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Bf=1500//width of flange, in mm
Bw=300//breadth of web, in mm
Df=100//thickness of flange, in mm
d=700//effective depth, in mm
sigma_cbc=5//in MPa
sigma_st=140//in MPa
m=18.66//modular ratio
Ast=8*0.785*25^2//eight 25 mm dia bars, in sq mm
//assume x < Df; find x using Bf(x^2)/2=mAst(d-x), which becomes of the form px^2+qx+r=0
p=Bf/2
q=m*Ast
r=-m*Ast*d
//solving quadratic equation
x=(-q+sqrt(q^2-4*p*r))/(2*p)//in mm
//x > Df; hence our assumption is incorrect; equating moments of area on compression and tension sides about N.A.
x=(m*Ast*d+Bf*Df^2/2)/(m*Ast+Bf*Df)//in mm
//to find critical depth of neutral axis
Xc=d/(1+sigma_st/(m*sigma_cbc))//in mm
//as x < Xc, beam is under-reinforced
sigma_cbc=sigma_st/m*x/(d-x)//in MPa
sigma_cbc_dash=sigma_cbc*(x-Df)/x//in MPa
//to find lever arm
z=d-(sigma_cbc+2*sigma_cbc_dash)/(sigma_cbc+sigma_cbc_dash)*Df/3//in mm
Mr=Bf*Df*(sigma_cbc+sigma_cbc_dash)*z/2//in N-mm
mprintf("Moment of resistance of the beam=%f kN-m", Mr/10^6)
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