ENERCALC Version 5.8 - Non-Current Retired Version

Series of Cantilevered Beams

Series of Cantilevered Beams

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Series of Cantilevered Beams

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This program analyzes and designs a series of statically determinate simple span and cantilevered beams. This type of framing arrangement is typically used in warehouse type structures where long runs of cantilevered and simple span beams provide an economical framing system. The economy of this type of framing system can be improved when the positive and negative moments are nearly equal in magnitude, thereby fully utilizing the beam.

 

Live load is automatically applied to various span combinations to give maximum reactions, shears, moments, and deflections. Using the column layout of the calcsheet, you can model a variety of different framing systems. The following span combinations can be used to model a line of beams having up to eight beams:

Single Cantilever Simple Span Single Cantilever
Simple Span Double Cantilever Simple Span
Simple Span Simple Span Simple Span

 

On each span, you can apply one uniform load, one partial length uniform load, and four point loads, each having dead and live components.

NOTE!!   When entering loads in the various calcsheet columns, keep in mind that the load is applied to beams and cantilevers located between the supports, NOT JUST TO THE BEAM REFERRED TO IN THE COLUMN TITLE. This enables you to simply specify the point load locations, and the program will determine if it applies to the simple span beam or the adjacent cantilevers.

 

The program also offers some general design options:

Automatic live load alternate span placement.
For laminated beams; specification of lamination thickness for automatic design.
Consideration of load duration factors for live and/or snow loads.
The program also offers two unique abilities:
Automatic Cantilever Balancing. This feature automatically adjusts cantilever lengths to balance the positive and negative moments.
Automatic Beam Depth Determination using the calculated moments and shears.

 

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Basic Usage

If this will be a design calculation, enter the lamination thickness that should be used when automatically calculating required beam depths.
Since this system of beams can have numerous arrangements of live load, set Skip Load Live to YES indicate if you wish the program to perform the extra calculations to place live loads in all possible locations for maximum values. Indicate the load duration factor for the type of loads you will be applying, and indicate if cantilever bracing should be assumed. If no bracing is used, all cantilevers will go through code checking with the unbraced length equal to 2*Cant. Span.
Enter the column spacing for the system of beams. All beams must be in line with one another, and up to eleven spans can be used. For more spans, try to look for symmetry and model accordingly. Then take a first trial estimate of the various cantilever lengths for the beams.
Although depth isn't required if you will be doing an automatic design, you must enter a beam width for each span. If you choose the auto design capability, the program will determine the depth (considering lamination increments) for you.
Use the Beam Design Data section to specify the material properties for the timber beam.
Up to nine loads can be applied between each column. The two uniform load entries allow a full length and partial length load to be applied. The partial length load can be used to apply a different load to the simple span beam than to the adjacent cantilevers. Point loads can be applied anywhere between the supports; the program uses the X-Dist. values to apply the load to the cantilever or simple beam.

 

Unique Features

With this program you can either analyze or optimize the design of a series of simple span and cantilever beams.

By specifying a cantilever at only one end of a double cantilever beam, you can simulate a Single Cant. - Simple Span - Single Cant. condition.
The program automatically checks the location of the point loads specified in Simple Span columns, and determines if they rest on the cantilever or simple span beam.
The maximum shear and reactions are calculated by skip loading.

 

When the program flag "Skip Load Live" is set to YES, the live load is placed on spans as follows:

For all Simple Span Beams , full live load is always placed on the entire span.
For maximum Cantilever  moments, live load is applied to the cantilever and adjacent simple span beam.
The following placements apply to cantilevered beams for calculating moments between supports and maximum end shears and reactions:
For Maximum Moment t, live load is not applied to cantilevers or simple span beams between adjacent columns. Live load is applied to the portion of the beam between supports.
For Maximum Left Shear , live load is applied to the left cantilever and the simple span beam is supported by the left cantilever. This value is then compared to the maximum left reaction (see below) minus this value.
For Maximum Left Reaction , live load is applied between supports, left cantilever, and simple span beam supported by the left cantilever. No live load is applied to the right cantilever or simple span beam supported by the right cantilever.

 

Example

The data entry for this example is shown in the screen captures that accompany the Data Entry Tabs and Results & Graphics Tabs sections to follow.

 

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Automatic Cantilever Length Optimization

Using the [Optimize Cantilevers] button in the toolbar at the top of the screen you can have the program automatically calculate the proper cantilever lengths to make the center span "Positive" moments approximately equal to the "Negative" moments at the end supports.  The program performs a cyclical modification of the cantilever lengths and examines the resulting end moments and center span moments.

 

This type of optimization is essential when designing these types of beam system because the greatest economy of member sizes is achieved.

 

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Automatic Member Selection

Using the [Design] button you can display a screen that will enable you to set design parameters and examine a database of wood members for selection of those that satisfy your criteria. This screen allows you to:

Specify maximum deflection ratios for dead and total loads.
Specify overstress limits for bending and shear forces.
Use "Go" to start the database search. The beam width and lamination thickness already present in the calcsheet will be used to determine a depth considering bending and shear stresses and deflections.

 

Here's the screen....

 

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Wood Section Database

On all the tabs labeled "Right", "Key", "Double", and "Left" you are provided with a button to select a wood section from the internal wood member database.

 

[Wood Section] button and entry

Use this button to display the database of wood sections. The database provides selections for sawn, glued-laminated, and manufactured lumber. Please refer to the previous chapter describing using database in the Structural Engineering Library.  Pressing [Wood Section] will display the following selection window:

 

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Data Entry Tabs

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

 

General Tab

 

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Wood Species : [Stress] button & entry

This allows you to use the built-in NDS & Manufactured lumber allowable stress database to retrieve allowable stresses. When you press the button you will see this selection window.  Please see the section earlier in this User's Manual that give information and usage for the databases.

 

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Fb : Base Allowable

Basic allowable bending stress to be used for design and analysis. This stress will be modified based by slenderness, size factor, and load duration factor.

 

Fv-Shear

Allowable shear stress to be used in design. This allowable will be modified by the load duration factor.

 

Elastic Modulus

Enter the modulus of elasticity to be used in determining deflections and calculation of F'b for laterally unbraced beams.

 

Load Duration Factor

Load duration factor to be applied to allowable bending and shear stresses. Application of this factor is in accordance with NDS.

 

Lamination Thickness

 

Should Live Load be "Skip" Loaded

Use this checkbox specifies whether the program's analysis should place the live load in different locations to determine maximum values. If unchecked dead and live load will always be placed on each span.

 

Are Cantilevers Braced

This checkbox specifies whether the program should consider all cantilevers to have an unbraced length equal to zero. This allows full stresses to be used for design and analysis. If CHECKED either the cantilever's span/thickness ratio is very low, or cantilever braces are being used. If NOT CHECKED an unbraced length equal to 2*Cant. Length is used to determine allowable stresses based on lateral buckling of the compression face.

 

 

Using the Beam Data Entry Tabs "Right", "Key", "Double", "Left'

At the top you will see the following tabs:

     Right Cant----Key #1----Double #1----Key #2---- .....

 

Each span condition is represented by the tab. All information for that beam is specified in that column. For example, if we want to analyze a beam with a cantilever off the right end, and that cantilever supports the left end of a simple span beam we would use the two left-most columns, labeled :

     Right Cant----Key #1

 

Use any column on the calcsheet to model your system of cantilevered beams.

 

On each tab you will see an entry called "Column Spacing". Think of the program as setting up column bays that support the system of beams. Because you will be modifying cantilever lengths it is far easier to enter the column locations and let the program recalculate key beam lengths automatically.

 

Also, when you enter partial length loads and point loads in the "Key Beam" tabs this program will automatically figure out whether the load is on the cantilevered portion or simple span portion of the beam system between those support.

 

Right Cant Tab

This tab is used to enter the information for the left-most beam in your cantilevered beam system.

It is named "Right Cant" because the beam ONLY has a cantilever to the right. The left end is bearing on a wall or other end support.
You do not need to use this tab if the left side of your cantilever system is a simple-span beam that bears on a support at the left and hangs on a cantilever on the right. In that case do not use this tab by setting the span to "0.0" and the "Key #1" tab is the left-most tab used in the calculation.

 

 

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Column Spacing

This is the distance between the supports for this beam.

 

Right Cantilever

This is the cantilever length for this beam that extends past the right support.  LOADS THAT WILL BE APPLIED TO THIS CANTILEVER ARE SPECIFIED ON THE "Key #1" TAB.  This is because the program operates on a column-to-column format. You specify the loads between columns and the program automatically figures out which member (cantilever portion or simple "key" beam) that the load actually is applied to based upon the loads' location.

 

Unbraced Length

Enter the unbraced length of the compression side of the beam that should be used to calculate Rb and the resulting allowable stress reduction factor "Cl".

 

Wood Section

See the information given previously on using the built-in wood section database.

 

You do not need to use the database !  You can enter any beam name in this entry and type in the beam Width & Depth. When you use the wood section database it merely fills in the beam name, depth, and width for you.

 

Beam Depth & Width

The actual beam Width and Depth to be used for calculation of section properties used in this design/analysis.

 

Uniform & Partial Length Loads

Uniform loads apply to the beam between the supports. Any loads that need to be applied to the cantilever must be entered on the adjacent tab.

Partial Length loads allow you to enter a starting and ending location as a distance from the left support. Values less than zero and grater than "Column Spacing" are not valid and will be automatically corrected for you.

 

Point Loads

Enter any point loads applied to the beam here. The "Location" is the distance from the left support. Values less than zero and grater than "Column Spacing" are not valid and will be automatically corrected for you.

 

 

Key Tabs

The data entry on this tab is essentially the same as the "Right Cant" tab except that no entry for cantilevers is available. Instead the actual span of the beam is shown. The "Actual Span" i calculated by subtracting the cantilevers specified on the adjacent tabs from the "Column Spacing" specified here.

 

Also, the loads that you specify here are applied to any beam portion that is in this "Column Spacing" area. Referring to the image below, this means the right cantilever specified on the "Right Cant" tab and the left cantilever specified on the "Double #1" tab.

 

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Double Tabs

The data entry on this tab is essentially the same as the "Right Cant" tab except entries for cantilevers off both ends of the beam are now available.

 

 

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Uniform & Partial Length Loads

Uniform loads apply to the beam between the supports. Any loads that need to be applied to the cantilever must be entered on the adjacent tab.

Partial Length loads allow you to enter a starting and ending location as a distance from the left support. Values less than zero and grater than "Column Spacing" are not valid and will be automatically corrected for you.

 

Point Loads

Enter any point loads applied to the beam here. The "Location" is the distance from the left support. Values less than zero and grater than "Column Spacing" are not valid and will be automatically corrected for you.

 

 

Results & Graphics Tabs

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

 

Results Tab

This tab shows all of the calculated values for the beam tab selected on the left.

 

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Moments

This is the maximum moments between end supports and at the cantilevers (if present).

 

For simple span beams on the "Key #?" tabs this moment is caused by dead and live loading. For cantilevered beams when the Skip Load flag is set to YES, the live load on the adjacent simple span beams and cantilevers is Skip Loaded to determine maximum moments.
For beams with left cantilevers (which are the "Double Cant" tabs and the "Left Cant" tab to the far right in the tab set) the moment at the beam's left support is induced by applying full dead and live load to the left cantilever AND the simple span beam it is supporting.
For beams with right cantilevers (which are the "Double Cant" tabs and the "Right Cant" tab to the far left in the tab set) the moment at the beam's right support is induced by applying full dead and live load to the right cantilever and to the simple span beam it is supporting.

 

F'b-Allow

Using the basic Fb entered under DESIGN DATA, the actual allowable bending stress is calculated considering Load Duration Factor, Size Factor, and reductions considering lateral buckling failure (caused by long unbraced lengths).

 

fb-Actual

Maximum moment divided by section modulus.

 

Maximum Shear

For cantilevered beams, this is the maximum shear over the support. For calculation of the maximum shear, the greater of:

A total of all forces acting on the cantilever
The maximum reaction minus the total of all forces acting on the cantilever.
For simple span beams it is simply the maximum end reaction.

 

fv-Actual

After calculations have determined the maximum shear magnitude at supports, all loads within a distance Beam Depth from the support (on the governing side of the beam) are subtracted, the result is divided by the beam's area, and then multiplied by 1.5 to arrive at this true shear stress.

 

Fv-Allow

Basic Fv entered under the DESIGN DATA section is multiplied by the load duration factor.

 

Center Deflection

Center Dead Load Deflection results from applying all dead loads to the beam and all contributing cantilevers and beams which the cantilevers support. Center Maximum Deflection depends upon the state of the Skip Load flag. If skip loading is not  used, dead and live loads are applied to all beams. If skip loading IS used, the live load is applied to the beam only between supports..... no cantilevers or beams they support are loaded with live load.

 

Cantilever Deflections

Maximum cantilever deflections (regardless of Skip Load flag) are calculated by applying dead and live load to the cantilever and adjacent simple span beam. No live load is applied to the beam between supports, BUT the opposite cantilever IS loaded with live load.

 

Maximum Reactions

These are calculated as follows:

For the left support t this value is calculated by applying full dead and live load to all portions of the beam between supports and the simple span beam to the left, and NOT APPLYING LIVE LOAD  to the right cantilever or the simple span beam immediately to its right.
For the right support this value is calculated by applying full dead and live load to all portions of the beam between supports and simple span beam to the tight, and NOT APPLYING LIVE LOAD  to the left cantilever or the simple span beam immediately to its left.
For the simple span beams, all loads are applied to the beam.

 

Cv

This item will display as "Cv" for glued laminated beams when the volume factor applies and as "Cf" for sawn or manufactured members when the size factor applies.

 

Rb

Slenderness ratio for the beam.

 

Le : Unbraced Length

This unbraced length entry ONLY APPLIES TO THE SIMPLE BEAM AND CENTER SPAN OF CANTILEVERED BEAMS. It is independent of the Are Cants. Braced general entry. This value helps the stress checking function to determine if the beam is short, intermediate, or long for purposes of allowable stress determination.

This entry is the unsupported compression edge length, corrected for span type per AITC/UBC code.

Use the following table as a guide.

Type of Beam Span and Nature of Load                    Value of Effective Length, Le Single

     Span beam, load concentrated at center                                  1.61 Lu

     Single Span beam, uniformly distributed load                            1.92 Lu

     Single Span beam, equal end moments                                  1.84 Lu

     Cantilever beam, point load at unsupported end                            1.69 Lu

     Cantilever beam, uniform load w/ point load at end                    1.69 Lu

     Single Span beam, any other load                                        1.92 Lu

 

 

 

 

Sketch Tab

This tab provides a sketch of the beam with loads and resulting values shown. Using the [Print Sketch] button will print the sketch in large scale on a single sheet of paper.

 

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Notes Tab

This tab contains some general notes about the usage of the results of this program.

 

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Printing Tab

This tab allows you to control which areas of the calculation to print. Checking a box will signal that the information described by the item will be printed. However, if there is no information in for a particular selection it will not be printed. So these checkboxes are best described as "If this particular area of the calculations contains data then print it".

 

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Sample Printout Page 1

 

CANTBEAM_PRT_1

 

Sample Printout Page 2

 

CANTBEAM_PRT_2