3. CALCULATION OF REQUIRED STIFFNESS OF HOUSING

Design Requirements

• Deflection at the center of the beam per unit length shall be less than 0.0001in/inch
• Angular twist of beam per inch of length shall be less than 2e-7 rad/inch

Design steps

1. Calculate minimum required bending moment of inertia of section based on the above data
2. Calculate minimum required torsional moment of inertia
3. Calculate the required cross sectional area

Calculations

1. Vertical stiffness calculation
2. Horizontal stiffness calculation
3. Torsional stiffness calculation
4. Compressive stiffness calculation





Vertical stiffness calculation
For the above case,
Length = 40"
Deflection= 40 * 0.0001 = 0.004"
E = 200 lb/sq.in
P = 32.9 lb


Since deflection is a function of L,E,I,P, the value of Ix can be easily calculated using the formulas of simply supported beam. The minimum required Ix = 47.9in^4




Horizontal stiffness calculation

The calculation is same as above
The required Bending stiffness Iy = 34 in^4





Torsional stiffness calculation

Torsional resistance (J) = Moment (M) / (G * allowable ang. twist)
The required torsional resistance = 70.2 in^4





Compressive stiffness calculation
For direct loading, Area(A) = Load (P) / (unit deflection * E)
The required c.s area to resist 785 lb of compressive load is 2.6in^2

Previous | Next Step | Input Data | Home Page