Integrating Eq. 1 we
get;
EI(dy/dx) =
66[x]^{2}/2  20[x]^{3
}/6 +20[x4]^{3}/6 
10[x8]^{2}/2 +C1
Eq.2
We do not have any
information about slope at the ends,
We continue
integrating Eq. 2 for finding deflection;
EIy =
66[x]^{3}/6  20[x]^{4
}/24 +20[x4]^{4}/24 
10[x8]^{3}/6 +C1x + C2
Now apply the condition for deflection at the supports;
at x=0, y=0 (neglect the terms which become negative with x=0)
we get C2=0;
Further at x=10, y=0; we get
0=11000  200000/24 + 1080  80/6 + 10C1
C1= 374.66
Therefore the equation for slope can be written as
EI(dy/dx) =
66[x]^{2}/2  20[x]^{3
}/6 +20[x4]^{3}/6 
10[x8]^{2}/2  374.66
and the equation for deflection would be
EIy =
66[x]^{3}/6  20[x]^{4
}/24 +20[x4]^{4}/24 
10[x8]^{3}/6  374.66x
Slope at x=5;
dy/dx = (37)/EI
Deflection at x=5;
y = (
1018)/EI
The value of moment
of inertia can be calculated by using
moment
of inertia calculator
I_{xx}
= 29008.3 cm^{4}
EI= (200x10^{9}
N/m^{2})x(29008.3
cm^{4} ) = 58016.6 kN m^{2}
substituting the
value of EI in the expressions for slope and deflection we get;
dy/dx = 37/58016.6 = 0.00064 rad.
y =  1018/58016.6 =  0.0175 m
(negative sign indicates that the deflection is downward)
You can also use our
Slope
deflection calculator for different combinations of load.
For other problems please visit our
Problem Solver^{New }
