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from sympy import *
init_printing(use_latex='mathjax')
from IPython import display
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display.SVG('oiq-exam-1.svg')
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from sdutil2 import SD, FEF
var('EI theta_a theta_b theta_c theta_d')
Mab,Mba,Vab,Vba = SD(6,EI,theta_a,theta_b) + FEF.p(6,180,4)
Mbc,Mcb,Vbc,Vcb = SD(8,2*EI,theta_b,theta_c) + FEF.udl(8,45)
Mcd,Mdc,Vcd,Vdc = SD(6,EI,theta_c,theta_d)
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Mab
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Solve equilbrium equations for rotations:
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soln = solve( [Mab,Mba+Mbc,Mcb+Mcd,Mdc],[theta_a,theta_b,theta_c,theta_d] )
soln
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Member end moments:
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[m.subs(soln) for m in [Mab,Mba,Mbc,Mcb,Mcd,Mdc]]
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Member end shears:
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[v.subs(soln).n(4) for v in [Vab,Vba,Vbc,Vcb,Vcd,Vdc]]
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Reactions:
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Ra = Vab
Rb = Vbc - Vba
Rc = Vcd - Vcb
Rd = -Vdc
[r.subs(soln).n(4) for r in [Ra,Rb,Rc,Rd]]
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# sum forces in vertical dirn.
(Ra+Rb+Rc+Rd - 180 - 45*8).subs(soln)
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# sum moments about left
(-Rb*6 - Rc*(6+8) -Rd*(6+8+6) + 180*4 + 45*8*(6 + 8/2.)).subs(soln)
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Ra.expand()
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