Meriam, Kraige & Bolton — Distributed Forces: Centroids and Centers of Gravity: Problem 5_132

⚡ Mecademy AIENG정역학 · ch5  Problem Statement A horizontal 350-mm-diameter water pipe is supported over a ravine by the cable shown. The pipe and the water within it have a combined mass of 1400 kg per meter of its length. Calculate the compression exerted by the cable on each support. The angles made by the cable with the horizontal are the same on both sides of each support. The span of the cable is 40 m and the sag is 2.5 m. Problem 5/132 (a) Calculation of the compression force C on each support 1. Formula: First, determine the weight per unit length of the pipe. Then, calculate the vertical component of the cable tension at the support, . For a parabolic cable (where the load is uniformly distributed horizontally), the vertical component at the support is: Given that the cable makes the same angle with the horizontal on both sides of the support, the total compression on the support is the sum of the vertical components from both segments: 2. Substitution: Mass per unit length: Gravitational acceleration: Weight per unit length: Total span: Substitute these into the compression formula: C w V V=w⋅ ( 2 L ) C C=2V=2⋅w⋅ = ( 2 L )wL m= ′ 1400 kg/m g= 9.81 m/s 2 w=m⋅ ′ g=1400⋅9.81=13734 N/m L=40 m C=13734 N/m×40 m 3. Calculation: Convert to kilonewtons: 4. Result: (to three significant figures) ● Final Conclusion: The total compression force exerted by the cable on each support is 549 kN. This value is equal to the total weight of the pipe for the entire span because each sup