Solving Stress Concentration for Elliptical Hole in Square Panel

[raunakm]

Homework Statement

Square panel , elliptical hole, uniform pressure p in x direction. calc stress at end of minor axis. pt A

L=40in p=10psi a=1in b=0.5 in t=0.2 in

Homework Equations

i know that stress at end will be max stress multiplied by stress conc. factor.
bt i don't know how to calc stress conc. factor for an elliptical hole

The Attempt at a Solution

Kt = stress x (1 + 2b/a)

is this correct?

 

[mgb_phys]

Can't read the diagram but it's normally 1+2(a/b) where a is the length and b is the width.
So as the width gets smaller or the length is longer - the concentration gets bigger!

Alternatively it's sqrt(crack_length/radius)

 

[Moetasim]

As a scientist, it is important to always provide a clear and comprehensive response. Firstly, the attempt at a solution is on the right track. The stress concentration factor for an elliptical hole in a square panel can be calculated using the equation Kt = stress x (1 + 2b/a), where a and b are the major and minor axis lengths of the ellipse, respectively. In this case, a = 1in and b = 0.5in.

However, it is also important to consider the type of loading and material properties in order to accurately calculate the stress at the end of the minor axis. In this problem, a uniform pressure is applied in the x-direction, which will result in a biaxial stress state at the end of the minor axis. The maximum stress can be calculated using the equation σmax = p*t/(π*a*b), where p is the applied pressure, t is the panel thickness, and a and b are the major and minor axis lengths of the ellipse, respectively.

Once the maximum stress is calculated, it can be multiplied by the stress concentration factor to obtain the stress at the end of the minor axis. It is also important to note that the stress concentration factor may vary for different loading conditions and material properties, so it is important to ensure that the correct equation is being used for the specific problem being solved.

In conclusion, the attempt at a solution is on the right track, but it is important to consider all relevant equations and factors in order to accurately calculate the stress at the end of the minor axis for an elliptical hole in a square panel.