Would you kindly answer this question.If the shaft must have one uniform diameter, determine the required minimum diameter of the shaft if the normal yield stress in the composite shaft must not exceed 450 MPa with a factor of safety equal to 1.8. Figure 1 shows a composite shaft ABCD acted upon horizontal forces. Themoduli of elasticity and the cross-section areas of the segments of the shaft arealso provided.Eal = 70 GPaAAB = 58 mm²Ecu = 126 GPaEst = 200 GPa%3D%3DABC = 77 mm2AcD = 39 mm²Сopper20kN8 kNAluminumSteel7 kNABD20kN8 kN450 mm300 mm400 mm

Answered: Image /qna-images/answer/452d0adc-7f2f-4598-9a49-8a8d9ff6ce3a.jpg

If the shaft must have one uniform diameter, determine the required minimum diameter of the shaft if the normal yield stress in the composite shaft must not exceed 450 MPa with a factor of safety equal to 1.8

If the shaft must have one uniform diameter, determine the required minimum diameter of the shaft if the normal yield stress in the composite shaft must not exceed 450 MPa with a factor of safety equal to 1.8

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter1: Tension, Compression, And Shear

Section: Chapter Questions

Problem 1.7.1P: A high-strength steel bar used in a large crane has a diameter d = 2.00 in. (sec figure). The steel...

See similar textbooks

Related questions

Q: The torque of 12kN m is applied to the 6-meter steel shaft's free end. The shaft must rotate at a…

Q: A 5-meter-long round steel rod has an outer diameter d (the rod is solid). The rod is subjected to a…

Q: The state of plane stress at a critical point in a steel machine bracket is shown. If the yield…

Q: determine the maximum length of the shaft using the maximum-shear-stress theory (Tresca yield…

Q: (a.) Determine the maximum length of the flexible shaft consists of a 5mm -diameter steel wire…

Q: A 2 m copper bar subjected to a tensile load 180 kN is suspended from a pin that is supported by two…

Q: A nylon thread is subjected to a 1.7-lb tension force. It is given that E = 0.5 × 106 psi and the…

A: Given data: Tension Force in nylon thread = F = 1.7 lb Young's Modulus of the thread = E = 0.5 x 106…

Q: The bearings at A and D exert only y and z components of force on the shaft as shown in Fig 7.…

Q: The five-bolt connection shown must support an applied load of P = 214 kN. If the average shear…

A: Given:number of bolts, n=5Applied force, P=214 KNAverage shear stress, σ=249 MPa

Q: The yield stress for a zirconium-magnesium alloy is sY = 15.3 ksi. If a machine part is made of this…

A: Given: The yield stress for a zirconium-magnesium alloy is sY=15.3 ksi The maximum principal stress…

Q: Part A Determine the shear strain at A relative to axes that are directed along AB and AD. Express…

A: Given, d1=0.38 ind2=0.5 in

Q: (a) determine the minimum factor of safety based on yielding according to the maximum- shear-stress…

Q: A tensile stress is to be applied along the long axis of a cylindrical copper rod that has a…

Q: A shaft is made of a steel alloy having an allowable shear stress of 10 ksi and the diameter of the…

A: Data givem - Shaft is made of steel alloy Allowable shear stress τallow = 10 ksi d = 1.2 inch…

Q: A shaft is made of an aluminum alloy having allowable shear stress of tallow = 100 MPa. If the…

A: Given Allowable shear stress = 100 MPa Diameter of shaft = 100 mm To find Maximum torque at 75 mm

Q: Q.3 A tensile stress is to be applied along the long axis of a cylindrical nickel rod that has a…

A: Given:Diameter of rod=D=11mmChange in diameter=∆D=2.5×10-3mmLet tensile axial force on rod=FWe…

Q: A spring was made by a steel wire of 25 mm diameter around a 175 mm diameter cylinder. determine the…

Q: If a shaft is made of a material for which sY = 75 ksi, determine the maximum torsional shear stress…

A: Given: The yield stress of the material is sY=75 ksi.

Q: A steel shaft is subjected to the torques shown. The shaft is solid with a diameter of 1 in and G =…

A: To find: (a) The internal torque in each segment. (b) The maximum shear stress (psi) in each segment…

Q: Determine maximum diameter of hole that can be punched through a plate of 10mm thick,if the punch…

Q: A flanged bolt coupling consists of nine ½ -in diameter bolts equally spaced around a bolt circle 15…

A: The torque capacity of the coupling is 5.522 kip•ft.

Q: The five-bolt connection must support an applied load of P = 2600 Ib. If the average shear stress in…

Q: The design of a machine element calls for a 40-mm-outer-diameter shaft to transmit 50 kW. If the…

A: As there are two shaft shown in figure but for figure b , d2 is not given so I have considered…

Q: The 25 mm diameter shaft is made of a material having an allowable shear stress of 80 MPa. If the…

Q: If a machine part is made of titanium (Ti-6A1-4V) and a critical point in the material is subjected…

A: Given Data: The principal stress is σ1. The principal stress is σ2=0.5σ1. The yield stress…

Q: The cylinder for a hydraulic press has an inside diameter of 300 mm and an outside radius of 260 mm.…

A: Given data, Internal diameter of the hydraulic cylinder, Di = 300 mm Outer radius of the cylinder,…

Q: The 12 kN.m torque is applied to the free end of the 5-m steel shaft. The angle of rotation of the…

Q: A shaft is subjected to an axial pull of 20N and transverse shear force of 10kN The yield strength…

A: Given: Pt1 =20 KN, Ps = 10 KN, σy = 250 MPa , μ =0.3 diameter of shaft, d =? cross…

Q: D esign and draw a cottered joint to join two rods safely to resist a load of 60 kN that acts along…

A: Given: The load, P = 60 kN The tensile stress, St = 60 MPa The crushing stress, Sc = 100 MPa The…

Q: Two shaft of diameter 50 mm are joined by a rigid flange coupling and transmit a torque in such a…

A: Here, Shaft diameter = dsh = 50 mm Allowable shear stress in shaft = τsh = 100 N/mm2 Pitch circle…

Q: Determine the diameter of a taper pin for use to fix a lever to a shaft, if it is to transmit a…

Q: determine the minimum bolt diameter that may be used for this connection.

Q: Two 20 mm steel shafts with a 100 MPa yield stress in shear are connected by a brass coupling with…

A: Given, d1 = 20 mmτsteel = 100 MPaτbrass = 60 MPaFOS = 2.1∴ τallow-steel = 1002.1 = 47.62 MPa&…

Q: A pipe has an outside diameter of 0.7 inches and inside diameter of 0.12 inches. A force of 411 lbs…

Q: tensile load of 8 kN is applied to a 1.6 mm long aluminum rod. The rod have stretched to a total of…

A: Stress: Stress is nothing but the force per unit area. It is represented by σ.& SI unit of…

Q: The puncher is to drive a 25 mm diameter hole to a steel plate. If the allowable axial stress of the…

Q: The applied shear force is V = 24 kip. 3 in. 1 in. V 3 in. 1 in. 1 in. Part A Determine the maximum…

Q: The cylinder for a hydraulic press has an inside diameter of 300 mm and an outside radius of 260 mm.…

Q: 2. An implant is made of a titanium alloy having an allowable shear stress of Tallow = 50 MPa. If…

Q: A 4-m long shaft transmits a torque of 5 kN-m. Determine the maximum torsional stress (TMax) of the…

A: Given: length of the shaft→L=4m torque transmitted→T=5 KN‐m=5000 N‐m outer diameter of the…

Q: A load P is supported by two (2) concentric steel springs. The inner spring consists of 40 turns of…

A: Answer: (a) The maximum load that the inner spring could carry is 2424.52 N. (b) The maximum load…

Q: The bell crank CBA is connected to a pin support B in double shear with 8-mm diameter pin B and to…

Q: The 10-mm-diameter steel bolt in (Figure 1) is surrounded by a bronze sleeve. The outer diameter of…

Q: Part A) A solid circular rod is used to transmit power from a motor to a machine. The diameter of…

Q: Two steel springs arranged as shown support a load P. The left spring consists of 12 turns of 20-mm…

Q: Q2: A cold drawn steel rod of circular cross- section is subjected to a variable bending moment of…

A: Calculate the mean bending moment,…

Q: How is the maximum shear stress determined with the torsion formula?

A: The formulae to calculate the shear stress from the Torsion formulae is as follows:

Q: shaft is subjected to an axial pull of 22N and transverse sheer force of 12KN The yield strength of…

A: Given: Axial load (P)=22N (Check the value is N or KN again)Transverse shear force (F)=12kNYield…

Concept explainers

Combined Loading

Any functioning component, such as machine parts, structural members, pressure vessels, and so on, are all under the influence of more than one force. When anybody is under the influence of more than one force such as shear forces, bending moments, axial forces, torsion, and so on, then such body is said to be under combined loading. A very practical example of combined loading is the crankshaft of an internal combustion engine (IC engine). The crankshaft of the IC engine is under high rpm, which is caused due to the torsional forces. Due to the presence of piston, counterbalances, and internal imbalances, the crankshaft experiences lateral forces and due to the rise in temperature, the crankshaft undergoes thermal expansion, which pulls the crankshaft along the axial direction and lateral direction. The presence of unbalanced loads along the periphery of the crankshaft also induces a bending moment.

Question

Would you kindly answer this question.

If the shaft must have one uniform diameter, determine the required minimum
diameter of the shaft if the normal yield stress in the composite shaft must not
exceed 450 MPa with a factor of safety equal to 1.8.

Figure 1 shows a composite shaft ABCD acted upon horizontal forces. The
moduli of elasticity and the cross-section areas of the segments of the shaft are
also provided.
Eal = 70 GPa
AAB = 58 mm²
Ecu = 126 GPa
Est = 200 GPa
%3D
%3D
ABC = 77 mm2
AcD = 39 mm²
Сopper
20kN
8 kN
Aluminum
Steel
7 kN
A
B
D
20kN
8 kN
450 mm
300 mm
400 mm

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

Similar questions

A thin-walled aluminum tube of rectangular cross section (sec fig me) has a centerline dimensions b = 6.0 in. and b = 4.0 in. The wall thickness t is constant and equal to 0.25 in. Determine the shear stress in the tube due to a torque T = 15 kip-in. Determine the angle of twist (in degrees) if the length L of the tube is 50 in. and the shear modulus G is 4.0 x 106 psi.
A statically indeterminate stepped shaft ACE is fixed at ends A and B and loaded by a torque TQat point C (see figure). The two segments of the bar are made of the same material, have lengths L4and LB, and have polar moments of inertia IAand Ipb. Determine the angle of rotation 4>of the cross section at Cby using strain energy. Hint: Use Eq, (3-55b) to determine the strain energy Urn terms of the angle d?. Then equate the strain energy to the work done by the torque to. Compare your result with Eq. (3-52) of Example 3-9.
A flying but tress transmit s a load P = 25 kN, acting at an angle of 60º to the horizontal, to the top of a vertical buttress AB (see figure). The vertical buttress has height h = 5.0 m and rectangular cross section of thickness t = 1.5 m and width b = 1.0 m (perpendicular to the plane of the figure). The stone used in the construction weighs y = 26 kN/m3. What is the required weight W of the pedestal and statue above the vertical buttress (that is, above section A) to avoid any tensile stresses in the vertical buttress?
A steel bar has a square cross section of width b = 2.0 in. (sec figure). The bar has pinned supports at the ends and is 3.0 ft long. The axial forces acting at the end of the bar have a resultant P = 20 kips located at distance e = 0,75 in, from the center of the cross section. Also, the modulus of elasticity of the steel is 29,000 ksi. Determine the maximum compressive stress max, in the bar. If the allowable stress in the steel is 18,000 psi, what is the maximum permissible length Lmaxof the bar?
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 propeller shaft for a small yacht is made of a solid steel bar 104 mm in diameter. The allowable stress in shear is 48 MPa, and the allowable rate of twist is 2.0° in 3.5 meters. (a) Assuming that the shear modulus of elasticity is G = 80 GPa, determine the maximum torque that can be applied to the shaft. (b) Repeat part (a) if the shaft is now hollow with an inner diameter of 5d18. Compare values to corresponding values from part (a).
A W410 × S5 steel column is compressed by a force P = 340 kN acting with an eccentricity e = 38 mm, as shown in the figure. The column has pinned ends and a length L. Also, the steel has a modulus of elasticity E = 200 GPa and yield stress y= 250 MPa. P = 340 kN If the length L = 3 m, what is the maximum compressive stress maxin (he column? If a factor of safety n =2.0 is required with respect to yielding, what is the longest permissible length Lmaxof the column?
A tie-down on the deck of a sailboat consists of a bent bar boiled at both ends, as shown in the figure. The diameter dBof the bar is 1/4 in., the diameter D Wof the washers is 7/8 in., and the thickness is of the fiberglass deck is 3/8 in. If the allowable shear stress in the fiberglass is 300 psi, and the allowable bearing pressure between the washer and the fiberglass is 550 psi, what is the allowable load P allowon the tie-down?
AW310 × 74 wide-flange steel column with length L = 3.8 m is fixed at the base and free at the top (see figure). The load P acting on the column is intended to be centrally applied, but because of unavoidable discrepancies in construction, an eccentricity ratio of 0.25 is specified. Also, the following data are supplied: E = 200 GPa, y = 290 MPa, and P = 310 kN. What is the maximum compressive stress max in the column? What is the factor of safety n with respect to yielding of the steel?
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 pinned-end column with a length L = 18 ft is constructed from a W12 x 87 wide-flange shape (sec figure). The column is subjected to a centrally applied load P1=180 kips and an eccentrically applied load P2=15 kips. The load P2acts at a distance s = 5.0 in. from the centroid of the cross section. The properties of the steel arc E = 29,000 ksi and y = 36 ksi. Calculate the maximum compressive stress in the column. Determine the factor of safety with respect to yielding.
The hollow drill pipe for an oil well (sec figure) is 6,2 in. in outer diameter and 0.75 in. in thickness. Just above the bit, the compressive force in the pipe (due to the weight of the pipe) is 62 kips and the torque (due to drilling) is 185 kip-in. Determine the maximum tensile, compressive, and shear stresses in the drill pipe.