Concept explainers
8–51 to
8–54 For the pressure cylinder defined in the problem specified in the table, the gas pressure is cycled between zero and pg. Determine the fatigue factor of safety for the bolts using the following failure criteria:
(a) Goodman.
(b) Gerber.
(c) ASME-elliptic.
Problem Number | Originating Problem Number |
8–51 | 8–33 |
(a)
The fatigue factor of safety for the bolts using Goodman criteria.
Answer to Problem 51P
The fatigue factor of safety for the bolts using Goodman criteria is
Explanation of Solution
Write the expression of the length of the material squeeze between the bolt face and washer face.
Here, the length of the material squeeze between the bolt face and washer face is
Write the expression for the length of the bolt.
Here the length of bolt is
Write the expression of the threaded length for hexagonal bolt.
Here, the threaded length is
Write the expression of the length of the unthreaded portion in grip.
Here, the length of the unthreaded portion in the grip is
Write the expression of the length of the threaded portion in grip.
Here, the length of threaded portion in the grip is
Write the expression of the major area diameter.
Here, the nominal diameter of the bolt is
Write the expression of the stiffness for the bolt.
Here, the bolt stiffness is
Write the expression of stiffness for the steel cylinder.
Here, the stiffness of the steel cylinder is
Write the expression for the stiffness of the cast iron pressure vessel.
Here, the stiffness of the cast-iron pressure vessel is
Write the expression for the stiffness of the member.
Here, the stiffness of the member is
Write the expression of joint constant.
Here, the joint constant is
Write the expression of initial tension in the bolt.
Here, the tensile stress area is
Write the expression of the effective area of the cylinder.
Here, the effective area of the cylinder is
Write the expression for the total force acting on the assembly.
Here, the total load acting on the assembly is
Write the expression for the load acting on each bolt.
Here, the number of bolt is
Write the expression for the initial stress in the bolt.
Write the expression for the average stress.
Write the expression for the mean stress.
Write the expression for factor of safety by Goodman criteria.
Here, the ultimate strength is
Conclusion:
Substitute
Refer to Table
Substitute
Substitute
Substitute
Substitute
Substitute
Refer to Table
Substitute
Substitute
Substitute
Substitute
Substitute
Refer to Table
Substitute
Substitute
Substitute
Substitute
Refer to Table
Refer to Table 8.11 “Metric Mechanical-Property Classes for Steel Bolts, Screws, and Studs” to obtain
Substitute
Substitute
Substitute
Substitute
Thus, the fatigue factor of safety for the bolts using Goodman criteria is
(b)
The fatigue factor of safety for the bolts using Gerber criteria.
Answer to Problem 51P
The fatigue factor of safety for the bolts using Gerber criteria is
Explanation of Solution
Write the expression for the factor of safety using Gerber criteria.
Conclusion:
Substitute
Thus, the fatigue factor of safety for the bolts using Gerber criteria is
(c)
The fatigue factor of safety for the bolts using ASME-elliptic criteria.
Answer to Problem 51P
The fatigue factor of safety for the bolts using ASME-elliptic criteria is
Explanation of Solution
Write the expression for the factor of safety using ASME-elliptic criteria.
Conclusion:
Substitute
Thus, the fatigue factor of safety for the bolts using ASME-elliptic criteria is
Want to see more full solutions like this?
Chapter 8 Solutions
Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)
- Q) A helical compression spring of a mechanism is subjected to Pas =120 N 19ad cycle. The diameter if the wire is 3 mm, with a spring index of € = 7 P, =4N and .The spring is made of oil-hardened and tempered steel, with”« ~ L0t dm Determine the factor of safety in fatigue loading.arrow_forwardDetermine the safe tensile load for fine series bolts of (a) M 24and (b) M 38. Assume that the bolts are not initially stressed and take the safe tensile stress as 450MPa.arrow_forwardThe figure gives the cross-section of a grade 25 cast-iron pressure vessel. A total of N bolts are to be used to resist a separating force of 150 kN. (a) Determine kb, km, and C. (b) Find the number of bolts required for a load factor of 2 where the bolts may be reused when the joint is taken apart. (c) With the number of bolts obtained in part (b), determine the realized load factor for overload, the yielding factor of safety, and the load factor for joint separation. Use (SI) units as it appliesarrow_forward
- A cap screw, ¾ in.-10-UNC-2, with a hexagonal head that is 9/16 in. thick, carries a tensile load of 3000 lb. If the material is AISI 1015, cold drawn, find the factor of safety based on ultimate strengths of a. the threaded shank, b. the head against being sheared off, and c. the bearing surface under the head. d. Is there any need to consider the strength of standard cap-screw heads in design?arrow_forwardA cap screw, ¾ in.-10-UNC-2, with a hexagonal head that is 9/16 in. thick, carries a tensile load of 3000 lb. If the material is AISI 1015, cold drawn, find the factor of safety based on ultimate strengths of a.the threaded shank, b.the head against being sheared off, and c.the bearing surface under the head. d.Is there any need to consider the strength of standard cap-screw heads in design?arrow_forwardA rotating shaft of 40×4 mm AISI 1018 cold-drawn steel tubing has a 6 mm diameter hole drilled transversely through it. Estimate the factor of safety guarding against fatigue and static failures using the Gerber and Langer failure criteria for the following loading conditions: a. The shaft is subjected to a completely reversed torque of 120 N.m in phase with a completely reversed bending moment of 150 N.m. b. The shaft is subjected to a pulsating torque fluctuating from 20 to 160 N.m and as steady bending moment of 150 N.m.arrow_forward
- A rigid block is supported by two cables having the same diameter of 4 mm. Cable S1 is made of AISI 1050 cold drawn steel with E=200,000 MPa, Sy=580 MPa, and Sult=690 MPa; cable S2 is made of AISI 1020 cold drawn steel with E=200,000 MPa, Sy=390 MPa, and Sult=470 MPa. Determine the maximum number of cycles n3 due to the following history of P.arrow_forwardUsing safety factor of (3) , determine a minimum diameter for the shaft shown in FIGURE 2. The shaft material AISI 1050 HR ( hot rolled ) steel . The power to be transmitted is (8 KW) at ( 900 rpm). The diameter of the pulley is (250 mm ) and the ratio of belt tensions is (2.5 ). (90 percent ) reliability is desired.arrow_forwardDesign and draw a protective type of cast iron flange coupling for a steel shaft transmitting ‘P is 17kW at ‘N is 350 r.p.m. and having an allowable shear stress of 40 MPa. The working stress in the bolts should not exceed 30 MPa. Assume that the same material is used for shaft and key and that the crushing stress is twice the value of its shear stress. The maximum torque is 25% greater than the full load torque. The shear stress for cast iron is 14 MPa.arrow_forward
- A bushed pin type flexible coupling is used to transmit 10 kW power at 720 rpm. The design torque is 150% of rated torque. The keys have square cross-section. The permissible stresses are: For shaft and key material, τ = 66.67 N/mm2 , σc = 200 N/mm2 ; For pin material, τ = 35 N/mm2 , σt = 133 N/mm2 ; For flange material τ = 16.67 N/mm2 . The permissible bearing pressure for rubber bushes is 1 N/mm2. The number of bushes is 4. Design the bushed pin flexible coupling. Explain Axle, Spindle, Counter shaft and line-shaft with their examples .arrow_forwardA bushed pin type flexible coupling is used to transmit 10 kW power at 720 rpm. The design torque is 150% of rated torque. The keys have square cross-section. The permissible stresses are: For shaft and key material, τ = 66.67 N/mm2, σc = 200 N/mm2; For pin material, τ = 35 N/mm2, σt = 133 N/mm2; For flange material τ = 16.67 N/mm2. The permissible bearing pressure for rubber bushes is 1 N/mm2. The number of bushes is 4. Design the bushed pin flexible coupling.arrow_forwardThe shaft of a belt drive is made of AISI C1020 as rolled steel. The belt tensions vary continuously during transmission at a constant tension ratio of 3:1; the maximum tight side tension being 400 lb and the minimum tight side tension is expected to be 160 lb, at a pulley diameter of 12 inches. For a Goodman factor of safety of 1.8, recommend the diameter of the shaft. Consider a machined surface and the effect of a hardened profile keyway in the shaft.arrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY