Fatigue Failure Resulting from Variable Loading

A rectangular filleced bar as shown in figure below is subjected to a fluctusting force $F$ that varies from $20N$ to $500$ N at the end of this bar at $\text{'}$ C $\text{'}.$ Another end of this bar at $\text{'}$ N $\text{'}$ are fixed to the wall. This har has a length of $110$ mm from $\text{'}A\text{'}$ to $\text{'}$B$\text{'}$ and $170$ mm from $\text{'}$ B $\text{'}$ to $\text{'}$ C $".$ This bar is made of AISI $1050$ cold$-$drawn steel. This bar has a thickness of $5$ mm $,$ a mactine surface finish and $90\%$ reliability. Clange the X$,$ Y and Z$,$ tem with your matric card number last three digits. Foe cumple. if your matrix card number is ADI$50179,$ X$=1.$ Y$=7$ and $Z=9.$

a$)$ Because this bar has a discontinuity geomerry at $"$B$\text{'},$ compute fatigue stres

$(2$ marls$)$

concentration factor, $K_{\frac{?}{?}}$ at this location.

b$)$ Calculate all stresses acting at $"A"$ and $\text{'}$ B $\text{'}$ location. Then determine which

$(6$ marls$)$

location from this two point will be the most critical.

c$)$ Determine endurance limits$,S,$ for this part at the critical location.

$(3$ marla$)$

d$)$ Calculate safety factor, $(N)$ of this pant by uxing modified Goodman line theories.

$(2$ mark$)$

Cinc a conclusion for your answer?

c$)$ Sketch the Goodman line, Yield $($Larger$)$ line and include it with the load line in

$(2$ marks$)$

fatigue diagram.

X$=0$

Y$=2$

Z$=8$