Introduction. Background

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1 Introduction Welcome to CFS, the comprehensive cold-formed steel component design software. The endless variety of shapes and sizes of cold-formed steel members, combined with the complex failure modes of this type of construction, results in difficult and time-consuming structural calculations to determine the strength of such members. Background The American Iron and Steel Institute (AISI) has issued numerous editions of the "Specification for the Design of Cold-Formed Steel Structural Members" over the years. The 1986 Edition introduced a significant change to member local buckling strength determination called the "Unified Approach". This approach requires the computation of effective widths of each element of the cross section, based on the slenderness of the element, the stress in the element, and the degree of edge stiffening. The effective section properties are then used to determine the strength. This is often an iterative process due to shifting of the neutral axis and thus changes in stress level. The first version of CFS was written in 1987 to assist the engineer in performing these calculations. From the start, the primary goal was to handle any general shape of uniform material thickness. The internal calculations were developed from mathematically rigorous derivations for arbitrary shapes, including integration through the bend radius segments and across the material thickness. Furthermore, the calculations of torsional properties, which are often crucial in the determination of member strength, use exact integrations for thin-walled sections that incorporate the bend radius segments as well. Just as important was the goal to make the application easy to use. A flexible method of defining cross section shapes was devised that simply requires the length and angle of consecutive connected elements, and the bend radius between each of them. Additionally, the interface was graphical to provide the user with immediate visual confirmation of the inputs as they are given. This Version The CFS application has evolved through changes in appearance, numerous enhancements, and changes to the AISI Specification. The 1996 Edition of the Specification for the Design of Cold-Formed Steel Structural Members combined Load Factor and Resistance Design (LRFD) and allowable stress design (ASD) into one specification. The 1999 Edition was published as Supplement No. 1 to the 1996 Edition, which further refined the Specification and added some new provisions. Subsequently, AISI worked with Canada (Canada Standards Association) and Mexico (CANACERO) to develop the 2001 Edition of the North American Specification for the Design of Cold-Formed Steel Structural Members. This was further revised in 2004 Supplement with several new provisions, and the incorporation of the Direct Strength Method as an Appendix. AISI published the 2007 Edition of the North American Specification, followed by the 2010 Supplement with some additional changes. The 2012 Edition was released in 2013 to incorporate the 2010 Supplement changes and various improvements to the scope of the design provisions. This version of CFS provides calculations from the 2012, 2010, 2007, 2004, and 2001 Editions, including ASD and LRFD methods (U.S. and Mexico) and the LSD method (Canada). Calculations for the ASD and LRFD methods from the 1999 Edition continue to be available in CFS. Also, the 2002 Edition of the ASCE Specification for the Design of Cold-Formed Stainless Steel Structural Members (ASCE-8-02) is used for ASD and LRFD methods with stainless steel materials. Responsibility It is strongly recommended that the user of this software have a good understanding of these specifications. CFS is intended to assist the engineer in performing the necessary structural calculations

2 for cold-formed steel structures, and to increase your productivity. However, it cannot replace responsible engineering practice and judgment. Great effort has been made to ensure that the computations performed by CFS are correct within the guidelines and assumptions stated in this documentation. The author takes no responsibility for any errors that occur. The interpretation of the output and the application of such data is solely the responsibility of the user. RSG Software, Inc NW Chipman Road Lee's Summit MO,

3 Overview The CFS application allows you to work with two types of objects: Section and Analysis. A Section is a geometric definition of a cold-formed steel cross sectional shape and its material properties. An Analysis is a configuration of cold-formed steel members, supports, and loads, for a simple beam, continuous beam, or beam-column arrangement. Sections Sections are composed of one or more individual cold-formed steel cross sectional shapes (parts) that together represent a beam or column member. Each part in a section is of uniform thickness with curved bends, and may be an open or closed shape. Parts are made up of elements that each define the flat portion of the shape, the radius at the bend, an optional hole size, and some behavior characteristics. Many useful editing features are available to quickly modify shapes. In addition to ordinary cut, copy, paste, insert, and delete functions, you may also rotate and mirror parts and entire sections, add stiffening ribs to elements of a section, and generate the second half of a symmetrical part. You may also undo and redo the last change you make. A section also has a specific set of material properties associated with it. CFS provides several carbon steel and stainless steel material types to choose from. Additionally, you may define a custom carbon steel or stainless steel material for a section. Analyses An Analysis is composed of members, supports, and loads. It may be used for analyzing simple beams, continuous beams, or beam-columns, with both vertical and horizontal transverse loads, as well as axial loads. Each member has an associated section, and all sections used in an analysis must be open (loaded) when working with the analysis. Member locations are defined independent from support locations. This approach provides a convenient way to define overlaps and multiple supports without numerous member segments and nodes. Supports may be horizontal, vertical, torsional, and rotational about both X and Y axes. Loads are grouped by loading type (dead, live, etc.), and numerous ASD, LRFD, and LSD load combinations may be defined. Transverse loads may be distributed (uniform or trapezoidal) or concentrated. Axial loads are defined by specifying both ends: the point of application and the point of restraint. Computations Several computations are available: Section Properties (full and net), Section Strength (axial, bending, and shear), Member Checks, and Web Crippling Checks. The output from any of these computations may be combined into reports for saving and printing. A finite strip elastic buckling analysis can be performed on any section containing one part. You may also display and print shear, moment, and deflection diagrams for an analysis.

4 Interface CFS is a Multiple Document Interface (MDI) application. This means that you may have several windows open at the same time. The main CFS window is a container for all the MDI windows. There are three types of windows in the MDI: Section Window, Analysis Window, and Report Window. Additionally there are two windows for defining inputs: Section Inputs and Analysis Inputs. These are `floating' windows that are displayed separate from the main CFS window. They may be moved outside the boundaries of the CFS window, and they may be closed and reopened at any time. There are also temporary `dialog' windows used for entering specific information to complete a task. Some examples are Section Wizard, Insert Ribs, Member Check Parameters, Web Crippling Parameters, and Analysis Wizard. The main CFS window contains a menu of commands at the top. These commands are used to perform specific tasks, and are grouped into the categories: File, Edit, View, Compute, Tools, Window, and Help. Many of the commands on these menus have shortcut keys which are displayed next to the command. Some of the menu commands are available in pop-up menus from the section window, analysis window, and input grids. A toolbar also provides quick access to many of the menu commands. Units Many inputs throughout the application are numerical with an associated unit of measure. Initially, these inputs use the units defined by the application defaults (see Options - Units). These inputs contain a drop-down list showing conversions to other units of the same type. You may select any of the values in the list, thereby changing the default unit for that specific input. You may also type in the value and the unit you want to use. If you start modifying an input and change your mind, you may press the Esc key to revert to the previous value. Tab Pages Several input windows contain multiple pages that are accessed with tabs. By clicking on a tab, you can change the displayed page. You may also use the Ctrl-Tab and Ctrl-Shift-Tab keys to cycle through the pages. Grid Inputs Many of the inputs for sections and analyses are organized in a tabular form, or grid. Grids behave very similar to spreadsheets. By positioning the cell pointer on the desired location, you may change the entry by just retyping it, or by editing it. An input can be made available to edit by either double-clicking on it or by pressing F2. Rows in a grid may be inserted, deleted, copied, pasted, etc. Several keys may be used for navigation and cell selection in a grid. Arrow keys, Page Up, Page Down, Home, and End all move the cell pointer around the grid. Using these keys while holding the Shift key extends the selection of cells. Ctrl-X, Ctrl-C, and Ctrl-V are used to cut, copy, and paste rows.

5 Working With Sections There are three ways to create a Section Window: create a new section with the Section Wizard, open an existing section (sct) file, or open a section from a section library (scl) file. The section window contains a graphic of the cross sectional shape. All the inputs for a section are contained in the Section Inputs window. These inputs are grouped into three categories, each on a separate page in the window. The Section Page contains inputs that apply to the entire section. The Part Page contains inputs that apply to each individual part. The Elements Page contains inputs that define the elements for each part. Many useful editing features are available to quickly modify shapes. In addition to ordinary cut, copy, paste, insert, and delete functions, you may also rotate and mirror parts and entire sections, add stiffening ribs to elements of a section, and generate the second half of a symmetrical part. You may also undo the last change you make. See the Edit menu. A section also has a specific set of material properties associated with it. These properties are defined on the Section Page, and apply to all parts in the section. CFS provides several carbon steel and stainless steel material types to choose from. Additionally, you may define a custom carbon steel or custom stainless steel material for a section. There are several computations that may be performed for a section. These are accessed from the Compute menu. Full and net section properties are computed using the Properties command. The fully braced strength is computed using the Strength command. A member check can be performed using the Member Check command. This check requires some additional inputs defining the member parameters and the internal forces. A web crippling check can be performed using the Web Crippling command. This check also requires some additional inputs defining parameters and loads. And finally, a finite strip elastic buckling analysis can be performed on any section containing one part.

6 Section Wizard - Screen 1 of 2 This window is displayed by selecting New Section from the File menu. The Section Wizard is used to easily create the geometry for many common shapes. Once you finish the Wizard, you have full editing capabilities for the section. The first screen of the Section Wizard is used to select the type of section you want to create. After you select the shape, press the Next button to proceed to the next screen (see Screen 2 of 2). If the shape isn't represented, you may define any shape by choosing `Custom', and then pressing the Finished button. This will create a section with no geometry, from which you may start building the shape you need.

7 Section Wizard - Screen 2 of 2 This window is displayed by selecting New Section from the File menu. The Section Wizard is used to easily create the geometry for many common shapes. After you finish the Wizard, you have full editing capabilities for the section. The second screen of the Section Wizard is used to define the geometric parameters applicable to the shape you selected (see Screen 1 of 2). All of the dimensional parameters of Section Depth, Flange Width, and Lip Length are measured to the outside intersection points, except for panel sections which dimension to the centerline of the thickness. Some of the inputs do not apply to every shape. Thickness (name) Thickness (value) Section Depth Flange Width Lip Length Radius Web Angle Lip Angle Rib Spacing Number of Spacings A selection of predefined thicknesses and corresponding default bend radii. If you select a different thickness name, the thickness and default bend radius are updated. The predefined thicknesses may be customized by selecting Options from the Tools menu. The design thickness of the part. If you enter a thickness that matches a predefined thickness, its corresponding default bend radius will be assigned. If it does not match a predefined thickness and the bend radius is less than the new thickness, the bend radius is set equal to the new thickness. The overall vertical dimension of the section. The width of the flange. This is usually the dimension of the horizontal element(s). For angle sections, it is the length of the legs. The length of the lip edge stiffener. The inside bend radius for all bends on the part. If some bends use a different bend radius, you may make these changes after the Section Wizard creates the section. The angle of the web, measured from the horizontal. The angle of the lip, measured from the horizontal. The horizontal distance from the center of one rib to the center of the next rib. This only applies to panel sections. The number of rib spacings in the panel. There is one more rib than the number of spacings.

8 Section Inputs - Section Page This window is displayed when you create a new section or open an existing section. It is displayed as a floating window separate from the main application window. Closing this window will not close the section itself and will not lose any information about the section. To redisplay this window (when a section is open), select Section Inputs from the View menu, or press F3. This page contains general inputs that apply to the entire section. See also Part Page, Elements Page, and Direct Strength Page. Description Project Revised Material Type Text describing the type of section. Text describing the use for the section. The date and time of the last revision to the section, and the name of the user that made the last revision. The user name comes from the Heading page of the Options window. The designation for the type of material of the section. When you select a different material, the yield strength and tensile strength inputs are updated to the defaults for that material. For carbon steels, these may then be changed if necessary. If you have created a custom material it will also be available to select from the list. Additionally, you may view detailed information about the material and customize it specifically for the current section by pressing the button next to the material type. Apply strength increase from cold work of forming: Indicates whether to calculate and apply the strength increase from cold work of forming. Not available for stainless steel materials. Yield Strength, Fy Tensile Strength, Fu J Override Cw Override The section material yield strength used for design calculations. For stainless steel materials, this represents the longitudinal compression yield strength and is not editable. The section material longitudinal ultimate tensile strength. For stainless steel materials, this is not editable. St. Venant torsion constant to be used instead of the value calculated by CFS, if the override is greater than the calculated value. This is useful for sections containing multiple parts that are connected such that the section torsion constant is larger than the sum of the individual part torsion constants, which generally happens when separate parts join to form a closed shape. The Section Wizard will compute and assign the appropriate value for applicable sections, however if you subsequently make changes to the inputs, this value will not be automatically updated. Torsional warping constant to be used instead of the value calculated by CFS, if the override is greater than zero. This is useful for sections containing multiple parts that are connected such that the section torsional warping constant is different from the sum of the individual part torsional warping constants. The Section Wizard will compute and assign the appropriate value for applicable sections, however if you subsequently make changes to the inputs, this value will not be automatically updated.

9 Connector Spacing For built-up sections of more than one part, this defines the spacing between shear connectors. It is used to adjust the KL/r for column members.

10 Section Inputs - Part Page This window is displayed when you create a new section or open an existing section. It is displayed as a floating window separate from the main application window. Closing this window will not close the section itself and will not lose any information about the section. To redisplay this window (when a section is open), select Section Inputs from the View menu, or press F3. A section may contain multiple parts that act together as a member. This page contains the inputs for each part of the section, one part at a time. See also Section Page, Elements Page, and Direct Strength Page. Part Name Thickness (name) Thickness (value) Default Inside Radius The name associated with the part, useful in built-up sections to identify the different parts more readily. The name may be changed to any name not already used in the section. To view the part inputs for a different part, select its name from the list. There is always one more entry in the list than there are parts currently defined. To add a part, select the last entry in the list and optionally rename it. You may delete a part by deleting its name and pressing Enter. A selection of predefined thicknesses and corresponding default radii. If you select a different thickness name, the thickness and default radius are updated. The predefined thicknesses may be customized by selecting Options from the Tools menu. The design thickness of the part. If you enter a thickness that matches a predefined thickness, its corresponding default radius will be assigned. If it does not match a predefined thickness and the default radius is less than the new thickness, the default radius is set equal to the new thickness. The inside bend radius used for new elements on the part. Changing this input will automatically change existing radii on the current part that were equal to the previous default radius. Centerline Dimensions When unchecked, element lengths and hole distances are measured to the outside intersection points. When checked, element lengths and hole distances are measured to the centerline intersection points. Changing this input automatically adjusts the element lengths and hole distances. Centerline dimensions are useful for panels and similar shapes that use the same centerline dimensions for different material thicknesses. Closed Part When unchecked, the part geometry is open, such as a channel or zee. When checked, the part geometry is closed, such as a tube. Placement of Part from Origin: X Y The horizontal position of the current part with respect to the section origin. This position may be defined as measured to the left edge, to the right edge, or to the center of gravity of the part. Positive X is to the right of the origin. The vertical position of the current part with respect to the section origin. This position may be defined as measured to the top edge, to the bottom edge, or to the center of gravity of the part. Positive Y is above the origin. Distance from Center of Gravity:

11 X Y The horizontal distance from the center of gravity of the current part to the extreme left and right edges of the part. The vertical distance from the center of gravity of the current part to the extreme lower (bottom) and upper (top) edges of the part.

12 Section Inputs - Elements Page This window is displayed when you create a new section or open an existing section. It is displayed as a floating window separate from the main application window. Closing this window will not close the section itself and will not lose any information about the section. To redisplay this window (when a section is open), select Section Inputs from the View menu, or press F3. Parts are made up of elements, each defining the geometry and behavior of a flat segment of the shape. This page contains the inputs for elements, one part at a time. See also Section Page, Part Page, and Direct Strength Page. Part Name Length Angle Radius Web The name of the part whose elements are currently displayed in the grid. The distance measured parallel to the element between the outside intersection points, or between the centerline intersection points if using centerline dimensions. To add an element to an open part, enter its length on the blank row after the last element. To add an element to a closed part, modify the length (or angle) of the last element. The length and angle of the added element on a closed part will always be determined by the program to close to the beginning of the first element. The direction of an element from the preceding element. An angle of 0 is horizontal to the right. Positive angles are measured counter-clockwise. The inside radius of the bend between the current element and the preceding element. The radius of the first bend on an open part has no relevance. The radius of the first bend on a closed part is the radius between the last element and the first element. Indicates the type of shear and web crippling behavior of the element. All web types other than 'None' have shear and web crippling strength. 'Cee', 'Zee', 'Hat', and 'Deck' are used for the web elements in those types of sections. 'Double' is used for webs restrained against rotation such as back-to-back Cees. 'Nested' is used for 'Zee' shapes that are overlapped at a support. 'Single' is a generic type for all other elements that should contribute to the shear and web crippling strength. Calculations using the 1999 AISI Specification and 2002 ASCE Specification treat 'Cee', 'Zee', 'Hat', and 'Deck' webs as 'Single' webs. Calculations using the 2001 AISI Specification treat 'Single' webs as 'Cee' webs. k Coefficient Hole Size Distance The plate buckling coefficient used to determine the effective width of the element under compression. Usually you may leave this as the default value of 0, which indicates the program should determine the appropriate value (see Element Behavior). This is useful for intermediate stiffeners or unusual situations. If you enter a non-zero plate buckling coefficient, it is applied using the compression width of the element and the maximum compressive stress in the element. You may not define a plate buckling coefficient and a hole in the same element. The size of the hole in the plane of the cross section. The default hole size of 0 indicates the element has no hole. The maximum hole size is 80% of the flat width of the element. You may not define a hole and a plate buckling coefficient in the same element. The distance from the beginning of the element to the center of the hole, measured from the outside intersection point, or from the centerline intersection point if using centerline dimensions.

13 Section Inputs - Direct Strength Page This window is displayed when you create a new section or open an existing section. It is displayed as a floating window separate from the main application window. Closing this window will not close the section itself and will not lose any information about the section. To redisplay this window (when a section is open), select Section Inputs from the View menu, or press F3. Parts are made up of elements, each defining the geometry and behavior of a flat segment of the shape. This page contains the inputs for elements, one part at a time. See also Section Page, Part Page, and Elements Page. Use Direct Strength Prequalified Section Pcrl/Py Pcrd/Py Mcrl/My Mcrd/My Vcr/Vy Check this box to use the Direct Strength Method of calculating section strength according to the AISI Specification. You must compute the elastic buckling behavior and enter the corresponding direct strength parameters in the table. You may use the Elastic Buckling feature from the Compute menu for sections consisting of one part. This tool allows you to select points directly from the buckling plot and transfer the values into the table. Check this box if the section complies with the geometric parameters of prequalified sections as defined in the Direct Strength provisions of the AISI Specification. The strength of prequalified sections is determined using a lower factor of safety or a higher resistance factor. The ratio of the critical elastic local buckling load to the compressive yield load. A value of 0 causes CFS to revert to the Main Specification provisions even if you check the box to Use Direct Strength. The ratio of the critical elastic distortional buckling load to the compressive yield load. A value of 0 causes CFS to revert to the Main Specification provisions even if you check the box to Use Direct Strength. The ratio of the critical elastic local buckling moment to the yield moment. A separate value is required for each direction of bending. A value of 0 causes CFS to revert to the Main Specification provisions even if you check the box to Use Direct Strength. The ratio of the critical elastic distortional buckling moment to the yield moment. A separate value is required for each direction of bending. A value of 0 causes CFS to revert to the Main Specification provisions even if you check the box to Use Direct Strength. The ratio of the critical elastic shear buckling force to the shear yield force. A separate value is required for vertical and horizontal shear. A value of 0 causes CFS to revert to the Main Specification provisions even if you check the box to Use Direct Strength.

14 Custom Material Properties - Carbon Steel Page This window is displayed when you press the... button on either the Material page of the Options window, or on the Section page of the Section Inputs window. If you came from the Options window, you are defining the default material for new sections; it does not affect any existing sections. If you came from the Section Inputs window, you are defining the material for the current section only. This page will appear if the original material was a carbon steel. See also Stainless Steel Page. Material Type Modulus of Elasticity, E Minimum Yield Strength Default Yield Strength The designation for the type of material of the section. AISI specifies this value to be ksi or 203,000 MPa for carbon steel. The minimum value of yield strength for this type of carbon steel. The default value of yield strength when using this type of carbon steel (usually the minimum yield strength). Minimum Tensile Strength The minimum value of tensile strength for this type of carbon steel. This also is used as a maximum value of yield strength. Maximum Tensile Strength The maximum value of tensile strength for this type of carbon steel. Default Tensile Strength Default Button Customize Button The default value of tensile strength when using this type of carbon steel (usually the minimum tensile strength). This button sets the material to the current default settings for the new sections (defined in the Options window). This button allows you to customize the material currently being displayed. You may modify the name of the material, but CFS will always place the name inside brackets to identify it as a material not originally provided with CFS. You may also modify any of the numerical inputs, with some limitations imposed by CFS. The customized material will then become your default material for new sections.

15 Custom Material Properties - Stainless Steel Page This window is displayed when you press the... button on either the Material page of the Options window, or on the Section page of the Section Inputs window. If you came from the Options window, you are defining the default material for new sections; it does not affect any existing sections. If you came from the Section Inputs window, you are defining the material for the current section only. This page will appear if the original material was a stainless steel. See also Carbon Steel Page. Material Type Property Directions Modulus, Eo Yield Strength, Fy Ramberg-Osgood Coefficient, n Tensile Strength, Fu Default Button Customize Button The designation for the type of material of the section. Stainless steel properties may vary in the different directions. Longitudinal is parallel to the direction the steel was produced in, which CFS assumes to be the direction of the longitudinal axis of a member. Transverse is perpendicular to the longitudinal direction, in the plane of the sheet. The initial modulus of elasticity, which is the slope of the stress-strain curve at zero stress. The yield strength of the material as determined by the offset. A coefficient indicating the linearity of the stress-strain curve (refer to the ASCE 2002 Specification, Appendix B). The coefficient for shear is used to determine the plasticity reduction factor for shear (Gs/Go) as computed using the same modified Ramberg-Osgood Equation, except that a offset is used instead of The tensile strength in the longitudinal direction. This button sets the material to the current default settings for the new sections (defined in the Options window). This button allows you to customize the material currently being displayed. You may modify the name of the material, but CFS will always place the name inside brackets to identify it as a material not originally provided with CFS. You may also modify any of the numerical inputs, with some limitations imposed by CFS. The customized material will then become your default material for new sections.

16 Section Window The section window displays a graphic of the section. Every open section has a corresponding section window, whether it was created as a new section with the Section Wizard, or opened from a section file or a section library. The graphic contains some markers in addition to the geometry. Each part in the section contains a dot at its center of gravity. The origin of the section is shown as a plus (+). After any computations, the principal axes are shown as perpendicular lines. The long line is the major axis and the short line is the minor axis. The shear center is identified as a plus with a circle. This window normally comes up in Selection Mode. In this mode, you may use the mouse to select parts and elements. Selected elements are shown highlighted in the graphic. You may select any element in the section simply by clicking on it. You may select multiple consecutive elements on a part by clicking on one element and dragging to another element. You may select an entire part by doubleclicking on it. A pop-up menu of edit commands is available by clicking with the right mouse button. In Selection Mode, you may also measure the distance between two points on the section. Hold the Ctrl key and click the first point. CFS will select the nearest endpoint, midpoint, or arc quadrant, and show a point marker in the window. Then hold the control key and click the second point to display distance information for the two points. You may zoom and pan the graphic using either the mouse or the keyboard. To switch to Zoom Mode, click on the small magnifying glass in the lower right corner of the window, or press F6. In Zoom Mode, anywhere you click in the graphic will shift to the center of the window and change magnification. Clicking with the left mouse button zooms in, and clicking with the right mouse button zooms out. You may also pan the graphic using the scroll bars. You may use the following keys to zoom and pan: F6 Home Esc Page Up Page Down Arrow Keys Ctrl-Arrow Keys Toggle between Zoom Mode and Selection Mode Zoom to 100% and center Zoom to 100% and center Zoom in Zoom out Pan Pan in larger increments

17 Elastic Buckling Parameters This window is displayed when you select Elastic Buckling from the Compute menu. After you enter the appropriate values and choose the appropriate settings, press the OK button and the Elastic Buckling Results will be displayed when the analysis is complete. The elastic buckling analysis uses the finite strip method to determine the magnitude of the forces at which elastic buckling occurs. These buckling forces are affected by the member length (half wave length) and the stress distribution. The analysis will determine forces corresponding to numerous member lengths, and identify the lengths that correspond to controlling buckling modes. The time to complete the analysis can take from a few seconds to several minutes depending on the complexity of the cross-section, the number of member lengths to calculate, and the speed of the computer. Start Length The smallest member length to consider in the buckling analysis. To capture local buckling, this should generally be less than 1/2 the width of the largest flat element. End Length Increment Size Stress Distribution The largest member length to consider in the buckling analysis. Intermediate lengths of 5 to 10 times the size of the section may exhibit distortional buckling. Greater lengths will reveal flexural and/or torsional buckling modes. The size of the length increments to use between the start length and the end length. The choices are: Small - each length is about times the previous length (20 increments in a 10x length range). Medium - each length is about 1.25 times the previous length (10 increments in a 10x length range). Large - each length is about 1.6 times the previous length (5 increments in a 10x length range). The vertical and horizontal sider bars are used to define the stress distribution you would like to apply to the cross-section. With both slider bars in the middle, uniform compression is applied. The vertical slider bar controls the moment about the X axis, where the top position produces a positive moment and the bottom position produces a negative moment. The horizontal slider bar controls the moment about the Y axis, where the right position produces a positive moment and the left position produces a negative moment.

18 Elastic Buckling Results The Elastic Buckling window is displayed when you choose Elastic Buckling from the Compute menu, define the parameters to use in the analysis, and then perform the analysis. The elastic buckling analysis uses the finite strip method to determine the magnitude of the forces at which elastic buckling occurs. This analysis involves dividing the section into several flat strips throughout the flat and curved portions of the section. The number of strips is automatically determined by CFS based on the size of the element and the stress distribution. More strips are used for larger elements with stress gradients. Fewer strips are used for smaller elements with uniform stress. This screen shows a plot of buckling stress vs. member length. The member length is shown on a horizontal logarithmic scale to provide greater resolution for the short wave-length behavior. The stress magnitude represents the maximum stress in the cross section, which is generally the maximum compressive stress, but may be the maximum tensile stress if bending about a non-symmetric axis. The magnitude of the stress and resulting forces is displayed in the upper right corner corresponding to the position of the X on the plotted profile. You can move the X to other locations on the profile to display the corresponding values by pressing the left and right arrow keys or clicking on the profile. The Copy Data button copies the plot profile data to the clipboard. This data can be pasted into another application such as Notepad, Word, or Excel.

19 Some specific locations on the profile have mode shapes available for display. You can move the X to the mode shape locations by holding the Ctrl key and pressing the left and right arrow keys. The Mode Shape button will display the mode shape, and subsequently pressing the Stress Plot button will return to the stress vs. length profile as shown above. This particular example illustrates a distortional buckling mode shape. Since it occurs at a local minima, the load ratio (P/Py) can be automatically be applied to the Direct Strength value for the section by clicking on the Direct Strength button. You just need to select whether it s a local or distortional buckling mode and click OK. To fill in additional direct strength values for the section, run the elastic buckling analysis for the other basic stress distributions (positive and negative bending about x and y axes). The Print button will print the elastic buckling results to the default printer. It contains the stress vs. length plot and each controlling mode shape. This printout is formatted for standard 8½x11 inch paper in portrait orientation. Other sizes and orientations should work, but may result in less effective use of the paper. To change the default printer, paper size, or orientation, press the Printer button.

20 Working With Analyses There are two ways to create an Analysis Window: create a new analysis with the Analysis Wizard or open an existing analysis (anl) file. The analysis window contains a graphic of the members, supports, and loads. Simple beams, continuous beams, beams with laps, and beam-columns are examples of the types of problems that can be analyzed. All the inputs for an analysis are contained in the Analysis Inputs window. These inputs are grouped into five categories, each on a separate page in the window. The General Page contains inputs and information for the analysis. The Members Page contains inputs that define the members in the analysis. The Supports Page contains inputs that define the member supports. The Loadings Page contains inputs that define loads applied to the members, and are grouped into different loadings. The Combinations Page contains inputs that define combinations of loadings to analyze. All geometric locations are input using a one-dimensional global coordinate system. Members, supports, and loads are all defined independently, so that members may span across multiple supports, and loads may span across multiple members. Node numbers and beam elements are assigned internally by CFS and are invisible to the user. The plot of the geometry is always shown with the members in a horizontal orientation, but the analysis is still valid for vertical columns. Each member has an associated section, and all sections used in an analysis must be open (loaded) when working with the analysis. The orientation of the section is as viewed from the left end of the member. Supports may be horizontal (X), vertical (Y), torsional (T), and rotational about both X and Y axes (Rx and Ry). CFS does not consider ends of overlapped sections or inflection points as support locations. If you want to consider these as support points, you must explicitly define them. Loads are grouped by loading type (dead, live, etc.), and numerous ASD and LRFD load combinations may be defined. Transverse loads may be distributed (uniform or trapezoidal) as well as concentrated, and may be in any direction perpendicular to the members. Axial loads are defined by specifying both ends: the point of application and the point of restraint. Once an analysis is defined, computations may be performed for one load combination at a time. The current combination on the Combinations Page of the Analysis Inputs is displayed in the analysis window. You may create shear, moment, and deflection diagrams, and you may also compute member checks and web crippling checks for any location. These are accessed from the Compute menu.

21 Analysis Wizard - Screen 1 of 4 This window is displayed by selecting New Analysis from the File menu. The Analysis Wizard is used to easily create the geometry and loads for many common beam and column configurations. Once you finish the Wizard, you have full editing capabilities for the analysis. The first screen of the Analysis Wizard is used to select the type of analysis you want to create. After you select the configuration, press the Next button to proceed to the next screen (see Screen 2 of 4). If the analysis configuration isn't represented, you may define any analysis by choosing `Custom', and then pressing the Finished button. This will create an analysis with no members, supports, or loads, from which you may start building the configuration you need.

22 Analysis Wizard - Screen 2 of 4 This window is displayed by selecting New Analysis from the File menu. The Analysis Wizard is used to easily create the geometry and loads for many common beam and column configurations. Once you finish the Wizard, you have full editing capabilities for the analysis. The second screen of the Analysis Wizard is used to define the parameters for members and supports. After you enter the parameters you want, press the Next button to proceed to the next screen (see Screen 3 of 4). Section Span Lengths Cantilever Length Lap Length Fixed End Supports Bearing Length Fastened Support Member Bracing Braced Flange Moment Reduction, R Rot. Stiffness The name of the section file to use for the members. This drop-down list contains all of the sections currently open in CFS. The length of each span, or distance between vertical supports, separated by commas (or periods if a comma is your decimal separater). You may enter up to 20 spans. The length of cantilever beyond the first and last supports. The length of beam overlap on each side of the supports. Only available for Multi-Span Beam with Laps. Indicates whether the extreme ends of the members are in rotation about both the X and Y axes. If checked, you cannot have a cantilever length. The length of bearing in the longitudinal direction (width of the supports). Indicates whether the bearing flanges are fastened to the supports. This can affect the web crippling strength at the support. Indicates the type of bracing between vertical supports: None, Mid-Point, Third- Points, Quarter-Points, or Fully Braced. This will create horizontal (X) and torsional (T) supports at the specified intervals. These brace points will restrain all flanges against twisting and lateral movement. For members having one flange fastened to deck, sheathing, roof system, or other continually connected system, select the flange that is attached: Bottom, Top, Left, or Right. Otherwise, select None. You can have both a braced flange and discrete member bracing at the same time. If there is a braced flange, enter the moment reduction factor as defined in the AISI or ASCE Specification for your situation. For example: R=0.70 for continuous span Z sections R=0.60 for continuous span C sections R=0.70 for simple span C or Z section, depth 6.5" R=0.65 for simple span C or Z section, 6.5" < depth 8.5" R=0.50 for simple span Z section, 8.5" < depth 12 R=0.40 for simple span C section, 8.5" < depth 12 The rotational stiffness provided to the braced flange by connection to the bracing material (deck, sheathing, etc.). This stiffness is incorporated in the distortional buckling calculations for the flange which is braced (bottom, top, left, or right). The units for this input are moment/radian/unit length (such as k- in/rad/in) which is then reduced to a force (such as k). Refer to the AISI

23 Specification and Commentary for more information on determining what value to use. Length, Lm The distance along the length of the member between discrete rigid restraints that restrict distortional buckling. If there are no discrete restraints for distortional buckling, leave this as a large value (such as the span length) and CFS will calculate the distortional buckling wavelength. If the member is fully restricted against distortional buckling, use Lm = 0. If the shape does not have a distortional buckling failure mode, the value of Lm has no effect. In cases where rotational stiffness is provided to the braced flange by connection to bracing material, Lm does not represent the spacing between fasteners. It is the distance between rigid restraints against distortional buckling, if they exist.

24 Analysis Wizard - Screen 3 of 4 This window is displayed by selecting New Analysis from the File menu. The Analysis Wizard is used to easily create the geometry and loads for many common beam and column configurations. Once you finish the Wizard, you have full editing capabilities for the analysis. The third screen of the Analysis Wizard is used to define the applied loads. After you enter the parameters you want, press the Next button to proceed to the next screen (see Screen 4 of 4). Tributary Width Include beam self-weight Dead Load Live Load Product Load Roof Live Load Snow Load Wind Load or Uplift Load Angle The width across which pressure loads are carried by the members in the analysis. For beams, this applies to all load types listed below. For columns, this only applies to the wind load. For beam arrangements, indicates whether to include the beam self-weight as an additional dead load. Not applicable to columns. Gravity load due to the weight of construction materials and permanent equipment, stated in force per unit area for beams, and force for columns. Gravity load due to intended use and occupancy, stated in force per unit area for beams, and force for columns. Gravity load due to intended use of product storage on racks, stated in force per unit area for beams, and force for columns. Gravity load due to intended use on roofs, stated in force per unit area for beams, and force for columns. Gravity load due to accumulation of snow, stated in force per unit area for beams, and force for columns. Transverse load due to wind, stated in force per unit area. For beams, this is an uplift force as is commonly applied to roof members. This input applies to beam analyses. A load angle of 90 degrees indicates vertical loads. The dead load, live load, roof live load, and snow load are applied as negative magnitudes, producing a download load. Wind uplift is applied as a positive magnitude, producing an upward load. Load angles other than 90 degrees can be used to simulate members installed at an angle (such as purlins). For example, rather than rotating a section by 30 degrees to reflect its installed angle, you should adjust the load angles by -30 degrees, and therefore enter a 60 degree load angle.

25 Analysis Wizard - Screen 4 of 4 This window is displayed by selecting New Analysis from the File menu. The Analysis Wizard is used to easily create the geometry and loads for many common beam and column configurations. Once you finish the Wizard, you have full editing capabilities for the analysis. The fourth screen of the Analysis Wizard is used to select the load combinations to include in the analysis. After selecting the load combinations you want, press the Finished button and the new analysis will be generated. The load combinations list includes several sets of commonly used load combinations, plus a set of custom load combinations if you defined any in the Options window. Under combinations to include, check or uncheck the applicable load combinations to your analysis problem. Each load combination has an associated design method (ASD, LRFD, or LSD). The current application setting for the design specification will determine which specification is actually applied to each combination. For example, if the selected specification is 2012 NAS - US (ASD), but the load combination is LRFD or LSD, then the specification applied to that combination would be 2012 NAS - US (LRFD). Check the box for Use Inflection Point Bracing if you want the analysis to treat inflection points as brace points. This setting will apply to all selected load combinations. So if you want some of them to be changed, you can get more specific on the Combinations page of the Analysis Inputs window.

26 Analysis Inputs - General Page This window is displayed when you create a new analysis or open an existing analysis. It is displayed as a floating window separate from the main application window. Closing this window will not close the analysis itself and will not lose any information about the analysis. To redisplay this window (when an analysis is open), select Analysis Inputs from the View menu, or press F4. This page contains general inputs and information for the analysis. See also Members Page, Supports Page, Loadings Page, Combinations Page, and Notes Page. Description Project Revised Text describing the type of analysis. Text describing the use for the analysis. The date and time of the last revision to the analysis inputs, and the name of the user that made the last revision. The user name comes from the Heading page of the Options window.

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