STRESS CONCENTRATION
ABSTRACT
Main purpose of this experiment is to simply determine the stress concentration factor in vicinity of the geometric discontinuity in a beam. For the detection of trends in strain form the notch several strain gages are used. This data is then used to empirically find the experimental strain on the opposite side in order to calculate the elastic stress concentration factor, k.
Introduction
Geometric irregularities on loaded members can dramatically change stresses in the structure that leads to a region of stress concentration. The abrupt change in cross sections cause the stress “flow lines” to crowd causing high stress concentration. To mitigate this phenomenon, smoother changes such as fillet radii are introduced in structural members that make the “flow lines” less crowded causing lower stress concentrations. A simple irregularity, a drilled hole, is studied within this experiment such that the effects of this feature can be analyzed and explored. Extensive research into the effects of these discontinuities, called "stress-risers" has been conducted previously. A standard means of computing the maximum theoretical stress around an irregularity is found by the stress concentration factor, K
The theoretical stress concentration factor, K is defined in terms of maximum (or peak) stress, σmax and nominal (or average or far-field) stress, σnom as:
K = σmax/σnom Eq-1
Using the hook’s law,
K = εmax/εnom Eq-2
For a hole, the maximum stress is always found at the closest position to the discontinuity. The nominal stress refers to the ideal stress based on the net area of the section.
The value for stress can be calculated with the following formula,
σ = 6P(L-x)/bt2 Eq-3
Where,
P is the magnitude of the force applied
L is the longitudinal length from the clamp to the load
x is the longitudinal distance from the clamp to the cross sectional area being inspected
b is the base dimension of the beam
t is the thickness of the beam
The nominal stress for a cross sectional area with a hole can be expressed as:
σ = 6P(L-x)/(b-d)t2 Eq-4
where d is the diameter of the hole
Procedure and Experimental Data
An aluminum beam of stated geometry was used in the experiment.
Beam Geometry
Material Type Al
Leangth, L 8
Width, H 1.5
Thickness, t 1/8
Semicircle radius, r 7/32
In measuring stress concentration with a strain gauge it was kept in mind that the gage tends to indicate the average strain in the area covered by the grid. The three gages was apeelid on the aluminum bar and readings were taken and recorded in table 1.
Measure the strain for three different loading values
Table 1. Experimental strain per load
Load
|
Load
|
Gage 1
Circle edge
|
Gage 2
Axial axis
|
Gage 3 far edge
|
P (gr)
|
P(lb)
| |||
100
|
0.22
|
1.16E-4
|
1.10E-4
|
0.52E-4
|
150
|
0.33
|
2.25E-4
|
2.02E-4
|
1.20E-4
|
200
|
0.44
|
3.26E-4
|
2.90E-4
|
1.75E-4
|
Results and Analysis
The above stated equation were used to calculate the stress values and later the strain values by applying the hook’s law and recording in the table below
Load
|
Load
|
Gage 1
Circle edge
|
Gage 2
Axial axis
|
Gage 3 far edge
|
Calculated Strain
|
K
|
P (gr)
|
P(lb)
| |||||
100
|
0.22
|
1.16E-4
|
1.10E-4
|
0.52E-4
|
1.9E-5
|
1.48
|
150
|
0.33
|
2.25E-4
|
2.02E-4
|
1.20E-4
|
2.96E-5
|
1.51
|
200
|
0.44
|
3.26E-4
|
2.90E-4
|
1.75E-4
|
3.9E-5
|
1.39
|
Conclusion
Overall this experiment, gone successful, due to the consistent stress concentration factor. Using three stress gages to notice the pressure focus pattern was also very useful. This research reveals how an abnormity can absolutely modify the pressure withdrawals and focus.
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