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clear
//
//
//Initilization of Variables
L=8000 //mm //Span of beam
w=40*10**6 //N/mm //udl
//I-section
//Flanges
b=100 //mm //Width
t=10 //mm //Thickness
D=400 //mm //Overall Depth
t2=10 //mm //thickness of web
//Calculations
//Let R_A and R_B be the Reactions at A & B respectively
R_A=w*2**-1*L*10**-9 //KN
//Shear force at 2m for left support
F=R_A-2*w*10**-6 //KN
//Bending Moment
M=R_A*2-2*w*10**-6 //KN-m
//M.I
I=1*12**-1*b*D**3-1*12**-1*(b-t)*(D-2*t2)**3 //mm**4
//Bending stress at 100 mm above N_A
f=M*10**6*I**-1*b
//Shear stress
q=F*10**3*(t*I)**-1*(b*t*(D-t)*2**-1 +t2*(b-t2)*145) //N/mm**2
p_x=-197.06 //N/mm**2
p_y=0 //N/mm**2
q=21.38 //N/mm**2
//Principal Stresses
P1=(p_x+p_y)*2**-1+(((p_x-p_y)*2**-1)**2+q**2)**0.5 //N/mm**2
P2=(p_x+p_y)*2**-1-(((p_x-p_y)*2**-1)**2+q**2)**0.5 //N/mm**2
//Max shear stress
q_max=(((p_x-p_y)*2**-1)**2+q**2)**0.5 //N/mm**2
//Result
printf("\n Principal Stresses are: %0.2f N/mm**2",P1)
printf("\n %0.2f N/mm**2",P2)
printf("\n Max shear stress %0.2f N/mm**2",q_max)
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