- #1

spggodd

- 38

- 0

## Homework Statement

My problem is how to calculate the Shear Flow Distribution through this open cross-section.

The section has a uniform thickness of 2mm and all other dimensions are on the attached picture.

There is also a 100 kN downwards force applied.

## Homework Equations

q(s) = q(s

_{0}) = {(I

_{xx}V

_{x}(z) - I

_{yx}V

_{x}(z)) / (I

_{yy}I

_{xx}- I

_{xy}

^{2})} ∫

^{s}

_{0}tx*ds - {(I

_{yy}V

_{y}(z) - I

_{yx}V

_{x}(z)) / (I

_{yy}I

_{xx}- I

_{yx}

^{2})} ∫

^{s}

_{0}ty*ds

Where the:

I terms are the second moment of areas.

V terms relate to the applied force.

t is the thickness

y is the distance to the overall centroid of the part from the centroid of the sub-section under consideration.

ds is the distance along the sub-section.

For the rectangular sections 1 - 4 I have simplified the equation to:

q(s)=q(s

_{0})-(V

_{y}(z)/I

_{xx})∫

^{s}

_{0}ty*ds

## The Attempt at a Solution

I have calculated the Second Moment of Area (500.172x10

^{-6}) m

^{4}

I have calculated all the shears flows up until point 4 on the diagram.

To the left of point 4 is a small rectangular area which I have chosen to neglect, therefore I am concentrating on the Shear Flow around a the remaining quarter annulus which will bring me back to the x-axis.

At point 4 I believe the initial shear stress = 90.168 N/mm based on my workings through the rest of the cross-section up to this point.

I am now stuck at the annulus and I can't seem to find anything in books or my course notes etc..

Thank you for your time.

Steve