rm(list=ls())
#
# Der Mohr'sche Spannungskreis
#
sigma3 <-  50  # kN/m^2    # 1. Hauptspannung
sigma1 <- 150  # kN/m^2   # 3. Hauptspannung
#
alpha <- 5    # ° Drehwinkel
alpha <- pi*alpha/180
#
# Der Kreis
#
narc <- 150
Arc <- seq(0,pi/2,pi/(2*narc))
fun_sigma <- function(sigma1,sigma3,Arc){
                0.5*((sigma1+sigma3)+(sigma1-sigma3)*cos(2*Arc))
             }
fun_tau   <- function(sigma1,sigma3,Arc){
                0.5*(sigma1-sigma3)*sin(2*Arc)
             }
tau   <- fun_tau(sigma1,sigma3,Arc)
sigma <- fun_sigma(sigma1,sigma3,Arc)
plot(sigma,tau,type="l",xlim=c(0,1.1*max(sigma)),asp=1,lwd=2,
       ylim=c(-5,1.2*max(tau)),pch=20,cex=0.8,col="darkgreen",
       main="Mohr-Coulomb'sche\nGrenzgerade",
       xlab=expression(paste("Normalspannung  ",sigma)),
       ylab=expression(paste("Scherspannung   ",tau)))
text(sigma[1],-5,expression(sigma[1]))
text(sigma[narc],-5,expression(sigma[3]))
#
# Scher- und Normalspannung der um alpha gedrehten Ebene
tau.p   <- fun_tau(sigma1,sigma3,alpha)
sigma.p <- fun_sigma(sigma1,sigma3,alpha)
points(sigma.p,tau.p,pch=16,cex=2,col="lightblue")
lines(c(0,sigma.p,sigma.p),c(tau.p,tau.p,0),lty=2,cex=1,col="blue")
text(sigma.p,-5,expression(sigma[p]),col="blue")
text(-4,tau.p,expression(tau[p]),col="blue")
lines(c(sigma[1],sigma[narc]),c(0,0),lty=3,col="red")
lines(c(sigma.p,sigma[narc]),c(tau.p,0),lty=3,col="red")
#text(sigma[narc]+cos(pi*beta/180)*20,3,expression(beta),col="red")
alpha.text.x <- sigma[narc]+(0.25*(pi/2-alpha)*(sigma1-sigma3))
text(alpha.text.x,2,expression(alpha),col="red")