=0.32 kN⋅m AR (0.4 m)− B 1.6 kN(0.85 m)+ 0.32 kN⋅m=0 R + A R − B 1.6 kN=0 0.4R = B 1.36−0.32=1.04⇒R = B = 0.4 1.04 2.6 kN R = A 1.6−2.6=−1.0 kN BM = B R × A 0.4 m M = B −1.0 kN×0.4 m=−0.4 kN⋅m M = B −400 N⋅m B−400 N⋅m (b) Distance to the left of at which the bending moment is zero 1. Formula: Define the bending moment for the region ( ) and solve for . 2. Substitution: 3. Calculation: from The distance to the left of is: 4. Result: ● Final Conclusion: The bending moment is zero at a distance to the left of point . (c) Construct the moment diagra