The composite shaft, consisting of aluminum, copper, and steel sections, is subjected to theloading shown in Figure Q3. The data of the shaft is listed in Table Q3.Table Q3: Segment data for composite shaftShaft segmentABВСCDMaterialAluminumCopperSteelModulus of elasticity (GPa)70125200Yield Strength (MPa)24070250Cross-sectional area (mm²)60754016 kN8 kN9 kN7 kNAD16 kN8 kN- 300 mm---- 400 mm-- 450 mmFigure Q3: Composite shaft to support axial loads(a)Draw internal normal force diagram for the shaft AD.(b)Determine the normal stress in each section and ascertain whether the shaft remains inan elastic condition.(c)Determine the displacement of end D with respect to C.

Answered: Image /qna-images/answer/837c8be1-63d1-433b-a74b-9e9da106db8c.jpg

The composite shaft, consisting of aluminum, copper, and steel sections, is subjected to the loading shown in Figure Q3. The data of the shaft is listed in Table Q3. Table Q3: Segment data for composite shaft Shaft segment CD AB BC Material Aluminum Copper Steel Modulus of elasticity (GPa) 70 125 200 Yield Strength (MPa) 240 70 250 Cross-sectional area (mm?) 60 75 40 16 kN 8 kN 9 kN 7 kN D 16 kN 8 kN - 300 mm---400 mm- 450 mm- Figure Q3: Composite shaft to support axial loads (a) Draw internal normal force diagram for the shaft AD. (b) Determine the normal stress in each section and ascertain whether the shaft remains in an elastic condition. (c) Determine tbe displacement of end D with respect to C

The composite shaft, consisting of aluminum, copper, and steel sections, is subjected to the loading shown in Figure Q3. The data of the shaft is listed in Table Q3. Table Q3: Segment data for composite shaft Shaft segment CD AB BC Material Aluminum Copper Steel Modulus of elasticity (GPa) 70 125 200 Yield Strength (MPa) 240 70 250 Cross-sectional area (mm?) 60 75 40 16 kN 8 kN 9 kN 7 kN D 16 kN 8 kN - 300 mm---400 mm- 450 mm- Figure Q3: Composite shaft to support axial loads (a) Draw internal normal force diagram for the shaft AD. (b) Determine the normal stress in each section and ascertain whether the shaft remains in an elastic condition. (c) Determine tbe displacement of end D with respect to C

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter3: Torsion

Section: Chapter Questions

Problem 3.7.5P: The propeller shaft of a large ship has an outside diameter 18 in. and inside diameter 12 in,, as...

See similar textbooks

Similar questions

.17 A mountain-bike rider going uphill applies torque T = Fd(F = l5lb, d = 4 in.) to the end of the handlebars ABCD by pulling on the handlebar extenders DE. Consider the right half of the handlebar assembly only (assume the bars are fixed at the fork at A). Segments AB and CD are prismatic with lengths L, = 2 in.andL3 = 8.5 in, and with outer diameters and thicknesses d01 = 1.25 in. 101 = 0.125 in. and d03 = O.87in.,i03 = 0.ll5in, respectively as shown. Segment BC’ of length L, = 1.2 in. however. is tapered, and outer diameter and thickness vary linearly between dimensions at B and C. Consider torsion effects only. Assume G = 4000 ksi is constant. Derive an integral expression for the angle of twist of half of the handlebar tube when it is subjected to torque T = Fd acting at the end. Evaluate ‘b1-, for the given numerical1ues.
A steel riser pipe hangs from a drill rig located offshore in deep water (see figure). (a) What is the greatest length (meters) it can have without breaking if the pipe is suspended in the air and the ultimate strength (or breaking strength) is 550 MPa? (b) If the same riser pipe hangs from a drill rig at sea, what is the greatest length? (Obtain the weight densities of steel and sea water from Table M, Appendix I. Neglect the effect of buoyant foam casings on the pipe.)
Solve the preceding problem for the following data: diameter LO m, thickness 48 mm, pressure 22 MPa, modulus 210 GPa. and Poisson's ratio 0.29
A large precast concrete panel for a warehouse is raised using two sets of cables at two lift lines, as shown in the figure part a. Cable 1 has a length L1 = 22 Ft, cable 2 has a length L2= 10 ft, and the distance along the panel between lift points Band D is d = 14 ft (see figure part b). The total weight of the panel is W = 85 kips. Assuming the cable lift Forces F at each lift line are about equal, use the simplified model of one half of the panel in figure part b to perform your analysis for the lift position shown. Find the required cross-sectional area AC of the cable if its breaking stress is 91 ksi and a factor of safety of 4 with respect to failure is desired.
A safety valve on the top of a tank containing steam under pressure p has a discharge hole of diameter d(see figure). The valve is designed to release the steam when the pressure reaches the value Pmax If the natural length of the spring, is L and its stiffness is k, what should be the dimension ft of the valve? (Express your result as a formula for h.)
Two circular aluminum pipes of equal length L = 24 in. arc loaded by torsional moments T (sec figure). Pipe I has outside and inside diameters d2= 3 in. and L2, = 2.5 in., respectively. Pipe 2 has a constant outer diameter of d2along its entire length L and an inner diameter of d1but has an increased inner diameter of d3= 2.65 in. over the middle third. Assume that E = 10,400 ksi, u = 0.33, and allowable shear stress ra= 6500 psi. Find the maximum acceptable torques that can be applied to Pipe 1; repeat for Pipe 2. If the maximum twist e of Pipe 2 cannot exceed 5/4 of that of Pipe 1, what is the maximum acceptable length of the middle segment? Assume both pipes have total length L and the same applied torque T. Find the new value of inner diameter d3of Pipe 2 if the maximum torque carried by Pipe 2 is to be 7/8 of that for Pipe L If the maximum normal strain in each pipe is known to bemax = 811 x 10-6, what is the applied torque on each pipe? Also, what is the maximum twist of each pipe? Use the original properties and dimensions.
A sign of weight W is supported at its base by four bolls anchored in a concrete footing. Wind pressure P acts normal to the surface of the sign; the resultant of the uniform wind pressure is force fat the center of pressure (C.P). The wind force is assumed to create equal shear forces F/4 in the y direction at each boll (see figure parts a and c). The overturning effect of the wind force also causes an uplift force R at bolts A and C and a downward force (— R) al bolts B and D (see figure part b). The resulting effects of the wind and the associated ultimate stresses for each stress condition are normal stress in each boll (h — 60 ksi); shear through the base plate (th = 17 ksi); horizontal shear and bearing on each bolt ( tfur = 25 ksi and cr^ = 75 ksi): and bearing on the bottom washer at B (or D) (abor = 50 ksi).
The propeller shaft of a large ship has an outside diameter 18 in. and inside diameter 12 in,, as shown in the figure. The shaft is rated for a maximum shear stress of 4500 psi. If the shaft is turning at 100 rpm, what is the maximum horsepower that can be transmitted without exceeding the allowable stress? If the rotational speed of the shaft is doubled but the power requirements remain unchanged, what happens to the shear stress in the shaft?
A cylinder filled with oil is under pressure from a piston, as shown in the figure. The diameter d of the piston is 1,80 in. and the compressive force F is 3500 lb. The maximum allowable shear stress t^^, in the wall of the cylinder is 5500 psi. What is the minimum permissible thickness t„± of the cylinder wall? (Sec figure
A cylindrical brick chimney of height H weighs w = 825 lb/ft of height (see figure). The inner and outer diameters are d1= 3 ft and d2= 4 ft, respectively. The wind pressure against the side of the chimney is p = 10 lb/ft2 of projected area. Determine the maximum height H if there is to be no tension in the brickwork.
A tubular shaft being designed for use on a construction site must transmit 120 kW at 1,75 Hz, The inside diameter of the shaft is to be one-half of the outside diameter. If the allowable shear stress in the shaft is 45 MPa, what is the minimum required outside diameter d?
A thin metal strip of total weight W and length L is placed across the top of a flat table of width L2as shown in the figure. What is the clearance S between the strip and the middle of the table? (The strip of metal has flexural rigidity EI.)