7/27/2019 Tutorial Fatigue

1/2

FUNDAMENTALS OF MACHINE DESIGN AND DRAWING (A.Y. 2013-2014)

TUTORIAL # 1 FATIGUE

EXERCISE # 1

Generate a Haigh diagram at infinite life for a steel material.Take: Rm =1180 MPa, Rp02 =880 MPa, D-1 =480 MPa - fatigue limit for alternate symmetric cycles (R= -1).

EXERCISE # 2

For a steel material, with fatigue limit for alternate symmetric cycles D-1=250 MPa and ultimate tensile

strengthRm =600 MPa, compute the alternate stress level corresponding to a life to failure of 105

cycles.

[a =339 MPa]

EXERCISE # 3

For a steel material (Rm=700 MPa, D-1=300 MPa) subjected to an alternate symmetric cycle with an

alternate stress level ofa=420 N/mm2, compute the number of cycles to failure.

[N=6.37 10

4cycles]

EXERCISE # 4

A solid circular shaft with diameter d=30 mm is subjected to a bending moment having of mean value

Mfm=600 Nm and alternating value Mfa=200 Nm.

The shaft is made from steel (Rm=1000 MPa, Rp02 =800 MPa, D-1 =450 MPa) with a machined surface

finish (RA = 1.6m).

Use the Haigh diagram to compute the factor of safety to infinite life. Consider both the case of average

stress constant and alternate stress varying with performance (CASE A) and the case of average stress and

alternate stress varying with performance (CASE B).

[SF=3.8 (case A); SF= 2.3 (case B)]

EXERCISE # 5

A 25 x 25 mm square bar with a rough lathe finish (RA = 6.3m) is subjected to a zero to maximum (stress

ratio R=0) tension cycle with Fmax=105

N.

Use the Haigh diagram (material steel: Rm=1180 MPa, Rp02=880 MPa, D-1=690 MPa) to compute the factor

of safety to infinite life.

[SF=4.8 (case A); SF= 3.8 (case B)]

EXERCISE # 6

A machined steel beam with solid circular cross section is subjected to an axial loading cycle between

Fmax=5105

N and Fmin=1105

N.

Use the Haigh diagram (Rm=1180 MPa, Rp02=880 MPa, D-1=680 MPa) to determine the diameter of the

beam which can ensure a factor of safety SF =1.5 with respect to yielding and SF=3 with respect to infinite

life (refer to the case of average stress and alternate stress varying with performance). Consider a machined

surface finish (RA=1.6 m).

For the designed beam, estimate the factor of safety to infinite life for the following axial loading cycles:

a) Fmax=0 N and Fmin=-7105

N;

b) Fmax=+3.5105

N and Fmin=-3.5105

N;

c) Fmax=+7105

N and Fmin=0 N.[d = 52 mm; a)SF= 4.5; b) SF=2.7; c) SF=2.0]

7/27/2019 Tutorial Fatigue

2/2

EXERCISE # 7

M M

r

F F

D d

A notched rotating shaft is subjected to a constant

bending moment Mf=250 Nm and to a constant axial

force F=30 kN. Compute the factor of safety withrespect to infinite life, considering that it is the

bending moment that may increase during operation.

Take: D=45 mm, d=40 mm, r=3 mm, RA= 0.8 m

Material properties: Rm =640 MPa, Rp02=420 MPa,

D-1=300 MPa

[SF=3.4 (CF=1; CS= 0.83; Kf= 1.57)]

EXERCISE # 8

A stepped rotating shaft, loaded by an end-load F, must endure under nominal working conditions.

Use the Haigh diagram to compute the factor of safety with respect to yielding and to infinite life.

Take: F = 3.5 kN, D = 45 mm, d = 38 mm, r = 1.5 mm, L = 180 mm, l = 90 mm.

Material: Rm = 900 MPa, Rp02 = 635 MPa, D-1= 450 MPa, RA= 1.6 m.

D

r

F

Notch geometry at support B

A B

L l

d

[Yielding SF= 10.7; infinite life SF= 3.4 (CF=0.95; CS= 0.85; Kf= 1.78)]