13. The velocity distribution for the flow of a Newtonian fluid between two fixed, wide, parallel plates is given by the equation u where U is the mean velocity, y is the distance from the centerline, and h is the distance between the two plates. For a fluid with a viscosity of 0.04 lb - s/ft, mean velocity of 2 ft/s and distance between the plates of 0.2 in, determine (a) the shear stress acting on the bottom wall, and (b) the shear stress acting through the centerline of flow.

Calculate the R-value for the following materials: a. 4 in. thick brick b. 10 cm thick brick c. 12 in. thick concrete slab d. 20 cm thick concrete slab e. 1 cm thick human fat layer

A structural member with a rectangular cross section as shown in the accompanying figure is used to support a load of 2500 N. What type of material do you recommend be used to carry the load safely? Base your calculations on the yield strength and a factor of safety of 2.0.

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?

The results of a tensile test are shown in Table 1.5.2. The test was performed on a metal specimen with a circular cross section. The diameter was 3 8 inch and the gage length (The length over which the elongation is measured) was 2 inches. a. Use the data in Table 1.5.2 to produce a table of stress and strain values. b. Plot the stress-strain data and draw a best-fit curve. c. Compute the, modulus of elasticity from the initial slope of the curve. d. Estimate the yield stress.

The data in Table 1.5.3 were obtained from a tensile test of a metal specimen with a rectangular cross section of 0.2011in.2 in area and a gage length (the length over which the elongation is measured) of 2.000 inches. The specimen was not loaded to failure. a. Generate a table of stress and strain values. b. Plot these values and draw a best-fit line to obtain a stress-strain curve. c. Determine the modulus of elasticity from the slope of the linear portion of the curve. d. Estimate the value of the proportional limit. e. Use the 0.2 offset method to determine the yield stress.

How does a tensile stress differ from a compressive stress?

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

In concrete work, Fuller and Thompson (1907) suggested that a dense packing of grains can be achieved if the percent finer (p) and grain size (D) are related by the following equation, where n is a constant varying in the range of 0.3-0.6. Dmax is the size of the largest grain within the soil. p=(DDmax)n100 This equation is sometimes used in roadwork for selecting the aggregates. a. For n = 0.5, show that the soil is well graded. b. If n = 0.5 and Dmax = 19.0 mm, find the percentages of gravel, sand, and fines within the soil. Use the Unified Soil Classification System.

A soil element beneath a pave ment experiences principal stress rotations when the wheel load, W, passes over it and moves away, as shown in Figure 10.51. In this case, the wheel load has passed over points A and B and is now over point C. The general state of stress at these points is similar to the one shown by a stress block at point D. The phenomenon of principal stress rotation influences the permanent deformation behavior of the pavement layers. Investigate how the magnitude and the orientations of the principal stresses vary with distance from the point of application of the wheel load. Consider the case shown in Figure 10.51. An unpaved aggregate road with a thickness of 610 mm and unit weight of 19.4 kN/m3 is placed over a soil subgrade. A typical single-axle wheel load, W = 40 kN, is applied uniformly over a circular contact area with a radius of R = 150 mm (tire pressure of 565 kN/m2). The horizontal and shear stresses at each point are calculated from a linear elastic finite element analysis for a two-layer pavement and are presented in the following table. a. Use Eq. (10.28) to calculate the vertical stress increases at soil elements A, B, and C that are located at radial distances 0.457,0.267, and 0 m, respectively, from the center of the load. Determine the total vertical stress (y) due to wheel load, the overburden pressure at each point, and enter these values in the table. b. Use the pole method to determine the maximum and minimum principal stresses (1 and 3) for elements A, B, and C. Also determine the orientation (s) of the principal stress with respect to the vertical. Enter these values in the table. c. Plot the variations of 1 and s, with normalized radial distance, r/R, from the center of loading.