Cumulative Fatigue Damage of a Machine Bracket A steel bracket of a machine is subjected to a reversed bending stress of S1 for n1 cycles, S2 for n2 cycles, and S3 for n3 cycles. Determine whether failure will occur. Given: S1 = 420 MPa, S2 = 350 MPa, S3 = 280 MPa n1 = 5,000 cycles, n2 = 20,000

Question

Cumulative Fatigue Damage of a Machine Bracket

A steel bracket of a machine is subjected to a reversed bending stress of [latex]S_{1}[/latex] for [latex]n_{1}[/latex] cycles, [latex]S_{2}[/latex] for [latex]n_{2}[/latex] cycles, and [latex]S_{3}[/latex] for [latex]n_{3}[/latex] cycles. Determine whether failure will occur.

Given: [latex]S_{1}[/latex] = 420 MPa, [latex]S_{2}[/latex] = 350 MPa, [latex]S_{3}[/latex] = 280 MPa

[latex]n_{1}[/latex] = 5,000 cycles, [latex]n_{2}[/latex] = 20,000 cycles, [latex]n_{3}[/latex] = 30,000 cycles.

Design Decisions: The bracket has a machined surface and Bhn = 200. Miner’s cumulative damage rule is used.

Accepted Answer

The appropriate limiting number of cycles corresponding, respectively, to the preceding stress values is, from Figure 7.18,

[latex]N_{1}[/latex] = 12,000 cycles, [latex]N_{2}[/latex] = 50,000 cycles, [latex]N_{3}[/latex] = 280,000 cycles

Applying Equation 7.36,

[latex] \frac{n_1}{N_1}+\frac{n_2}{N_2}+\cdots=1 [/latex] (7.36)

[latex] \frac{5,000}{12,000}+\frac{20,000}{50,000}+\frac{30,000}{280,000}=0.924 [/latex]

Comment: Since 0.924 < 1, the member is safe.

Question 7.6: Cumulative Fatigue Damage of a Machine Bracket A steel brack...

Related Answered Questions

Camshaft Fatigue Design of Intermittent-Motion Mechanism Figure 7.16 illustrates a rotating camshaft of an intermittent-motion mechanism in its peak lift position. The cam exerts a force P on the follower, because of a stop mechanism (not shown), only during less than half a shaft revolution. ...

Verified Answer:

Allowable Fully Reversed Load of an Actuating Rod A round rod is subjected to an axial tensile force Fm. Calculate the limiting value of the completely reversed load Fa that can be applied with a ½ in. eccentricity without causing fatigue failure at 10^6 cycles Given: The diameter of the rod ...

Verified Answer:

Verified Answer:

Endurance Limit for a Stepped Shaft in Reversed Bending Rework Example 7.1 for the condition that the critical point on the shaft is at a diameter change from d to D with a full fillet where there is reversed bending and no torsion, as shown in Figure 7.10. Given: d = 1 5/8in., D = 1 7/8 in., ...

Verified Answer:

Fatigue Life of Instrument Panel with a Crack A long plate of an instrument is of width 2w and thickness t. The panel is subjected to an axial tensile load that varies from Pmin to Pmax with a complete cycle every 15 s. Before loading, on inspection, a central transverse crack of length 2a is ...

Verified Answer:

Verified Answer:

Design of a Cylindrical Pressure Vessel for Fluctuating Loading A thin-walled cylindrical pressure vessel of diameter d is subjected to an internal pressure p varying continuously from pmin to pmax. Determine the thickness t for an ultimate strength Su, modified endurance limit Se, and a safety ...

Verified Answer: