I'm working on a problem but I've hit a road block..(adsbygoogle = window.adsbygoogle || []).push({});

Then the cross section of the piece is here:

The first part of the problem is to determine Iy, Iz, and Iyz of the member.. I found the y value of the centroid to be 2.8587" and the z value of the centroid to be 1.0734" using the bottom left corner as the origin. From there I did the following:

Iz = 1/12(5)(.5)^{3}+ 2.5(.25 - 2.8587)^{2}+ 1/12(.625)(7.5)^{3}+ 4.6875(.3125 - 1.0734)^{2}

and something similar for Iy and Iyz. All said and done I got

Iz = 48.112 in^{4}

Iy = 13.163 in^{4}

Iyz = -14.266 in^{4}

Anywho, I then used that to get:

Where I1 = 53.196 in^{4}

and I2 = 8.0788 in^{4}

Radius of gyration:

Rmax = 2.7205 in

Rmin = 1.0602 in

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The next part of the problem is to find the max stress (be it tensile or compressive) at the far left hand side. I calculated the reaction force of the support to be 6562.5 lbf in the negative Y direction (the opposite of V_{y}in picture 2) and no moments at all which makes sense considering that the far left side is essentially "exposed" to air.

Am I correct to treat this like V_{y}is simply negative? Another part of me wants to say that the reaction force from the support is applied to the bottom of the member and I don't know if that changes anything or not..

It seems that the max stress will be solely from the shear stress caused by the support force? I'm trying to figure that out but my book only covered shear stress for symmetrical beams. I remember my professor saying something about using just the webbing for the shear analysis(?) Like treat it as if only the vertical, 8 inch high, .625 inch thick webbing was there then do a simple shear analysis on that piece.. Can somebody point me in the right direction please?

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# Strength of Materials- Asymmetric, simply supported beam problem

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