diff options
Diffstat (limited to '3683/CH3/EX3.12/Ex3_12.sce')
-rw-r--r-- | 3683/CH3/EX3.12/Ex3_12.sce | 25 |
1 files changed, 25 insertions, 0 deletions
diff --git a/3683/CH3/EX3.12/Ex3_12.sce b/3683/CH3/EX3.12/Ex3_12.sce new file mode 100644 index 000000000..7d4365df5 --- /dev/null +++ b/3683/CH3/EX3.12/Ex3_12.sce @@ -0,0 +1,25 @@ +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
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