6.1 A beam of length 10 m is symmetrically placed on two supports 7 m apart. The loading is 15 kN/m between the supports and 20 kN at each end. What is the central deflection of the beam? E = 210 GN/m²; I = 200 × 10-6 m². [6.8 mm]

EB and FG are two planes inside a soil element ABCD as shown in Figure 10.50. Stress conditions on the two planes are Plane EB: EB = 25 kN/m2; EB = +10 kN/m2 Plane FG: FG = 10 kN/m2; FG = 5 kN/m2 (Note: Mohrs circle sign conventions for stresses are used above) Given ; = 25, determine: a. The maximum and minimum principal stresses b. The angle between the planes EB and FG c. The external stresses on planes AB and BC that would cause the above internal stresses on planes EB and FG

Determine the factor of safety against bottom heave for the braced cut described in Problem 15.18. Use Eqs. (15.66) and (15.70). For Eq. (15.70), assume the length of the cut, L = 18 m. 15.18 Refer to Figure 15.51 in which = 17.5 kN/m3, c = 60 kN/m2, and center-to-center spacing of struts is 5 m. Draw the earth pressure envelope and determine the strut loads at levels A, B, and C. FIG. 15.51

For the beam shown: (a) determine the distance a for which the maximum positive and negative bending moments in the beam are equal; and (b) draw the corresponding shear and bending moment diagrams for the beam.

The cross section of a braced cut supporting a sheet pile installation in a clay soil is shown in Figure 14.22. Given: H = 12 m, clay = 17.9 kN/m3, = 0, c = 75 kN/m2, and the center-to-center spacing of struts in plan view, s = 3 m. a. Using Pecks empirical pressure diagrams, draw the earth-pressure envelope. b. Determine the strut loads at levels A, B, and C.

An astronaut has a mass of 68 kg. What is the weight of the astronaut on Earth at sea level? What are the mass and the weight of the astronaut on the Moon, and on Mars? What is the ratio of the pressure exerted by the astronauts shoe on Earth to Mars?