A sector-shaped sluice gate having a radius of curvature of 5.4 m is as shown. The center of curvature C is 0.9m vertically below the lower edge A of the gate about which the gate is constructed to turn. If the water level is 2.4m above the lower edge of the gate, determine the magnitude of the total force (in kN) acting on the gate using the General Solution.

A steel beam, of lengths a= 6 m and b= 3 m and a hollow box cross section, is supported by a hinge support A and roller support B, see Figure Q.1. The width and height of the cross section are 200 mm and 300 mm, respectively, and the wall thickness of the cross section is 5 mm. The beam is under a distributed load of the intensity that linearly varies from q = 0 kN/m to q = 3.1 kN/m for AB span; and is constant with q= 3.1 kN/m for BC span. The Young's modulus of steel is 200 GPa. Part A Calculate: A y, v a 5 mm 200 mm Figure Q.1 9 S B 300 mm b с X

Figure 3 shows a cross section of a dam with parabolic face, the vertex of the parabola being at O. The axis of the parabola is vertical. The centroid of half parabolic cross section of water is 4.68m from the vertical through O. Water level in front of the dam is 50 m. 125m Af Figure 3 The magnitude of the resultant force on 1 m length of the dam is 11.9x10 N 11.9 x10³ KN 12.9 x10³ N 12.9 x10³ KN None of the above

Problem # 1: A hollow shaft has an outside diameter 60 mm and a wall thickness of 1.25 mm. The maximum shear stress in the shaft must be limited to 150 MPa. Use G = 43 000 MPa. Determine: (a) the maximum power that can be transmitted by the shaft if the rotation speed must be limited to 20 Hz. (b) the magnitude of the angle of twist in a 700-mm length of the shaft when 30 kW is being transmitted at 8 rpm.