Calculation of internal forces in ribs

When calculating internal forces in a rib (see the procedure below to learn how to switch this feature on), a 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 of the appropriate effective width of the slab. The effective width of the slab is then used to determine internal forces from the slab that must be added to the internal forces calculated in the rib itself. The internal forces in the slab are transformed into the local coordinate system of the rib before the integration.

T

the centre of gravity of the whole substitute T-section

T1

the centre of gravity of the left hand side part of the effective width

T2

the centre of gravity of the right hand side part of the effective width

T3

the centre of gravity of the original rib

image\ResultsInRib.gif

The coordinates of centres of gravity are used to determine lever arms in Y and Z direction:

Lever Arm Z1 = T1z – Tz

Lever Arm Y1 = T1y – Ty

Lever Arm Z2 = T2z – Tz

Lever Arm Y2 = T2y – Ty

Lever Arm Z3 = T3z – Tz

Lever Arm Y3 = T3y – Ty

Lever Arm Z = Tz – 0z

Lever Arm Y = Ty – 0y

The final internal forces in the rib can be calculated from the formulas 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 +

Vz slab, left * (Lever Arm Y1)+ Vz slab, right *(Lever Arm Y2)

 

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;

The procedure to recalculate internal forces in the rib

  1. Open service Results.

  2. Select function Beams > Internal forces on beams.

  3. Select the 1D member(s) where the results should be displayed.

  4. Select the quantity to be displayed.

  5. In the property dialogue select option Rib.

  6. Press button Refresh to see the result diagram.