Mohr's Circle: Difference between revisions

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Mohr's circle is a tool for analyzing element stress. The drawing below shows mohr's circle and some of the relavent points of interest.

Given a state of stress, $(σ_{x}, σ_{y}, τ_{x y})$ , we can calculate the principle stresses,

$σ_{1} = \frac{1}{2} (σ_{x} + σ_{y}) + \frac{1}{2} \sqrt{{(σ_{x} - σ_{y})}^{2} + 4 τ_{x y}^{2}}$

$σ_{2} = \frac{1}{2} (σ_{x} + σ_{y}) - \frac{1}{2} \sqrt{{(σ_{x} - σ_{y})}^{2} + 4 τ_{x y}^{2}}$

Revision as of 16:47, 4 July 2006 view source Stephens (talk \| contribs) Bureaucrats, Administrators 1,090 edits m →Mohr's Circle for 2D ← Older edit		Latest revision as of 16:47, 4 July 2006 view source Stephens (talk \| contribs) Bureaucrats, Administrators 1,090 edits mNo edit summary
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	<math>\sigma_2=\frac{1}{2}\left(\sigma_x+\sigma_y\right)-\frac{1}{2}\sqrt{\left(\sigma_x-\sigma_y\right)^2+4\tau_{xy}^2}</math>		<math>\sigma_2=\frac{1}{2}\left(\sigma_x+\sigma_y\right)-\frac{1}{2}\sqrt{\left(\sigma_x-\sigma_y\right)^2+4\tau_{xy}^2}</math>

			==Mohr's Circle for 3D==