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Diffstat (limited to '3864/CH5/EX5.12/Ex5_12.sce')
-rw-r--r-- | 3864/CH5/EX5.12/Ex5_12.sce | 87 |
1 files changed, 87 insertions, 0 deletions
diff --git a/3864/CH5/EX5.12/Ex5_12.sce b/3864/CH5/EX5.12/Ex5_12.sce new file mode 100644 index 000000000..755716ee5 --- /dev/null +++ b/3864/CH5/EX5.12/Ex5_12.sce @@ -0,0 +1,87 @@ +clear +// +// + + +//Initilization of Variables +L_AC=2 //m //Length of AC,CD,DB +L_DB=2 +L_CD=2 +F_C=40 //KN //Force at C +w=20 //KN/m //u.d.l +L=6 //m //span of beam + +//Let E*I=X +X=15000 //KN-m**2 + + +//Calculations + +//Let V_A & V_B be the reactions at A & B respectively +//V_A+V_B=80 + +//Taking Moment B,M_B +V_A=(F_C*(L_CD+L_DB)+w*L_DB*L_DB*2**-1)*L**-1 //KN +V_B=80-V_A //KN + +//Taking Moment at distance x from A +//M_x=33.333*x-40*(x-2)-20*(x-4)**2*2**-1 +//EI*(d**2/dx**2)=33.333*x-40*(x-2)-10*(x-4)**2 + +//Integrating above equation we get +//EI*(dy/dx)=C1+33.333*x**2*2**-1-20*(x-2)**2-10*3**-1*(x-4)**3 + +//Again Integrating above equation we get +//EI*y=C2+C1*x+33.333*x**3*6**-1-20*3**-1*(x-2)**3-10*12**-1*(x-4)**4 + +//At +x=0 +y=0 +C2=0 + +//At +x=6 +y=0 +C1=-760*6**-1 + +//Assuming Deflection to be max in portion CD and sustituting value of C1 in equation of slope we get +//EI*y=C2+C1*x+33.333*x**3*6**-1-20*3**-1*(x-2)**3-10*12**-1*(x-4)**4 +//0=-126.667+33.333*x**2**-1-20*(x-2)**2 + +//After rearranging and simplifying further we get + +//x**2-24*x+62=0 +//From above equations +a=1 +b=-24 +c=62 + +y=(b**2-4*a*c)**0.5 + +x1=(-b+y)*(2*a)**-1 +x2=(-b-y)*(2*a)**-1 + +//Taking x2 into account +x=2.945 //m +C1=-126.667 +C2=0 + +y_max=(C2+C1*x+33.333*x**3*6**-1-20*3**-1*(x-2)**3)*X**-1 //mm + +//Max slope occurs at the ends +//At A, +//EI*(dy/dx)_A=-126.667 +//At B +//EI*(dy/dx)_B=126.667+33.333*6**2*2**-1-20*4**2-10*2**3 +//After simplifying Further we get +//EI*(dy/dx)_B=73.3273 + +//Now Max slope is EI(dy/dx)_A=-126.667 +//15000*(dy/dx)_=-126.667 + +//Let Y=dy/dx +Y=-126.667*X**-1 //Radians + +//Result +printf("\n Maximum Deflection for Beam is %0.4f mm",y_max) +printf("\n Maximum Slope for beam is %0.4f radians",Y) |