Frame Subjected to Vertical Forces
Objective: Verification of the determination of elements with forced or constricted deformation at buckling.
Initial data file: Energy94B.SPR
Problem formulation: The plane frame is subjected to 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 No. 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÷3 |
1÷3 |
|
Numbers of finite elements with the negative energy |
4÷6 |
4÷6 |