Meriam, Kraige & Bolton — Distributed Forces: Centroids and Centers of Gravity: Problem 5_105

⚡ Mecademy AIENG정역학 · ch5  Problem Statement Determine the shear-force and bending-moment distributions produced in the beam by the concentrated load. What are the values of the shear and moment when ? Problem 5/105 (a) Shear-force and bending-moment distributions ● Calculation Process 1. Determine External Reactions: First, we find the reaction forces at supports and . Summing moments about point : Summing vertical forces: 2. Shear Force Distribution (): For the first segment (): For the second segment (): 3. Bending Moment Distribution (): For the first segment (): Since at the pin support , . Thus, . x=l/2 A BA M = ∑ A 0⟹B (l)− y P = ( 3 2l )0 B = y 3 2P F = ∑ y 0⟹A + y B − y P=0 A = y P− = 3 2P 3 P V0≤x< 3 2l V=A = y 3 P < 3 2l x≤l V=A − y P= − 3 P P= − 3 2P M0≤x< 3 2l M=V dx= ∫ dx= ∫ 3 P + 3 Px C 1 M(0)=0AC = 1 0M= 3 Px For the second segment (): Since at the roller support : 4. Final Formula: ● Final Conclusion: The shear force is constant at for the first two-thirds of the beam and drops to for the last third. The bending moment increases linearly to a maximum of at and then decreases linearly to zero at the right end. (b) Values of shear and moment when ● Calculation Process 1. Identify Relevant Segment: The point is in the first segment because (since ). 2. Substitute Value for Shear (): Using the equation for the first segment: 3. Substitute Value for Moment (): Using the equation for the first segment: ● Final Conclusion: At mid-span (), the internal shear force i