Structural Dynamics and Vibration in Practice

Appendix B

Calculation of Flexibility Influence Coefficients

Flexibility influence coefficients for simple beams in bending or torsion can be calculated easily using the following methods. The bending case is considered first.

The potential energy, U_B, due to bending, in a beam, is

(B1)

where the integration is carried out over the whole length of the beam, and

M is the bending moment as a function of x;

x is the distance along the beam;

E is the Young’s modulus and

I is the second moment of area of the cross-section.

Since

(B2)

where is the ...