2.2.Beams Structural Problems:

2.2.Beams

structural members supporting loads applied structural members supporting loads applied at various points along the member

at various points along the member

Structural Problems:

Remember…

Relations among load, shear, and bending moment

Example: Draw the shear & bending-moment diagrams for the simply supported beam

V=dM/dx

at x=L/2 V=0 & M=M

^max

Deflection of Beams

Structural Problems:

The curvature of a plane curve at a point Q(x,y) of the curve

elastic curve characterizing the

shape of the deformed beam

2.2.Two-Dimensional Beam

Structural Problems:

Structural Problems:

A beam element

2 Degree of freedom at each

node

4 nodal values for a beam

element

3rd-order polynomial with

4 unknown coefficients

Finite Element Formulation of Beams:

Structural Problems:

Structural Problems:

Kji

Kii Kij

Kjj

The stiffness matrix [K](e) for any member (element) of the

beam (for both of local & global coordinates)

Load Matrix:

Structural Problems:

Two ways to formulate the nodal load matrices:

(1) minimizing the work done by the load (2) computing the beam's reaction forces

V(x)

Structural Problems:

Structural Problems:

Example:

Structural Problems:

2.2.1.Modeling Beam in ABAQUS:

Structural Problems:

Beam cross-sectional axis system

Abaqus Analysis User’s Manual/ 26.3.4 Beam element cross-section orientation

Available beam profiles

Abaqus/CAE User’s Manual/ 12.2.2 Defining profiles