# Homework Help: Maximum stress

1. Aug 23, 2011

### qwerty0123

trying yo figure this out:
the graph of stress concentration factor K for flat bars with a circular hole geometries are shown in the diagram link below. a load of 50kN is applied to the plate. the width of the plate b=100mm with a thickness of t=10mm

find the maximum stress for the following:
1. plate without hole
2. plate with hole (diameter 50mm)
3. how much is SCF? well k=nominal stress / maximum stress but im not sure how to get the maximum stress, is it s chart or the graph below?
http://imageshack.us/photo/my-images/15/scfvk.jpg/

this is what i have done so:
stress=P/A
p=50X10^3
A=(b-d)h = 50mm x 10mm = 500mmsquared = 0.0005m squared??

so nominal stress is = 50x10^3/0.0005 = 6000???

2. Aug 23, 2011

### qwerty0123

ive found the stress for the plate without the hole to be:
P/A
=
P/bt= 50000/0.001
=
50MPa

3. Aug 23, 2011

### qwerty0123

cant do the second bit though
cant find the correct area either

4. Aug 23, 2011

### PhanthomJay

Pick out the stress concentration factor based on the given dimensions and solve for the max stress near the hole using your formula.

5. Aug 23, 2011

### qwerty0123

how do i do that?

6. Aug 23, 2011

### PhanthomJay

Stress concentration factors are derived from the Theory of Elasticity. In this example, the stress concentration factor is plotted on the y axis and the d/b ratio is plotted on the x axis. Find the correct value of d/b on the x axis, and move up vertically until you hit the curve (hint, the SCF is somewhere in between 3 and 2.5). Once you determine the SCF, then use the formula given in the chart to calculate the max stress near the hole. Note that the reference (nominal) stress is calculated based on the cross section area of the plate minus the cross section area of the hole. You would get different SCF factors if you use the stress on the plate without the hole as your reference stress. I assume the graph given is given correctly.

7. Aug 24, 2011

### qwerty0123

i've got d/b to be 0.5 since d=50 and b=100 d/b=50/100 = 0.5
using the graph i get 2.2?

8. Aug 24, 2011

### PhanthomJay

Oh yeah that's about right I gave a bad hint because I wasn't looking at the graph and going from my incorrect memory of it from an earlier viewing, Sorry. So now that the SCF is 2.2, calculate the max stress near the hole using the formula given on the chart.

9. Aug 24, 2011

### qwerty0123

haha thats ok.....ive managed to get the maximum stress as 110MPa
since 2.2x50MPa = 110 000 000

thats part 2 done but what about part 3 the SCF?

10. Aug 24, 2011

### PhanthomJay

But the SCF factor is based on the nominal stress using the net section area at the hole, not the gross section area. Your answer is not correct.
You just told me that the SCF is 2.2!