From 7f60ea012dd2524dae921a2a35adbf7ef21f2bb6 Mon Sep 17 00:00:00 2001
From: prashantsinalkar
Date: Tue, 10 Oct 2017 12:27:19 +0530
Subject: initial commit / add all books

---
 3683/CH3/EX3.11/Ex3_11.sce | 27 +++++++++++++++++++++++++++
 1 file changed, 27 insertions(+)
 create mode 100644 3683/CH3/EX3.11/Ex3_11.sce

(limited to '3683/CH3/EX3.11')

diff --git a/3683/CH3/EX3.11/Ex3_11.sce b/3683/CH3/EX3.11/Ex3_11.sce
new file mode 100644
index 000000000..34b03a4d7
--- /dev/null
+++ b/3683/CH3/EX3.11/Ex3_11.sce
@@ -0,0 +1,27 @@
+Bf=1500//width of flange, in mm
+Df=150//thickness of flange, in mm
+d=600//effective depth, in mm
+sigma_cbc=7//in MPa
+sigma_st=230//in MPa
+m=13.33//modular ratio
+Ast=1964//in sq mm
+Asc=1140//in sq mm
+top_cover=50//in mm
+//to find critical depth of neutral axis
+Xc=d/(1+sigma_st/(m*sigma_cbc))//in 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
+sigma_cbc=sigma_st/m*x/(d-x)//in MPa
+sigma_cbc_dash=sigma_cbc*(x-top_cover)/x//stress in concrete at level of compression steel, in MPa
+//taking moments about tensile steel
+Mr=Bf*x*sigma_cbc*(d-x/3)/2+(1.5*m-1)*Asc*sigma_cbc_dash*(d-top_cover)//in N-mm
+mprintf("Moment of resistance of the beam=%f kN-m", Mr/10^6)
+//answer given in textbook is incorrect
-- 
cgit