Meriam, Kraige & Bolton — Distributed Forces: Centroids and Centers of Gravity: Problem 5_173

⚡ Mecademy AIENG정역학 · ch5  Problem Statement The design of a floating oil-drilling platform consists of two rectangular pontoons and six cylindrical columns which support the working platform. When ballasted, the entire structure has a displacement of 26,000 tons (expressed in long tons of 2240 lb). Calculate the total draft of the structure when it is moored in the ocean. The specific weight of salt water is . Neglect the vertical components of the mooring forces. Problem 5/173 (a) Calculation of the total draft 1. Formula: First, calculate the total displacement weight and then the required submerged volume based on Archimedes' principle for flotation equilibrium: The total submerged volume is the sum of the volume of the submerged portions of the pontoons and columns. Assuming the pontoons are fully submerged (): where: is the number of pontoons. , , are the dimensions of each pontoon. is the number of cylindrical columns. is the diameter of each column. is the specific weight of salt water. 2. Substitution: h 64 lb/ft 3 h W V sub W=Displacement (long tons)×2,240 lb/ton B=W⟹γ V = swsub W⟹V = sub γ sw W h>25 ft V = sub V + pontoons V columns_sub V = sub (N ⋅ p L⋅w⋅t)+[N ⋅ c ⋅ 4 πD 2 (h−t)] N = p 2 L=350 ftw=40 ftt=25 ft N = c 6 D=30 ft γ = sw 64 lb/ft 3 W=26,000×2,240=58,240,000 lb V = sub = 64 58,240,000 910,000 ft 3 Volume of pontoons if fully submerged: 3. Calculation: Since , the pontoons are indeed fully submerged, so the draft . Required submerged volume from the col