## Endurance Limit

A mechanism has a 0.5 inch diameter rod made from a AISI 1012 hot rolled steel plate. The steel has a yield strength of 210 MPA and an ultimate tensile strength of 375 MPa. Determine the effect of the fatigue stress concentration factor on the endurance limit if the fatigue stress concentration factor K = 1.125 is used for a bolt hole located at the rod's end.

##
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__**Hint**

**Hint**

$$$S_{endurance}=K_{endurance}\cdot S_{endurance}'$$$

$$$S_{endurance}'=(0.5)(S_{ultimate})$$$

$$$K_{endurance}=\frac{1}{K_{fatigue}}$$$

$$K_{fatigue}$$
will adversely affect the endurance limit.

$$$K_{endurance}=\frac{1}{K_{fatigue}}=\frac{1}{1.125}=0.889$$$

There are two equations to determine the endurance limit. However,
$$S_{ultimate}$$
, which is given as 375 MPa, is less than or equal to 1400 MPa, the equation is:

$$$S_{endurance}'=(0.5)(S_{ultimate})=(0.5)(375 \:MPa)= 187.5 \:MPa$$$

Solving for
$$S_{endurance}$$
:

$$$S_{endurance}=K_{endurance}\cdot S_{endurance}'=(0.889)(187.5\:MPa)=166.7\:MPa$$$

166.7 MPa