@@ -871,12 +871,12 @@ The von Mises stress can be determined from the net axial and shear stress as fo
871871 Principal Stresses
872872^^^^^^^^^^^^^^^^^^
873873
874- For a cross section subjected to axial force, shear in the :math: `x` and :math`y` axes which are
874+ For a cross section subjected to axial force, shear in the :math: `x` and :math: `y` axes which are
875875perpendicular to the centroidal (:math: `z`) axis, and moments about all three axes, there are no
876876axial stresses in the :math: `x` or :math: `y` axes, and so the stress tensor is given by:
877877
878878.. math ::
879- \textbf {\sigma } = \begin {bmatrix} 0 & 0 & \tau _{zx} \\
879+ \boldsymbol {\sigma } = \begin {bmatrix} 0 & 0 & \tau _{zx} \\
880880 0 & 0 & \tau _{zy} \\
881881 \tau _{xz} & \tau _{yz} & \sigma _{zz}
882882 \end {bmatrix}
@@ -889,7 +889,7 @@ matrix through a coordinate transformation. Since this is the basic eigenvalue p
889889principal stresses are then given by:
890890
891891.. math ::
892- \det (\textbf {\sigma } - \lambda \textbf {I}) = 0
892+ \det (\boldsymbol {\sigma } - \lambda \textbf {I}) = 0
893893
894894 Of which the characteristic polynomial can then be written:
895895
@@ -899,9 +899,9 @@ Of which the characteristic polynomial can then be written:
899899 where the stress invariants :math: `I` are then given by [5]:
900900
901901.. math ::
902- I_1 &= \textnormal (\textbf {\sigma }) = \sigma _{zz} \\
903- I_2 &= \frac {1 }{2 }\left [ (\textnormal (\textbf {\sigma })^2 - \textnormal (\textbf {\sigma }^2 )) \right ] = -\tau _{zx}^2 - \tau _{yz}^2 \\
904- I_3 &= \det (\textbf {\sigma }) = 0
902+ I_1 &= \textnormal (\boldsymbol {\sigma }) = \sigma _{zz} \\
903+ I_2 &= \frac {1 }{2 }\left [ (\textnormal (\boldsymbol {\sigma })^2 - \textnormal (\boldsymbol {\sigma }^2 )) \right ] = -\tau _{zx}^2 - \tau _{yz}^2 \\
904+ I_3 &= \det (\boldsymbol {\sigma }) = 0
905905
906906 and thus, the cubic polynomial reduces to a quadratic, the two roots of which are then the first
907907and third principal stresses (with :math: `\sigma _2 = 0 `):
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