Chapter. Steel Member Design

Transcription

1 Chapter Steel Member Design The steel member design modules can be used for elastic and plastic design of structural steel members. Several modules act as post-processors for the frame analysis modules, facilitating integrated frame analysis and design. Steel Member Design 4-1

2 Quick Reference Steel Member Design using PROKON 33 Steel Member Design for Axial or Combined Stress 45 Plastic Frame Design Error! Bookmark not defined. Crane Gantry Girder Design Error! Bookmark not defined.6 Plate Girder Design Steel Member Design

3 Steel Member Design using PROKON A variety of steel member design modules are included in the PROKON suite. These are considered useful tools when designing members using either elastic or plastic methods. Elastic member design When designing struts and ties, you can post-process frame analysis results using the member design module for axial stress, Strut. Similarly, the member design module for combined stress, Com, can be used to design members subjected to both axial force and moment, or beam-columns. Plastic frame design The Plastic Frame Design module can be used to design steel frames using plastic design methods. The same module can also optimise sections for better economy. Girder design Specialised modules are available for designing crane gantry girders and plate girders. Steel Member Design using PROKON 4-3

4 Steel Member Design for Axial or Combined Stress The steel member design modules are suitable for the following design tasks: Use Strut for checking and optimising steel members subjected to axial stress only, e.g. truss members. Com is used for checking and optimising steel members subjected to a combination of axial and uniaxial or biaxial bending stresses, e.g. beams and columns in frames. The steel member design modules primarily act as post-processors for the frame analysis modules. Both modules also have an interactive mode for the quick design or checking of individual members without needing to perform a frame analysis. 4-4 Steel Member Design using PROKON

5 Theory and application A brief background is given below regarding the application of the design codes. Design scope The steel member design modules can design hot-rolled sections subjected to axial stress or a combination of axial and bending stresses. Strut can be used to design any hot-rolled section for axial stress. Because the design procedure is relatively simple, design results are presented in tabular format. This feature makes the program especially useful when designing of a large number of struts and ties. Com can design hot-rolled double symmetric sections and channels subjected to axial and bending stress. Non-symmetric sections like angles are not supported. More design checks need to be performed for each member requiring more detailed output. Strut and Com use a similar design approach. Although there may seem to be a degree of overlapping in their design features, the two modules rather complement each other with specialised individual design functions. You will typically use them to design the different components of the same structure, e.g. design a roof truss in Strut and its supporting columns in Com. Note: Support for cold-formed sections is not provided. However, hot-rolled hollow circular and rectangular sections may be designed with the programs if such sections are deemed to have relatively thick walls with a resulting low risk of local buckling. Tapered sections The current versions of Strut nor Com cannot design tapered sections, e.g. haunches in portal frames. When evaluating members with varying sections, the section type at the first node is used over the whole length of the member. Design codes The program designs axially loaded steel members according to the following design codes: AISC LRFD (Strut only). BS CSA S M89. Eurocode (Strut only). SABS (allowable stress design). SABS (limit state design). Steel Member Design using PROKON 4-5

6 Units of measurement The steel design modules support the following units of measurement: Metric. Imperial (Strut only). The preferred unit of measurement can be selected using the Units command on the File menu. Symbols Where possible, the same symbols are used as in the design codes: A ne /A g : Effective area factor with which the gross sectional area must be multiplied to obtain the effective sectional area, reduced for fasteners holes. The factor applies to elements subjected to tensile axial stress only. K e : Factor with which the member length is multiplied to obtain the effective length for lateral torsional buckling (Com only). K v : Factor with which the member length is multiplied to obtain the effective length for buckling about the v-v (weakest) axis of the member (Strut only). K x : Factor with which the member length is multiplied to obtain the effective length for buckling about the x-x axis of the member. K y : Factor with which the member length must be multiplied to obtain the effective length for buckling about the local y-y axis of the member. AISC LRFD (Strut only): BS : F : Applied axial force (kn or kip). F y : Specified minimum yield strength of steel (MPa or ksi). F u : Specified minimum tensile strength of steel (MPa or ksi). L / r : Slenderness ratio. P u : Ultimate axial stress (MPa or ksi). P n : Allowable axial stress based on the slenderness ratio (MPa or ksi). S c : Actual axial stress in member (MPa or ksi). 4-6 Steel Member Design using PROKON

7 CSA S M89: F : Applied axial force (kn or kip). L / r : Slenderness ratio. M : Applied moment (knm or kipft). M a : Maximum buckling moment in presence of axial load (knm or kipft). M b : Lateral torsional buckling resistance moment (knm or kipft). M c : Moment resistance in the absence of axial force (knm or kipft). m : Equivalent uniform moment factor. n : Slenderness correction factor. P c : Allowable axial stress based on the slenderness ratio (MPa or ksi). P y : Design strength of steel (MPa or ksi). S c : Actual axial stress in member (MPa or ksi). Z : Elastic modulus (mm³ or in³). C e : Euler buckling strength (kn or kip). C r : Factored compression resistance (kn or kip). C u : Ultimate compression force (kn or kip). L / r : Slenderness ratio. F u : Ultimate strength of steel (MPa or ksi). F y : Design yield strength of steel (MPa or ksi). M cr : Elastic buckling moment (knm or kipft). M r : Factored moment resistance (knm or kipft). M u : Ultimate bending moment (knm or kipft). T r : Factored tensile resistance (kn or kip). T u : Ultimate tensile force (kn or kip). U 1 : Capacity factor to account for moment gradient and second-order effects. Z pl : Plastic modulus (mm³ or in³). ω 1 : Equivalent uniform bending moment factor. ω 2 : Moment gradient factor giving increased moment resistance of laterally unsupported members. Eurocode (Strut only): Steel Member Design using PROKON 4-7

8 F : Applied axial force (kn or kip). f y : Design yield strength of steel (MPa or ksi). L / i : Slenderness ratio. P c : Allowable axial stress based on the slenderness ratio (MPa or ksi). S c : Actual axial stress in member (MPa or ksi). SABS : f cr : 0.6 times the Euler buckling stress (MPa or ksi). f y : Design yield strength of steel (MPa or ksi). L / r : Slenderness ratio. f y : Design yield strength of steel (MPa or ksi). P c : Allowable axial stress based on the slenderness ratio (MPa or ksi). P mc : Allowable compressive bending stress (MPa or ksi). P mt : Allowable tensile bending stress (MPa or ksi). S c : Actual axial stress in member (MPa or ksi). S t : Average axial tensile stress (MPa or ksi). S mc : Maximum compressive bending stress (MPa or ksi). S mt : Maximum tensile bending stress (MPa or ksi). ω : Coefficient allowing for varying bending moment. SABS : C e : Euler buckling strength (kn or kip). C r : Factored compression resistance (kn or kip). C u : Ultimate compression force (kn or kip). L / r : Slenderness ratio. f u : Ultimate strength of steel (MPa or ksi). f y : Design yield strength of steel (MPa or ksi). M cr : Elastic buckling moment (knm or kipft). M r : Factored moment resistance (knm or kipft). M u : Ultimate bending moment (knm or kipft). T r : Factored tensile resistance (kn or kip). 4-8 Steel Member Design using PROKON

9 T u : Ultimate tensile force (kn or kip). U 1 : Capacity factor to account for moment gradient and second-order effects. Z pl : Plastic modulus (mm³ or in³). ω 1 : Equivalent uniform bending moment factor. ω 2 : Moment gradient factor giving increased moment resistance of laterally unsupported members. Sign conventions Member design is done in the local element axes. Bending about the x-x axis generally corresponds to strong axis bending and bending about the y-y axis to weak axis bending. For non-symmetric sections like angles, the x-x and y-y axes are horizontal and vertical with the v-v axis representing the weakest axis. Tip: The exact orientation of the v-v axis of a mono-symmetric section can be determined using the Section Properties Calculation module, Prosec. Axial force and moment The local axes system and force directions are defined as follows: Axial force: The local z-axis and axial force is chosen in the direction from the smaller node number to the larger node number. A positive axial force indicates compression and a negative force tension. Bending: Moments about the x and y-axes represent bending about the section's strong and weak axes respectively. Positive moments are taken anticlockwise in all diagrams. P-delta effects Design codes generally allow stability effects to be taken into account in buckling checks by reducing design capacities or amplifying design moments or axial forces. Trusses are normally not sensitive to sway. However, in any structure, if you judge P-delta effects to be an important part of the analysis, you should perform a second order frame analysis. Steel Member Design using PROKON 4-9

10 Second order analyses The desirability of a second order analysis is echoed in the various design codes: AISC LRFD: Section C1 states that an analysis of second order effects is required for frames. This is done by second order elastic analysis or first order analysis with amplification factors B 1 and B 2. BS : Accounts for stability effects by amplification of design moments by suggesting a more exact approach in clause CSA S M89: Desirability is expressed in clause Eurocode : See clause SABS : Encourages second order analysis of frames with sway by limiting the coefficient for variable bending moment, ω, to no less than 0.85 in the absence of second order analysis. SABS : Same as CSA S M89. The programs do not make automatic adjustments to take account of stability effects. If deemed necessary, you should conduct a second order analysis using the Plane Frame Analysis or Space Frame Analysis modules. When post-processing a second order frame analysis, Com also performs a second order analysis for each member. This generally results in more economic design of sections. Design parameters Different design parameters can be set for each group of elements designed: Effective area factor When an element is subjected to a tensile axial force, allowance should be made for the reduction in sectional area due to fastener holes. The various design codes follow similar approaches for calculating the effective area factor: AISC: Guidance is given in section B3. BS : See clauses 3.3 and 3.4. CSA S M89: When calculating the allowable tensile force, allowance is made for reduction of the effective net area for shear lag (clause 12.3). The effective area is thus effectively a function of the yield strength and ultimate strength of the steel (clause 13.2). Eurocode : See clause SABS : See clauses 5.3 and Steel Member Design using PROKON

11 SABS : The same clauses apply as for CSA S M89. Effective length factors for struts and ties The effective length factors depend on the degree of restraint to be expected at each end of compression members. Guidelines are given in the codes: AISC: See section E1. BS : Refer to clause and Appendix D. CSA S M89: See clause 9.3 and Annex C. Eurocode : See clause SABS : See clause and Appendix E. SABS : The same clauses apply as for CSA S M89. Considering a plane truss, the effective length L x relates to in-plane buckling. For struts where rotational fixity is provided by the connection, e.g. two or more fasteners or a welded connection, a value between 0.70 and 0.85 is usually appropriate. Where rotation at the joints are possible, e.g. single bolted connection, a value of 1.0 would normally be applicable. The effective length L y relates to buckling out of the vertical plane. This phenomenon can often govern the design of the top and bottom chords of a truss that can buckle in a snakelike S pattern, giving an effective length equal to unrestrained length. Lateral restraints are normally provided to reduce this effective length. For example, with braced purlins connected to the top flange of the truss, the effective length could be taken equal to the purlin spacing. The effective length L v relates to buckling about the v-v axis, i.e. the weakest axis, and requires special attention. Because movement about the v-v axis requires movement about both the x-x and y-y axes, L v is usually set equal to the least of L x and L y. Effective length factors for beam-columns The codes give similar guidelines: AISC: See section E1. BS : Refer to clause guidance on factors to use for members in bending. Refer to clause and Appendix D for members in compression. CSA S M89: Refer to clauses 9.1 to 9.4 and Annexes B and C. Eurocode : See clause SABS : See clause for flexural members. Refer to clause and Appendix E for compression members. SABS : Same as for CSA S M89. Steel Member Design using PROKON 4-11

12 Note: CSA S M89 and SABS clause allows the effective length factor for compression members to be reduced to 1.0 if a second-order frame analysis has been performed. A second order analysis will therefore normally yield a more economic design. Consider a typical portal frame subjected to dead and live load. The effective length L x relates to buckling in the plane of the portal, i.e. about the strong axis of each member. The length L y relates to out-of plane buckling, i.e. weak axis buckling. This value is typically set equal to the distance between restraining purlins and sheeting rails. The effective length L e relates to lateral torsional buckling of a member s compression flange about its weak axis. The length depends on the distance between restraints of the compression flange. For rafters with purlins restraining the top flange, L e can therefore be set equal to L y in zones of sagging moment. However, if the rafter is relatively deep and no special precautions are taken, the purlins could possibly have no effective restraint on the bottom flange. Therefore, where the bottom flange is in compression, i.e. zones of hogging moment, longer effective lengths for lateral torsional buckling will apply. Note: The current versions of Strut and Com cannot design tapered sections. The use of haunches in the sketch is merely for the sake of explaining the effective lengths. See page 5 for more detail Steel Member Design using PROKON

13 Slenderness limits The different codes specify similar slenderness ratios for members in compression, typically 200. For tension members, a maximum slenderness ratio of 300 is generally used. When launching Strut or Com, the slenderness limits given by the selected design code will be used by default. You are free to alter the maximum slenderness ratio for each individual load case or combination if required. For example, in the case where uplift due to wind is dominant, the maximum slenderness ratio may possibly be increased, e.g. SABS clause 8.4 and BS clause allows a slenderness ratio of 250. Steel Member Design using PROKON 4-13

14 Member design techniques The programs have two basic modes of operation: Read and post-process the frame analysis results. Alternatively, you can do an independent interactive design of one or more members. Uses and limitations of the member design modules Strut considers only axial forces during the design any prevailing bending moments are ignored. This means that you should use the program for the design of trusses and truss-type sub-structures of frames only, i.e. where members experience predominantly axial forces. Use Com when working with members that have significant bending moments. This program can however not design non-symmetrical sections like angles. Such members are typically used for constructing trusses or bracing frames and often have negligible bending moments, making Strut the appropriate design tool. Reading and post-processing frame analysis results Given the nature of the different frame analysis modules, selective compatibility exists between the various frame analysis and the steel member design modules: Strut designs members for axial stress only and can therefore read the results of Plane Frame Analysis, Space Frame Analysis and Space Truss Analysis. The Grillage Analysis and Single Span Beam Analysis modules are used to analyse beams and are therefore excluded. Com designs members for combined axial and bending stress can therefore read the results of Plane Frame Analysis, Grillage Analysis, Space Frame Analysis and Single Span Beam Analysis. The Space Truss Analysis is used to analyse trusses with axial forces only and is therefore supported by Strut instead. Design steps Working through the input and design pages, the frame design procedure can be broken up into the following steps: The Input page: Defining design tasks by choosing a design approach, selecting members to be designed, setting the design parameters and selecting load cases and slenderness limits. The concept of tasks is described in detail on page 17. The Members page (Com only): Define internal nodes and enter effective lengths. Refer to page 17 for detail. The Design page (Com only): Evaluating the design results. See page 17 for detail. The Calcsheet page: Accumulate design results. See page 17 for detail Steel Member Design using PROKON

15 Re-analysis of the frame Having evaluated the various member sizes, you may find it necessary to return to the original frame analysis and make some changes to section sizes. Before exiting the member design module, first save the task list using the Save command on the File menu. After re-analysing the frame, you can return to the member design module and recall the task list to have the modified structure re-checked without delay. Note: For a task list to be re-used with a modified frame, a reasonable degree of compatibility is required. Tasks that reference specific laterally supported nodes, for example, will require modification if relevant node numbers have changed. Interactive design of members As an alternative to the above procedure, individual members can be designed without needing to perform a frame analysis. To enable the interactive design mode: In Strut, select the Interactive page. In Com, select Interactive input of data on the Input page. Design steps Working through the input and design pages, the interactive design procedure can be broken up into the following steps: The Interactive page (Strut) or Input page (Com): Choose a design approach, set the design parameters and enter the element loads. In Strut, results are displayed interactively on the same page. Refer to page 17 for a detailed explanation. The Design page (Com): Evaluate the design results. More detail is given on page 17. The Calcsheet page: Accumulate design results to print or send to Calcpad. See page 17 for detail. Steel Member Design using PROKON 4-15

16 Tasks input On entering Strut or Com, it defaults to reading the last compatible frame analysis for post-processing. You can then choose to: Read and post-process the frame analysis results: Define one or more design tasks by grouping members with relevant design parameters. Interactive design: Ignore the frame analysis and interactively input and design members. The pages that follow describe the use of the programs for reading and post-processing frame analysis results. Information regarding interactive design is given on page Choosing the data input and design mode In Com, the appearance of the Input page determined by your selection of the mode of operation: If you choose to read and post-process the results of the frame analysis modules, you will use the Input page to define design tasks. However, if you opt for interactive design of members, the Input page displays a table for entering member geometry and loading. The appearance and behaviour of Strut is slightly different: The Input page is used to manage design tasks for post-processing frame analysis output. The Interactive page is used for entering data pertaining to interactive design of members. Reading frame analysis output files You can select another frame output file or view the current file: Read data from: Use this option to load the output of a different frame module than the one displayed. Click the box and select the relevant file from the list or enter a file name. View output: To display the current frame analysis output file. Defining design tasks Central to the process of post-processing frame analysis results, are design tasks. By grouping selective members with their relevant design parameters into one or more design tasks, you should find it easy to manage the vast amount of frame analysis data generated for larger frames Steel Member Design using PROKON

17 The design of a frame should be simplified by breaking it into one or more manageable tasks. Each task then defines a group of members to be designed together with the relevant design parameters to be used. Once you have defined one or more design tasks, the Calcsheet page (Strut) or Design page (Com) is enabled viewing that page automatically performs all design tasks. After having carefully defined a number of tasks, you can save the task list to disk for later re-use. This means that you can return to the relevant frame analysis module, make some changes to the structure, re-analyse it and then repeat the previous design tasks by simply reloading the task list. Defining tasks To define design tasks, you have to select or enter the following information: 1. Select a design approach. 2. If you choose to select the lightest section, then also choose a profile to use. 3. Select the members to be designed. 4. Enter the design parameters. 5. Select the load cases to be considered. To save a task, enter a Task title and click Add task. Once added to the task list, a task will be automatically performed when you go to the Calcsheet page. Define as many tasks as necessary to design the frame in the required detail. Steel Member Design using PROKON 4-17

18 Modifying design tasks To modify an exiting task: 1. Click Task title to display a list of defined tasks. 2. Select the task you want to modify. 3. Make the necessary changes to the selected members, design parameters etc. 4. Click Update task to save the changes. Deleting tasks To remove a task from the list, first select the task and then click Delete task. To save the complete task list to disk, use the Save commands on the File menu. Note: In Com, saving the task list with File Save also saves the intermediate nodes and effective lengths entered in the Members page Steel Member Design using PROKON

19 Selecting a design code The current selected design code is displayed in the status bar. To select a different design code, use the Code of Practice command on the File menu or click the design code on the status bar. Choosing a design approach Depending on what you would like to achieve, e.g. preliminary sizing or final design checks, you can choose between the following design approaches: Select lightest sections: Elements are optimised for economy using mass as the criterion. Specify the type of section to be used, e.g. equal leg angles, using Profile (F5). If you are unsure about the section sizes to use or want to do some preliminary sizing, this is the probably best approach to follow. Evaluate current sections: The sections specified in the original frame analysis are checked. This approach is best suited for final design checks. Note: The section type selected under Profile (F5) is used when the design approach is set to Select lightest section. However, the selected section type has no bearing on the design when the approach is set to Evaluate current sections. Selecting members for design in Strut Use the Element groups (F6) function to select one or more element groups from the list or by clicking members in the picture. Lateral supports are assumed at all nodes. If certain nodes are not laterally supported, you can indicate them as follows: Use the Laterally unsupported (F7) function to indicate those nodes that are supported all other nodes are then assumed to by unsupported. The program uses the shortest path between the specified nodes to identify the relevant elements. Leave a blank line to end a series of supported nodes or use the New group function to start a new series of laterally supported nodes. You can manually enter node numbers or click them on the picture. Steel Member Design using PROKON 4-19

20 The following apply to the calculation of effective lengths when you indicate laterally unsupported members: L y is based on the cumulative length between the specified supported nodes. L x and L v remain a function of the individual element lengths between adjacent nodes. Tip: To keep the design of a large truss manageable, consider using more tasks and specifying fewer nodes at a time. Selecting members for design in Com Use the Element groups (F6) function to select one or more element groups from the list or by clicking members in the picture. A lateral supports is assumed at each node. If certain internal nodes are not laterally supported, you can indicate them on the Members page. Refer to page for detail. Setting the design parameters Use the Design parameters (F8) function to enter appropriate design parameters and material properties. You can select a different set of design parameters with each task. Note: In Com, effective length factors are entered on the Members page. Refer to page 1730 for details on entering effective lengths in Com. Selecting load cases and limiting slenderness ratios When loading the last frame analysis results, the program automatically displays a list of all load cases and combinations that can be designed and also the default slenderness limits for struts and ties. In the Maximum L/r ratios (F9) table, you can exclude any load case or combination from the current design task by clicking its right-most column. A cross next to a load case means that the particular load case will be included. Tip: In the frame analysis modules you can also select to analyse load combinations only. The analysis output will then be more compact due to the omission of individual load case results. You are free to modify the slenderness limit for each individual load case or combination as required. In the case where uplift due to wind is dominant, for example, you may be able to set a higher slenderness limit. The code requirements regarding slenderness limits are discussed on page Steel Member Design using PROKON

21 Controlling design output The amount of information that will be added to the Calcsheet page can be controlled using the Settings function on the Input page: In Strut, you can select whether all members should be added to the Calcsheet or only a number of most critical members. In Com, you can choose between showing detailed calculation with or without diagrams or a summary of results. Steel Member Design using PROKON 4-21

22 Interactive input The interactive design mode offers an alternative method of designing members. Instead of performing a frame analysis and then and post-processing the results, you can enter member length and forces and design them interactively. To enable the interactive design mode: In Strut, select the Interactive page. In Com, select Interactive input of data on the Input page. The pages that follow describe the use of the programs for interactive member design. The procedure to reading and post-processing frame analysis results is explained on page 15 Selecting a design code The current selected design code is displayed in the status bar. To select a different design code, use the Code of Practice command on the File menu or click the design code on the status bar. Choosing a design approach Depending on what you would like to achieve, e.g. preliminary sizing or final design checks, you can choose between the following design approaches: Select lightest sections: Using mass as the criterion, the most economical section size will be determined for each member. The type of section that will be selected will be as specified above. Specify the type of section to be used, e.g. equal leg angles, using Profile (F5). This approach is very useful for if one is unsure about the section sizes to use or if one wants to do some preliminary sizing. Evaluate current sections: This approach allows you to specify a section size for each member. Use the Profile (F5) function to select a section. Setting the design parameters In Com, use the Effective lengths (F6) function to enter effective length factors. Use Design parameters (F8) to enter appropriate design parameters. All members designed in a particular interactive session use the same set of design parameters Steel Member Design using PROKON

23 Specifying slenderness limits Use the Maximum L/r ratios (F9) function to enter appropriate maximum allowable slenderness ratios for compression and tension. Entering member lengths and forces in Strut Use as many lines as necessary to enter member lengths and axial forces: L: Length of the member (m or ft). F: Axial force (compression positive) (kn or kip). Designation: Profile or section chosen using Profile (F5). With select lightest section enabled, you only need to choose the type of profile. With Evaluating current section selected, you should select a section for evaluation. Note: All entered forces and moments are ULS design values. For allowable stress design with SABS , you should enter working loads. Steel Member Design using PROKON 4-23

24 Entering member lengths and forces in Com One or more lines of information can be entered for each member. The program automatically accumulates multiple lines of loads for the same member. The following input data is required: Name: A descriptive name for each member. L: Length of the member (m or ft). F: Axial force with compression being positive (kn or kip). X/Y: Axis of bending relating to the values that follow next. Use as many lines as necessary to define the loading on the member about the x-x and y-y axes. M1: Moment applied at the left end (anti-clockwise positive) about the X or Y axis (knm or kipft). M2: Moment at the right end (anti-clockwise positive) (knm or kipft). W1: Distributed load at the left end. The load works over the whole length of the member load and varies linearly between the left and right ends (downward positive) (kn/m or kip/ft) Steel Member Design using PROKON

25 W2: Value of distributed load on right side (kn/m or kip/ft). P: Point load applied on the member (downward positive) (kn or kip). A: Position of the point load, measured from the left end (m or ft). Note: All entered forces and moments are ULS design values. For allowable stress design with SABS , you should enter working loads. The profile of the members to evaluate is chosen using the Profile (F5) function. On opening the Design page, the lightest section will be chosen for each member. Lighter or heavier sections of the same profile can then be browsed as required. Viewing design results Similar design criteria are applied in Strut and Com. The presentation of the design results are however done quite differently. Refer to page 17 for detail. Steel Member Design using PROKON 4-25

26 Beam-column member definition In Com, internal nodes and effective lengths are defined on the Members page. The data entered on the Members page is applicable to all design tasks defined on the Input page. To use different effective lengths for different design tasks lateral support group tasks with identical effective lengths and save them in separate files. Defining internal nodes An internal node is defined as a node in-between the end nodes of a member. When you add internal nodes, the program joins relevant members to allow for easy input of effective lengths Adding an internal node You can add internal as follows: Enter internal node numbers in the table or click them with the mouse. Use the Auto Select function to let the program detect all internal nodes. Removing an internal node You can remove an internal node by deleting it form the list or by clicking it again in the picture. Consolidation of members With the addition of each internal node, the relevant node is removed by joining the two adjacent members into a single member. The table of members is continuously updated to show the new member layout. The program uses the following guidelines to decide which members to join at an internal node: For the automatic selection of internal nodes, adjoining members must have the same section. Only members with an included angle greater than 100 (where 180 corresponds to a perfectly straight member) are joined. Where members of different sections intersect, the larger section defines the main member that should be joined. Where two or more members intersect, the internal node is taken to belong to one of the intersecting members only. The chosen member will be the straightest member or, if the same, the first in the table of members Steel Member Design using PROKON

27 Entering effective lengths Enter effective length factors as follows: Apply the same value of K x, K y or K e to all members by clicking the Kx, Ky en Ke buttons in the table heading. Enter the effective length factors for individual elements. Note: The list of internal nodes and effective length factors are automatically saved when you save the task list. See page 17 for detail. Tip: You can quickly find a member in the table by pressing Ctrl+F. Enter the member name by referring to one or both of its end node numbers. Steel Member Design using PROKON 4-27

28 Design results In Strut the design results are shown on the Calcsheet page. In Com, select the Design page to perform all design tasks and display the design results. All specified load cases and combinations are considered for each member designed. Unless a very large number of elements and load cases are involved, the design procedure will normally be completed almost instantaneously. By default, the results for the design task active on the Input page are displayed. The results of any other design task can be displayed by selecting the task from the list (see description below). If an interactive member design was performed, the displayed results will be for the interactive design task instead. The design criteria The following criteria are used in the design: The interaction formulae given by the relevant design code are used to evaluate the effect of axial stress or combined effect of axial stress and bending stress. In calculating the allowable stresses, the program takes account of the member slenderness and effective tension area. The slenderness ratio checked against the specified maximum allowable slenderness ratio for compression and tension. Note: Strut designs members for axial stress only and ignores any bending stresses. Viewing design results in Strut The design results are given in tabular format with OK and FAIL remarks to indicate success or failure. The mass of each group of elements is summarised below the relevant table. The results of each new design are appended to the bottom of the existing output. Viewing results in Com The complete interaction formulae are displayed for the critical load case of the first member of the first design task. Individual calculations have OK and FAIL remarks to indicate success or failure. To view the results of another task, member, section or load case: Use the Up and Down buttons to move up or down the list of available options. Tasks and load cases are listed in the order of definition. Sections are ordered by mass. Alternatively click the item, i.e. sections, and use the Up and Down arrow keys. Alternatively click the relevant input box and select an item from the list that drops down Steel Member Design using PROKON

29 Adding results to the Calcsheet page In Strut, the design results are automatically displayed on the Calcsheet page. In Com, the following options are available when adding design results to the Calcsheet page: Member to Calcsheet: Add the current displayed member only. Task to Calcsheet: Add the design results of all members in the current task, including those members not currently displayed. All tasks to Calcsheet: Add all members of all tasks. Note: The level of detail of the information added to the Calcsheet can be set using the Settings function on the Input page. Refer to page 17 for detail. Steel Member Design using PROKON 4-29

30 Calcsheet The design results of all tasks are grouped on the Calcsheet page for sending to Calcpad or immediate printing. Use the Output settings function on the Calcsheets page and Settings function on the Input page for the following: Embed the Data File in the calcsheet for easy recalling from Calcpad. Clear the Calcsheet page. Recalling a data file If you enable the Data File option before sending a calcsheet to Calcpad, you can later recall the design by double-clicking the relevant object in Calcpad. A data file embedded in Calcpad is saved as part of a project and therefore does not need to be saved in the member design module as well Steel Member Design using PROKON

31 Plastic Frame Design The Plastic Frame Design module can perform a linear elasto-plastic analysis of any general two-dimensional framed structure. The program can be used in the following plastic design modes: The plastic collapse mechanism and load factors can be determined for a series of load combinations. The frame s plastic behaviour can be optimised to achieve more economical sections. Elastic design of a steel frames can be done using the Plane frame Analysis or Space Frame Analysis modules in conjunction with the steel member design modules axial and combined stress, Strut and Com. See Chapter 4 for detail. Steel Member Design using PROKON 4-31

32 Theory and application The following text explains the sign conventions used and gives a brief background of the analysis techniques. Design scope The use of plastic design methods is normally limited to the design of continuous beams and single storey frames with rigid joints, e.g. portal frames. It may also be acceptable to use plastic methods for designing some braced multi-storey planar frames. Determining plastic mechanisms The program performs an elasto-plastic analysis of plane frames. A rational analysis approach is followed to obtain a true collapse mechanism for each load case or combination: 1. A linear elastic analysis is performed to determine the position of the first plastic hinge. 2. The bending moment at that position is then limited to the relevant plastic moment while the position of the next hinge is calculated. 3. The procedure is repeated to obtain more plastic hinges. 4. If the formation of further plastic hinges results in the bending moment at one of the existing hinges to decrease, that hinge is removed and elastic behaviour re-instated at that position. 5. The procedure is repeated until a collapse mechanism forms. Analysis modes Depending on the analysis module used, the following types of analysis can be performed: Linear analysis: Basic linear elastic analysis. A linear analysis procedure is typically performed markedly faster than a plastic analysis. It therefore is recommended that you verify the basic integrity of the frame input by performing a linear analysis prior to attempting a plastic analysis. Plastic analysis: Choose between evaluating the adequacy of the frame as entered or optimising the section sizes. When optimising, the program will search for a more economic configuration of sections. The plastic modulus, Z pl, is used as the criterion for section economy. Two design modes are available during plastic analysis: No optimisation: Evaluate the frame with sections as entered and calculate the adequacy against collapse for each load combination Steel Member Design using PROKON

33 Optimise sections: Optimise the frame s plastic behaviour by determining more economical sections. Design codes The program uses general plastic theory. Working within their scope, the program can be considered to support the following design codes: BS CSA S M89. Eurocode SABS SABS Note: SABS use an allowable stress design method for elastic design. For plastic design, however, it adopts an ultimate limit state design method. Sign conventions Frame input and output uses a mixture of global axis and local axes values. Global axes The global axis system is nearly exclusively used when entering frame geometry and loading. Global axes are also used in the analysis output for deflections and reactions. The global axes are defined as follows: The X-axis is chosen to the right. The Y-axis points vertically upward. A positive vertical load thus works up and a negative load down. Using a right-hand rule, the Z-axis points out of the screen. Local axes Steel Member Design using PROKON 4-33

34 Local axes are used in the output for element forces. You can also apply loads in the direction of a beam element s local y-axis. The local axis system is defined as follows for beam elements: The local z-axis and axial force is chosen in the direction from the smaller node number to the larger node number. The x-axis is taken parallel to the global Z-axis, i.e. pointing towards you. A rotation about the x-axis is thus always anti-clockwise. The y-axis is taken perpendicular to the x and z-axes, using a right-hand rule. Beam element forces The element forces are given in the local element axis system. The following conventions apply to beam elements: The axial force, P z, is taken in the z-direction. The shear force, V y, is taken in the y-direction. The moment, M xx, is taken about the x-axis, i.e. anti-clockwise. Note: In this manual the global and local axes are written in uppercase and lowercase respectively. Units of measurement The following units of measurement are supported: Units Metric Imperial Distance mm, m ft, inch Force N, kn lb, kip Use the Units commands on the Options menu to change the units for the current analysis: Set Units: Changes the units of measurement without altering the input data. Convert Units: Changes the units and converts all numeric data from the old to the new units of measurement Steel Member Design using PROKON

35 Input Work through the relevant Input pages to enter the frame geometry and loading: General input: Select the analysis type and special analysis parameters. Nodes input: Frame coordinates. Beams input: Join nodes with beam elements. Beam sections input: Enter properties or read sections from the database. Spring elements input: For special effects, optionally enter spring elements. Supports input: External supports. Nodal loads input: Point loads and moments. Beam element loads input: Uniform distributed, triangular and trapezium loads on beams. Load combinations input: Group dead, live and wind loads in load combinations. Alternative methods of generating frame analysis input are discussed on page 17. Viewing the frame You may want to enlarge portions of the picture of the structure or rotate it on the screen. Several functions, all of which are described in detail in Chapter 2, are available to help you using pictures of the frame: Use the Zoom buttons to zoom into a part of the structure or view it from another angle. Use the View Point Control to set a new view point or camera position. The Options menu makes the following additional functions available: Graphics: Select whether you want items like node numbers and supports to be displayed. Choose whether you want all beam elements or only a certain type to be displayed. Steel Member Design using PROKON 4-35

36 Display the structure with full 3D rendering, e.g. to verify section orientations. 3D rendering is automatically suppressed when viewing output. Choose quick or detailed rendering. Quick rendering is faster than the detailed method, but you may find that some surfaces are drawn incorrectly. All surfaces are drawn as polygons. You can choose to make the surfaces transparent or have them filled and outlined. Tip: The Graphics options and 3D rendering function can also be accessed using the buttons next to the displayed picture. Views: You can save the current view point and view plane. The current view s name is displayed on the picture. To re-use a saved view, click the view name on the picture to drop down a list of saved views. The functions described above can also be used when viewing output. Contour diagrams, for example, are drawn as polygons. You can therefore use the Graphics options setting for polygons to change their appearance. Views defined during input are also available when viewing output and vice versa Steel Member Design using PROKON

37 Saving and printing pictures Any picture can be saved or printed using the relevant buttons next the picture. Pictures on the Input and Output pages can also be added to the Calcsheets. Tip: You can zoom into a picture and print, save or add the picture to the Calcsheets. General input The General input page handles several important analysis parameters. Analysis type Choose between performing a simple linear elastic analysis or a plastic analysis. Refer to page 17 for an explanation of the analysis modes. Plastic design parameters You need to set the following analysis parameters when performing a plastic analysis: Plastic analysis tolerance: The plastic analysis is an iterative procedure. The analysis is deemed to have converged once the total strain energies of two sequential iterations differ by less than the specified tolerance. Maximum number of iterations: The analysis procedure calculates as many hinges as necessary to form a plastic mechanism. You can terminate the analysis at an earlier stage. A complex analysis that takes a very long time to converge can also be forced terminate earlier. To force the analysis to end before the formation of the final collapse mechanism, you can limit the maximum number of iterations to be performed. Own weight The own weight of the frame can be calculated using the entered cross-sectional areas and member lengths. If you specify a load case, the own weight is calculated and added to the other loads of that case. The following are points of importance: By default the own weight of the frame is set to not be included in the analysis. Be sure to select the appropriate load case for own weight or, alternatively, to include the frame s own weight in the values of the loads entered. The list of load cases from which you can select is based on the load cases defined on the Nodal loads and Beam loads input pages. You may thus prefer to specify the own weight load case only after completing all other input for the frame. However, you can also enter Steel Member Design using PROKON 4-37

38 the own weight load case at the start of the frame input process in which case you may ignore the warning message (that the load case does not exist). Tip: If you wish to use own weight in its own separate load case, you can do so by defining an empty load case. You can enter a zero load at any node number, for example, and then select that load case as the one to use for own weight. Parametrics The parametric plastic frame input modules are suitable for the rapid generation of complete input files for some typical structures. Because the resulting input data is presented in the normal way on the input pages, you are free to edit and append to the data as necessary. Input generated this way can optionally be appended to existing data you can therefore repeatedly use the parametric input modules to generate complicated structures. Note: Plasdes is not limited to analysing only those frames generated by the parametric modules. The program can treat any general two-dimensional frame. The parametric modules merely serve to simplify input of typical frames. Adding input data to the Calcsheets You can append the input tables (as they appear on the screen) to the Calcsheets by clicking the Add input tables to Calcsheets button. You can add a picture from any input pages to the Calcsheets by clicking the Add to Calcsheets button next to the picture in question. Title A descriptive name for the frame. It should not be confused with the file name you use when you save the input data Steel Member Design using PROKON

39 Nodes input Use as many lines as necessary to enter the nodes defining the frame. A unique number must be assigned to each node. The node number is entered in the No column, followed by the X and Y-coordinates in the X and Y columns. If you leave X or Y blank, a value of zero is used. You are allowed to skip node numbers to simplify the definition of the frame. You may also leave blank lines in the input to improve readability. If a node number is defined more than once, the last definition will be used. Error checking The program checks for nodes lying at the same coordinate. If a potential error is detected, an Error list button will appear. Steel Member Design using PROKON 4-39

40 Generating additional nodes When defining a node, you can have additional nodes generated at regular intervals. Example: The Y-coordinate of node 4 is left blank. Therefore, node 4 is put at the coordinate (0.805,0). The No of is set to 2, meaning that two additional nodes are generated. Setting Increment to 7 means that the node numbers are incremented by seven. Therefore, node 4 is copied to node 11 and node 11 is copied to node 18. The values in the X-inc and Y-inc columns set the distance between copied nodes. The coordinates 4 to 18 are horizontally spaced at m to the right at m downward, i.e. along the X and negative Y-axis respectively. The coordinates of the additional nodes are thus (1.945,-0.472) and (3.085,-0.944). An alternative method to generate equally spaced nodes is to use the Inc to End option. This method allows you to define two nodes and then generate a number of nodes in-between: Use the same procedure as above to define the first node s coordinates. Set the values of X-inc, Y-inc and Z-inc to the total coordinate difference to the last node and enable the Inc to End option. The last node s coordinates are then first calculated and the specified number of intermediate nodes then generated. Second order generation Once you have defined one or more nodes in the table, you can copy that relevant line s nodes by entering a ' 'character in the No column of the next line. Then enter the number of additional sets of nodes to be generated in the No of column and the coordinate increments in the X-inc and Y-inc columns. Second order generation example: 4-40 Steel Member Design using PROKON

41 The following nodes are generated: No X Y Block generation A group of nodes can be repeated by entering a B in the No column followed by the first and last table line numbers in which the nodes were defined. Separate the line numbers with a '. Block generation example: The nodes defined in lines 11 to 26 are copied twice. Node numbers are incremented by thirty for each copy. The X and Y-coordinate increments are 10 m and zero respectively. To copy one line only, simply omit the end line number, e.g. 'B10'to copy line 10 only. Tip: The current line number is displayed in the status bar at the bottom left of the program's window. The block generation function may be used recursively. That means that the lines specified may themselves contain further block generation statements. Moving nodes To move a group of nodes to a new location without generating any new nodes, use the block generation function and set No-of to '1'and Inc to '0'. Arc generation A group of nodes can be repeated on an arc by entering an 'A'in the No column, followed by the start and end line numbers. Enter the centre of the arc in the X and Y columns and use the X-inc column to specify the angle increment about the Z-axis. Example: All nodes defined in lines 5 to 9 of the table will be repeated eleven times on an imaginary horizontal arc. The centre point of the arc is located at the coordinate (10.0,1.5). The node Steel Member Design using PROKON 4-41

42 number increment is set to 5, i.e. node number 3 becomes node 8, etc. The rotation angle between the generated groups of nodes is 30 degrees about the Z-axis, i.e. anti-clockwise on the screen using a right-hand rule. To copy one line only, simply omit the end line numbers, e.g. A12 to copy line 12 only. Note: The arc generation function may be used recursively. Rotating nodes To rotate a group of existing nodes without generating any new nodes, use the arc generation function and set the No-of to 1 and Increment to 0. Mirror Nodes of a plane frame or grillage can be mirrored horizontally or vertically by entering an M in the No column, followed by the start and end line numbers. Mirror example: All nodes defined in lines 5 to 9 are mirrored about a vertical (horizontal for a grillage) line through X=10 m. Node numbers are incremented with 5. By specifying a Y or Z-value instead of an X-value, nodes can be mirrored about a horizontal line passing through the specified Y or Z-value. Deleting nodes Nodes can be deleted by entering Delete in the Inc to end column. This can be especially handy if you have generated a large group of nodes and then need to remove some of them again. Example: Nodes 15 and the additional nodes 18 and 21 are deleted Steel Member Design using PROKON

43 Beam elements input A beam or frame element is defined by entering the node numbers at each end, separated with a '. For example, '3 9'is the element linking nodes 3 and 9. The elements themselves are not numbered. A series if elements can be input in a string, e.g. ' '. If the node number increment of a series is constant, you can replace intermediate nodes with two ' 'characters. In the string above, nodes 2 to 22 has a constant increment of four. Therefore, the string can be rewritten as ' '. The node increment of four is derived from '2-6'. An element definition must include a section number entered in the Section Name column. The section name is used to identify the relevant section. The actual section properties for each section number defined on the Beam Sections input page. Steel Member Design using PROKON 4-43

44 Section orientation The local y-z plane of an element is taken in the global X-Y plane. The principle can be illustrated by considering an I- section in its normal orientation. For this case, the web will always be considered to be in a vertical plane. A section can be rotated through ninety degrees by selecting the alternative orientation when reading it from the section database. Tip: Enable full 3D rendering in the Graphics options to view the true beam orientation. End fixity The fixity at each end of an element, i.e. continuous or pinned, must also be defined in the Fixity columns. Pins are modelled on the element itself and not on the node. External pinned supports should be defined on the Supports input table. External supports are described in the next section. The following types of end fixities can be specified: Fixed: Specify F to provide full rotational continuity. If you leave the field blank, F is assumed. Pinned: Use P to for no rotational restraint, i.e. a pin. Note: To retain compatibility with the Dos version, you may also use 0 or 1 instead of F and P respectively. Entered fixities are applied at an element s lower node number (designated as the left end) and higher node number (the right end). The order of the node numbers entered in the first column of the table has no bearing on the application of the fixity codes. To define a pin only at the two remote ends of a group of elements, enable the Group fix option by entering a Y. In this case the normal convention of smaller and larger node numbers does not apply. Instead, pins are put at the remote ends in the same order that the nodes have been entered Steel Member Design using PROKON

45 Example: The group of elements from node 42 to 24 is continuous except for the pins used at nodes 42 and 24. If the Group fix is left blank or N is entered, the normal individual element fixity mode is assumed. Tip: Element fixity can be displayed graphically on the screen. For this, edit the Graphics options to disable the Elements Continuous option. When using pins, you should take care to ensure overall stability of the frame. Consider two elements on a straight line with pins at all three relevant nodes, for example. The centre node will be unrestrained for rotation about the element axis, resulting in instability during the analysis. Note: Do not use an internal pin on an element to model an external support that allows free rotation. Rather allow the beam to be fixed to the node and define a simple support on the Support input page. Tapered beams The current version of Plasdes does not support tapered sections. Rigid links You can use rigid links to rigidly fix sub-structures to each other. To define a rigid link, enter R in the Section Name column. Rigid links are modelled as very stiff beams. The stiffness of a rigid link is determined by multiplying the maximum stiffnesses of the other beams with a factor, typically one thousand. Rigid link example: Rigid links are defined between nodes 12 and 24, 14 and 26 and 16 and 26. Steel Member Design using PROKON 4-45

46 Generating additional elements You can generate additional elements with the same section and fixity code values using the No of extra and Node No Inc columns. Example: The elements between nodes 251 and 266 are copied ten times with the node numbers decrementing by five with each copy. Block generation A group of elements can be repeated by entering a B in the No column. Then enter the first and last table line numbers in which the elements were defined, separated with a '. Block generation example: All elements defined in lines 11 to 26 will be copied twice with a node number increment of thirty. The copied elements will use the same section number and fixity codes as the original elements. To copy one line only, simply omit the end line number, e.g. 'B11'to copy line 11 only. Tip: The current line number is displayed in the status bar at the bottom left of the program's window. The block generation function may be used recursively. The group of lines referenced may thus contain block generation statements. Tip: When entering a complicated structure it may help to leave a few blank lines between groups of elements. Not only will it improve readability, but it will also allow you to insert additional nodes at a later stage without upsetting block and arc generations. Deleting beams Beam elements can be deleted by entering a special section name 'Delete'. This can be especially handy if you have generated a large group of elements at regular increments and need to remove some of them again Steel Member Design using PROKON

47 Example: Elements and are deleted. Note: The display of selected beam element groups can be activated or suppressed by editing the Graphic options. Error checking The program checks for duplicate elements and elements with zero length. It also checks that a section number is assigned to each element. If an error is detected, an Error list button will be displayed. Beam sections input Section properties should be assigned to all section names used on the Beam elements input page. The following properties are required for all sections: Cross sectional area, A. Second moment of area about the local x-axis, I xx. Plastic modulus about the local x-axis, Z xx. Each section should also have an associated material selected. If no section or material properties are entered, the values applicable to the previous line in the table are used. Reading sections from the database Use the Section database function to display and select sections from database. You can add your own sections, e.g. plate girders, to the database using the procedures described in Chapter 2. Entering haunches Haunched sections are entered by appending the haunch depth to the section designation. To add a haunch of 280 mm to a 305x102x66 BS taper flange I-section, enter 305x102x66 (0.280h). The overall depth is then taken to be 305 mm mm = 585 mm. Tip: You can verify your definition of haunches by enabling 3D rendering. Refer to page for 15 more detail. Steel Member Design using PROKON 4-47

48 Note: Although haunched sections can be entered, Plasdes does not support analysis of members with tapered sections. A tapered haunch in a typical portal frame, for example, should be modelled by entering one or more members that approximate the stiffness of the actual haunch. Own weight If a material s definition includes a density value, the own weight of a member is calculated automatically and added to the load case specified on the General input page Steel Member Design using PROKON

49 Selecting materials Each section should have an associated material. To add one or more materials to a frame analysis data file, click Materials. Open the relevant material type screen and select the materials that are required for the current frame input. After adding the selected materials to the input, you can select them by clicking the Material column to drop down a list. Adding materials to the global database The procedure to permanently add more materials to the database is described in Chapter 2. Spring elements input You can use spring elements to provide elastic links between sub-structures. In theory, two nodes connected with a spring element should have the same coordinates. The program will warn if this is not the case and still allow you to continue. Note: By default the Spring elements input page is not visible. This behaviour can be changed using the Advanced command on the Options menu. Enter linear spring constants in the Kx, Ky and Kz columns and rotational spring constants in the Rx, Ry and Rz columns. The orientation of a spring element is defined by entering a bearing between any two nodes that do not necessarily need to be connected to the same or other spring elements as well. The directions of the axes are defined as followed: A spring element s x-axis is taken in the direction of the orientating nodes. The y-axis defined in the same way as for a normal beam element, i.e. perpendicular to spring element in a vertical plane. The z-axis is taken perpendicular to the x and y-axes using aright-hand rule. Spring element example: Spring elements are defined between nodes 16 and 116, 17 and 117 up to 19 and 119. The spring elements are aligned parallel to the imaginary line joining nodes 3 and 4. Steel Member Design using PROKON 4-49

50 Tip: Spring elements can also be made "rigid" so as to force two nodes to have the same translation and/or rotation. In the above example, a very large value for K x would cause nodes 16 and 116 to have identical displacements in the direction described by nodes 3 and 4. Supports input Frames require external supports to ensure global stability. Supports can be entered to prevent any of the three degrees of freedom at a node, i.e. translation in the X and Y-directions and rotation about the Z-axes. You can also define elastic supports, e.g. an elastic soil support, and prescribed displacements, e.g. foundation settlement. Enter the node number to be supported in the Node No column. In the next column a combination of the letters X, Y and z can be entered to indicate the direction of fixity. Use capitals and lowercase to define restraint of translation and rotation respectively, e.g. XYz means fixed against movement in the X and Y-direction and rotation about the Z-axis. Note: The use of lowercase for rotational restraints should not be confused with the convention of using lowercase for local element axes Steel Member Design using PROKON

51 Tip: To enter a simple support with no moment restraint, you should enter XY or Y. If you want to repeat the supports defined on the previous line of the table, you need only enter the node number, i.e. you may leave the Fixity column blank. If the XYZxyz column is left blank, the supports applicable to the previous line will be used automatically. Prescribed displacements and elastic supports Use the X, Y and Rz columns to enter prescribed displacements and rotations in the direction of the X or Y-axis or about the Z-axis. Being a global support condition, the effect of the prescribed displacement is not considered to be a separate load case. Instead, the effect of prescribed displacements is added once only to the analysis results of each load case and load combination. Elastic supports, or springs, are defined by entering spring constants in the X, Y and z columns. The spring constant is defined as the force or moment that will cause a unit displacement or rotation in the relevant direction. Enter an S in the P/S column to indicate that an entered value is a spring constant rather than a prescribed displacement. If you leave the P/S column blank, the entered values are taken as prescribed displacements. Note: The display of supports can be activated or suppressed by editing the Graphic options. Error Checking The program does a basic check on the structural stability of the frame. If a potential error is detected, an Error list button will appear. Note: You cannot define an elastic support and a prescribed displacement at the same node because it will be a contradiction of principles. Generating additional supports Additional supports and prescribed displacements can be generated using the Number of extra and Node number inc columns. The procedure is similar to that described on page 17 for generating additional nodes. Steel Member Design using PROKON 4-51

52 Nodal loads input Loads on beam elements are categorised as nodal loads, i.e. loads at node points, and element loads, i.e. loads between nodes. Uniform distributed loads can be applied to shell elements. All loads are organised in load cases, e.g. DL for own weight, ADL for additional dead loads, LL for live load, etc. Load cases apply equally to the various load input screens, meaning that you can build up a load case using different types of loads. To define a load case, type a descriptive name for each load case in the Load Case column. Use up to six characters to describe each load case. If the load case name is not entered, the load case applicable to the previous line in the table is used. The load case at the cursor position is displayed graphically. Press Enter or Display to update the picture. A nodal load can, as its name implies, only be applied at a node. If a point load is required on an element, use the Beam loads input table instead. Sign conventions 4-52 Steel Member Design using PROKON

53 Nodal loads are applied parallel to the global axes an explanation of the sign conventions are given on page 17. Tip: For a typical steel frame or roof truss, it may be easiest to define a node at each purlin position. Roof loads transferred via the purlins can then be entered as nodal loads. Error checking The program checks that specified nodes have indeed been defined in the Nodes input table. If an error is detected, an Error list button will appear. Generating additional nodal loads Additional nodal loads can be generated using the Number of extra and Node number inc columns respectively. Block generation of nodal loads You can use the block function to copy blocks of nodal loads. The procedure is similar to that for generating additional nodes see page 17 for more detail. Beam element loads input Distributed loads and point loads on beam elements are all referred to as element loads. The Nodal loads input page provides the easiest way of applying point loads and moments at nodes. Use up to six characters to enter a descriptive name for each load case in the Load Case column. Then enter the element string of nodes in the Beam element definition column. Entering the beam element definition follows the same convention used as for the Elements input table see page 17 for detail. Sign conventions Depending on the selected load direction, beam loads are applied parallel to the global axes or parallel to the local y-axis the definitions of the global and local axes are given on page 17 and 17 respectively. The load direction is entered in the Direction column. Enter a global direction 'X'or 'Y'. Element loads are applied to the relevant projected length of the elements. Therefore, if a 'Y' load is entered for a vertical element, for example, the resulting load will therefore be zero. Note: Positive vertical loads act upward and negative loads act downward. Steel Member Design using PROKON 4-53

54 For a distributed load, entered in the load intensity at the smaller and larger node numbers in the W-begin and W-end columns respectively. If the load is constant over the length of the element, W-end may be left blank. Error checking The program checks that element definitions match previously defined elements. If an error is detected, an Error list button will appear. Generating additional element loads The No of extra and Node number Inc columns can also be used to generate additional element loads. Block generation of beam loads You can use the block function to copy blocks of beam loads. The procedure is similar to that used to generating additional beam elements see page 17 for detail Steel Member Design using PROKON

55 Load combinations input You can model practical scenarios by grouping load cases together in load combinations. Enter the load combination name in the Load comb column, followed by the load case name and relevant load factors. Use up to six characters for a descriptive load combination name. If the Load comb column is left blank, the load combination is taken to be the same as for the previous line of the table. The load cases to consider in a load combination are entered one per line in the Load case column. Enter the relevant ultimate and serviceability limit state load factors in the ULS factor and SLS factor columns. Tip: You may leave one or more blank lines between load combination definitions to improve readability. The ultimate and serviceability limit states are used as follows: Deflections are calculated using the entered SLS loads. A set of reactions is also calculated at SLS for the purposes of evaluating support stability and bearing pressures. A second set of reactions and all element forces are determined using the entered ULS forces. Steel Member Design using PROKON 4-55

56 Note: Unlike elastic design, which is done using an allowable stress design technique, plastic design to SABS is done at ultimate limit state. Refer to clause 12.2 and Table 30 for guidance on load factors to be used. Error checking The program only checks that valid load cases are specified. It has no knowledge of the design code that will be used in the member design and therefore does not check the validity of the entered load factors Steel Member Design using PROKON

57 Alternative frame input methods Alternative means of frame input are available: Parametric input: Modules are available for the rapid generation of input for typical frame structures. Graphical input: Structures can be drawn in Padds or another CAD system and converted to frame analysis input. Parametric input A number of typical frames can be input by entering a number of parameters. The Parametrics input modules do most of the data input. See page 17 for more detail on the Parametrics. Note: Plasdes is not limited to modelling only those frames generated by the parametric modules. Instead, the parametric modules merely serve to simplify input of some typical frames. Graphical input In some situations it may be easier to define a frame s geometry graphically. With Padds you can draw a frame and then generate a frame analysis input file. Using Padds for frame input To use Padds to define a frame s geometry: 1. Use Padds to draw the frame. Alternatively import a DXF drawing from another CAD system. 2. The frame should be drawn to scale using millimetres as unit. Identify different beam sections by using different pen numbers. 3. Use the Generate input command on the Macro to display the drawing conversion options. Choose the Plasdes as the target frame analysis module and press OK to start the conversion procedure. The resultant frame analysis input file will be compatible with both the Dos and Windows versions of Plasdes. The file is saved in the working folder as a last plastic analysis file, e.g. Lastpl.s Close Padds. Tip: To see a graphical input example, open..\prokon\data\demo\inputgen.pad in Padds. Importing DXF drawings Steel Member Design using PROKON 4-57

58 You can also use your favourite CAD system to save a frame s geometry in a 2D drawing and then use the Import DXF file command on the File menu to convert it to frame input. The same basic rules apply as given above: The drawing should be to scale. You should use millimetre units. Different pen numbers should be used for different beam sections. Typical problems experienced include the following: Polylines may not be recognised correctly. Break or explode polylines into single lines before saving the DXF file. Blocks may not import correctly and may need to be broken or exploded into individual entities. Using AutoCAD, lines colours set by layer translates to the default pen number. Rather set colours using pen numbers to ensure correct section numbering. If you experience problems importing a DXF file saved using a brand new version of your CAD system, it may help saving the file as an older DXF file version, e.g. version Steel Member Design using PROKON

59 Analysis On completing the frame input, you should set the analysis options before commencing the actual analysis. Analysis options Use the General input page to select the analysis mode: Linear analysis: Basic linear elastic analysis. A linear analysis procedure is typically performed markedly faster than a plastic analysis. It therefore is recommended that you verify the basic integrity of the frame input by performing a linear analysis prior to attempting a plastic analysis. Plastic analysis: Choose between evaluating the adequacy of the frame as entered or optimising the section sizes. When optimising, the program will search for a more economic configuration of sections. The plastic modulus, Z pl, is used as the criterion for section economy. Note: The results of an optimising plastic analysis should not be regarded as a final solution. You should return to the input data and enter the suggested or other preferred sections and then re-analyse the frame as a final check. On the Analysis page, select the following: Output file: Enter an output file name or accept the default file name, e.g. Pasdes.out. Analyse load combinations only: Enable this option if the results of only the load combinations are required. Generally one would require results for the load combinations only. However, you may have a special need to view the results of specific load cases as well. Disable this option to include the results for the individual load cases as well. Steel Member Design using PROKON 4-59

60 Analysing the structure To analyse the structure, open the Analysis page and press Start Analysis. The analysis progress of displayed to help you judge the time remaining to complete the analysis. After a successful analysis, the deflected shape is displayed for the first load case or load combination. Error checking during analysis During the input phase, the frame geometry and loading data is checked for errors. Not all reported errors are necessarily serious. To define duplicate elements between two nodes, for example, could be an accidental error on your side. However, the program is quite capable of dealing with a situation like this and will therefore allow the analysis procedure to continue. Other input errors could be serious enough to prevent an analysis from being completed successfully. Nodes with no elements, for example, have no restraints and will cause numeric instability during the analysis. The first step of any analysis is the final verification of the input data. In the case of critical errors still present, a warning message will be displayed. If you then choose to not proceed with the analysis, you will be taken to the input table with the error. However, choosing to proceed and ignore the warning, will have an unpredictable result. Fixing errors that occurred during the analysis Even if all input data seems valid, numeric errors may still occur during an analysis. For example, if you entered incorrect section properties, such as a very small E-value, the mistake may go by unnoticed. However, the analysis will then yield an invalid value in the stiffness matrix or extremely large deflections. The same applies to the stability of the frame. Although the frame may appear stable, some combinations of internal hinges may result in some nodes being unstable. If an error was detected during the analysis, a warning will be displayed. The cause of the error should become clear when studying the output file: The text at the end of the output file normally gives the reason for the error. If the output file seems complete, the problem will require more careful attention. Scan all output tables for excessively large or small values Steel Member Design using PROKON

61 Viewing output The analysis results can be viewed graphically or in tabular format. Output data, including graphics and tabled values, can be selectively appended to the Calcsheets using the Add to Calcsheets function on each output page. Viewing output graphics Diagram can be displayed for the following: Deflections: Deflections are generally small in relation to dimensions of the structure, especially in the case of linear analyses. To improve the visibility of the deflection diagram, you can enter a screen magnification factor. You can optionally display the deflected shape without the original geometry. Beam element forces: Axial forces: The force is shown as expanded red and blue lines. Compression forces are shown in red and tension forces in blue. The distance of a line from the element centre line is in proportion to the size of the axial force. Moments: Bending moments about the local x and y-axes. A plot factor can also be entered to enlarge or reduce the bending moment diagram on the frame. Shear: Shear force diagrams are drawn for the local y and x-directions. A beam element s shear force diagram is constructed by viewing it with its local z- axis pointing to the right. Since the direction of the z- axis depends on the node numbers, irregular numbering of nodes can Steel Member Design using PROKON 4-61

62 result in apparent inconsistent signs used in the shear force diagrams. Refer to page 1736 for detail on the sign conventions used for beam element forces. Envelopes: Enter a series of elements and select the load case and combinations to include in the envelopes. Envelopes are drawn using the values as tabulated from the output file. Positive moments, for example, are drawn below the line and negative above. Because members of different orientations can be included in the same envelope, no simple distinction is made between tension and compression faces of members. Tip: When working with complicated frames, you may prefer adding one or more zoomed pictures to the Calcsheets instead of a single cluttered picture. To do this, simply into a picture and then use the Add to Calcsheets function. Viewing output tables Open the Output file page for a tabular display of the frame analysis output file. You can filter the information appended to the Calcsheets by enabling or disabling the relevant sections. The Find output function allows you to quickly locate any section of the output file Steel Member Design using PROKON

63 Calcsheets Frame analysis output can be grouped on a calcsheet for printing or sending to Calcpad. To include a particular component of the output in the calcsheets, view the relevant output information and then click Add to Calcsheets. Recalling a data file The Data File is automatically included in the calcsheet sent to Calcpad. You can later recall the frame by double-clicking the relevant object in Calcpad. A data file embedded in Calcpad is saved as part of a project and therefore does not need to be saved in the frame analysis module as well. Steel Member Design using PROKON 4-63

64 4-64 Steel Member Design using PROKON

65 Crane Gantry Girder Design The Crane Gantry Girder Design module can be used to design and optimise multi-span crane gantry girders with one or two cranes. Girders may be continuous or simply supported. The program supports multiple combinations of main beams and capping beams, including standard I-sections, plate girders and box girders. Steel Member Design using PROKON 4-65

66 Theory and application A brief background is given below regarding the application of the theory and principles given by the design codes. Design scope Crane gantry girders are generally constructed from rolled I-beams or welded plate girder. Channel capping beams are often used to stiffen top flanges. The program can check and optimise crane gantry girders made of rolled or welded I-sections or box sections with or without capping beams. One or two simultaneous cranes can be specified. The design procedure for crane gantry girders is similar to that used for statically loaded girders. The various loading codes recognise the varying degree of duty of different types of crane and give parameters for horizontal transverse effects. Especially in the case of heavier duty cranes, certain aspects of the design and construction may require special consideration. Design codes The program designs plate girders according to the following design codes: BS CSA S M89. SABS (allowable stress design). SABS (limit state design). Symbols Where possible, the same symbols are used as in the design codes. A list is given below. A : Cross-sectional area (mm 2 ). b : Width of capping beam top flange (mm). b bot : Width of main beam bottom flange (mm). b top : Width of main beam top flange (mm). C w : Warping torsional constant (mm 4 ). h : Height of section (mm). I xx : Second moment of area about major axis (mm 4 ). I yt : Second moment of area top flange only (mm 4 ). I yy : Second moment of area about minor axis (mm 4 ) Steel Member Design using PROKON

67 J : St. Venant s torsional constant (mm 4 ). r 1 : Radius between flange and web (mm). r 2 : Outside radius at end of taper flange in (mm). r y : Radius of gyration about minor axis (mm). t f bot : Main beam bottom flange thickness (mm). t f top : Main beam top flange thickness (mm). t w : Web thickness (mm). Z pl : Plastic section modulus about major axis (mm 3 ). Z pt : Top flange plastic modulus about minor axis (mm 3 ). Z yt : Top flange section modulus about minor axis (mm 3 ). ß : Angle between web and inside taper flange surface ( ). Stresses, forces and related entities BS : F : Applied axial load (kn). M : Applied moment (knm). M a : Maximum buckling moment in presence of axial load (knm). M b : Lateral torsional buckling resistance moment (knm). M c : Moment resistance in absence of axial load (knm). CSA S M89.: m : Equivalent uniform moment factor. n : Slenderness correction factor. P c : Compression resistance (kn). p y : Design strength of steel (MPa). C r : Factored compression resistance (kn). C u : Ultimate compression force (kn). f y : Yield strength (MPa). M r : Factored moment resistance (knm). M u : Ultimate bending moment (knm). U 1 : Capacity factor to account for moment gradient and second-order effects. The value depends on the bending moment diagram and the member stability. Steel Member Design using PROKON 4-67

68 SABS : V r : Factored shear resistance (kn). V u : Ultimate shear force moment (kn). 1 : Equivalent uniform bending moment factor. 2 : Moment gradient factor giving increased moment resistance of laterally unsupported members. f cr : 0.6 times the Euler buckling stress (MPa). f y : Yield strength (MPa). P c : Allowable axial compressive stress (MPa). P co : Maximum allowable axial compressive stress (MPa). P mc : Allowable compressive bending stress (MPa). P mco : Maximum allowable compressive bending stress (MPa). SABS : c : Average axial compressive stress (MPa). mc : Maximum compressive bending stress (MPa) : Coefficient allowing for varying bending moment. C r : Factored compression resistance (kn). C u : Ultimate compression force (kn). f y : Yield strength (MPa). M r : Factored moment resistance (knm). M u : Ultimate bending moment (knm). U 1 : Capacity factor to account for moment gradient and second-order effects. The value depends on the bending moment diagram and the member stability. V r : Factored shear resistance (kn). V u : Ultimate shear force moment (kn). 1 : Equivalent uniform bending moment factor. 2 : Moment gradient factor giving increased moment resistance of laterally unsupported members Steel Member Design using PROKON

69 Design parameters Various design parameters need to be set when designing a crane gantry girder: Effective lengths The codes give guidelines for determining effective length factors for flexural members: BS : Refer to clause guidance on factors to use for members in bending. Refer to clause and Appendix D for members in compression. CSA S M89: Refer to clauses 9.1 to 9.4 and Annexes B and C. SABS : See clause for flexural members. Refer to clause and Appendix E for compression members. SABS : Same as for CSA S M89. Steel Member Design using PROKON 4-69

70 Input Design input comprises five categories: General parameters: Design parameters including general characteristics of the girder, load factors, support conditions. Main beam sections: Dimensions and material properties of main beams sections. Capping beam sections: Dimensions and material properties of optional capping beams. Spans: Section composition and lengths along the length of the girder. Crane data: Capacity, weight and dimensions of each crane. General parameters Various design parameters, some of which depend on the code used, should be entered. General design parameters Spans can be made continuous or simply supported. If this entry is left blank, full continuity at supports is assumed. Modulus of elasticity. The entered value is used for all main beam and capping beam sections. The rail height is used as eccentricity when applying horizontal crane loads. The effective length factor for a typical span relates to effective length for lateral torsional buckling. This will depend on the degree of fixity at the supports and the de-stabilizing effect of applied loads. During the analysis each crane is moved step-wise across the beam to determine the force and deflection envelopes. A larger step can be used for an initial analysis and a smaller step for the final design. A smaller step size will yield a more accurate analysis and smoother output diagrams but will result in a longer analysis time. ULS load factors: Dead load factor: Factor by which the dead load, i.e. the self-weight of the girder, bridge and crab, is to be multiplied to obtain the ultimate limit state design load. Live load factor: Factor by which the live loads are to be multiplied Combined live load factor: Factor by which both the horizontal and vertical live loads must be multiplied if they are considered as acting together. This factor is usually smaller than the normal live load factor. When designing a girder for two cranes, enter the minimum spacing between the cranes Steel Member Design using PROKON

71 You can choose to make either end of the girder pinned (simply supported), fixed (built-in) or free (cantilevered). Dynamic load factors and deflection limits By default, the tabled values are set to those given by the selected design code: Vertical: Amplification factor for vertical loading per wheel, including the effect of impact. Horizontal surge: Factor for transverse force due to acceleration and braking of the crab. The program assumes that surge forces are transmitted via the wheel flanges. The full effects of such forces are applied perpendicular to the crane track. Misalignment: For the effects of misalignment of the bridge s wheels or the crane tracks. The misalignment forces are applied as two equal opposing forces. Skewing: Allows for skewing of the bridge. Skewing forces are applied as two equal opposing forces. L/D vertical: Vertical deflection limit, given as a ration of the span length. L/D horizontal: Horizontal deflection limit. Note: The program does not include the effects of horizontal force due to acceleration, braking or force exerted on end stops. Design options Two design approaches are available: You can choose to evaluate the capacity of entered beam sections to carry the specified loads. The main beams and capping beam sections can be optimised to obtain the lightest sections capable of resisting the design loads. Main beam sections Enter the properties for all the main beam sections that will be used in the analysis. You can read the properties of any standard I, H, square or rectangular hollow section from the database. Plate girder and box girder sections can also be used as main beams. The properties for these should be entered manually. Only fields relevant to the type of section need be completed: The designation column is optional and is used to describe a section. For square and rectangular hollow sections only h, b-top and t f -top are required. Steel Member Design using PROKON 4-71

72 The value for r2 and ß applies to sections with tapered flanges only. Each main beam section must be given a unique number for easy reference when defining the girder. Capping beams section data Main beam sections may optionally have channels or flat plates as capping beams. Enter each section that will be used during the analysis. Standard channels can be read from the database and flat plates can be defined by entering values for h and b. Each capping beam section must be given a unique number for easy reference when defining the girder. Main and capping beam sections are numbered independently. The various sections are combined when defining the girder geometry. Spans The data for a typical span comprises a span number, span length, main beam section number and, if required, capping beam section number. Information required for each span: 4-72 Steel Member Design using PROKON

73 Length : The length of a segment (m). Segment lengths are added to get the total length of the girder. Section M : Main beam section number. Section C : Capping beam section number. Leave blank if no capping beam is used. Any combination of previously defined main and capping beams may be used. However, you should take care that the capping beam will correctly fit over the main beam. Crane data Enter the loading and dimensional data for the cranes. In the case of a single crane analysis, simply leave the information for the second crane blank. Capacity : The rated lifting capacity of crane (T, i.e. 10 kn units). Class : The crane class designates it s type of use: Class Type of use 1 Light duty and hand operated cranes 2 Medium duty cranes 3 Heavy duty cranes 4 Extra heavy duty cranes Weight bridge : Weight of the bridge assembly (kn). Weight crab : Weight of the crab assembly (kn). The crab is defined as the portion that can move across the bridge. Tip: If the exact value of the crab weight is not known, a value of 15% of the capacity of the crane will usually be a reasonable estimate. Wheel spacing : Spacing between the bridge wheel assemblies (m). Wheel load : For web buckling and crippling checks, the maximum load that any single wheel will exert on the girder is required. This value should be obtained from the manufacturer's technical data. Steel Member Design using PROKON 4-73

74 Viewing analysis output The analysis output is displayed graphically. To view the detailed design calculation, select the Calcsheets page. You can view the following results and use the mouse to read values from the diagrams: The vertical and horizontal deflected shape of the crane gantry girder. Ultimate limit state bending moment diagrams about the X-X (horizontal) and Y-Y (vertical) axes. Bending moment diagrams are drawn on the tension face of the girder. Vertical and horizontal shear force diagrams. To append a deflection, moment or shear force diagram to design results on the Calcsheets page, first display the diagram and then click Add to Calcsheets Steel Member Design using PROKON

75 Calcsheet The design results of all tasks are grouped on a calcsheet for printing or sending to Calcpad. The design calculations include the following: Section properties for each combination of main beam and capping beam sections used. Web buckling and crippling checks for each section. Design checks for each span, including checks for the critical section and overall member strength. The design output shows the complete interaction formulae, with the zero values for axial force. If required, the output equations can be edited to include bending about the minor axis. To edit an equation, select it in the calcsheet, right-click it and choose Edit. Recalling a data file You can later recall the design by double-clicking the Data File object in Calcpad. Because a data file is embedded in the calcsheets sent Calcpad and saved as part of a project, you normally will not need to explicitly save your plate girder input using the Save command on the File menu as well. Steel Member Design using PROKON 4-75

76 4-76 Steel Member Design using PROKON

77 Plate Girder Design The Plate Girder Design module can be used to design I-shaped welded plate girders. The program checks the behaviour of girders under specified loading and gives guidance regarding bearing and intermediate stiffeners. Plate Girder Design 4-77

78 Theory and application A brief background is given below regarding the application of the theory and principles given by the design codes. Design scope Welded plate girders can often be effectively and economically used as flexural sections. Modern mechanised manufacturing and automated welding techniques have simplified the production of plate girders greatly, boosting their popularity. The program is capable is designing I-shaped sections with identical or different top and bottom flanges. You can also make the section properties vary along the length of the girder to model a tapered element. Tapered sections CSA S M89 and SABS do not cover the design of tapered sections. You can however choose to use the approach given by BS to design tapered elements. Bi-axial bending moment Plate girders are normally used to resist high bending moments and/or vertical shear forces. The program correspondingly assumes that these effects would govern the design and does not explicitly perform the checks for bi-axial bending moment. The design output shows the complete interaction formulae, with the zero values for bending moments about the minor axis. If required, the output formulae can be manually adjusted to include bending about the minor axis. Buckling under axial compression The program assumes that the effect of axial compression is small and therefore uses the full moment capacity for bending about the major axis. No capacity reduction is made on account of buckling about the major axis. Design codes The program designs plate girders according to the following design codes: BS CSA S M89. SABS (allowable stress design). SABS (limit state design) Plate Girder Design

79 Symbols Where possible, the same symbols are used as in the design codes. A list is given below. General design parameters A : Cross-sectional area (mm 2 ). B bot : Width of bottom flange (mm). B top : Width of top flange (mm). C w : Warping torsional constant (mm 4 ). f yf : Yield strength of flange (MPa). f yw : Yield strength of web (MPa). h : Total height of section (mm). I x : Second moment of area about major axis (mm 4 ). I y : Second moment of area about minor axis (mm 4 ). J : St. Venant torsional constant (mm 4 ). r y : Radius of gyration about minor axis (mm). T b : Bottom flange thickness (mm). T t : Top flange thickness (mm). T w : Web thickness (mm). Z cx : Compression flange section modulus about major axis (mm 3 ). Z tx : Tension flange section modulus about major axis (mm 3 ). Z plx : Plastic section modulus about major axis (mm 3 ). Z ply : Plastic section modulus about minor axis (mm 3 ). Z y : Section modulus of entire section about minor axis (mm 3 ). Stresses, forces and related entities BS : A g : Gross sectional area (mm 2 ). F : Applied axial load (kn). M : Applied moment (knm). M a : Maximum buckling moment in presence of axial load (knm). M b : Lateral torsional buckling resistance moment (knm). Plate Girder Design 4-79

80 M c : Moment resistance in absence of axial load (knm). CSA S M89.: m : Equivalent uniform moment factor. n : Slenderness correction factor. P c : Compression resistance (kn). p y : Design strength of steel (MPa). C r : Factored compression resistance (kn). Cu : Ultimate compression force (kn). Mr : Factored moment resistance (knm). Mu : Ultimate bending moment (knm). U1 : Capacity factor to account for moment gradient and second-order effects. The value depends on the bending moment diagram and the member stability. Vr : Factored shear resistance (kn). Vu : Ultimate shear force moment (kn). ω1 : Equivalent uniform bending moment factor. ω2 : Moment gradient factor giving increased moment resistance of laterally unsupported members. SABS : f cr : 0.6 times the Euler buckling stress (MPa). P c : Allowable axial compressive stress (MPa). P co : Maximum allowable axial compressive stress (MPa). P mc : Allowable compressive bending stress (MPa). P mco : Maximum allowable compressive bending stress (MPa). σ c : Average axial compressive stress (MPa). σ mc : Maximum compressive bending stress (MPa) SABS : ω : Coefficient allowing for varying bending moment. C r : Factored compression resistance (kn). Cu : Ultimate compression force (kn). Mr : Factored moment resistance (knm) Plate Girder Design

81 Mu : Ultimate bending moment (knm). U1 : Capacity factor to account for moment gradient and second-order effects. The value depends on the bending moment diagram and the member stability. Vr : Factored shear resistance (kn). Vu : Ultimate shear force moment (kn). ω1 : Equivalent uniform bending moment factor. ω2 : Moment gradient factor giving increased moment resistance of laterally unsupported members. Design parameters Various design parameters need to be set when designing a plate girder: Effective lengths The effective length of a member depends on the degree of restraint to be expected at each end of the member. The program assumes that the effect of axial compression is relatively small and hence uses the full bending capacity for bending about the major axis. However, the program allows you to specify positions of restraints for lateral torsional buckling of the compression flange. You can apply a different effective length factor to each unsupported length, e.g. different factors for a cantilever end and internal continuous lengths. Guidelines given in the codes include: BS : Refer to clause guidance on factors to use for members in bending. Refer to clause and Appendix D for members in compression. CSA S M89: Refer to clauses 9.1 to 9.4 and Annexes B and C. SABS : See clause for flexural members. Refer to clause and Appendix E for compression members. SABS : Same as for CSA S M89. Plate Girder Design 4-81

82 Bending moment factors A flexural member s lateral torsional behaviour is influenced by the shape of its bending moment diagram. This phenomenon is acknowledged by the design codes through their introduction of special design factors: BS : The equivalent uniform moment and slenderness correction factors, m and n, may not be less than 0.43 and 0.65 respectively. CSA S M89: The equivalent uniform bending moment, ω 1, may not be less than 0.4 and the moment gradient factor, ω 2, may not be higher than 2.5. SABS : The values of the coefficient for varying bending moment, ω, may not be less than 0.4. For members subjected to sway, ω should not be taken less than SABS : Same as for CSA S M89. The program automatically calculates the above factors and restrict their values to the minimum and maximum values specified Plate Girder Design

83 Input Design input comprises five categories: General: Design parameters, supports and axial load. Sections: Dimensions and material properties of section webs and flanges. Spans: Section variations and lengths along the length of the girder. Loads: Ultimate loads. Lateral supports: Compression flange supports. General parameters Various design parameters, some of which depend on the code used, should be entered: The shape of a flexural member s bending moment diagram influences its lateral torsional stability. The design codes use different design factors to accommodate this phenomenon. See page 17 for more details. The entered support width is used to calculate local buckling and crushing of the girder s web at every support. Specify whether the program should calculate and add the girder s own weight in the analysis. You can choose to make either end of the girder pinned (simply supported), fixed (built-in) or free (cantilevered). Enter an axial force, with a positive force denoting compression (kn or kip). Note: Although the program allows you to enter an axial force, it does not check for buckling under axial load. The effect of axial compression is assumed to be so small as not to cause a reduction in the moment capacity for bending about the major axis. Sections You can define a variety if I-section by entering the dimensions for the web and top and bottom flanges. If different grades of steel are used for the flanges and web, you should enter the appropriate yield strengths for each. Each section should be given a unique number for easy reference when defining the girder. Plate Girder Design 4-83

84 Spans The plate girder is entered as one more continuous segments. Up to twenty segments may be defined by entering the following values in the Section Lengths input table: Length: The length of a segment (m or ft). Segment lengths are added to the right hand side of the girder. Section Left/Right: Section numbers to be used at left and right ends of a segment. You can define a tapered section by specifying different section numbers for the left and right ends. Note: CSA S M89 and SABS do not cover the design of tapered sections. When designing such elements, the program gives the option to use the weakest portion of such elements or to design of them using the approach given by BS Loads Applied loads may comprise distributed loads, point loads and moments. Positive forces and moments are taken to work downward and anti-clockwise respectively: Wleft : Distributed load intensity (kn/m or kip/ft) applied at the left-hand starting position of the load. If you do not enter a value, the program will use a value of zero. Wright : Distributed load intensity (kn/m or kip/ft) applied on the right-hand ending position of the load. If you leave this field blank, the value is made equal to Wleft, i.e. a uniformly distributed load is assumed. P : Point load (kn or kip). M : Moment (knm or kipft). a : The start position of the distributed load, position of the point load or position of the moment (m or ft). The distance is measured from the left-hand edge of the girder. If you leave this field blank, a value of zero is used, i.e. the load is taken to start at the left-hand edge of the beam. b : The end position of the distributed load, measured from the start position of the load (m or ft). Leave this field blank if you want the load to extend up to the right-hand edge of the girder Plate Girder Design

85 Note: Applied forces are taken to be design loads at ultimate limit state. For allowable stress design according to SABS , you should enter working loads. Lateral supports Specify the positions of lateral support by entering the unsupported lengths. A unique effective length factor can also be entered for each length. Refer to page 174 for more details. Note: The program always draws the specified lateral supports on the top flange. During the analysis, however, these positions are taken to define lateral supports of the compression flange, whether it is the top or bottom flange that is actually in compression. Plate Girder Design 4-85

86 Viewing analysis output The analysis output can be viewed graphically. To view the detailed design calculation, select the Calcsheets page. You can view the following results and use the mouse to read values from the diagrams: The deflected shape of the plate girder. Ultimate limit state bending moment diagram. The bending moment diagram is drawn on the tension face of the girder. Ultimate limit state shear force diagrams. Bending stresses at ultimate limit state. The stresses in the top and bottom flanges are shown in red and yellow respectively. The shear stresses at ultimate limit state together with the shear capacity for various web stiffener spacings. The actual stresses are shown in red and the shear capacities in blue Plate Girder Design

87 Calcsheet The design results of all tasks are grouped on a calcsheet for printing or sending to Calcpad. The calcsheets include a Data File for easy recalling of the analysis from Calcpad. The design output shows the complete interaction formulae, with the zero values for bending moments about the minor axis. If required, the output equations can be edited to include bending about the minor axis. To edit an equation, select it in the calcsheet, right-click it and choose Edit. Recalling a data file You can later recall the design by double-clicking the Data File object in Calcpad. Because a data file is embedded in the calcsheets sent Calcpad and saved as part of a project, you normally will not need to explicitly save your plate girder input using the Save command on the File menu as well. Plate Girder Design 4-87