Mohr's Circle is a graphical method used to determine principal stresses, maximum shear stress, and stress transformations from a given 2D stress state. A circle is drawn on a normal stress (σ) vs. shear stress (τ) plane, with the center at ((σx + σy) / 2, 0) and a radius derived from the stress components. It is an essential tool in mechanical and civil engineering for visualizing how stress components change under coordinate rotation.
#' anyplot.ai
#' mohr-circle: Mohr's Circle for Stress Analysis
#' Library: ggplot2 3.5.1 | R 4.4.1
#' Quality: 89/100 | Created: 2026-05-30
library(ggplot2)
library(ragg)
# Theme tokens (Imprint palette — theme-adaptive chrome)
THEME <- Sys.getenv("ANYPLOT_THEME", "light")
PAGE_BG <- if (THEME == "light") "#FAF8F1" else "#1A1A17"
INK <- if (THEME == "light") "#1A1A17" else "#F0EFE8"
INK_SOFT <- if (THEME == "light") "#4A4A44" else "#B8B7B0"
INK_MUTED <- if (THEME == "light") "#6B6A63" else "#A8A79F"
IMPRINT_PALETTE <- c(
"#009E73", # 1 brand green — circle + principal stress markers
"#C475FD", # 2 lavender
"#4467A3", # 3 blue — point A
"#BD8233", # 4 ochre — max shear stress points
"#AE3030", # 5 matte red — point B
"#2ABCCD", # 6 cyan
"#954477", # 7 rose
"#99B314" # 8 lime
)
# Stress state (MPa) — structural member under combined axial and shear loading
sigma_x <- 80
sigma_y <- -20
tau_xy <- 40
# Mohr's circle parameters
center_x <- (sigma_x + sigma_y) / 2
radius <- sqrt(((sigma_x - sigma_y) / 2)^2 + tau_xy^2)
sigma_1 <- center_x + radius
sigma_2 <- center_x - radius
tau_max <- radius
two_theta_p <- atan2(tau_xy, (sigma_x - sigma_y) / 2) * 180 / pi
# Circle path (360 points)
theta_seq <- seq(0, 2 * pi, length.out = 360)
circle_df <- data.frame(
x = center_x + radius * cos(theta_seq),
y = radius * sin(theta_seq)
)
# Arc showing 2θp angle (measured from horizontal to line C to A at center)
arc_r <- radius * 0.28
arc_seq <- seq(0, two_theta_p * pi / 180, length.out = 80)
arc_df <- data.frame(
x = center_x + arc_r * cos(arc_seq),
y = arc_r * sin(arc_seq)
)
mid_angle <- two_theta_p * pi / 360
arc_label_x <- center_x + arc_r * 1.5 * cos(mid_angle)
arc_label_y <- arc_r * 1.5 * sin(mid_angle)
# Build labels using paste0 with unicode escapes so Edit tool can match ASCII source
sigma_sym <- "σ"
tau_sym <- "τ"
theta_sym <- "θ"
deg_sym <- "°"
sub1 <- "₁"
sub2 <- "₂"
label_A <- paste0("A (", sigma_sym, "x=", sigma_x, ")")
label_B <- paste0("B (", sigma_sym, "y=", sigma_y, ")")
label_s1 <- paste0(sigma_sym, "1=", round(sigma_1, 1))
label_s2 <- paste0(sigma_sym, "2=", round(sigma_2, 1))
label_tmax <- paste0(tau_sym, "max=", round(tau_max, 1))
label_2tp <- paste0("2", theta_sym, "p=", round(two_theta_p, 1), deg_sym)
# Grid lines with alpha (major and minor differentiated)
grid_color <- adjustcolor(INK, alpha.f = 0.08)
grid_color_minor <- adjustcolor(INK, alpha.f = 0.05)
p <- ggplot() +
# Reference lines through center
geom_hline(yintercept = 0,
color = adjustcolor(INK_SOFT, alpha.f = 0.55),
linewidth = 0.5, linetype = "dashed") +
geom_vline(xintercept = center_x,
color = adjustcolor(INK_SOFT, alpha.f = 0.55),
linewidth = 0.5, linetype = "dashed") +
# Diameter line connecting A and B (passes through center C)
annotate("segment",
x = sigma_x, y = tau_xy, xend = sigma_y, yend = -tau_xy,
color = INK_MUTED, linewidth = 0.8, linetype = "dotted") +
# Mohr's circle (primary element — Imprint brand green)
geom_path(data = circle_df, aes(x = x, y = y),
color = IMPRINT_PALETTE[1], linewidth = 1.5) +
# Arc showing angle 2θp
geom_path(data = arc_df, aes(x = x, y = y),
color = INK_SOFT, linewidth = 0.7) +
# Center point (filled circle marker)
annotate("point", x = center_x, y = 0,
color = INK, fill = PAGE_BG, size = 3.5, shape = 21, stroke = 0.8) +
# Principal stress points sigma1, sigma2 (where circle meets sigma-axis)
annotate("point", x = sigma_1, y = 0,
color = "white", fill = IMPRINT_PALETTE[1], size = 5.5, shape = 23,
stroke = 0.5) +
annotate("point", x = sigma_2, y = 0,
color = "white", fill = IMPRINT_PALETTE[1], size = 5.5, shape = 23,
stroke = 0.5) +
# Maximum shear stress points (top and bottom of circle)
annotate("point", x = center_x, y = tau_max,
color = "white", fill = IMPRINT_PALETTE[4], size = 4.5, shape = 24,
stroke = 0.5) +
annotate("point", x = center_x, y = -tau_max,
color = "white", fill = IMPRINT_PALETTE[4], size = 4.5, shape = 25,
stroke = 0.5) +
# Stress point A (sigma_x, tau_xy) — upper right
annotate("point", x = sigma_x, y = tau_xy,
color = "white", fill = IMPRINT_PALETTE[3], size = 5.0, shape = 21,
stroke = 0.5) +
# Stress point B (sigma_y, -tau_xy) — lower left
annotate("point", x = sigma_y, y = -tau_xy,
color = "white", fill = IMPRINT_PALETTE[5], size = 5.0, shape = 21,
stroke = 0.5) +
# Label A: positioned to the left+above to stay within panel
annotate("text", x = sigma_x - 3, y = tau_xy + 6,
label = label_A,
color = IMPRINT_PALETTE[3], hjust = 1, vjust = 0, size = 3.8) +
# Label B: positioned to the right+below to stay within panel
annotate("text", x = sigma_y + 3, y = -tau_xy - 6,
label = label_B,
color = IMPRINT_PALETTE[5], hjust = 0, vjust = 1, size = 3.8) +
# Label sigma1: centered below intersection (outside lower arc)
annotate("text", x = sigma_1, y = -9,
label = label_s1,
color = INK, hjust = 0.5, vjust = 1, size = 3.8) +
# Label sigma2: centered below intersection (outside lower arc)
annotate("text", x = sigma_2, y = -9,
label = label_s2,
color = INK, hjust = 0.5, vjust = 1, size = 3.8) +
# Label tmax: to the left of top point (toward center)
annotate("text", x = center_x - 3, y = tau_max + 4,
label = label_tmax,
color = IMPRINT_PALETTE[4], hjust = 1, vjust = 0, size = 3.8) +
# Label 2thetap angle: near midpoint of arc
annotate("text", x = arc_label_x, y = arc_label_y,
label = label_2tp,
color = INK_SOFT, hjust = 0, vjust = 0.5, size = 3.0) +
coord_fixed(ratio = 1, clip = "off") +
labs(
x = paste0("Normal Stress ", sigma_sym, " (MPa)"),
y = paste0("Shear Stress ", tau_sym, " (MPa)"),
title = "mohr-circle · r · ggplot2 · anyplot.ai"
) +
theme_minimal(base_size = 8) +
theme(
plot.background = element_rect(fill = PAGE_BG, color = PAGE_BG),
panel.background = element_rect(fill = PAGE_BG, color = NA),
panel.grid.major = element_line(color = grid_color, linewidth = 0.3),
panel.grid.minor = element_line(color = grid_color_minor, linewidth = 0.15),
panel.border = element_rect(color = INK_SOFT, fill = NA, linewidth = 0.25),
axis.title = element_text(color = INK, size = 10),
axis.text = element_text(color = INK_SOFT, size = 8),
plot.title = element_text(color = INK, size = 12, face = "plain"),
plot.margin = margin(40, 50, 20, 30, "pt")
)
ggsave(
filename = sprintf("plot-%s.png", THEME),
plot = p,
device = ragg::agg_png,
width = 6,
height = 6,
units = "in",
dpi = 400
)
Runnable source as JSON, for any HTTP client: https://api.anyplot.ai/specs/mohr-circle/ggplot2/code. Any spec id and library id listed in llms-full.txt fit the same URL shape; every URL below is complete and callable.
{
"spec_id": "mohr-circle",
"language": "r",
"library": "ggplot2",
"page": "https://anyplot.ai/mohr-circle/r/ggplot2",
"hub": "https://anyplot.ai/mohr-circle",
"code_json": "https://api.anyplot.ai/specs/mohr-circle/ggplot2/code",
"spec_json": "https://api.anyplot.ai/specs/mohr-circle",
"render_light_png": "https://storage.googleapis.com/anyplot-images/plots/mohr-circle/r/ggplot2/plot-light.png",
"render_dark_png": "https://storage.googleapis.com/anyplot-images/plots/mohr-circle/r/ggplot2/plot-dark.png",
"quality_score": 89.0,
"license": "MIT",
"guide": "https://anyplot.ai/llms.txt"
}Part of Mohr's Circle for Stress Analysis on anyplot.ai.