This wiki explains the complete workflow to perform the Direct Analysis Method using RAM Elements.

1.1 Introduction

In order to use the Direct Analysis Method, the next steps are required:

Definition and creation of Notional Loads. This is done in order to consider de geometric imperfections during analysis.
Applying Stiffness Reductions. Reduction factors should be applied to members to consider the inelastic behavior.
Running a Second Order Analysis. A second order analysis considering both P-D and P-d effects must be performed.

The applications of these steps will be done using a benchmark example provided by the AISC Design Examples v15.1.

1.2 Example

This example corresponds to AISC Example C.1A.

1.2.1. Model data

Open the “Example C.1A.retx” model. The structure is a moment frame as shown in the following figure:

The beams are loaded for Dead Load (0.4 kip/ft) and Live Load (1.2 kip/ft).

1.2.2. Definition and creation of Notional Loads

Go to Home tab, then go to Load Conditions > Add/Edit and click the button Add and edit notional load cases button:

The Notional load cases manager dialog will be displayed:

As the example model is a 2D model, unselect Z Direction. For this example, use the default values for the Gravity load factor. Let the Gravity load cases for notional loads selected for both DL and LL as all gravity loads for both conditions must be considered for the creation of notional loads. Then click on Generate and the notional load cases will be created as follows:

Click on the OK and these two new load cases will be added to the Load Conditions:

Click on the OK button of the Load Condition window to accept these new load cases.

Now, the model has notional load forces automatically generated for dead and live load respectively:

The program converts automatically all loads applied for the gravity load cases: self-weight, point loads, distributed loads, pressure load, etc. into similar load (self, point, etc.) but applied as a lateral load using the direction and factors provided in the Notional load cases manager dialog. These notional loads are regenerated each time the model is analyzed, so you do not need to recreate these load cases when the source gravity loading changes.

1.2.3. Load Combinations

To consider the combined effects of gravity and notional loads, the program requires some steel design type load combinations. Use the Load Combination Generator tool to generate a set of steel design combos, ASCE 7-16 LRFD is appropriate in this case.

1.2.4. Stiffness Reductions

Go to the Members spreadsheet, then go to Stiffness reduction button:

In this spreadsheet the user is able to enter the stiffness reduction factor for the selected members. RAM Elements also provides some tools to speed up the process. For this example, click on the Assign stiffness reductions factor tool:

The following dialog will be displayed:

By default, both the Axial and Flexural stiffness reduction factors are selected. Those values are according to the AISC-360 specification. However, these values can be modified according to any specification required.

By clicking on the OK button, the values are set into the spreadsheet:

1.2.5. P-Delta and P-delta effects

With the two previous steps completed (Notional Loads and Stiffness Reductions), it is time to run a second order analysis.

Click on the Analyze model button located at the top left of the screen (or go to Process > Analyze model). In the Analysis dialog, select the option to run a P-D Analysis:

In order to include P-d effects, members need to be segmented to capture the translation and rotation effects. For this, go to the FEM tab and check the option Minimum number of segments:

Note 1.-

Tests indicate that 4 segments are required to account the member second order effects, higher values do not provide much more accuracy in results and could produce a model unnecessarily large.

Note 2.-

Members, like beams, with very low axial loads, can be ignored for P-d effects. In that sense, it is possible to avoid a member to be segmented during analysis: go to Members spreadsheet, in the first button Connectivity and description go to the column Ignore segmentation and check the members that not require to be segmented.

1.2.6. Results

All the steps to perform the Direct Analysis Method are completed!

After the analysis is performed, check some results like combined bending moments:

As it is possible to see, the values match exactly those presented in Example C.1A of the AISC Design Examples v15.1, page C-5.

Direct Analysis Method