1. Four forces are applied to point P as shown. Knowing that F₁ = 50 lb, F2 = 20 lb and F4 = 70 lb, find the magnitude of F3 and the angle 0 such that point P remains in equilibrium. Fi F3 50 0 F4 120° チュ NOT SHARE

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

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.

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.

A 9 ft wide and infinitely long flexible strip load of 800 lb/ft2 is placed on an elastic medium as shown in Figure P8.7. Find the vertical stress increase at points A, B, and C located 3 ft below the surface.

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?

Refer to Figure 10.46. A flexible circular area of radius 6 m is uniformly loaded. Given: q = 565 kN/m2. Using Newmarks chart, determine the increase in vertical stress, z, at point A. Figure 10.46

Repeat Problem 10.12 for q = 700 kN/m2, B = 8 m, and z = 4 m. In this case, point A is located below the centerline under the strip load. 10.12 Refer to Figure 10.43. A strip load of q = 1450 lb/ft2 is applied over a width with B = 48 ft. Determine the increase in vertical stress at point A located z = 21 ft below the surface. Given x = 28.8 ft. Figure 10.43

Bourdon-type pressure gauges are used in thousands of applications. A deadweight tester is a device that is used to calibrate pressure gauges. Investigate the operation of a deadweight pressure tester. Write a brief report to discuss your findings.