| Product(s): | RAM Structural System | |

| Version(s): | 13.00.00.00 or later | |

| Area: | Analysis | |

| Original Author: | Bentley Technical Support Group |

Semirigid diaphragms are meshed into quadrilateral plates within RAM Frame or Ram Concrete Analysis using the properties of the deck defined in RAM Modeler. For composite and non-composite decks, the Effective Thickness, Poisson’s Ratio, and Elastic Modulus in the Diaphragm box are used for the plate properties.

For concrete slabs, the Concrete Slab Thickness, Poisson’s Ratio, and Elastic Modulus are used for the shell properties. In addition, the Cracked Factor – Bending can be used to modify the out-of-plane stiffness and the Cracked Factor – Diaphragm can be used to modify the in-plane stiffness.

In some older versions of the software the Cracked Factor - Bending was applied to the deck thickness, affecting the deck out-of-plane inertia cubically. That was changed in 14.06 so that the cracked factor is now applied to linearly reduce the deck out-of-plane stiffness.

Currently, it is not possible to model an orthotropic material.

The in-plane stiffness of metal decks is a function of many parameters, including as warping and fastener patterns. The Steel Deck Institute has published a method for calculating diaphragm deflection using the shear stiffness parameter (G`) in their diaphragm design manual. This method is typically reproduced in deck manufacturer's catalogs. The parameter G’ has units of kip/in. Some deck manufacturers, such as Verco, use a similar parameter that has units of in/kip and is essentially the inverse of G’.

An effective Elastic Modulus can be calculated using the shear stiffness parameter G’ and other diaphragm properties. An example of this calculation using a Vulcraft deck can be found here

One simple option is to use the gage thickness of the deck for the effective thickness and a typical value for Possion’s ratio of steel materials (0.3), but this results in a very thin deck that can deflect tremendously in RAM Frame analysis or result in instabilities. For that reason it is usually better to **increase the deck gage thickness by a factor of 10 or more while reducing the elastic modus by the same factor.**

Some engineering judgment is required when determining the properties of composite decks and concrete slabs defined as semirigid diaphragms, because cracking can affect the stiffness. ACI 318-11 Section 10.10.4.1 lists approximate effective moment of inertias that are permitted for various structural members. Although there is not a factor for diaphragms, the factors listed for walls may be most appropriate for use with diaphragms. ACI states that 0.7Ig should be used for uncracked walls and 0.35Ig should be used for cracked walls. You could run a hand calculation on your diaphragm to get an idea of what the stresses might be and compare those stresses to the modulus of rupture. Alternatively, you could envelope the stiffness and run the model twice: once with 0.35Ig and once with 0.7Ig. For a concrete slab, the factor should be entered as the Cracked Factor – Diaphragm defined with the deck properties. For a composite deck, the factor should be incorporated into the effective thickness that is defined with the deck properties. For example, if you have 4 inches of concrete above the flutes and want to use 0.35Ig, the effective thickness would be 0.35 * 4 = 1.4 inches.

For composite slabs, most engineers ignore the stiffness of the metal deck and enter the Elastic Modulus and Poisson’s Ratio for concrete. Some engineers ignore the concrete within the flutes and use the thickness of the concrete above the deck as the effective thickness. Other engineers consider a portion of the concrete and modify the effective thickness accordingly.

The size of the shells and the number of finite element nodes in the model is controlled by the Max Distance between Nodes on Mesh Line parameter defined in RAM Frame – Criteria – General. There is a trade-off between the mesh size and the time required to complete the analysis. In general, a finer mesh yields more accurate results, but requires a longer analysis. If you are not sure what mesh size to use, run a few iterations with smaller and smaller maximum distances. The displacements should converge. Once the change in the displacements is negligible, you know your mesh size is adequate.

The program also has the ability to use the slab edge or the perimeter beams/walls as the diaphragm boundary in RAM Frame – Criteria - Diaphragm. If there are small slab edge offsets, the elements between the perimeter beam and the slab edge will be poorly meshed. In these situations, use the perimeter beams/walls as the diaphragm boundary.

In Ram Frame, only the lateral members are considered in the finite element model (see RAM SS Analysis Types for details). RAM Frame ignores the stiffness of gravity members. As a result, any beam that needs to stiffen the diaphragm through its axial rigidity needs to be defined as a lateral member. The program assumes that the semirigid diaphragm is connected to the beam at the beam centroid.

RAM Gravity calculates the gravity load tributary to the lateral members and applies them as point loads or line loads in the finite element analysis in RAM Frame.

When out-of-plane stiffness is considered, the one-way deck acts as a slab and can span from support-to-support and share load with interconnected frame beams. As the out-of-plane stiffness of the semirigid diaphragm increases relative to the beams, more load will be directed out of the beams, into the deck, and transferred into the supports through bending of the diaphragm. For details see How does the diaphragm out-of-plane stiffness affect behavior?

For a flat, semirigid diaphragm with little or no out-of-plane stiffness these effects will be minimal. For sloped, semirigid diaphragms or concrete decks, the effect on the member forces can be significant.

Consider gabled roof framing modeled as lateral members meshed with a semirigid diaphragm. The in-plane stiffness of the sloping diaphragm has a component in the vertical plane of the rigid beam. As a result, the diaphragm acts as a deep beam, props up the ridge beam, and decreases the shear and forces in the beam. Similarly, the horizontal thrust under the gravity loads will be resisted by the diaphragm and not the gable frame. There really is no way to get accurate gravity forces for this configuration in RAM Frame while using a semirigid diaphragm. It is best to size the beam for gravity loads in RAM Frame with the diaphragm assigned as flexible. If the member is part of the lateral force resisting system, you would then take these gravity forces and combine them manually with the semirigid analysis lateral forces and design the beam by hand.

Lateral loads applied to sloped semirigid diaphragms are applied in the XY plane, not in the plane of the diaphragm. When the diaphragm is sloped, a component of the applied load acts out-of-plane of the diaphragm. This force component can cause significant out-of-plane deformation since the stiffness of gravity members is ignored. This is especially true when the semirigid dipahragm is an untopped metal deck, which has very little out-of-plane stiffness. The only way to control the diaphragm displacements is to model the gravity members as lateral so their stiffness is not ignored. However, this will impact the forces in the actual lateral force resisting system.

By default, program generated seismic and wind story forces using the calculated fundamental periods and frequencies in each direction. The calculated periods and frequencies are based on the mass and stiffness of the structure and are determined using an Eigen Analysis.

In the Eigen Analysis, mass is distributed spatially at each finite element node when semirigid diaphragms are used. Mass is not lumped at the center of mass (or an eccentric location) as is done when rigid diaphragms are used. Each node has two lateral degrees of freedom: x-translation and y-translation. As the mesh size decreases, the number of degrees of freedom increases. This also increases the analysis time and can increase the number of mode shapes that the program is attempting to find. For static lateral cases, only the fundamental mode in the x and y directions is needed. For dynamic cases, at least 90% mass participation in the x and y directions is required (ASCE7). Mass participation and the calculated periods and frequencies for each mode can be reviewed using the Periods & Modes Report in RAM Frame. If you have a semirigid diaphragm, you can often reduce the analysis time by creating an Eigen Solution load case and limiting the number of periods considered to a number that includes the fundamental modes (static load cases) or satisfies the 90% mass participation requirement (dynamic load cases).

When a semirigid diaphragm has little out of plane stiffness, mode shapes associated with the vertical vibration of the deck may be included in the analysis. Typically, these modes have large periods, low frequencies, and very low mass participation in both the x and y directions. If the vertical vibration modes are the predominant modes considered in the analysis, then erroneous story forces can be calculated. The following are options can be used to prevent vertical vibration modes from skewing the lateral analysis:

- Use the option to include out-of-plane stiffness in RAM Frame – Criteria – Diaphragm. In some cases, especially with sloping diaphragms, this might not completely alleviate the issue, however.
- Model all framing as framing members so that their stiffness is considered in RAM Frame.
- If only static lateral load cases are used, explicitly define the periods and frequencies instead of using the calculations values. That way the calculated periods and frequencies are not required unless you have created a dynamic load case. If you are unsure of what frequencies or periods to enter, you could run the model with rigid diaphragms using the calculated values. The Loads and Applied Forces Report in RAM Frame reports the fundamental period and frequency in each direction.
- In version 14.06 or later, use Ritz vectors instead of Eigen Vectors in the Eigen Analysis (RAM Frame – Criteria – General). Using the Ritz vector approach has helped to eliminate the presence of these diaphragm flapping mode shapes in some cases.

Yes, this feature was added in release 15.05. Use the Reports menu - Diaphragm Forces. After this the program will put you into plan view if you are not already in plan view. Then cut a section using the mouse wherever you would like to get forces. Use the shift key to align your section with the global axis. Generally, it's best to cut a section fully across a slab or a part of the slab such that the slice created a complete free-body, but partial cuts are allowed.

If the diaphragm properties are too soft it causes the program to calculate huge deformations and/or very long mode shapes that are out of range of expected values and this, in turn, leads to some results being reported as 0 or -nan ("not a number"). Revise the diaphragm properties to be reasonable, or make the diaphragm flexible/pseudo flexible in such a case.

Example for Calculating Effective Elastic Modulus for Semirigid Diaphragms

RAM Frame - Criteria - Diaphragms

RAM Frame - Pseudo Flexible Diaphragms

How does the diaphragm out-of-plane stiffness affect behavior?