# Overview

Tilt-up walls are thin concrete panels. When a slender wall is subjected to axial compression and out-of-plane bending, second order effects must be considered. ACI 318 permits an amplified first order approach, elastic second order approach, or inelastic second order approach. ACI 318 also provides an alternative analysis for slender walls which is an amplified first order approach and is the basis of ACI 551.2R. RAM Structural System has implemented an elastic second order analysis to handle the slender wall problem.

In addition to the elastic second order analysis, several features where implemented to facilitate the in-place analysis and design of tilt-up structures in a 3D model.

- Distributed wall self-weight
- Gaps (joints) can be assigned to provide analytical separation from adjacent panels
- Assignment of eccentricity parameter for automatic application of out-of-plane gravity moments
- Pressure loads on walls
- Mechanism to isolate out-of-plane behavior
- Asymmetrical wall reinforcement for different cover on interior and exterior faces
- Net section consideration for reveals

# Wall Self-Weight Criteria

By default, self-weight of walls is computed by story and applied at the top of the member. This is conservative but can lead to excessive out-of-plane 2^{nd} order effects in slender walls. An option in RAM Manager – Criteria – Self Weight has been added to distribute wall self-weight to the finite element mesh. Rather than applying self-weight to the top of the physical wall, self-weight is applied to the top of each shell finite element within the wall.

# Modeling Tilt-Up Walls

Since the tilt-up wall analysis is performed in RAM Frame, all tilt-up walls to be considered in the analysis must be modeled as lateral walls. To distinguish tilt-up concrete walls from cast-in-place concrete walls (default assumption), a type property was added to the wall layout and change properties dialogs. When tilt-up is selected, the gap properties are available and can be assigned to either end. Exposure is assigned to the wall faces and impacts reinforcement cover in RAM Concrete Wall.

When modeling tilt-up walls that have a physical joint between panels, the gap assignment is used to provide analytical separation between the walls rather than physical modeling the separation. Gaps are displayed in plan as orange rectangles with tails that point toward the wall they are modeled on. In elevation, gaps are displayed as bold orange lines with tabs pointing to the interior of the wall they are modeled in. A gap only needs to be assigned to one wall end at a joint but can be assigned to both wall ends to facilitate rapid modeling. However, this can lead to ambiguous conditions for supported members at joints. RAM Modeler – Integrity – DataCheck will flag these conditions as errors when they occur.

When a wall is modeled on a floor layout, the i-end of the wall is the end that has the lesser X coordinate, or lesser Y coordinate if the X coordinate are the same, regardless of which point is clicked on first when modeling the wall. The primary face of the wall is on the right side as you walk from the i-end to the j-end of the wall. When looking at a wall in elevation, you are always looking at the primary face. RAM Modeler – Options – Show Wall allows the primary face and exposure properties to be turned on in the graphical display. The primary face arrow points away from the primary face. Labels for Exterior and Interior exposure assignments are displayed on the corresponding face.

# Cracked Factor For Out-Of-Plane Bending

An elastic second order analysis requires consideration for cracked regions on the wall. Stiffness after cracking is a function of internal forces and the placement of reinforcement. Wall reinforcement is not determined until after the analysis is performed and designed in RAM Concrete Wall. Therefore, the RAM Frame analysis relies on a cracked factor assigned to the wall that is applied to all finite elements to approximate the cracking effects. The cracked factor (bending) shown in the Add Concrete Wall dialog above modifies wall out-of-plane stiffness in the RAM Frame analysis.

ACI 318 permits the use of a reduced moment of inertia with an elastic second order analysis to account for cracking. ACI 551.2R states that a panel at ultimate load conditions typically exhibits cracks over most of the height and that testing and analytical studies confirm that assuming Ec Icr over the full panel correlates closely with test results. ACI 318 alternative analysis for slender walls provides an equation for the cracked moment of inertia which is typically less than 0.35 Ig.

The cracked factor (bending) factor requires engineering judgement. It should represent an effective out-of-plane moment of inertia for a factored load analysis (conditions at strength failure) with a reduction for uncertainty. It is recommended that the engineer start with a conservative cracked factor to avoid underestimating the 2^{nd} order effects and later refine the cracked factor if more accuracy is desired.

# Assigning Wall Eccentricity

Wall eccentricities are assigned automatically when a wall is modeled based on the default criteria specified in RAM Modeler – Set Defaults – Eccentricities. After a wall has been modeled, the eccentricity assignment can be changed using Layout – Wall – Change Eccentricity. Note that wall eccentricity applies to all walls, but currently moments due to the eccentricity are only considered on lateral walls in the RAM Frame analyses. The eccentricity is measured orthogonal to the plane of the wall and is applied to all loads from one way decking and supported gravity beams/joists. If a rigid link is assigned to a gravity beam supported by a wall, the rigid link overrides the eccentricity assignment.

# Wall Pressure Loads

Wall pressures are added in elevation mode in RAM Modeler. A lateral load case is created in Prop Table – Lateral Load Cases. There is an option to Lock Diaphragm Displacements which is a separate property for each load case. When this option is selected, the diaphragm will not displace in the RAM Frame analysis when the load case is analyzed. The purpose of this option is to isolate out-of-plane behavior from in-plane behavior. For example, the wind pressure producing out-of-plane bending in a wall is often a components and cladding load that is not necessary to be considered for the main lateral force resisting system. By preventing the diaphragm from displacing, the engineer can model the components and cladding wind pressures on all walls in a single load case and no in-plane forces will be produced in the 3D analysis. This option is ineffective for a flexible diaphragm.

Pressure properties are created in Prop Table – Lateral Loads – Wall Pressure Loads. Pressures are always applied orthogonal to the plane of the wall. Hence, you define the magnitude of the pressure and whether it acts towards or away from the primary face. In elevation mode, you are looking at the wall primary face. The direction towards is into the screen. Pressure can be defined explicitly as top and bottom pressures (linearly varying between top and bottom based on elevation) or as an inertia force based on the wall weight and fraction of gravity to consider.

Once a lateral load case and pressure property have been defined, pressures can be assigned by referencing a load case, selecting a load property, and applying it to the walls. Hatching and labels with the assignments will be displayed.

Wall openings have a distribution property to determine how to handle the portion of the wall pressure that exists over the opening. The pressure can be distributed to the vertical or horizontal sides of the opening, or completely ignored. Openings are created and changed in elevation mode in RAM Modeler.

# RAM Frame Analysis Criteria

By default, wall out-of-plane stiffness is ignored in RAM Frame. Out-of-plane stiffness can be turned in RAM Frame Analysis – Criteria – General. Typically tilt-up walls are pinned at the base for out-of-plane behavior, so the release rotational fixity option should be selected as well. Convergence on theoretical results occurs as the mesh sizes decreases and may require the default maximum distance between nodes to be reduced. However, reducing the mesh size will increase the analysis time.

When gravity moments due to eccentricity and lateral pressures are applied to walls, diaphragms cannot be assigned as flexible or pseudo-flexible because these are no diaphragm conditions. Without a diaphragm, there is nothing for the wall to lean against in the finite element analysis. If there are gravity moments due to eccentricity, you will encounter an instability in the analysis or massive displacements. Similarly, pressures on the wall will produce excessive displacements unless the diaphragm displacements are locked (not applicable to flexible diaphragms) unless your intent is to look at a cantilevered walls with fixed bases.

# RAM Frame Elastic Second Order Analysis

The creation of story force cases for in-plane analysis in RAM Frame and the analysis of individual load cases is no different than previous versions of RAM Structural System. After the load cases have been analyzed, the elastic second order analysis is performed in RAM Frame Analysis – Load Combinations mode. The Combinations menu has Custom, Strength, and Service Combinations. The Custom Combinations are the superimposed load case results that are not analyzed. The Strength and Service combinations are considered in the Advanced Analysis. The engineer should only create advanced analysis combinations for conditions where an iterative analysis is required. For example, assume that a single wind pressure case was created for the components and cladding forces that will control the out-of-plane design, and generated story force wind cases were created for the main force resisting system in-plane design. Small p-delta effects are negligible for the in-plane design and the P-Delta implementation in Frame Analysis Load Cases mode is adequate for any big P-Delta effects that impact in-plane behavior. Therefore, the advanced analysis combinations can only include combinations that include the out-of-plane pressure case as shown below.

The criteria defined in Load Cases mode is used in the load combination analysis, as well. Some criteria will cause the analytical model for a gravity case to be different than a lateral load case. This would present a problem for the analysis of a load combination that contains both cases. Errors will be thrown when these conditions occur. The user will need to change the selections in Load Cases mode before proceeding with the load combination analysis.

Additional criteria that is only relevant to elastic second order analysis exists in RAM Frame Analysis -Load Combinations mode – Criteria – Advanced Analysis. As discussed previously, the cracked section factors entered in RAM Modeler are intended to be used for a strength analysis. When analyzing service conditions, the crack factors can be relaxed. Rather than entering separate cracked factors for strength and service combinations, a single cracked factor modifier is entered for service combinations (see Service Analysis section below). Live load reduction can be turned enabled or disabled. Trouble shooting criteria for the iterative analysis is available to assist in achieving convergence.

The advanced analysis is performed by going to Process – Advanced Analysis, selecting the combinations to consider, and then clicking OK. If advanced combinations have not been defined or no valid combinations are selected, the combination type will have a red status light.

Viewing and reporting of load combination analysis results requires selection of the appropriate load combination type to consider. Reports and onscreen results only consider the active output mode load combination type. Similarly, the Frame Shear Wall Forces module has a dialog to select the combination type for envelope results.

# Service Analysis

The service combination analysis in RAM Frame Analysis Load Combination mode is an elastic 2nd order analysis that scales the cracked factors assigned in RAM Modeler by the service multiplier in Criteria - Advanced Analysis. The service analysis in the ACI Alternative Method for Out-of-Plane Slender Wall Analysis is an iterative bilinear interpolation that considers the displacement at the cracking moment with the gross moment of inertia and the displacement at the nominal moment with the cracked moment of inertia. The out-of-plane displacements in RAM Frame will be larger than displacements calculated using ACI slender wall for practical moments. If the maximum nodal displacement in RAM Frame for the service combination exceeds displacement limits, a more detailed analysis should be performed prior to changing wall stiffness.

If the maximum service moment in the wall considering 2nd order effects is below 2/3 the cracking moment, then the wall remains uncracked for the service combination per ACI slender wall. The RAM Frame service combination analysis can be repeated using the gross moment of inertia for the wall. To force the service analysis to use the gross moment of inertia, the service modifier should be larger than 1 divided by the bending cracked factor assigned in RAM Modeler.

If the maximum service moment in the wall considering 2nd order effects is above 2/3 the cracking moment, then the wall has cracked at some point during the iterative analysis. For cases when the first order moment is larger than 2/3 the cracking moment, the difference between the ACI method and the RAM Frame 2nd order analysis is minimized. The RAM Frame results can used directly. For cases when the first order moment is smaller than 2/3 the cracking moment, the difference between the ACI method and the RAM Frame 2nd order analysis can be significant. The RAM Frame results are conservative, but hand calculations may be necessary to improve accuracy.

# RAM Concrete Wall

RAM Concrete Shear Wall has been renamed RAM Concrete Wall in v17.00. The program was enhanced to allow reinforcement to be placed asymmetrically and consider reveals. In addition, consideration of the advanced analysis strength combinations and tilt-up reinforcement cover have been added.

The generated and custom load combinations superimpose the load case results to create a load combination force. Assuming the 2^{nd} order analysis was performed for out-of-plane forces only, the generated and custom combinations should only consider in-plane cases. The strength load combinations considered in the elastic 2^{nd} order analysis can be selected for design in RAM Concrete Wall – Load Combinations – Advanced. All selected combinations are considered in the design of all section cuts.

The criteria in Concrete Wall – Criteria – Design Criteria has options for cover and bar placement at wall face. Tilt-Up walls use the minimum cover requirements for precast. Exterior faces assume weather exposure that require additional cover per ACI 318. RAM Concrete Wall – Assign – Wall Panel Clear Cover allows the engineer to override the global cover criteria. Tilt-up walls typically have the vertical bars closest to the wall face to maximize the out-of-plane flexural capacity for a wall spanning vertically. Previous versions assumed the vertical bars were inside the horizontal bars. Therefore, separate placement options exist for the Cast-In-Place and Tilt-Up wall types.

Concrete Wall – Assign – Wall Pane Reveal Depths allows a depth to be specified that impacts bar placement and the concrete section considered in design. For example, if a wall is 10” thick with 1” of clear cover and there is a 0.75” reveal on the primary face, the cover to the bars closest to the primary face is measured from inside the reveal depth. If the vertical bars are closest to the face, the distance from the face of the 10” wall to edge of the vertical reinforcement edge is 1.75”. The reveal depth is applied to all section cuts in the wall panel. The concrete section considered in strength calculations excludes the reveal depths.

Critical horizontal sections for in-plane forces typically occur at the bottom of walls and openings. For out-of-plane design, critical horizontal sections will often occur mid-height where the out-of-plane moment is the largest. The program does not attempt to locate the maximum out-of-plane moment and add a section cut at that location. The engineer is required to add cuts where they are desired to be checked. If it is not obvious where the critical section for out-of-plane flexure will occur over the height of the wall, the engineer can use maximum cut spacing parameters in the section cut generator to create multiple cuts over the height of the wall. However, increasing the number of section cuts will increase the design time.

The Concrete Wall – Process – View/Update dialog and section cut design summary report include an out-of-plane shear check. Reveal locations and accurate bar placement can be visualized in the section view. Axial-flexure interaction has always considered weak axis moments in the wall. Pure out-of-plane bending occurs with a beta angle of 90 or 270 degrees.