Slide 1

COORDINATE TRANSFORMATIONS

T is referred to as the transformation matrix.Transformation from Global to Local Coordinate Systems

Transformation from Local to Global Coordinate Systems

Example: Determine the transformation matrices for the members of the truss shown

Member 1: the joint 1 is the beginning joint and joint 2 is the end joint for member 1.

for any member with the positive directions of its local x and y axes oriented in the positive directions of the global X and Y axes, respectively, the transformation matrix always equals a unit matrix, I.

Example:For the truss shown , the end displacements of member 2 in the globalcoordinate system are

Calculate the end forces for this member in the global coordinate system. Is the member in equilibrium under these forces?

MEMBER STIFFNESS RELATIONS IN THE GLOBAL COORDINATE SYSTEMQ = kuLocal Stiffness

Force Transformation

Member Stiffness in Global Coordinate System

a stiffness coefficient Kij represents the force at the location and in the direction of Fi required, along with other end forces, to cause a unit value of displacement vj, while all other end displacements are zeroSolve Example 3.5 by using the member stiffness relationship in the global coordinatesystem, F = Kv.

Member End Forces in the Global Coordinate System: By applying the relationship F = Kv