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RAM SS Semirigid Diaphragms [TN]

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Current Revision posted to Structural Analysis and Design Wiki by Seth Guthrie on 9/17/2013 12:14:23 AM

RAM SS Semirigid Diaphragms [TN]

RAMStructuralSystem,TechNote,RAMFrame,selectservices

  
 Applies To 
  
 Product(s):RAM Structural System
 Version(s):13.00.00.00 or later
 Environment: N/A
 Area: N/A
 Subarea: N/A
 Original Author:Bentley Technical Support Group
  

 

 

 

 

 

 

 

 

Semirigid Diaphragms in RAM Frame

General

Semirigid diaphragms are discussed in section 6.12.3 of the Ram Frame Analysis documentation.

Diaphragm Flexibility

ASCE 7-05 Section 12.3 (note IBC 2006 Section 1613.6.1 modifies this slightly) discusses diaphragm flexibility. Diaphragms should be analyzed as semirigid unless they can be idealized as flexible or rigid. A diaphragm idealized as rigid is assumed translate and rotate as a rigid membrane. That is, there are no relative horizontal displacements between nodes attached to a rigid diaphragm and the nodal rotations about the vertical axis are always the same. In RAM Frame, even if the diaphragm is sloped the rigid diaphragm constraint is applied to a horizontal plane. The distribution of story shears to the individual frames/walls is a result of the analytical behavior which depends on the relative rigidities of the individual frames/walls. If the load is not applied through the center of rigidity then there will be a torsional moment on the diaphragm. A diaphragm idealized as flexible has no stiffness and there is no torsional moment. Shears should be distributed to the individual frames/walls based on tributary area. A semirigid diaphragm is somewhere between these idealized cases. An infinitely stiff semirigid diaphragm will behave like a rigid diaphragm and a complete lack of stiffness in the diaphragm will result in behavior similar to a flexible diaphragm. The figure below was taken from http://www.gostructural.com/article.asp?id=1131and is a nice flowchart for determining if your diaphragm can be idealized as flexible or rigid.

 

You can understand what the code is trying to do by thinking about a continuous beam with spring supports. With pinned supports, the reactions under any loading will be pretty much the same regardless of the beam stiffness. However, if the support deformation is not negligible (springs), then the reactions will be highly dependent on the beam stiffness unless the beam is extremely flexible or rigid relative to the spring stiffness.

The criteria for determining if a diaphragm can be idealized as flexible are pretty clear in ASCE 7-05. Section 12.3.1.1 basically says that untopped metal decks and wood diaphragms should be considered flexible unless you have moment frames. If you do have moment frames, Section 12.3.1.3 can be used to determine if the diaphragm can be considered flexible. The requirements for idealizing a diaphragm as rigid are not as straight forward because concrete slabs and concrete topped decks must have a span to depth ratio less than 3 and not have any horizontal irregularities that are defined in ASCE 7-05 Table12.3-1. RAM Frame does not determine if you have a horizontal irregularity. However, the output can be used to help determine if you have an irregularity. For example, RAM Frame Analysis > Process > Results > Drift at a Point or Drift at Control Points can be used to look at rigid diaphragm displacements at locations other than the center of mass. The displacements at the center of mass are shown in the RAM Frame Analysis > Reports > Story Displacements.


Semirigid Diaphragm Stiffness

The deck property tables in RAM Modeler require that you enter an Effective Thickness, Poisson's Ratio, and Modulus of Elasticity for non-composite and composite decks. For concrete slabs, the Modulus of Elasticity is calculated from the concrete properties. You still specify Poisson's Ratio and the Slab Thickness. There is an additional parameter that allows you to apply a diaphragm cracked section factor for concrete slabs.

ASCE 7-05 does not provide guidance as to what the stiffness of semirigid diaphragms should be. The stiffness of untopped steel roof decks is a function of many parameters including warping and fastener patterns. The Steel Deck Institute has published a method for determining a shear stiffness parameter (G`) in their diaphragm design manual. This method is typically presented in the deck manufacturer's catalogs. RAM Frame requires a modulus of elasticity be defined and the shear modulus is calculated based on Poisson's Ratio. Appendix A shows a method to approximate the effective modulus of elasticity for untopped steel decks and provides an example for a Vulcraft deck.  This effective modulus should be used in conjunction with a deck thickness equal to the gage of the sheet metal. 

Concrete slab and composite deck stiffness require engineering judgment. ACI 318-02 Section 10.11.1 provides effective moment of inertias for various structural members. There isn't a factor for diaphragms but the wall factors are probably the most appropriate. 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 you just need to enter the factor for the diaphragm cracked section factor. For a composite deck you would incorporate the cracked factor into the assumed effective thickness. For example, if you have 4 inches of concrete above the flutes and want to use 0.35Ig the effective thickness is 0.35 * 4 = 1.4 inches. It is probably appropriate to enter the Modulus of Elasticity and Poisson's Ratio for concrete and ignore the stiffness of the steel deck. If you want to consider a portion of the concrete within the flutes you should modify the effective thickness accordingly.

The maximum distance between nodes in the mesh specified in RAM Frame > Criteria > General will impact the behavior in the model. 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. If you have small slab edge offsets the elements within the edge will be poorly meshed. In these situations use the perimeter beams/walls as the diaphragm boundary.


Effectofbeamsconnectedtothediaphragm

InRamFrame,onlythelateralmembersareconsideredinthefiniteelementmodel(seeRAMSSAnalysisTypesfordetails).Consequently,anybeamthatneedstostiffenthediaphragmthroughitsaxialrigidityneedstobedefinedasa
lateralmember.

Dynamic Analysis with Semirigid Diaphragm

RAM Frame ignores the stiffness of gravity members in the finite element analysis. When a semirigid diaphragm has little out of plane stiffness you may see mode shapes associated with the vertical vibration of the deck. There are options in RAM Frame > Criteria > Diaphragm to include out-of-plane stiffness and/or include gravity columns and walls as springs to help prevent these mode shapes from occurring. In some scenarios, primarily with sloping diaphragms, this might not completely alleviate the issue. In these situations you may have to model all of the framing as lateral members so that their stiffness is considered in RAM Frame. Please note, static wind and seismic cases default to using calculated frequencies and periods. These calculated values require an Eigen solution (dynamic analysis). A simple work around would be to explicitly define the frequencies and periods rather than use the calculated value. That way the Eigen solution is 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 force report shows the frequencies and periods used in the wind and seismic cases.

Mass is distributed spatially when semirigid diaphragms are used.  It is not lumped at the center of mass (or eccentric location) like a rigid diaphragm.  Therefore, there are many more mass degrees of freedom in the model.  Also, since the mass distributed spatially, there are no rotational mass degrees of freedom.  If you have semirigid diaphragms, create an dynamic - Eigen solution load case and reduce the number of periods the program attempts to find.  In general three times the number of diaphragms is a reasonable number of modes to start with.  Then, review the periods and modes report and ensure that you have at least 90% mass participations (minimum per ASCE 7) in the X and Y directions.


Analytical Behavior of Semirigid Diaphragms Under Gravity Loads

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. A semirigid diaphragm has stiffness and will impact the forces in your lateral members. For a flat diaphragm with no out-of-plane stiffness these effects will be minimal. Including out-of-plane stiffness in the diaphragm will have a significant impact on the member forces. Essentially, the diaphragm will behave as a flange at the beam centerline. However, the forces in the diaphragm are not included in the beam results. You get into a scenario where the diaphragm is now acting like a slab and is spanning from column to column and is sharing the beam load. This is probably not the behavior that you are looking for and the results will not be correct.

When the diaphragm is sloped the impact on the member forces is even more significant. Consider gabled roof framing modeled as lateral members. The ridge beam will see very little bending because it is being propped up by the diaphragm which has a large stiffness component in the vertical plane of the ridge beam. The diaphragm acts like a deep beam and ends up taking the majority of the load and spans from column to column. Similarly, the gable frame which normally would resist the horizontal trust under gravity loads will see little load. 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.

 

Analytical Behavior of Sloped Semirigid Diaphragms Under Lateral Loads

Lateral loading applied to sloped semirigid diaphragms is applied in the XY plane, not in the plane of the diaphragm. Therefore, a component of the applied load acts out of the plane of the diaphragm. The stiffness of gravity members is ignored and significant out-of-plane deformations might be observed depending on the diaphragm stiffness. In particular, this is a problem when trying to simulate metal deck stiffness as described in Appendix A. Appendix A is a method to approximate the in-plane stiffness of metal decks and the resulting diaphragm properties will yield very little out-of-plane stiffness. Currently, it is not possible to model an orthotropic material or specify different stiffness factors in-plane and out-of-plane. 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.


Semirigid Diaphragms for Two Way Slabs

Out-of-plane stiffness is assumed when the deck is two way. There are some general concerns in RAM Frame for these diaphragms. The distribution of gravity loads is determined by meshing the diaphragm and then the program calculates the gravity load that is tributary to each node. . Gravity columns/walls are ignored in the Frame finite element analysis. If you have gravity columns and/or walls, the gravity forces on the lateral members will be inaccurate unless you utilize the consider gravity columns/walls as springs options. However, utilizing this option will have an impact on the lateral analysis as well. The following concepts apply to one way decks with out-of-plane stiffness considered, too.

Consider a five story shear wall building with two way 8 inch concrete slabs. Here is the typical plan.

The moments at the base of the walls for a lateral load case in the X direction are 13555 k-ft and the shears are 242 kips. If you run the same load case and include the gravity columns as springs the moments drop to 11163 k-ft but the shears stay the same. The rotation of the building is being resisted by the gravity column springs and out-of-plane diaphragm stiffness. You would get similar results if you modeled all of the columns as pinned lateral columns. As the out-of-plane stiffness of the diaphragm and axial stiffness of the columns increase the moments in the walls would decrease. Conversely, if there was negligible diaphragm stiffness the moments would not change. In the RAM Concrete Shear Wall Module all of the forces, including gravity forces, come from RAM Frame. If you intend to design the shear walls in RAM Concrete it is important to recognize how the Frame results will be impacted when the diaphragm is semirigid and out-of-plane stiffness is being considered.

Appendix A

See Also

Product TechNotes and FAQs

Structural Product TechNotes And FAQs

RAMSS Two Way Decks

External Links

Bentley Technical Support KnowledgeBase

Bentley LEARN Server

Comments or Corrections?

Bentley's Technical Support Group requests that you please confine any comments you have on this Wiki entry to this "Comments or Corrections?" section. THANK YOU!


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