3 Hh

zw zw

25 ft

FIGURE 5.37 Configuration of the unbraced eight-story frame.

2. Output data

• joint displacement

• member forces

5.5.4.3 Type of Elements

The analysis library consists of three elements: a plane frame, a plane truss, and a connection. The connection is represented by a zero-length rotational spring element with a user-specified nonlinear moment-rotation curve. Loading is allowed only at nodal points. Geometric and material nonlinearities can be accounted for by using an iterative load-increment scheme. Zero-length plastic hinges are lumped at the element ends.

5.5.4.4 Locations of Nodal Points

The geometric dimensions of the structures are established by placing joints (or nodal points) on the structures. Each joint is given an identification number and is located in a plane associated with a global two-dimensional coordinate system. The structural geometry is completed by connecting the predefined joints with structural elements, which may be a frame, a truss, or a connection. Each element also has an identification number.

The following are some of the factors that need to be considered in placing joints in a structure:

1. The number of joints should be sufficient to describe the initial geometry and the response behavior of the structures.

2. Joints need to be located at points and lines of discontinuity (e.g., at changes in material properties or section properties).

3. Joints should be located at points on the structure where forces and displacements need to be evaluated.

4. Joints should be located at points where concentrated loads will be applied. The applied loads should be concentrated and act on the joints.

5. Joints should be located at all support points. Support conditions are represented in the structural model by restricting the movement of the specific joints in specific directions.

6. Second-order inelastic behavior can be captured by the use of one or two elements per member corresponding to the following guidelines:

• Beam member subjected to uniform loads: two elements

• Column member of braced frames: two elements

• Column member of unbraced frames: one element.

5.5.4.5 Degrees of Freedom

A two-joint frame element has six displacement components as shown in Figure 5.34. Each joint can translate in the global x- and y-directions, and rotate about the global z-axis. The directions associated with these displacement components are known as degrees of freedom of the joint. A two-joint truss element has four degrees of freedom as shown in Figure 5.35. Each joint has two translational degrees of freedom and no rotational component.

If the displacement of a joint corresponding to any one of its degrees of freedom is known to be zero (such as at a support), then it is labeled an inactive degree of freedom. Degrees of freedom where the displacements are not known are termed active degree of freedoms. In general, the displacement of an inactive degree of freedom is usually known, and the purpose of the analysis is to find the reaction in that direction. For an active degree of freedom, the applied load is known (it could be zero), and the purpose of the analysis is to find the corresponding displacement.

There are no "built-in" units in PAAP. The user must prepare the input in a consistent set of units. The output produced by the program will conform to the same set of units. Therefore, if the user chooses to use kips and inches as the input units, all the dimensions of the structure must be entered in inches and all the loads in kip. The material properties should also conform to these units. The output units will then be in kips and inches, so that the frame member axial force will be in kips, bending moments will be in kip-inches, and displacements will be in inches. Joint rotations, however, are in radians, irrespective of units.

5.5.4.7 Input Instructions

In this section, the input sequence and data structure used to create an input file called P.DAT are described. The analysis program, PAAP, can analyze any structures with up to 300 degrees of freedom, but it is possible to recompile the source code to accommodate more degrees of freedom by changing the size of the arrays in the PARAMETER and COMMON statements. The limitation of degree of freedom can be solved by using dynamic storage allocation. This procedure is common in finite element programs [41,42], and will be used in the next release of the program.

The input data file is prepared in a specific format. The input data consists of 13 data sets, including five control data, three section property data, three element data, one boundary condition, and one load data set:

1. Title

2. Analysis and design control

3. Job control

4. Total number of element types

5. Total number of elements

6. Connection properties

7. Frame element properties

8. Truss element properties

9. Connection element data

10. Frame element data

11. Truss element data

12. Boundary conditions

13. Incremental loads

Input of all data sets are mandatory, but some of the data associates with elements (data sets 6-11) may be skipped depending on whether the use of the element. The order of data sets in the input file must be strictly maintained. Instructions for inputting data are summarized in Table 5.7.

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