5. Mohr Circle

Tobias Stephan

2025-10-03

library(structr)
library(ggplot2)

Some basic calculations:

# Define the magnitudes of the principal stress axes
s1 <- 1025 # maximum stress, sigma 1
s2 <- 400 # intermediate stress, sigma 2
s3 <- 250 # minimum stress, sigma 3

# Differential stress
diff_stress(s1, s3)
#> [1] 775

# Mean stress
mean_stress(s1, s3)
#> [1] 637.5

# Shear stress at given angle
shear_stress(s1, s3, theta = 35)
#> [1] 364.1309

# Normal stress at given angle
normal_stress(s1, s3, theta = 35)
#> [1] 504.9672

# Angle of fracture for given coefficient of internal friction
fracture_angle(mu = 0.6)
#> [1] 60.48188

To plot the Mohr circle:

ggMohr(sigma1 = s1, sigma2 = s2, sigma3 = s3, unit = "MPa") +
  theme_classic()