Question
Download Solution PDFएक समतल प्रतिबल की स्थिति पर विचार कीजिए, जहाँ σx = 3 Pa, σy = 1 Pa और τxy = 1 Pa है। मुख्य निर्देशों में से एक x-अक्ष के संबंध में ________ होगा।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
\({\sigma _{1,2}} = \left( {\frac{{{\sigma _x} + {\sigma _y}}}{2}} \right) + \left( {\frac{{{\sigma _x} - {\sigma _y}}}{2}} \right)\cos2\theta + {\tau _{xy}}\sin2\theta \)
\(\tau _{xy}^* = - \left( {\frac{{{\sigma _x} - {\sigma _y}}}{2}} \right)\sin2\theta + {\tau _{xy}}\cos2\theta \)
At the principal plane, the value of shear stress is 0. i.e.\(\tau _{xy}^* =0\)
Calculation:
Given:
\(\tau_{xy}^*=0\)
\( - \left( {\frac{{{\sigma _x} - {\sigma _y}}}{2}} \right)\sin2\theta + {\tau _{xy}}\cos2\theta = 0\)
\(\left( {\frac{{{\sigma _x} - {\sigma _y}}}{2}} \right)\sin2\theta = {\tau _{xy}}\cos2\theta \)
\(\left( {\frac{{3 - 1}}{2}} \right)\sin2\theta = \cos2\theta \)
\(\sin2\theta = \cos2\theta \)
\(\tan2\theta=1\)
\(2\theta=45^\circ\)
\(\therefore \theta = {22.5^\circ}\)
Last updated on Jun 13, 2025
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