# Mohr Circle Calculations

### Description

These functions are used to calculate the different parameters associated with Mohr Circle:

`sigmaTrans`

performs stress-transformation calculations at a specific angle of inclination`MohrCircle.calc`

performs calculations associated with the Mohr Circle (stress transformation over a range of angles)`MohrCircle.plot`

creates a plot of the Mohr Circle for a given state of stress`sigma13`

calculates the magnitudes and orientations of the principal stresses`tauMax`

calculates the magnitude and orientation of the maximum in-plane shear stress

### Usage

1 2 3 4 5 6 7 8 9 | ```
sigmaTrans(theta, sigmaX = NA, sigmaZ = NA, tauXZ = NA,
sigma1 = NA, sigma3 = NA)
MohrCircle.calc(sigmaX = NA, sigmaZ = NA, tauXZ = NA,
sigma1 = NA, sigma3 = NA,
theta = seq(from = 0, to = 180, by = 1))
MohrCircle.plot(sigmaX = NA, sigmaZ = NA, tauXZ = NA,
sigma1 = NA, sigma3 = NA, metric = TRUE)
sigma13(sigmaX, sigmaZ, tauXZ)
tauMax(sigmaX, sigmaZ, tauXZ)
``` |

### Arguments

`sigmaX` |
normal stress acting in the horizontal direction |

`sigmaZ` |
normal stress acting in the vertical direction |

`tauXZ` |
shear stress acting on the same plane as sigmaX |

`sigma1` |
major principal stress |

`sigma3` |
minor principal stress |

`theta` |
angle of inclination (degrees) [see details below] |

`metric` |
units, if TRUE units are SI, if FALSE units are English |

### Details

For sigmaTrans, MohrCircle.calc, and MohrCircle.plot, One of the following two sets of data must be entered:

sigmaX, sigmaZ, and tauXZ

sigma1 and sigma3

In functions sigmaTrans and MohrCircle.calc, if theta is entered in conjunction with sigmaX, sigmaZ, and tauXZ, it is interpreted as the angle of inclination above the horizontal. If theta is entered in conjunction with the principal stresses, then it is interpreted as the angle of inclination above the major principal plane.

Note that theta is required for sigmaTrans, optional for MohrCircle.calc, and not used in MohrCircle.plot, sigma13, and tauMax.

### Value

`sigmaTrans`

outputs a two-element list containing the results of the stress-transformation calculations:sigma = normal stress on an inclined plane

tau = shear stress on an inclined plane

`MohrCircle.calc`

outputs a five-element list containing Mohr Circle calculations:C = center of Mohr circle

R = radius of Mohr circle

sigma = vector of normal stresses for Mohr circle

tau = vector of shear stresses for Mohr circle

theta = vector of angles (deg)

`MohrCircle.plot`

produces a plot of Mohr Circle; no numerical calculations are output from the function.`sigma13`

outputs a four-element list containing the magnitudes and directions of the principal stresses:sigma1 = magnitude of major principal stress

sigma3 = magnitude of minor principal stress

theta1 = direction of major principal stress (deg)

theta3 = direction of minor principal stress (deg)

`tauMax`

outputs a two-element list containing the magnitude and direction of the maximum in-plane shear stress:tauMax = maximum in-plane shear stress

theta = angle of maximum in-plane shear stress

### Author(s)

James Kaklamanos <kaklamanosj@merrimack.edu> and Kyle Elmy <ElmyK@merrimack.edu>

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 | ```
## Example code for Stress Transformation
sigmaTrans(sigmaX = 80, sigmaZ = 120, tauXZ = 20, theta = 78)
## Example code for Mohr Circle Calculations
MohrCircle.calc(theta = 20, sigmaX = 80, sigmaZ = 120, tauXZ = 20)
## Example code for Mohr Circle Plot
MohrCircle.plot(sigmaX = 80, sigmaZ = 120, tauXZ = 20, metric = FALSE)
## Example code for Principal Stresses
sigma13(sigmaX = 80, sigmaZ = 120, tauXZ = 20)
## Example code for Maximum In-Plane Shear Stress
tauMax(sigmaX = 80, sigmaZ = 120, tauXZ = 20)
``` |