## Diaphragms

Diaphragms provide lateral load distribution functions, and are necessary for automatic Wind and Seismic load generation. There are three fundamental types of diaphragms in structural modeling:

Note:

For additional advice on this topic, please see the RISA News webpage at risa.com/news. Type in Search keywords: Diaphragms.

 RISA-3D Rigid Diaphragm RISAFloor linked with RISA-3D Includes Rigid and Flexible Diaphragms

#### Rigid Diaphragms

Rigid diaphragms represent a plane of very high rigidity. Rigid diaphragms distribute load to elements which connect to them solely based on the stiffness of the elements. They achieve this by tying all of the joints within the diaphragm plane together for both translation and rotation, but only within the plane of the diaphragm. This is typical behavior for most slabs and decks, which attribute vertical loads based on the tributary area of their supporting members.

Note:

• Older versions of RISA-3D had a diaphragm option called "Planar". This option was removed due to a lack of real-world applicability to any structure.
• There is no rigid diaphragm design in the program. This is strictly an analysis tool.
• Sloped rigid diaphragms are not supported. Therefore rigid diaphragms always exist in a flat horizontal plane.

Loads applied within the plane of a diaphragm will be attributed to all elements which connect to the diaphragm. The amount of load which each element takes is proportional to its stiffness. Diaphragms are capable of both translation and rotation, so the torsional effects of the moment arm between the center of load and the center of rigidity are accounted for. This is also true for a dynamic mass which is offset from the center of rigidity.

Because a rigid diaphragm is part of the stiffness matrix, an explicit Center of Rigidity is not calculated or reported. Internally, the program creates a hidden set of rigid links which interconnect all of the joints in the diaphragm, therefore preserving the diaphragm's rotational degree of freedom (something which traditional nodal slaving is incapable of).

###### Connectivity

All joints which fall within the plane of the diaphragm automatically become connected to it. Joints may be intentionally disconnected from the diaphragm by checking the Detach From Diaphragm box in the Joint Coordinates spreadsheet. If a boundary condition exists within the plane of a diaphragm it will act as a restraint for all of the joints connected to the diaphragm.

Rigid Diaphragms must be defined along the Global Axes, therefore they can only exist in the XY, XZ, or YZ planes. If rigid behavior is desired along a plane other than these, a semi-rigid diaphragm (made of plates) with a large stiffness value can be used instead.

###### Rigid Diaphragm Stiffness

The stiffness of the rigid diaphragm is set to a unitless value of 1 x 107 by default. This value has been calibrated as providing the best behavior for most models. It can be adjusted from within the diaphragms spreadsheet, however adjusting this value is only recommended in the following circumstances:

1. The lateral stiffness of elements which pass through the diaphragm is sufficiently large to cause the rigid diaphragm to behave as a semi-rigid diaphragm (i.e. the translations of the joints within the diaphragm do not correspond to a uniform rotation about one point). If this is the case, try a diaphragm stiffness of 1 x 108.
2. The dynamics solver is not converging. In this case try reducing the diaphragm stiffness to 1 x 106, however be sure to confirm that the diaphragm is not behaving semi-rigidly (see #1)
3. The program has generated a warning that the sum of the reactions does not equal the total applied load. In the case of points on the diaphragm which have a very close proximity to each other, the stiffness of the internally generated rigid link between them may approach the stiffness of a boundary condition. If this happens the model can have Ghost Reactions, which are points which act as boundary conditions (dumping load out of the model) without any notification. In this case try reducing the diaphragm stiffness to 1 x 106, however be sure to confirm that the diaphragm is not behaving semi-rigidly (see #1)

To adjust the diaphragm stiffness either right-click on the diaphragms spreadsheet and select Set Diaphragm Stiffness, or click on the button.

###### Rigid Diaphragms in a RISA-3D Only Model

With RISA-3D's diaphragm feature, a node can be defined within a given plane as the diaphragm node, and all points in that plane will be rigidly connected to each other with internal rigid links. Thus, each node will rotate and translate as one rigid body and exhibit rigid diaphragm behavior. RISA-3D's rigid diaphragm feature is discussed further in the Diaphragm Modeling Tips section.

###### Rigid Diaphragms in a Combined RISAFloor/RISA-3D Model

A RISA-3D model that is linked up to RISAFloor has an automatic rigid diaphragm analysis and design. Each individual slab/deck polygon is converted to a rigid diaphragm within RISA-3D. Therefore, it is possible to have multiple independent diaphragms at any given floor elevation.

#### Semi-Rigid Diaphragms

A semi-rigid diaphragm is one which distributes loads based on both the stiffness of elements which connect to it and on the stiffness of the diaphragm itself.

###### Semi-Rigid Diaphragms in a RISAFloor/RISA-3D Model

The Semi-Rigid diaphragm in RISA-3D will help you distribute the lateral forces based on the stiffness of the slab. When RISA-3D is integrated with RISAFloor the program can create a Semi-Rigid diaphragm automatically. The Semi-Rigid diaphragm is defined in Diaphragm Parameters in a Beam Supported Floor and the Slab Definitions spreadsheet in a Concrete Floor Slab. During the integration between RISAFloor and RISA-3D, the program creates a mesh of FEA plate elements within the edges of the slab. The thickness of the plates is defined by the slab/diaphragm defined in RISAFloor. The plate elements are automatically submeshed so that they attach to all vertical elements (columns and walls) as well as any new members or loads added into the RISA-3D model. Below shows an example of a simple L-shaped building with the mesh displayed. For further display information see the Model Display Options - Diaphragms topic..

When the model is in RISA-3D, the mesh size is controlled by the Model Settings - Solution Tab -Semi-Rigid Mesh . For RISAFloor ES models, the slab stiffness can be reduced based on the Icr factor in the RISAFloor Slabs spreadsheet and the Use Cracked Slabs checkbox in the Model Settings in RISA-3D. The Icr slab stiffness only affects the out-of-plane stiffness. For further information on cracked slabs, see Elevated Slabs - Analysis. The top of the columns are fixed to the diaphragm using links to distribute the forces over a 12"x12" area rather than a single column node. For further information see the Column Meshing section of the help.

###### Semi-Rigid Modeling Tips for Concrete Floor Slabs

Lateral Elements: When modeling with a Semi-Rigid diaphragm, it's important to make all columns and walls Lateral. This will bring all the columns and walls into RISA-3D which will support the slab as the vertical loads are applied. In RISA-3D, the program will apply both lateral and vertical loads to the diaphragm for analysis of the lateral system. This is different than Rigid diaphragms because only the lateral resisting system needs to be transferred into RISA-3D.

Reinforcement Design: RISA-3D will not design the reinforcement for the slab. The reinforcement is designed in RISAFloor and is based on the vertical loads. However, you can find forces in the slab in RISA-3D using the tools listed below.

1. Contours: The contours will display the global axis forces over the slab.  See the Model Display Options - Diaphragms section for further information on display of the contours. The contours can be used to find the high and low forces as needed for reinforcement design.
2. Internal Force Summation Tool (IFST): There is an IFST Slab tool that allows you to find forces from a point on the submesh to another point on the slab.  This tool can be used to "cut" across the slab and will finds forces along the "cut". This is the same tool that is used internally in RISAFloor to find Auto-Design Cuts inside the Design Strips. For further information on this tool, see the IFST Topic.
###### Semi-Rigid Modeling Tips for Beam Supported Floors

Vertical Loads: The semi-rigid diaphragm has no self weight or out-of-plane stiffness. Internally the plates are modeled with the "Plane Stress" flag turned on so that there is no stiffness out-of-plane. Self weight of the diaphragm is handled through the decks, see Loading for further information. The diaphragm is used for only in-plane load distribution.

Diaphragm Material:The Semi-Rigid diaphragm material uses the General Materials.  There are a list of default General Materials, however you can add to this list to match your diaphragm. See Materials for further information on creating your own General Material.

Diaphragm Thickness:The Semi-Rigid diaphragm thickness should be selected based on the approximate stiffness you expect from the slab or deck for lateral loading. The semi-rigid diaphragm is modeled using isotropic plates. Therefore, there is no association with the deck direction for the semi-rigid diaphragms. If your diaphragm is truely one-way, you may consider using a Flexible diaphragm.

###### Semi-Rigid Diaphragms for RISA-3D Only Models

RISA-3D does not have the ability to automatically define a Semi-Rigid diaphragm. However, Semi-Rigid diaphragms can be represented in the model using plates.

A semi-rigid diaphragm is modeled with plates, and requires you to model and submesh the plates appropriately. In order to adequately mesh your plates it is good to be familiar with Plate-Member Interaction. Plates are modeled using general materials, so the first step is to set up a material with the material properties of your diaphragm.

Next, model your plates using the specified material, and with an accurate thickness. Be sure to check the “Plane Stress” option. This makes it so that the plates only have stiffness within their own plane, and as a result won’t add any composite bending strength to the beams in the plane of the diaphragm.

Note:

• When meshing a floor diaphragm around members, you want to make sure that the corners of your plates meet at members. Otherwise, when applying surface loads to plates, the members will not see that load.
• Sloped semi-rigid diaphragms are not supported. Therefore rigid diaphragms always exist in a flat horizontal plane at the ceiling level.

#### Flexible Diaphragms

Flexible diaphragms distribute loads to elements which connect to them solely based on the tributary area of the element within the plane of the diaphragm.

###### Flexible Diaphragms in a RISA-3D Only Model

The diaphragm feature in RISA-3D cannot be used to create a flexible diaphragm. To consider a flexible diaphragm in RISA-3D there are a couple of options. The main option is to manually calculate how much force is going to each frame or shear wall in the lateral system and apply that load directly to those elements as a point or distributed load. Another option is to essentially use a semi-rigid path to use plates with an equivalent thickness and material properties as your diaphragm. You may choose a very small equivalent thickness which will still be semi-rigid, but much closer to flexible than rigid.

###### Flexible Diaphragms in a Combined RISAFloor/RISA-3D Model

A flexible diaphragm can be defined in a combined RISAFloor/RISA-3D model. For wood diaphragms, the program will actually design the sheathing and nail spacing, incorporating the code specified design tables from the NDS/IBC. See the Diaphragms - Analysis & Results topic for more information on how the design works and how loads are attributed both for wind and seismic loads. The diaphragm can be defined as flexible when drawing the deck edge or from the Diaphragms spreadsheet.

Note:

• Flexible diaphragms cannot be defined on an elevated slab floor.

Flexible diaphragms within RISAFloor/RISA-3D are used solely as load-attribution devices, and do not exist as elements within the stiffness matrix, unlike rigid or semi-rigid diaphragms. Flexible diaphragms have no stiffness, and are incapable of transferring load from one element within them to another. Thus, members that do not have lateral resistance out of plane are susceptible to stability issues. To increase stability in a model with a flexible diaphragm it may be necessary to add small springs in the out-of-plane directions on the frames at the tops of the columns. This will stabilize the members while generally having a minimal effect on the analysis of the model.

###### Ceiling Diaphragm (Sloped Roofs)

When a flexible diaphragm is applied to a sloped roof in RISAFloor, a setting exists to specify whether a ceiling diaphragm is present.

The load attribution for the flexible diaphragm will occur only for Lateral Members from RISAFloor when a ceiling diaphragm is not specified. This is illustrated above where the lateral load follows the rafters. When a ceiling diaphragm is specified, it is necessary to draw in collector beams at the ceiling elevation so that the load can be carried directly the columns or walls at the base of the sloped members. With a ceiling diaphragm, the sloped members will not experience any lateral load directly. Note that the same total amount of lateral force will be applied regardless of this setting. This only controls whether the lateral load is applied to the sloped members, or in a horizontal flat plane.

#### Diaphragms Spreadsheet - General Tab

The Diaphragms Spreadsheet contains diaphragm information and may be accessed by selecting Diaphragms on the Spreadsheets menu under Data Entry. Alternatively, it can be accessed by clicking the button on the Data Entry Toolbar.

For RISA-3D models there are two different versions of the Diaphragms spreadsheet. One version is for models which have been created in RISA-3D, the other is for models which are linked to RISAFloor.

###### RISA-3D Only

Joint Label defines the master joint for the diaphragm. For diaphragms in the ZX plane, the diaphragm will be created at the Y-coordinate of the specified joint. Similarly, XY diaphragms will use the joint's Z coordinate, and YZ diaphragms will use the joint's X coordinate.

When the Inactive box is checked the diaphragm will be ignored by the program. This is a convenient way to disable diaphragms without deleting them.

You may designate any floor level as a No Wind / Drift (i.e. mezzanine) level in order to omit it from the generated wind load calculation and the drift calculations.

Note:

• Previous versions of RISA-3D had a Type field that had a Membrane and Planar option. The Planar option has been removed and all diaphragms are Membrane. Only the in-plane rigidity is in play and not the out-of-plane rigidity.
• There are not semi-rigid or flexible options for RISA-3D as a standalone program.

Elevation displays the elevation of the diaphragm. This is the same elevation as the floor which the diaphragm was created on.

Mass displays the dynamic mass tributary to the diaphragm. This mass is used to calculate seismic forces for both static and response spectra methods.

Mass MOI displays the dynamic mass moment of inertia of the diaphragm. This moment of inertia is used to calculate seismic forces for response spectra analysis.

Center of Mass displays the X and Z coordinates of the center of mass of each diaphragm. This is the location at which static (equivalent lateral force) seismic loads are applied for each diaphragm.

Eccentricities are the percent of length/width of the diaphragm which are used to place "accidental eccentric" seismic loads for each diaphragm. This only applies to the static (equivalent lateral force) procedure. See ASCE 7-16, Section 12.8.4.2 for more information.

When the Inactive box is checked the diaphragm will be ignored by the program. This is a convenient way to disable diaphragms without deleting them.

You may designate any floor level as a No Wind/ Drift (i.e. mezzanine) level in order to omit it from the generated wind load calculation and the drift calculations.

Diaphragm displays the diaphragm label. This label is used for the naming of Diaphragm Regions.

Type specifies whether the diaphragm is Rigid (Membrane) or Flexible for a Beam Supported Floor or Rigid (Membrane) or Semi-Rigid for Concrete Floor Slab. If a diaphragm has been defined as Flexible within RISAFloor it can be toggled between Rigid and Flexible in RISA-3D.

Region lists the diaphragm regions for each diaphragm. Diaphragm regions are used for the design of wood flexible diaphragms, and are also useful for explicitly defining how flexible load attribution is to be performed.

Design Rule specifies the Design Rule which is assigned to each region. Only the information on the Diaphragms tab of the Design Rules Spreadsheet is considered.

SGAF is the specific gravity adjustment factor for the design of wood flexible diaphragms. For more information see AF&PA NDS SDPWS, Table A4.2, Note 2. This value defaults to 1, however it should be manually changed if the framing supporting the wood flexible diaphragm is not Douglas Fir-Larch or Southern Pine.

Note:

#### Diaphragm Modeling Tips

###### Modeling a Rigid Diaphragm in RISA-3D

In the Diaphragms spreadsheet, enter the joint in the Joint Label column that the diaphragm will be defined by. Designate the Plane the diaphragm will act.

Internally, the Rigid Diaphragm ties all nodes at that elevation together with Rigid links.

To view the diaphragm, click the Toggle Display of Diaphragms button . This allows you to visually see the location of the diaphragms. Inactive diaphragms will not show up graphically.

From here the Wind and Seismic load generators can be run.

Members in the plane of the diaphragm will have no axial load attributed to them. This is because the internal rigid links that are created to achieve rigid behavior take the entire load. In these cases, the axial loads in these members will need to be considered outside of the program.

###### Openings in a RISA-3D Only Model

If there are openings within the defined diaphragm, where portions of the structure are not rigidly connected, it is possible to disconnect those locations from the diaphragm in the Joint Coordinates spreadsheet.

###### Use of Rigid Diaphragms with the Top of Member Offset

Never use Top of Member Offsets with the diaphragm feature. This combination will almost surely make the forces in the member incorrect. This is because a Vierendeel-type truss is created, where the internal rigid links created by the diaphragm feature acts as a top flange and the member acts as the bottom flange. What now is drawn as a single member has multiple internal members influencing these forces.

###### Partial Diaphragms in a RISA-3D Only Model

There may be times when you want to model a partial diaphragm, i.e., a diaphragm that extends over only a portion of a floor or plane.  For example, let’s say you are trying to model a floor that is composed of a relatively rigid section (thick concrete slab) and a relatively flexible section (corrugated steel decking).  You would like a way to model a rigid diaphragm for only the rigid portion of the floor.

To accomplish this, you may specify that a joint or group of joints be detached from the diaphragm.  This may be accomplished by selecting the Detach from Diaphragm option in the Joint Coordinates spreadsheet or double-click a joint and specify it in the Information dialog.

Another way this can be done is to offset the elevations of the joints that comprise the rigid floor section so that they are all a little higher or a little lower than the surrounding floor.  The offset only needs to be slightly larger than the Merge Tolerance, since this is the tolerance for other joints to be on the same plane as the master joint.  This works because the rigid diaphragm feature will only rigidly connect joints that are at the same elevation as the master joint.  The other joints, which are on the flexible portion of the floor and are now at a different elevation than the master joint, will not be incorporated into the diaphragm. This can also be used for a "twin tower" situation where you want each tower to act independently of the other.

###### Partial Diaphragms in a Combined RISAFloor/RISA-3D Model

For buildings where a flexible diaphragm and rigid diaphragm occur on the same floor you can model the diaphragms using separate slab edges. This will require a gap between the framing of the two diaphragms however, such that load will not automatically be shared between the diaphragms.

Below is a screenshot of the gap for example:

###### Sloped Roof Flexible Diaphragms (RISAFloor/RISA-3D Integration)

The flexible diaphragms at sloped roofs require members that are in the horizontal plane to attribute load to. These members must exist at the base roof elevation. For that reason in the example below the program reports "Loads are not attributed for Diaphragm". In the direction perpendicular to the ridge there are no members for the program to attribute the wall wind loads to, so no loads are attributed to the diaphragm at all in that direction.

To correct this issue, simply draw horizontal bracing in the structure which can pick up the load and transmit it to the main lateral force resisting system.

For additional advice on this topic, please see the RISA News webpage at risa.com/news. Type in Search keywords: Sloped Roofs.