Journal of
Faculty of Civil Engineering

JOURNAL OF FACULTY OF CIVIL ENGINEERING 21, 2012.y., pp. 29-40

	UDC: 517.957:624.072.2
	CC-BY-SA 4.0 license
	Author : Aleksandar Borković
	Summary:
	As shown in Part one, equations of statical equilibrium of Bernoulli-Euler beam are derived according to von Karman theory. In this Paper elements of tangent stiffness matrix and vector of unbalanced forces are given for beams of type k and g. Standard procedure for derivation of this elements is numerical integration. By usage of the built-in Wolfram Mathematica functions for symbolic integration, these elemens are derived in closed-form. Presented procedure is validated through four numerical examples by comparison with commercial FEM packages ABAQUS and SAP2000. Classicalgeometricallynonlinear problems of plane beam structures are given: softening and stiffening of construction as well as their cobination that takes place for shallow arches. Boundary conditions and geometry are varied for better insight into presented problems.
	Keywords:
	Bernoulli-Eulerbeam, tangent stiffness matrix, vector of unbalanced forces, beam of type k, beam of type g