Calculation of internal forces in ribs
You can find the link between the internal forces calculated for the entire T-section, and for the beam and slab separately below.
When calculating the internal forces in a rib (see the procedure below to learn how to switch this part on), the substitute T-section is used to calculate the results.
The web of this T-section is formed by the rib-beam itself, the flange of the T-section is made with the right effective width of the slab.
The effective width of the slab has to be used to determine the internal forces of the slab that have to be added to the internal forces, calculated in the rib itself.
The coordinates of the hearts are used as lever arms in Y and Z direction:
The final internal forces in the rib can be calculated with the formulae below:
- N = Nbeam + Nslab,left + Nslab,right
- Vy = Vy,beam + Vy,slab,left + Vy,slab,right
- Vz = Vz,beam + Vz,slab,left + Vz,slab,right
- Mx = Mx,beam + Mx,slab,left + Mx,slab,right
- My = My,beam + My,slab,left + My,slab,right + Nslab,left * (lever arm Z1) – Nslab,right * (lever arm Z2) + Nbeam * lever arm Z3
- Mz= Mz,beam + Mz,slab,left + Mz,slab,right + Nslab,left * (lever arm Y1) – Nslab,right * (lever arm Y2) + Nbeam * lever arm Y3
What is the influence of the effective width on the internal forces?
The effective width that is taken into account for the results, calculated as a rib, can be entered in the properties panel of the beam.
For this another value can be entered both for a reinforcement calculation and for a calculation of the internal forces.
Of course the influence of the effective width will only be perceptible in the results if the option 'Rib' is ticked on (see also FAQ Influence of option rib).
When asking for the results in the slab, the internal forces will be zero over the effective width because it will be calculated already when asking for the results in the rib.
The calculated normal force in the rib, depends on the effective width.
The effective width has an influence on the flange width of the T-section that is considered. So this has an influence on the surface of the slab that is calculated.
The normal force Nslab is calculated by multiplying the tension in the slab with the considered surface of the slab and will in this way depend on the effective width.
The effect of the effective width is perceptible when asking for Nrib, because Nrib is the sum of Nbeam and Nslab.
This has the following results for the considered example:
- The first figure shows the normal forces Nbeam
- The second figure shows the normal forces Nrib with a effective width of 0,5 m
- The third figure shows the normal forces Nrib with a effective width of 1 m
Please note that with a effective width equal to the headway between the ribs (1 m), the resulting normal force is zero. This is logic since no exterior normal forces appear.
The effective width also plays an important role when determining Mrib.
Nslab will also influence Mrib because of its lever arm (see calculation internal forces in rib described above).