# Determination of shear field stiffness and application in Consteel

- Tartalmak

Shear fields are used in daily practice in Germany for the design of structures by considering the stabilization effect of trapezoidal decking connected to bar elements. Such stabilization effect can be taken into account only when software with special bar elements with 7 degrees of freedom are used. In Consteel the possibility to consider shear fields at finite element level has been implemented.

Additionally several producer and standard specific methods to calculate the stiffness of a shear field have been included.

In this post we would like to provide general information about the included methods to calculate the stiffness of a given shear field.

At the end through a sample building the different calculation methodes will be introduced.

**Determination of shear stiffness in case of panels produced by Hoesch [1]**

The recommended method uses the following formula (DIN 18807, Schardt/Strehl method):

(1)

S: stiffness of the shear field [kN]

K_{1}: parameter specific to the selected panel [m/kN]

K_{2}: parameter specific to the selected panel [m^{2}/kN]

L: length of the shear field parallel to the direction of the panel ribs [m]

a: applicable effective width [m]

Figure 1. shows the sketch of a general building showing the dimensions used in the previous formula. The method assumes that panels on all 4 edges along the boundary of the considered shear field are fixed to supporting structures with adequate spacing.

The values K_{1} and K_{2} have been specified by the producer for each panel type in function of its thickness. These values can be found on the website of the producer or in official application certificates.

Important to note, that such certificates have a certain validity of application, therefore it is always recommended to double check the validity of the values considered by Consteel.

The S value determined with formula (1) is valid if the trapezoidal sheet is fixed at each rib to the supporting structure. The S value shall be multiplied with 0.2 in case of fixations in every second rib only.

**Determination of shear stiffness in case of panels produced by Fischer [2]**

The recommended method uses the following formula (improved Schardt/Strehl method) (2). The formula contains 3 additional parameters (K_{1}*, K_{2}* and e_{L}) in comparison with the classical method, to consider the effect of the fixations of the panels.

(2)

S: stiffness of the shear field [kN]

K_{1}: parameter specific to the selected panel [10-4*m/kN]

K_{2}: parameter specific to the selected panel [10-4*m^{2}/kN]

K_{1}*: parameter specific to the selected panel [10-4*1/kN]

K_{2}*: parameter specific to the selected panel [10-4*m^{2}/kN]

e_{L}: distance between fixations lengthwise [m]

L: length of the shear field parallel to the direction of the panel ribs [m]

a: applicable effective width [m]

The method assumes that panels on all 4 edges along the boundary of the considered shear field are fixed to supporting structures with adequate spacing.

The S value determined with formula (2) is valid if the trapezoidal sheet is fixed at each rib to the supporting structure. The S value shall be multiplied with 0.2 in case of fixations in every second rib only.

**Determination of shear stiffness in case of panels produced by Arcelor [3]**

The recommended method uses the following formula (3) (Bryan/Davies method):

(3)

S: stiffness of the shear field [kN]

K_{1}’: parameter specific to the selected panel [m/kN]

K_{2}’: parameter specific to the selected panel [m^{2}/kN]

K_{1}*: parameter specific to the selected panel [1/kN]

K_{2}*: parameter specific to the selected panel [m^{2}/kN]

L_{s}: length of the shear field parallel to the direction of the panel ribs [m]

α_{1}, α_{2}, α_{3}: additional parameters depending on the number of panel spans defined in tables

α_{4}: additional parameter depending on the number of panel splices lengthwise

a: applicable effective width [m]

The method assumes that panels on all 4 edges along the boundary of the considered shear field are fixed to supporting structures with adequate spacing.

The S value determined with formula (3) is valid if the trapezoidal sheet is fixed at each rib to the supporting structure. The S value shall be multiplied with 0.2 in case of fixations in every second rib only.

**Determination of shear stiffness according to Eurocode 3 [4]**

The recommended method uses the following formula (4):

(4)

S: stiffness of the shear field [kN]

t: thickness of the panel [mm]

h_{w}: depth of the panel [mm]a: applicable effective width [m]

b_{roof}: length of the shear field parallel to the direction of the panel ribs (width of the roof) [mm]

The method doesn’t require that panels are fixed on all 4 edges along the boundary of the considered shear field are fixed to supporting structures. As a minimum fixation to directly stabilized structures (2 sides) with adequate spacing is required.

The S value determined with formula (4) is valid if the trapezoidal sheet is fixed at each rib to the supporting structure. The S value shall be multiplied with 0.2 in case of fixations in every second rib only.

**Examples to determine shear field stiffness values**

Parameters:

L=25 m (length of the shear field parallel to the direction of the panel ribs)

n=5 (number of frames)

a=5 m (bay spacing)

B=12 m (span)

The sample building is shown on Figure 2. In this building there are no purlins use, a deep corrugated trapezoidal decking is placed above the rafters. The complete roof of the building has been assumed to work as a shear field. In order to ensure this, the panels are fixed to the rafters and also to longitudinal beams located at the eaves. The panels are assumed to be connected over the ridge to form a continuous diaphragm with appropriate connecting elements (red lines). The panels are fixed at each rib to the supporting structure. It is important to note, that in such case the complete roof decking will have global stabilization role and therefore future changes such as additional openings can only be made in accordance with the approval of a structural engineer.

**Hoesch panel (Schardt/Strehl method)**

Applied panel:

- Hoesch T 135.1
- 0.75 mm thick positive orientation, normal fixation

Extract of the table for the determination of additional parameters:

Values of parameters specific to the chosen panel from approval document:

- K
_{1}=0,274 [m/kN] - K
_{2}=54,836 [m^{2}/kN]

Stiffness value of the shear field applicable to an intermediate frame (fixation in every rib) (5):

(5)

Stiffness value of the shear field applicable to an endwall frame (fixation in every rib) (7):

(6)

**Fisher panel (improved Schardt/Strehl method)**

Applied panel:

- Fischer 135/310
- 0.75 mm thick positive orientation, normal fixation

Extract of the table for the determination of additional parameters:

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