Frame Subjected to Various Vertical Forces

Objective: Verification of the determination of elements with forced or constricted deformation at buckling.

Initial data file:  Energy94A.SPR

Problem formulation: The plane frame is subjected to different vertical nodal forces. Find elements with positive and negative energy for the first buckling mode.

References: Perelmuter A.V., Slivker V.I., Design Models of Structures and Possibilities of Their Analysis. — M, DMK-Press, 2007, § 9.4.

Initial data:

E = 2.1·107  t/m2	- elastic modulus,
Р = 1 t	- value of the concentrated force.
Bar cross-sections	- I-beams №40 (bending in the plane of the frame occurs with respect to the axis with the minimum moment I = 667 cm4, А = 72,6 cm2, iy = 3,03 cm, Wy = 86,1 cm3).

 

Finite element model: Design model – general type system, 6 bar elements of type 2, 7 nodes.

Design model (with the numbers of elements and loads)

 

Results in SCAD:

Values of the energy

 

Comparison of solutions:

Parameter	Theory	SCAD
Numbers of finite elements with the positive energy	1÷5	1÷5
Numbers of finite elements with the negative energy	6	6