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How are the internal forces calculated in the ribs (+ influence of effective width)?

The link between the internal forces calculated for the entire T-section, and for the beam and slab seperately, is the following (explanation from help):
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 = N beam + N slab, left + N slab, 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 + N slab, left * (Lever Arm Z1) – N slab, right * (Lever Arm Z2) + N beam * Lever Arm Z3;
Mz = Mz beam + Mz slab, left + Mz slab, right + N slab, left * (Lever Arm Y1) – N slab, right * (Lever Arm Y2) + N beam * 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 window 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.

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 N, slab 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 N, rib, because N, rib is the sum of N, beam and N, slab.

This has the following results for the considered example:
The first figure shows the normal forces N, beam.
The second figure shows the normal forces N, rib with a effective width of 0.5m.
The third figure shows the normal forces N, rib with a effective width of 1m.

Please note that with a effective width equal to the headway between the ribs (1m), 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 M, rib.
N, slab will also influence M, rib because of its lever arm. (see calculation internal forces in rib described above)

Reference number: 
ESA1406
Software: 
FAQ Category: 
Results
Access Type: 
Free User