Mohr Circle Calculations

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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

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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:

    1. sigmaX, sigmaZ, and tauXZ

    2. 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:

    1. sigma = normal stress on an inclined plane

    2. tau = shear stress on an inclined plane

  • MohrCircle.calc outputs a five-element list containing Mohr Circle calculations:

    1. C = center of Mohr circle

    2. R = radius of Mohr circle

    3. sigma = vector of normal stresses for Mohr circle

    4. tau = vector of shear stresses for Mohr circle

    5. 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:

    1. sigma1 = magnitude of major principal stress

    2. sigma3 = magnitude of minor principal stress

    3. theta1 = direction of major principal stress (deg)

    4. 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:

    1. tauMax = maximum in-plane shear stress

    2. theta = angle of maximum in-plane shear stress

Author(s)

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

Examples

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##  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)