This program provides horizontal force distribution analysis for a rigid diaphragm laterally supported by up to 60 walls. X and Y axis forces may be applied to a center of mass location, and that force distributed to all walls after the rotational stiffness analysis has been completed.

 

All lateral forces are distributed to each wall on the basis of relative rigidities and wall locations. Lateral shear forces, induced torsional forces, and minimum eccentricity are considered after determining the location of the center of rigidity. The user may enter dimensions for walls of homogeneous materials for use in calculating relative stiffness's.

 

The program provides analysis for one level only. For structures where walls are symmetrically placed on many levels, a calculation may be performed for each level and results added to determine shears and overturning moments for each wall. When determining center of mass (where the lateral force is applied) on successively lower levels when walls are NOT all in line, a new center of mass position should be calculated based upon wall forces acting from the diaphragm from the level above and combined with the force at that level.

 

 

 

Basic Usage

 

 

 

 

 

 

 

 

 

 

Unique Features

This program uses a numerical approach to determine center of rigidity location and to distribute lateral forces to each wall. Because walls may be located at any angle, a rigorous stiffness analysis is made calculating each wall's stiffness about both axes and combining the stiffness's of all the walls to determine a center of rigidity location.

 

Assumptions & Limitations

Because this program performs a very complex stiffness matrix analysis for all walls, the traditional method of listing separate components of direct and torsional shears is not applicable. Also, the program internally adds and subtracts the additional accidental eccentricity (based on both maximum dimensions) about each axis to calculate maximum force to each wall. The results in one final force value being displayed for each wall.

 

Coordinate System

Please note that a STRICT X-Y coordinate system should be used to ensure that the analysis is properly carried out. When setting up an X-Y coordinate axis, please follow the standard Cartesian model with the diaphragm located such that X increases to the right and Y increases up. Unless another method is necessary, this will perform very well (but the program can handle variations).

 

Example

The data entry for this example is shown in the screen captures that accompany the Data Entry Tabs and Results & Graphics Tabs sections to follow. Here is the sketch showing the angular orientation of the walls. Please see the table of wall input values for the exact locations.

 

 

Data Entry Tabs

This set of tabs provides entries for all input in this calculation. While you are entering data and switching between these tabs you can view the desired resulting information on the tabs on the right-hand side of the screen (calculated values, sketches, diagrams, etc.). A recalculation is performed after any entry data is changed. After each data entry you can view the results on the right-hand set of tabs.

 

General Tab

 

 

Loading : XX Shear, YY Shear

Calculate the total lateral force to be applied at the center of mass of the diaphragm. We have provided individual entries for each direction, to allow for different lateral forces in each direction. For multi-story buildings in seismic and/or high wind areas, the building code specifies a non-linear distribution of base shear force (for multiple levels) which should be considered. You can use the Multi Story Seismic Force Distribution and Multi Story Wind Force Distribution programs to help you with this analysis.

 

Load Application

Forces Act Separately : The maximum applied shear value will be the maximum force from each shear force acting separately along each axis.

Forces Act Together : Both XX and YY axis shear forces will be applied to the diaphragm simultaneously to calculate the maximum forces to each wall.

 

Minimum Applied Shear Eccentricity

This specifies the minimum accidental (additional) eccentricity that should always be used for determining torsional forces on the diaphragm. Entering 5" specifies 5% minimum accidental eccentricity for a direction. For a 100' maximum dimension this would result in a 5'-0" minimum eccentricity between center of mass and center of rigidity.

 

Distance to Center of Mass

Enter the X and Y distance from the datum point to where the Shear Force is applied. The center of rigidity (+/-5% accidental eccentricity) is compared with this location to determine overall diaphragm torsions.

 

Maximum Dimensions

This value represents the diaphragm's maximum dimension along the X and Y-axis, and is used to determine the minimum eccentricity of the applied shears by multiplying it by the "Minimum Applied Shear Eccentricity".

 

Wall Data Tab

This tab is used as the main data entry location for all wall data. The entry items at the bottom of the screen let you edit the highlighted item in the list directly. To Add a wall you must use the button.

 

 

Add, Change Delete Buttons

These buttons control the table of values for all the walls. Each button works on the wall line currently highlighted. When pressing Add or Change a window is displayed very similar to the one shown below. Using this window you can specify the information for the wall.

 

Since the program considers each wall to be of one material with uniform properties throughout you simply need to specify the Thickness, Height, Width, and Elastic Modulus to specify the stiffness of the wall.

 

The "Length" dimension is used by the program as the axis to report shear along the wall. Although the program calculates shear both along and perpendicular to the wall (width direction) the length is assumed to be what you are interested in and the final shear results are given along that direction.

 

Thickness

This is the thickness of the wall and should be the smaller plan view cross sectional dimension of the wall.

 

Length

This is the length of the wall and should be the larger plan view cross sectional dimension of the wall. This is the length which would normally be considered to be stiffer and brace the diaphragm against lateral forces. Each wall's thickness (and length) is used to calculate the moment of inertia about each axis, depending on how the Fixity item is specified (see below). This dimension is perpendicular to the axis used to measure the wall angle.

 

NOTE..... Before examining components of each wall's stiffness about each axis, for calculation of the wall stiffness matrices, deflection constants are calculated using IMAJOR and IMINOR. The typical deflection equation:

 

                  P/E[h3/(inertia *value) + 2.64h/A]

 

will set value = 12 for Fixed/Fixed walls and 3 for Fixed/Pinned walls.

 

Height

This is the height of the wall from the next lower datum point. Because the program does not "know" that there is any consistent reference elevation on the floor below you are free to enter a different height.

 

X Distance to C.G.,   Y Distance to C.G.

This is the distance from the center of resistance of the wall from your datum point. The center of resistance is the dimensional plan view center of the wall.

 

Wall Angle CCW

This is the rotation of the wall's length axis. It is measured in degrees rotated counter-clockwise from the "X" axis which is assumed to be horizontal to the model. For example, a 12" thick x 5'-0" long wall (in plan view) that is rotated 90 degrees is oriented up & down and is parallel with the "Y" axis.

 

Elastic Modulus

This is the elastic modulus of the wall. You can modify this value to "play" with a wall's stiffness that will result in a linear effect on the walls stiffness.

 

Wall End Fixity

Select Fixed-Fixed when the wall's top and bottom end rotations are completely restrained by boundary elements (such as by walls above, large footing, etc.). When one end of the wall is free to rotate select Fixed-Pinned. This entry will modify the calculation of each wall's rigidity (1/deflection).

 

Modeling hints

You can use this program to model all types of shear resisting elements. Note that Thickness and Elastic modulus have a direct linear effect on the wall stiffness.  The length and height values have a non-linear effect (see stiffness equations to follow).

 

 

Results & Graphics Tabs

This set of tabs provides the calculated values resulting from your input on the "Data Entry Tabs". Because a recalculation is performed with each data entry, the information on these tabs always reflects the accurate and current results, problem sketch, or stress/deflection diagram.

 

Results Tab

This tab shows the major calculated values for the system of walls entered.

 

 

 

Distance to Center of Rigidity

This is the calculated distance from the datum (0,0) point to the center of translational rigidity of the system of walls.

The center of rigidity is calculated by:

 

Accidental Eccentricity

This value is the entered maximum X and Y dimensions multiplied by the minimum eccentricity value/100 =(CR-CM)+ Accidental

 

Using the calculated center of rigidity and accidental torsion values that cause maximum wall loads, these are the eccentricities used to calculate X-X and Y-Y axis torsions.

 

Torsional Moments from Y-Y Shear

Using the specified Y-Y applied shear force and applying it at an eccentricity equal to :

       Center of Mass - Minimum Eccentricity - Distance to Center of Rigidity)

the applied torsional moments on the diaphragm are calculated. These torsional moments are then used to determine the force along the length axis of the wall needed to resist it using the calculated stiffness's of all walls in the system.

 

Wall Forces Tab

This is a summary of information table that shows wall number, eccentricity of wall's resisting center to diaphragm's center of rigidity, and the direction and torsional shear components calculated for the wall.

 

These components are then analyzed in all of their combinations to see which combination gives the maximum force parallel to the "length" of the wall.

 

 

 

 

 

Eccentricity

This is the distance from the walls geometric center (entered as input as "Wall C.G. Location") to the calculated "Center of Rigidity" of the system of walls you have entered.

 

Direct Shears & Torsional Shears

 

Max. Shear Along Length

Considering the center of rigidity for the entire system of walls, the maximum force to each wall is calculated by:

 

Because of the stiffness matrix approach for determining rigidities and deflections, the actual number of forces calculated for each wall is 32....one for each axis (2), one for each applied load (2), and two for each accidental eccentricity (8). This equals 2 * 2 * 8 = 32 forces for each wall.

 

For each wall, the force applied to the wall in each direction is summarized as direct and torsional shear, with the governing eccentricity of the applied load that created the torsional shears shown.

 

The table is difficult to understand when loads are applied along both axis at once, so we recommend only applying a load along one axis for each run and printout.

 

 

Sketch Tab

This tab provides a sketch of the beam with loads and resulting values shown. Using the [Print Sketch] button will print the sketch in large scale on a single sheet of paper. The buttons at the bottom of the tab control the display of additional information.

 

 

Sample Printout