CE 8 ProbSet 1 PDF [PDF]

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CE 8 PROBSET 1 Instructions. Present complete solution. Show the free-body diagram. Take a photo of the solution and upload on LMS as Offline Assignment. Should you have any questions, please don’t hesitate to ask. Hydrostatic Forces on Submerged Planes 1) A rectangular gate, 1.60 m wide and 2.0 m wide is hinged along A, and subjected to water pressure to its left side, as shown. Determine the: (a) magnitude and location of the hydrostatic force acting on the gate; (b) minimum force applied to the normal gate at the end B that will just open it. ​ANS: F = 69.40 kN; e = 11 cm; P​min​ = 38.60 kN



2) A horizontal tunnel, diameter 3 m, is closed at one end by a vertical gate. Calculate the magnitude and location of the total force on the gate when the tunnel is 1/2 full. ​ANS: F = 22.10 kN 3) Gate AB is 3.20 m long. Find the horizontal force H to hold the gate in equilibrium. (Width of AB is 2.0m). ANS: ​H = 24.50 kN



4) Figure shows a gate AB in the form of a circular arc with a central angle of 60 degree, and with one end resting on the crest of a dam. The water surface is flushed with the upper end of the gate. Find F​V​ and F​H​ on AB and their locations. Consider a gate length of 3m normal to the plane of the paper. ​ANS: F​H​ = 44.04 kN; y​p​ = 1.155 m; F​V​ = 14.73 kN



Stability of Gravity Dams 5) A gravity dam has a triangular cross section, with the upstream face vertical and with the impounded water flushed with the crest. The height of the structure is 8m while its base is 6 m long. If there is no hydrostatic uplift and the friction coefficient between the base and the foundation is 0.80, find the : (a) the maximum and minimum soil pressure along the base; (b) factors of safety against sliding and overturning. (Specific of concrete is 23,540 N/m​3​). ​ANS: σ​max​ = 143.62 kPa; σ​min​ = 44.75 kPa; F.S. vs Sliding = 1.44 ; F.S. vs OT = 2.67 6) A masonry dam has a trapezoidal cross section, 25m high, crest width 3 m and base length 18 m. The upstream face slopes down 12 m in 25 m and the downstream face slopes down 3 m in 25m . If water at the upstream face stands flushed with the crest, and assuming no hydrostatic uplift, compute : (a) F.S. vs. O.T.;(b) soil pressures at the heel and toe of the dam; (c) Location of the point along the base where the resultant force intersects it. (Specific gravity of concrete is 2.40). ​ANS: F.S. vs OT = 2.57; (b) σ​max​ = 95.65 kPa , σ​min​ = 10.60 kPa (c) x = 5.24 m (from the toe / outside the MT) 7) The upstream face of a concrete dam with a trapezoidal cross section has a SS 1H: 10V, while the downstream face has a SS 1H:2V. The dam is 52 m high, with a crest width of 7m. Water stands 50 m at the upstream side. At a distance of 15 m from the toe, drains are located, at which location the pressure due to hydrostatic at the zero, then increasing linearly to full hydrostatic at the heel. Specific weights of water and concrete are respectively, 9.81 KN/m3 and 23.54 KN/m​3​. Find the : (a) location of the resultant force; (b) factors of safety vs. sliding and overturning. ​ANS: (a) x = 13.20 m (from the toe / within the MT) (b) F.S. vs. Sliding = 1.42; F.S . vs. OT = 1.81



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