initial commit / add all books

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+Bf=1450//width of flange, in mm

+Df=120//thickness of flange, in mm

+d=400//effective depth, in mm

+m=13.33//modular ratio

+Ast=1800//in sq mm

+Asc=450//in sq mm

+top_cover=30//in mm

+M=200*10^6//in N-mm

+//assume x>Df; equating moments of area on compression and tension sides about N.A.

+x=(m*Ast*d+Bf*Df^2/2+(1.5*m-1)*Asc*top_cover)/(m*Ast+Bf*Df+(1.5*m-1)*Asc)//in mm

+//we find that x<Df, hence our assumption that x>Df is wrong

+//to find x using Bf(x^2)/2 + (1.5m-1)Asc(x-d')=mAst(d-x), which becomes of the form px^2+qx+r=0

+p=Bf/2

+q=m*Ast+(1.5*m-1)*Asc

+r=-(m*Ast*d+(1.5*m-1)*Asc*top_cover)

+//solving quadratic equation

+x=(-q+sqrt(q^2-4*p*r))/(2*p)//in mm

+//as x<Xc, beam is under-reinforced; let stress in concrete at level of steel be equal to 'a' times the stress in concrete at top

+a=(x-top_cover)/x

+//taking moments about tensile steel

+sigma_cbc=M/(Bf*x*(d-x/3)/2+(1.5*m-1)*Asc*a*(d-top_cover))//in MPa

+sigma_st=m*sigma_cbc*(d-x)/x//in MPa

+sigma_sc=1.5*m*a*sigma_cbc//in MPa

+mprintf("Stress in concrete=%f N/mm^2\nStress in tension steel=%f N/mm^2\nStress in compression steel=%f N/mm^2",sigma_cbc,sigma_st,sigma_sc)

+//answer in textbook is incorrect