Endurance Limit of a Torsion Bar A round torsion bar machined from steel is under reversed torsional loading. Because of the design of the ends, a fatigue stress-concentration factor Kf exists. Estimate the modified endurance limit. Given: The diameter of the bar is d = 1⅝ in. and Kf = 1.2. The

Question

Endurance Limit of a Torsion Bar

A round torsion bar machined from steel is under reversed torsional loading. Because of the design of the ends, a fatigue stress-concentration factor [latex]K_{f}[/latex] exists. Estimate the modified endurance limit.

Given: The diameter of the bar is [latex]d[/latex] = 1⅝ in. and [latex]K_{f}[/latex] = 1.2. The operating temperature is 500°C maximum.

Assumption: Reliability is 98%.

Design Decision: The bar is made of AISI 1050 cold-drawn steel.

Accepted Answer

From Table B.3, we find the ultimate strength in tension as [latex]S_{u}[/latex] = 100 ksi. Then, applying Equation 7.4, the endurance limit of the test specimen is

[latex] S_{e s}^{\prime}=0.29 S_u=0.29(100)=29 ksi [/latex]

By Equation 7.7 and Table 7.2, the surface finish factor is

[latex] C_f=A S_u^b=2.7(100)^{-0.265}=0.80 [/latex]

The reliability factor corresponding to 98% is [latex]C_{r}[/latex] = 0.84 (Table 7.3). Using Equation 7.9, the size factor [latex]C_{s}[/latex] = 0.85. Applying Equation 7.11,

[latex] C_s=\left\{\begin{array}{ll} 0.85 & (13 mm 50 mm ) \quad(D>2 in .) \end{array} ight. [/latex] (7.9)

[latex] C_t=\left\{\begin{array}{cc} 1 \quad T \leq 450 ^{\circ} C & \left(840 ^{\circ} F ight) \ 1-0.0058(T-450) & 450 ^{\circ} C

[latex] C_t=1-0.0058(500-450)=0.71 [/latex]

Hence, the endurance limit for design is found to be

[latex] \begin{aligned} S_{e s} &=C_f C_r C_s C_t\left(1 / K_f ight) S_{e s}^{\prime} \ &=(0.80)(0.84)(0.85)(0.71)(1 / 1.2)(29) \ &=9.8 ksi \end{aligned} [/latex] (b)

Table 7.2 Surface Finish Factors [latex]C_{f}[/latex]
	[latex]A[/latex]
Surface Finish	MPa	ksi	[latex]b[/latex]
Ground	1.58	1.34	−0.085
Machined or cold drawn	4.51	2.7	−0.265
Hot rolled	57.7	14.4	−0.718
Forged	272.0	39.9	−0.995

Table 7.3 Reliability Factors
Survival Rate (%)	[latex]C_{r}[/latex]
50	1.00
90	0.89
95	0.87
98	0.84
99	0.81
99.9	0.75
99.99	0.70

Question 7.1: Endurance Limit of a Torsion Bar A round torsion bar machine...

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