- 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
- Calculate minimum required bending moment of inertia of section based on the above data
- Calculate minimum required torsional moment of inertia
- Calculate the required cross sectional area
- Vertical stiffness calculation
- Horizontal stiffness calculation
- Torsional stiffness calculation
- 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

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