Matrix Method of Structural Analysis

Matrices are used in solving structural mechanics problems. The structural Mechanics problems can be expressed in the form of linear simultaneous

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

A - 6: Matrix Method of Structural Analysis (Continued)

Matrices are used in solving structural mechanics problems. The structural mechanics Problems can be expressed as linear simultaneous equation. By solving these equations Using computer, these problems can be solved. Consider a rectangular prism. Governing equations are given in the following in the form of matrices:

where,

E = elastic modulus = modulus of elasticity = Young’s modulus, kg/ sq mm

G = shear modulus = E, kg / sq mm 2(I + v)

L = member length, mm

V = Poisson’s ratio

Iy = moment of inertia about Y – Y axis, mm Ù 4

Iz = moment of inertia about Z – Z axis, mm Ù 4

J = polar moment of inertia, mm Ù 4

A = area, sq mm

Fx = force in X – direction, kg

Fy = force in Y – direction, kg

Fz = force in Z – direction, kg

Mx = moment about X – X axis, kg - mm

My = moment about Y – Y axis, kg – mm

Mz = moment about Z – Z axis, kg – mm

Dx = deflection in X – direction, mm

Dy = deflection in Y – direction, mm

Dz = deflection in Z – direction, mm

qx = rotation about X – axis, radian

qy = rotation about Y – axis, radian

qz = rotation about Z – axis, radian