Machine Design  II (ME 308 Lab)
Rigidity Analysis
and
The following analysis explains the successive integration (double integration) method. It shows how to find both the deflections and slopes in the vertical direction (yaxis).
You are required to complete the required calculations and to find the slopes and deflections in the horizontal direction (zaxis) by yourself.
In the double integration method, the following equations form the basis for the analysis:
Load Equation 

Shear Equation 

Moment Equation 

Slope Equation 

Deflection Equation 
………………….. eqn. 1
………………….. eqn. 2
………………….. eqn. 3
………………….. eqn. 4
………………….. eqn. 5
………………….. eqn. 6
Equations 1 through 6
above involve 6 unknowns (C_{1}, C_{2}, C_{3}, C_{4}, C_{5} & C_{6}), and hence, 6 boundary
conditions are needed to solve for the 6 unknowns. The 6 boundary conditions are as
follows:
The 6 boundary conditions above are applied to the 6 equations (equations 1 through 6 ) and the resultant equations are solved simultaneously to find the 6 unknowns (C_{1} through C_{6}). 
Note:
The equations can be solved easily using any of the available math software like
Mathcad, Maple, Mathematica or Matlab
where:
where:
where:
REPEAT the same procedure to find the deflection of the shaft and slopes in the horizontal (zdirection) and then finally check against the rigidity criteria given.