What is the procedure used by STAAD.Pro in computing the stiffness matrix of a tapered beam?
1. Define the static deflection curves of a beam due to unit displacement at each of its 12 degrees of freedom while maintaining the displacements at the remaining 11 degrees of freedom as 0. These curves are usually referred to as shape functions.
2. Using the principle of virtual work, calculate each term of the stiffness matrix. This is an integral involving E (modulus of elasticity), I (moment of inertia for the applicable axis), and the product of the second derivative of the two shape functions which are relevant to the specific stiffness matrix term being generated. The integration is performed over the full length of the member.
Simpson's method is used in performing the integration. STAAD uses 100 integration points over the member length. The moment of inertia is calculated at the start and end of each integration point.