2. Two solid cylindrical rods AB and BC are welded together at B and loaded as shown below. Knowing the average normal stress must not exceed 200 ksi in either rod, determine the smallest allowable values of the diameter d, and d₂. 30 kips 15 kip d 30 kips •4ft. 6:ft: Figure 2

The steel beam ABCD shown is supported at C as shown and supported at B and D by steel bolts each having a diameter of 8 mm. The lengths of BE and DF are 50 and 60 mm, respectively. All dimensions are given in millimeters. Prior to loading, the nuts are just in contact with the beam, which is horizontal. A force of 2 kN is applied at point A. For steel, E = 209 GPa. Determinethe stresses in the cables and the deflections of points A, B and D if (a) beam ABCD is considered to be rigid, and (b) beam ABCD is elastic with a second area moment of I = 200 mm^4

The steel beam ABCD shown is simply supported at A and supported at B and D by steel cables each having a diameter of 12 mm. A force of 20 kN is applied at point C. For steel E = 209 GPa. Determine the stresses in the cables and the deflections of points B, C and D if (a) Beam ABCD is considered to be rigid (b) Beam ABCD has a second-area moment of I = 800,000 mm².

Each of the three solid steel shafts has a diameter of 20 mm. Shafts AB and EF are 600 mm long, whereas shaft CD is 300 mm long. The pitch radii of gears B, C, and F are 30, 80 and 50 mm, respectively. For steel E = 200 GPa and v=0.3. If torque of 10 N.m is applied to shaft AB as shown, determine the shear stresses in each shaft and the angle through which each gear rotates.

A 60-mm diameter solid steel shaft is simply supported at its ends on bearings A and E. Pulley C receives power from a motor through a belt with belt tensions as shown. The power is transmitted through the shaft and delivered to the belts on pulleys B and D. For pulley D, belt tension on the loose side is 15 percent of the tension on the tight side. The three pulleys are keyed to the shaft. Pulley C is of diameter 100 mm and pulleys B and D are of diameter 200 mm. The belt on pulley B is at 45° from the negative z direction. The shaft lengths AB, BC, CD and DE are in mm and shown in the figure below. (a) At the critical location on the shaft, find the principal stresses and maximum shear stress. Ignore transverse shear stress due to V in this problem

3(a). Both portions of the rod ABC are made of an aluminum for which E = 60 GPa. Knowing that the magnitude of P is 3 kN, determine (a) the value of Q so that the deflection at A is zero, (b) the corresponding deflection at B. Figure 3 1.5mm diameter 1.0m FO 50mm diameter 15.m 3(b). The rod ABC of Figure 3 is made of an aluminum for which E= 60 GPa. Knowing that P=10 kN and Q = 50 kN, determine the deflection of (a) point A, (b) point B. C/n

A 42-lb, 0.8-ft-diameter, 1-ft-tall cylindrical tank slides slowly down a ramp with a constant

A cantilever beam shown in the accompanying figure is used to support a load acting on a balcony. The deflection of the centerline of the beam is given by the following equation:

The rigid structure BCD is supported as shown. Assume a = 5.6 ft, b=4.4ft, c= 2.8 ft, d= 1.6 ft, and = 40°. Tie rod (1) is attached at A and C with double shear pin connections, while the pin at B is attached with a single shear connection. The pins at A, B, and C each have a diameter of 0.500 in. and an ultimate shear strength of 73 ksi, and tie rod (1) has diameter of 0.875 in. and a yield strength of 39 ksi. Determine the allowable load P that may be applied to the rigid beam if an overall factor of safety of 1.6 is required.

2. A 1/8" radius steel rod that is 2 ft long has a 20,000 in-lbs external torque applied. [J = (T4)/2] A. What is the polar moment of inertia for the rod? B. If the Modulus of Rigidity for the steel bar is 18 X 10³ Ksi, what is the expected twist of the bar in degrees?