Calculations are similar to the calculations of a rectangular beam and include the evaluation of forces in a beam and at nodes of a panel (slab). Forces are subsequently reduced to the center of gravity of a new T-section.
The axis passes through the center of gravity of the panel.
To calculate the forces of a panel, multiply forces at the panel nodes (common nodes of the panel and the beam) by the effective slab width (simplified approach). While positioning the beam with respect to the slab, offsets are considered (also relative offsets). In the following example, obtained reduction results of a T-section were shifted from the panel plane by the offset equal to the distance of the center of gravity of the panel and the center of gravity of the T-section.
The reduction of forces to the center of gravity of the T-section are as follows:
M = Mb + Mp * B + Np * B * e1 + Nb * e2
Q = Qb + Qp * B
N = Nb + Np * B
where:
B = beff1+b+beff2
Defining the center of gravity of a T-section
A static moment calculated at the center of gravity of the panel (a beam and its offset are only manipulated with)
S = b*h*(offset)
A = (beff1+b+beff2)*hpl + b*h
The center of gravity shifted with respect to the center of gravity of the panel:
Z = S / A
where:
b - beam width
h - beam height
beff1, beff2 - effective slab widths
hpl - slab height (panel thickness)
offset - offset of the beam with respect to the panel.
NOTES:
- Note should be taken that there may be common parts of the area of the panel and the beam; unfortunately, they are counted twice in calculations, which leads to the growth of rigidity of the T-beam. In consequence, forces and deflections are smaller
- Panel results are read at nodes of finite elements; mesh refinement has effect on the results
- In the model the axis of the T-section is the axis of the center of gravity of the panel
- Multiplying the relevant forces in the panel by the assumed effective slab width is a simplification. In consequence, results are approximated.