23.Matrix Method of Piping Analysis

23.Matrix Method of Piping Analysis

Matrices are used in solving structural mechanics problems. The structural mechanics problems can be expressed in the form of linear simultaneous equations. Consider a one dimensional problem.

The above can be written as: Force Vector = Stiffness Matrix x Displacement Vector Solution for structural problem can be obtained from this equation.

Matrices are used in solving structural mechanics problems. The structural mechanics problems can be expressed as linear simultaneous equations. By solving these equations using computer, these problems can be solved. Consider a rectangular prism. Consider a two dimensional problem. The governing equations are given in the following.

E = Elastic modulus = Young's modulus, kg/sq mm

L = length, mm

I = moment of inertia, mm ^ 4

A = area, sq mm

Fx = force in X - direction, kg

Fy = force in Y - direction, kg

Mz = moment about Z - direction, kg - mm

Δx = deflection in X - direction, mm

Δy = deflection in Y - direction, mm

θz = rotation about Z - axis, radian