1246 WordsMay 7, 20165 Pages

THEORITICAL FORMULATION AND FAMILIARIZATION STUDY OF GEOMETRICALLY NONLINEAR ANALYSIS OF TRUSS SYSTEMS
PREAMBLE
Successful implementation of the procedures in computer programs requires a thorough understanding of the associated algorithms. It is important to familiarize with the theoretical formulations along with pertinent equations. A brief description about the procedure is presented in the following sections.
MEMBER FORCE – DISPLACEMENT RELATIONS Case 1: Member orientation coinciding with Global Coordinate System
Consider a member of plane truss undergoing deformation as shown in the Fig.4.1 Figure 4-1: Deformation and Member axial Force
The displacement can be expressed as u = L – L’
Axial stress and axial strain is given by σ = Q/A and Ɛ = u/L
The stress- strain relation is given by: σ = E Ɛ Q= [(E A)/L]u
Case 2: Member with arbitrary orientation in Global Coordinate System
The deformation and member axial force in Local coordinate system are shown in Figure 4.2.
Figure 4-2: Deformation and member axial force in Local coordinate system
Let (xb,yb) and (xe,ye) be the global coordinates of the joints in the undeformed configurations. Member length of undeformed configuration is given by
L = √((x_b -x_e )^2+(y_b- y_e )^2 )
Let the displacement components in global directions at ends ‘b’ and ‘e’ be (v1,v2) and (v3,v4) respectively. The deformed member length is expressed as
〖L 〗^ '= √([(x_e+v_3 )-(x_b+v_1 )

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