Realization of the stiffness matrix of statically indeterminate trusses and 20 bar sensitivity penalty method using Mathcad

Abstract

This paper examines the stiffness matrix of two-dimensional statically indeterminate truss structures.  Using Mathcad, a stiffness matrix analysis of a truss problem is completed as a template for other sorts of problems.  This allows learners to understand the stiffness matrix theory and rapidly acquire the basic concepts of analysis theory.  As is shown in the example, the transformation of the matrix is apparent and the overall structure of the stiffness matrix can be easily constructed.  Unknown reactions and member forces caused by unknown displacement were calculated as well.  In addition, the problem of the 20 bar boundary condition sensitivity penalty method explained in the example 2 for structure analysis.  Although this process is difficult to acquire due to complex procedures, it is beneficial for students because they can check for errors using Mathcad.

Keywords: truss, stiffness matrix, Mathcad, penalty method, structure analysis