# Alternative to Gamma Method: Flexible Composite Beam as Framework Model

## Technical Article on the Topic Structural Analysis Using Dlubal Software

### Technical Article

Besides the standardized gamma method, you can display the semi-rigid composite beams also as a framework model.

In comparison with the gamma method, the framework m has, among others, the following advantages:

• Any position and spacing of the fasteners
• Independent of the number of supports and the conditions of support

#### Modeling

A T-section (web NH C24, flange LH D50) is to be modeled. In addition, the web and the flange are to be connected by coupling members with releases (rigid members) to as many discrete points as possible in order to detect identical deflections of both elements. The next step is to place a member into position where the fastener is situated. These are rigidly attached to the web and the flange and are shown by definable flexural stiffness / shear stiffness of the fasteners. A release is placed at the level of the composite joint.

#### Determining Bending Stiffness

As mentioned above, the bending stiffness of the stiffness members is determined to take into account the shear flexibility of the fastener. For this, you can use the formulas shown in the picture that result from the structural systems. In the figure above, the bending stiffness was determined neglecting the web and flange stiffness. In the figure below, the web and flange stiffness are taken into account.

The resulting value can be easily edited in the Member Type ‘Definable Stiffness’ with no need to create an effective cross‑section. The moduli of displacement can be determined according to Table 7.1 of EN 1995-1-1. According to Table 7.1 of EN 1995-1-1, a modulus of displacement of 3469 kN/m results for a screw d = 6 mm. If this value is inserted into the equation from Figure 02 (neglecting the flange stiffness), the result is an effective bending stiffness of 0.601 kN/m². The strain stiffness as well as the shear stiffness can be set to "infinite" with a high value.

#### Another alternative (RFEM only)

Another way to calculate compliant composite beams with members is to use line releases. This option is explained here.

#### Dipl.-Ing. (FH) Gerhard Rehm

Product Engineering & Customer Support

Mr. Rehm is responsible for the development of products for timber structures, and provides technical support for customers.

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• Updated 26 May 2021

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