Completed an example with matching results. Starting to understand.

I am beginning to understand how to iterate over series of neutral axis
locations and curvature values to generate a P-M Interaction diagram.

This is a very rudamentary example but just working through the basics to
understand.

The example is from Design of Concrete Structure by Nilson, Darwin, Dolan
pp. 274-276. I didn't implement the whole thing just used it to check
logic in a few places.

example.py

@@ -0,0 +1,57 @@
+import math
+import matplotlib.pyplot as plt
+
+c_start = 0.0
+c_end = 20.0
+num_steps = 100
+c_step = (c_end-c_start)/num_steps
+
+eu = 0.003
+Es = 29000000
+fy = 60000
+fc = 4000
+Ec = 57000*math.sqrt(4000)
+h = 20
+b = 12
+d = 17.5
+dp = 2.5
+As = 2.0
+Asp = 2.0
+
+P = []
+M = []
+
+for x in range(num_steps):
+    if x == 0:
+        c = c_step
+    else:
+        c = c + c_step
+
+    phi = math.log(eu/c, 10)
+
+    a = 0.85*c
+    es = eu*(d-c)/c
+    fs = min(Es*es,fy)
+    esp = eu*(c-dp)/c
+    fsp = min(Es*esp,fy)
+    C = 0.85*fc*a*b
+    Pn = C-fs*As+fsp*Asp
+    Mn = C*(h/2-a/2)+Asp*fsp*(h/2-dp)+As*fs*(d-h/2)
+
+    out = ('c: {8}\na: {0}\nes: {1}\nfs: {2}\nesp: {3}\nfsp: {4}\nC: {5}\nPn:'
+        '{6}\nMn: {7}'.format(a,es,fs,esp,fsp,C,Pn,Mn,c))
+    print out
+
+    pause = raw_input(">")
+
+    P.append(Pn)
+    M.append(Mn)
+
+
+plt.plot(M,P,".")
+
+plt.show()
+
+def beta1(fc):
+    return 0.85-0.05*(fc-4000)/1000
+