A) 3\[\sigma \]
B) 2\[\sigma \]
C) \[\sigma \]
D) Zero
Correct Answer: B
Solution :
\[{{\sigma }_{1,2}}=\frac{1}{2}({{\sigma }_{d}}+{{\sigma }_{b}})\pm \frac{1}{2}\sqrt{{{({{\sigma }_{d}}-{{\sigma }_{b}})}^{2}}+4{{\tau }^{2}}}\] \[=\frac{1}{2}(-\sigma +\sigma )\pm \frac{1}{2}\sqrt{{{(-\sigma -\sigma )}^{2}}+4\times 3{{\sigma }^{2}}}\] \[=0\pm \frac{1}{2}\sqrt{4{{\sigma }^{2}}+12{{\sigma }^{2}}}\] \[=\pm \,\,2\sigma \] Maximum compressive stress \[=2\sigma \]
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