mods.stress_transformation

Module Contents

Functions

average_normal_stress(sigma_x, sigma_y)	Calculate the average normal stress.
normal_stress_transform(sigma_x, sigma_y, tau_xy, theta)	Calculate the normal stress on an inclined plane.
shear_stress_transform(sigma_x, sigma_y, tau_xy, theta)	Calculate the shear stress on an inclined plane.
principal_stress(sigma_x, sigma_y, tau_xy)	Calculate the principal stress.
principal_stress_angle(sigma_x, sigma_y, tau_xy)	Calculate the principal stress angle.
maximum_in_plane_shear_stress(sigma_x, sigma_y, tau_xy)	Calculate the maximum in-plane shear stress.
maximum_in_plane_shear_stress_angle(sigma_x, sigma_y, ...)	Calculate the maximum in-plane shear stress angle.
mohrs_circle(sigma_x, sigma_y, tau_xy)	Calculate the center and radius of the Mohr's circle.
mohrs_circle_plot(sigma_x, sigma_y, tau_xy)	Plot the Mohr's circle.
mohrs_circle_stress(sigma_x, sigma_y, tau_xy, theta)	Calculate the normal and shear stresses on an inclined plane.
mohrs_circle_stress_plot(sigma_x, sigma_y, tau_xy, theta)	Plot the normal and shear stresses on an inclined plane on the Mohr's circle.
mohrs_circle_plane_angle(sigma_x, sigma_y, tau_xy, theta)	Calculate the angle of the plane that has the normal and shear stresses on the Mohr's circle.
mohrs_circle_plane_angle_plot(sigma_x, sigma_y, ...)	Plot the angle of the plane that has the normal and shear stresses on the Mohr's circle.

mods.stress_transformation.average_normal_stress(sigma_x, sigma_y)

Calculate the average normal stress.

Parameters:

• sigma_x (float) – Normal stress in the x direction.

• sigma_y (float) – Normal stress in the y direction.

Returns:

Average normal stress.

Return type:

float

mods.stress_transformation.normal_stress_transform(sigma_x, sigma_y, tau_xy, theta)

Calculate the normal stress on an inclined plane.

Parameters:

• sigma_x (float) – Normal stress in the x direction.

• sigma_y (float) – Normal stress in the y direction.

• tau_xy (float) – Shear stress in the x-y plane.

• theta (float) – Angle of the inclined plane in degrees.

Returns:

Normal stress on the inclined plane in the x’ and y’ directions.

Return type:

tuple

mods.stress_transformation.shear_stress_transform(sigma_x, sigma_y, tau_xy, theta)

Calculate the shear stress on an inclined plane.

Parameters:

• sigma_x (float) – Normal stress in the x direction.

• sigma_y (float) – Normal stress in the y direction.

• tau_xy (float) – Shear stress in the x-y plane.

• theta (float) – Angle of the inclined plane in degrees.

Returns:

Shear stress on the inclined plane.

Return type:

float

mods.stress_transformation.principal_stress(sigma_x, sigma_y, tau_xy)

Calculate the principal stress.

Parameters:

• sigma_x (float) – Normal stress in the x direction.

• sigma_y (float) – Normal stress in the y direction.

• tau_xy (float) – Shear stress in the x-y plane.

• stress_type (str) – ‘max’ for major principal stress, ‘min’ for minor principal stress.

Returns:

Major and minor principal stresses.

Return type:

tuple

mods.stress_transformation.principal_stress_angle(sigma_x, sigma_y, tau_xy)

Calculate the principal stress angle.

Parameters:

• sigma_x (float) – Normal stress in the x direction.

• sigma_y (float) – Normal stress in the y direction.

• tau_xy (float) – Shear stress in the x-y plane.

Returns:

Principal stress angle in degrees.

Return type:

float

mods.stress_transformation.maximum_in_plane_shear_stress(sigma_x, sigma_y, tau_xy)

Calculate the maximum in-plane shear stress.

Parameters:

• sigma_x (float) – Normal stress in the x direction.

• sigma_y (float) – Normal stress in the y direction.

• tau_xy (float) – Shear stress in the x-y plane.

Returns:

Maximum in-plane shear stress.

Return type:

float

mods.stress_transformation.maximum_in_plane_shear_stress_angle(sigma_x, sigma_y, tau_xy)

Calculate the maximum in-plane shear stress angle.

Parameters:

• sigma_x (float) – Normal stress in the x direction.

• sigma_y (float) – Normal stress in the y direction.

• tau_xy (float) – Shear stress in the x-y plane.

Returns:

Maximum in-plane shear stress angle in degrees.

Return type:

float

mods.stress_transformation.mohrs_circle(sigma_x, sigma_y, tau_xy)

Calculate the center and radius of the Mohr’s circle.

Parameters:

• sigma_x (float) – Normal stress in the x direction.

• sigma_y (float) – Normal stress in the y direction.

• tau_xy (float) – Shear stress in the x-y plane.

Returns:

(center, radius) of the Mohr’s circle.

Return type:

tuple

mods.stress_transformation.mohrs_circle_plot(sigma_x, sigma_y, tau_xy)

Plot the Mohr’s circle.

Parameters:

• sigma_x (float) – Normal stress in the x direction.

• sigma_y (float) – Normal stress in the y direction.

• tau_xy (float) – Shear stress in the x-y plane.

Returns:

Mohr’s circle plot.

Return type:

matplotlib.pyplot.plot

mods.stress_transformation.mohrs_circle_stress(sigma_x, sigma_y, tau_xy, theta)

Calculate the normal and shear stresses on an inclined plane.

Parameters:

• sigma_x (float) – Normal stress in the x direction.

• sigma_y (float) – Normal stress in the y direction.

• tau_xy (float) – Shear stress in the x-y plane.

• theta (float) – Angle of the inclined plane in degrees.

Returns:

(sigma_n, tau_n) on the inclined plane.

Return type:

tuple

mods.stress_transformation.mohrs_circle_stress_plot(sigma_x, sigma_y, tau_xy, theta)

Plot the normal and shear stresses on an inclined plane on the Mohr’s circle.

Parameters:

• sigma_x (float) – Normal stress in the x direction.

• sigma_y (float) – Normal stress in the y direction.

• tau_xy (float) – Shear stress in the x-y plane.

• theta (float) – Angle of the inclined plane in degrees.

Returns:

Normal and shear stresses on the inclined plane on the Mohr’s circle.

Return type:

matplotlib.pyplot.plot

mods.stress_transformation.mohrs_circle_plane_angle(sigma_x, sigma_y, tau_xy, theta)

Calculate the angle of the plane that has the normal and shear stresses on the Mohr’s circle.

Parameters:

• sigma_x (float) – Normal stress in the x direction.

• sigma_y (float) – Normal stress in the y direction.

• tau_xy (float) – Shear stress in the x-y plane.

• theta (float) – Angle of the inclined plane in degrees.

Returns:

Angle of the plane that has the normal and shear stresses on the Mohr’s circle in degrees.

Return type:

float

mods.stress_transformation.mohrs_circle_plane_angle_plot(sigma_x, sigma_y, tau_xy, theta)

Plot the angle of the plane that has the normal and shear stresses on the Mohr’s circle.

Parameters:

• sigma_x (float) – Normal stress in the x direction.

• sigma_y (float) – Normal stress in the y direction.

• tau_xy (float) – Shear stress in the x-y plane.

• theta (float) – Angle of the inclined plane in degrees.

Returns:

Angle of the plane that has the normal and shear stresses on the Mohr’s circle.

Return type:

matplotlib.pyplot.plot