Determine the fatigue factor of safety of the design using DE-Goodman criterion

A thin tubular shaft with a circular cross section (see figure) and with inside diameter 100 mm is subjected to a torque of 5000 N · m. If the allowable shear stress is 42 MPa, determine the required wall thickness t by using (a) the approximate theory for a thin-walled tube and (b) the exact torsion theory for a circular bar.

Repeat Problem 11.2-3 assuming that R= 10 kN · m/rad and L = 2 m.

The steel axle of a large winch on an ocean liner is subjected to a torque of 1.65 kN · m (see figure). What is the minimum required diameter dminif the allowable shear stress is 48 M Pa and the allowable rate of twist is 0.75º/m? (Assume that the shear modulus of elasticity is 80 G Pa.) Repeat part (a) if the shaft is now hollow with an inner diameter of 5d/8, Compare dminvalues to corresponding values from part (a)

At a machined shaft shoulder the small diameter d is 1.100 in, the large diameter D is 1.65 in, and the fillet radius is 0.11 in. The bending moment is 1260 Ib; . in and the steady torsion moment is 1100 lb; . in. The heat-treated steel shaft has an ultimate strength of Sut = 105 kpsi and a yield strength of S, = 82 kpsi. The reliability goal for the endurance limit is 0.99. a) Determine the fatigue factor of safety of the design using each of the fatigue failure criteria described in this section b) Determine the yielding factor of safety Solution:

The shaft shown in the figure is machined from AISI 1040 CD steel. The shaft rotates at 1600 rpm and is supported in rolling bearings at A and B. The applied forces are F1 = 2500 lbf and F2 = 2500 lbf. The location of critical bending moment from 10.5" from point A, where bending moment is 14 750 lbf·in. Determine the minimum fatigue factor of safety based on achieving infinite life. Yield strength is 71 kpsi. If infinite life is not predicted, estimate the number of cycles to failure. Also check for yielding. Note: for the given ratio of r/d = 0.0625/1.625 = 0.04, D/d = 1.875/1.625 = 1.15 the stress concentration is given by K, =1.95. Also, use the correction of the endurance limit based on the surface factor, ka, size factor, kb, and loading factor, ke -8 in- -8 in- -8 in- 3 in -10 in- -10 in in All fillets in R. 1/4

The section of shaft shown in the figure is to be designed to approximate relative sizes of D=1.5d, and r=0.125d. The shaft is to be made of AISI 1035 CD steel and the groove is machined. The shaft is subjected to a completely reversed bending moment of 800 lbf.in, accompanied by a steady torque of 500 lbf.in. The shaft is to be used at 400°F and is expected to have a reliability of 0.99. Use a design factor of 2 and size the shaft for an infinite life using the Modified Goodman criterion. Determine the minimum diameter 'd'.

3. Bearing reactions R1 and R2 are exerted on the shaft shown in the figure, which rotates at 950 rev/min and supports an 8-kip bending force. Use a 1095 HR steel. Specify a diameter d using a design factor of nd = 1.6 for a life of 10 hr. The surfaces are machined. R₁ F=8 kip -10 in-5 in- +5 in- d/10 R. 1.4d I in R₂ -20 d/5 R. ЈӘН

2. At a machined shaft shoulder the small diameter d is 25mm the large diameter D is 40mm, and the fillet radius is 2.5 The bending moment is 2300N mm and the steady torsion moment is 1800 N mm The heat-treated steel shaft has an ultimate strength of Sut- 850Mpa The reliability goal is 099 (ka- 0.786, kb 0.870, ke 0.814) Determine the fatigue factor of safety of the design described in this section

A 1.50-in.-diameter solid shaft is subjected to an axial force of P = 1700 lb, a horizontal shear force of V = 180 lb, and a concentrated torque of T = 2200 lb-in., acting in the directions shown. Assume L = 7.5 in.  Section properties for the shaft are A = 1.7671 in.2, J = 0.497 in.4, Iy = Iz = 0.2485 in.4, and Q = 0.2812 in.3.  Determine the normal and shear stresses at point K, and show these stresses on a stress element.