Meriam, Kraige & Bolton — Distributed Forces: Centroids and Centers of Gravity: Problem 5_134

⚡ Mecademy AIENG정역학 · ch5  Problem Statement Strain-gage measurements made on the cables of the suspension bridge at position A indicate an increase of 480,000 lb of tension in each of the two main cables because the bridge has been repaved. Determine the total weight w' of added paving material used per foot of roadway. Problem 5/134 (a) Determination of total added weight per foot of roadway ● Calculation Process 1. Present Final Formula: For a suspension bridge cable supporting a load uniformly distributed along the horizontal, the shape is a parabola. The tension at any horizontal distance from the center is given by: where is the horizontal tension, is the horizontal load per unit length for one cable, is the span, and is the sag. The slope of the parabolic cable is . Since there are two main cables, each cable supports half of the total added roadway weight , so the increase in load per cable is . The increase in tension at point is: 2. Substitute Values: From the diagram: Span Sag Increase in tension at per cable, Horizontal distance of point from the center: w ′ T x T=T 0 1+ ( dx dy ) 2 T = 0 8h wL 2 w Lh = dx dy L 2 8hx w ′ Δw= 2 w ′ A ΔT = A 16h wL ′2 1+ ( L 2 8hx A ) 2 L=2500 ft h=500 ft AΔT = A 480,000 lb Ax = A − 2 L 600=1250− 600=650 ft Substituting these values: 3. Partial Operations: Calculate the slope term at : Calculate the tension factor: Simplify the equation for : 4. Final Calculation: ● Final Conclusion: The total added weight of the paving material us