Structural E - Book
Contents
Introduction
Loads
Materials
Shapes and Sizes
Design
Structural Engineering
Stress Analysis
Detailing
Drafting
Documentation
Beam Formulas
Frame Formulas
Material Properties
Standard Shapes and Properties
Combined Properties
Matrix Method of Structural Analysis
Stress Limits
Deformation Limits
Foundations
Structural Steel Design an per Is : 800 - 2007
A Hundred Questions on Boilers
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
Equations.
Figure 1: Spar Subjected to Axial Tension
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:
 
 
A-6: Matrix Method of Structural Analysis (Continued)
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