Where are the moment distribution method and matrix displacement method applicable respectively?

Moment distribution method: a numerical asymptotic method based on displacement method, published by H. Cross in 1932, is mainly used for stress analysis of rigid-connected structures (such as continuous beams and rigid frames).

Matrix displacement method is suitable for statically indeterminate and statically indeterminate structures. Matrix displacement method is a method of arranging basic parameters in matrix form in structural mechanics calculation, taking node displacement as the basic unknown quantity.

Extended data

The basic idea of torque distribution method

(1) Fix the node, add a rigid arm on node O to control the rotation, and calculate the fixed-end bending moment generated by the load at each rod end respectively. The algebraic sum of the fixed-end bending moments of each rod acting on a node is called the moment;

(2) Loosen the joint, cancel the nonexistent rigid arm, let the joint rotate, and calculate the distribution torque of each rod from the torque according to the distribution coefficient of each rod;

And (3) transmitting torque, namely transmitting the torque to the far end of each rod according to the distributed torque and the transmission coefficient of each rod to obtain each transmitted torque. According to this law, the distribution, transmission and calculation are repeated until the torque value of the rod end is obtained with sufficient accuracy.

Finally, the rod end torque is equal to the sum of fixed end torque, distribution torque and transmission torque.

For the rigid frame with lateral displacement, the method developed from the moment distribution method can also be applied to the calculation, such as the moment distribution method of single-span rigid frame without shear distribution method and additional shear balance equation, but its application scope is limited or inconvenient, so the iterative method is often used for the general rigid frame with lateral displacement.