How to calculate relative stiffness in moment distribution method?
Answers
Explanation:
Take a prismatic beam with fixed ends.
Apply a unit rotation on one of the ends and keep fixed the other end. If you neglect shear deformations, results a moment of 4*E*I/L in the rotated end and 2*E*I/L in the other end. E=elasticity modulus, I=moment of inertia, L=length of beam. (Verify it by the force method!) In the case of the fixed-freely supported beam, you get a moment of 3*E*I/L for unit rotation of the fixed end. (This is easier to verify.)
These are the real stiffness coefficients of a beam. In the moment distribution method you are not directly working with rotations. If you apply a rotation, 1/(4*E), you get the practical or conventional stiffness coefficients I/L, 1/2*I/L and 3/4*I/L, which can be used to distribute and transmit moments proportionally with the stiffness factors of the members.