1 files changed, 89 insertions, 0 deletions
diff --git a/3683/CH19/EX19.7/Ex19_7.sce b/3683/CH19/EX19.7/Ex19_7.sce
new file mode 100644
index 000000000..de5c0cd3e
--- /dev/null
+++ b/3683/CH19/EX19.7/Ex19_7.sce
@@ -0,0 +1,89 @@
+l=7//span, in m
+fck=15//in MPa
+fy=250//in MPa
+b=300//assume, in mm
+W=35//live load, in kN/m
+Wu=1.5*W//in kN/m
+Mu=Wu*l^2/8//in kN-m
+d=(Mu*10^6/0.149/fck/b)^0.5//in mm
+d=1.1*d//increase depth by 10% for self-weight
+d=750//assume, in mm
+c=50//cover, in mm
+D=d+c//in mm
+W1=(b/10^3)*(D/10^3)*25//self-weight, in kN/m
+W2=35//live load, in kN/m
+W=W1+W2//in kN/m
+Wu=1.5*W//in kN/m
+Mu=Wu*l^2/8//in kN-m
+d=(Mu*10^6/0.149/fck/b)^0.5//<750 mm, hence OK
+d=750//in mm
+//steel
+//Xu=0.87*fy*Ast/0.36/fck/b = a*Ast
+a=0.87*fy/0.36/fck/b
+//using Mu=0.87 fy Ast (d-0.416 Xu), we get a quadratic equation
+p=0.87*fy*0.416*a
+q=-0.87*fy*d
+r=Mu*10^6
+Ast=(-q-sqrt(q^2-4*p*r))/2/p//in sq mm
+//provide 20 mm dia bars
+n=Ast/0.785/20^2
+//provide 8-20 mm + 2-18 mm dia bars
+Ast=8*0.785*20^2+2*0.785*18^2//in sq mm
+pt=Ast/b/d*100//pt=1.34
+Vu=Wu*l/2//in kN
+Tv=Vu*10^3/b/d//in MPa
+//for M15 and pt=1.34
+Tc=0.65//in MPa
+//as Tv>Tc, shear reinforcement required
+//provide 6 mm stirrups
+Vus=Vu-Tc*b*d/10^3//in kN
+Asv=2*0.785*6^2//in sq mm
+Sv=Asv*0.87*fy*d/Vus/10^3//in mm
+Sv=130//assume, in mm
+Svmin=Asv*fy/0.4/b//in mm
+Svmin=115//assume, in mm
+Sv=min(Sv,Svmin)//in mm
+mprintf("Summary of design:\nBeam size - %d x %d mm\nCover - 50 mm\nSteel - 8-20 mm + 2-18 mm dia bars\nStirrups - 6 mm dia @ %d mm c/c",b,D,Sv)
+//deflection check
+Ec=5700*sqrt(fck)//in MPa
+Es=2*10^5//in MPa
+m=Es/Ec
+fcr=0.7*sqrt(fck)//in MPa
+//using b x x/2 = m Ast (d-x), we get a quadratic equation
+//solving the quadratic equation
+p=b/2
+q=m*Ast
+r=-m*Ast*d
+x=(-q+sqrt(q^2-4*p*r))/2/p//in mm
+x=290//assume, in mm
+z=d-x/3//in mm
+Ir=b*x^3/12+b*x*(x/2)^2+m*Ast*(d-x)^2//in mm^4
+Igr=b*D^3/12//in mm^4
+yt=D/2//in mm
+Mr=fcr*Igr/yt//in N-mm
+M=W*l^2/8*10^6//in N-mm
+Ieff=Ir/(1.2-Mr/M*z/d*(1-x/d)*b/b)//in mm^4
+//Ir>Ieff
+Ieff=Ir//in mm^4
+W1=W*l//in kN
+u1=5/384*(W1*10^3)*(l*10^3)^3/Ec/Ieff//short-term deflection, in mm
+//long-term deflection
+//(i) deflection due to shrinkage
+k3=0.125//for simply supported beam
+pt=1.34//in %
+pc=0//in %
+k4=0.65*(pt-pc)/sqrt(pt)
+phi=k4*0.0003/D
+u2=k3*phi*(l*10^3)^2//in mm
+//(ii) deflection due to creep
+Ecc=Ec/(1+1.6)//in MPa
+//assuming a permanent load of 60%
+W2=0.6*W*l//in kN
+u3=5/384*(W2*10^3)*(l*10^3)^3/Ecc/Ieff//in mm
+u4=5/384*(W2*10^3)*(l*10^3)^3/Ec/Ieff//in mm
+u5=u3-u4//in mm
+u=u1+u2+u5//total deflection, in mm
+v1=l*10^3/250//permissible deflection, in mm
+v2=l*10^3/350//in mm
+//assuming half the shrinkage strain occurs within the first 28 days, the deflection occurring after this time
+v3=u2/2+u5//< permissible value, hence OK