Chapter General Applications - Ahmed Mansourahm531.com/Prokon and EQ course/Prokon Manual/Chap-08.pdf · Chapter General Applications The ... • The section is then sub-divided into

General Applications 8-1

Chapter

General Applications

The general analysis modules can be used to calculate section properties, wind pressures on buildings and evaluate drainage systems of building roofs.


Quick Reference

General PROKON Analysis Tools 3 Section Properties Calculation 5 Wind Pressure Analysis 17 Gutter and Down pipe Design 23


General PROKON Analysis Tools

The PROKON suite includes a number of simple analysis tools to simplify everyday calculations. These include:

• Section Properties Calculation: For the calculation of bending and torsional properties of any generalised section.

• Wind Pressure Analysis: For determining the free stream velocity pressure on a building.

• Gutter Design: Use this module to design a drainage system for a roof by sizing a gutter, outlet and down pipe.


Section Properties Calculation 8-5

Section Properties Calculation

The Section Properties Calculation module, Prosec, is used to calculate the bending and torsional properties of any arbitrary section. The section can be solid or have openings.


Theory and application

An overview is given below regarding the theories used to calculate section properties.

Scope Prosec can be used to calculate the properties of any arbitrary section. The section can be solid or have openings. For bending property calculation, the program uses a simple technique of division into sub-sections. The Prandtl membrane analogy is used to determine the torsional section properties, including the shear centre, St. Venant torsional constant and torsional warping constant.

Sign convention A simple Cartesian sign convention applies:

• X-coordinates are taken positive to the right and negative to the left.

• Y-coordinates are taken positive upward and negative downward.

Units of measurement All input and output values are used without a unit of measurement. Whether you define a section using sizes for millimetres, metres, inches or feet, the output will effectively be given in the same unit of measurement.

List of symbols Below is a list of symbols used for the bending and torsional section properties:

Bending properties

A : Area of the cross section.

Ixx, Iyy : Second moment of inertia about X and Y-axis.

Ixy : Deviation moment of inertia.

Iuu, Ivv : Second moment of inertia about major axis and minor axis.

Ang : Anti-clockwise angle from the X-axis to the U-axis.

Zxx : Elastic section modulus in relation to the top or bottom edge.

Zyy : Elastic section modulus in relation to the left or right edge.

Zuu : Minimum section modulus in relation to the U-axis.

Zvv : Minimum section modulus in relation to the V-axis.


Zplx, Zply : Plastic modulus about X and Y-axis.

Xc : Horizontal centroid position measured from the leftmost extremity of the section.

Yc : Vertical centroid position measured from the bottom most extremity of the section.

rx, ry : Radius of gyration about the X or Y-axis.

ru, rv : Radius of gyration about the U or V-axis.

Xpl : Horizontal distance from leftmost extremity to centre of mass.

Ypl : Horizontal distance from topmost extremity to centre of mass.

Torsional properties

τ : Shear stress.

X : Horizontal position of shear centre from the leftmost extremity of the section.

Y : Vertical position of shear centre from the bottom of the section.

J : St. Venant torsional constant.

Zt : Torsional modules.

Cw : Warping torsional constant.


Input

A section is defined by entering one or more shapes in the input table. A shape may comprise straight lines and arcs or may be a circle. When more than one shape is entered, the shapes will accumulate and form one section. You can create openings by entering negative shapes that are subtracted from the section.

Note: If preferred, section input can be done graphically. Use Padds to draw a polygon to scale or import a DXF drawing from another CAD system. Then generate an input file for Prosec.

Entering a section The Code column is used for categorise the data that follows in the next columns:

’+’ : The start of a new polygon or circle. An absolute reference coordinate must be entered in the X/Radius and Y/Angle columns.

’–' : Start of an opening. An absolute reference coordinate must be entered in the X/Radius and Y/Angle columns.

'R' : Indicates a line drawn with relative coordinates.

'L' : Indicates a line drawn with absolute coordinates.

'A' : An arc that continues from the last line or arc. The arc radius and angle are entered in the X/Radius and Y/Angle columns respectively. The angle is measured clockwise from the previous line or arc end point.

'C' : A circle with the radius entered in the X/Radius column.

Tip: If the Code column is left blank, relative coordinates are used.

The X/Radius and Y/Angle columns are used for entering coordinates, radii and angles:

X : Absolute or relative X-coordinate. Values are taken positive to the right and negative to the left.

Radius : Radius of a circle or an arc.

Y : Absolute or relative Y-coordinate. Values are taken positive upward and negative downward.

Angle : Angle that an arc is extending through.

Note: If the X/Radius or Y/Angle column is left blank, a zero value is used.


Entering a shape A shape has two basic components:

• A reference coordinate, which gives the starting point of a polygon or the centre of a circle.

• One or more entries defining the polygon’s coordinates of lines and arcs or a circle’s radius.

After entering each coordinate, the image of the polygon updated.

Note: The starting point of a polygon is also used as the ending point and the polygon is closed automatically. It is therefore not necessary to re-enter the starting coordinate to close a polygon.


The reference coordinate

Every polygon has a start point and every circle has a centre point. These points are called reference points and are entered as absolute coordinates:

• In the Code column, enter either a ’+’ or ’–' to indicate the start of a new shape. Entering a '+' means that the shape will be added to the section. Likewise, a '–' means that the shape will be subtracted, e.g. an opening.

• Enter the absolute values of the reference coordinate in the X/Radius and Y/Angle columns.

Coordinates defining the polygon

Given a reference coordinate, two or more additional coordinates are required to define the shape of a polygon. In the case of a circle, only a reference coordinate and radius is required. A coordinate may be entered using absolute or relative values:

• If the Code column is left blank, the coordinate is taken relative from the last point entered.

• Set the Code to 'L' if you want to enter an absolute coordinate.

• The coordinate values are entered in the X/Radius and Y/Angle columns. A negative X or Y-coordinate must be preceded by a minus sign. The plus sign before a positive X or Y-coordinate is optional.

• A circular arc is defined by setting the Code to 'A' and entering the radius in the X/Radius column. The arc is then taken to extend from the end point of the last line or arc, starting at the angle that the previous line or arc ended and extending through the angle specified in the Y/Angle column.

• Define a circle by setting the Code to 'C' and entering the coordinate for the centre point. On the next line, enter the radius in the X/Radius column.

Note: You can rotate by choosing Settings.

Procedures for entering shapes Step-by-step procedures for entering typical section Codes are given below:

Entering a polygon comprising straight lines

A polygon is defined by entering a start point followed by a few lines of additional coordinates. The polygon can be defined using relative or absolute coordinates or both.

Using relative coordinates:


• Define the start position of the polygon by setting the Code to ’+’ and entering the absolute coordinate in the X/Radius and Y/Angle columns.

• Next, leaving the Code column blank, enter the consecutive corner points of the polygon in the X/Radius and Y/Angle columns. By leaving the Code column blank, the entered coordinates are set to relative coordinates.

Using absolute coordinates:


• For each following coordinate, enter an L in the Code column and enter the absolute coordinate values in the X/Radius and Y/Angle columns.

Entering a polygon comprising lines and arcs

A polygon with one or more arcs is defined in a similar way as a normal polygon:


• Define straight lines by entering the consecutive corner points using relative or absolute coordinates.

• For an arc, set the Code to A and enter its radius and angle in the X/Radius and Y/Angle columns. The arc will be taken to extend from the previous line/arc through the specified angle. A positive angle is taken as a clockwise rotation and a negative angle as an anti-clockwise rotation.

Tip: If an arc is to start at a certain angle, simply precede it with a short line at that angle.

Entering a circle

A circle is defined by entering the centre point followed by its radius in the next line:

• Define the centre point of the circle by setting the Code to ’+’ and entering the absolute X and Y-coordinates. If you leave either of the coordinates blank, a value of zero is used.

• On the next line, set the Code to C and enter the radius of the circle in the X/Radius column.

Note: A circle should be considered as a complete shape. If a circle has to be incorporated in another shape, a polygon with arcs should be used.


Entering an opening

An opening is defined exactly like any other shape, with the exception that it is entered as a negative shape:

• Define the start position of the polygon by setting the Code to ’–' and entering the absolute coordinate in the X/Radius and Y/Angle columns.

• Define lines, arcs or a circle by entering the relevant points as described in the examples above.


Analysis

Two separate analysis procedures are used to calculate the bending and torsional section properties. The bending analysis is completed almost instantaneously. However, the torsional analysis procedure uses a sophisticated finite difference analysis technique and therefore takes longer to complete.

Analysis settings Click Settings to adjust the analysis settings applicable to the bending and torsional analyses:

• Rotation angle: Enter an angle if you wish to calculate the bending properties for a rotated section.

• Poisson ratio: The ratio influences the torsional shear stress distributions in a section. It therefore also has an effect on the position of the shear centre and warping torsion constant.

Material Poisson Ratio

Aluminium 0.16

Concrete 0.20

Steel 0.30

• Number of equations: For determination of the torsional section properties, the finite difference mesh is sized to yield approximately the specified number of equations. More equations will take longer to solve, but may yield better accuracy, especially when analysing thin-walled sections.


Calculating bending section properties The bending section properties are calculated using a simple method of division into sub-sections:

• Circles and arcs are first converted to polygons with approximately the same shapes. The program uses lines at 30° angle increments for this purpose.

• The section is then sub-divided into a series of trapeziums and the properties are calculated for each trapezium.

• The global section properties are finally calculated through summation of the values obtained for each trapezium.


Calculating torsional section properties A sophisticated finite difference analysis method is used for calculating the torsional section properties. The Prandtl membrane analogy is used for determining the Y and X-shear stresses and J, the St. Venant torsional constant. The membrane is modelled using a finite difference mesh.

The shear stress distributions in the Y and X-directions are determined for a unit load applied in the Y-direction. The shear centre is then calculated by considering the moment of shear stresses about the centre of mass.

The torsional constant, J, is taken as twice the volume below the membrane. The maximum slope of the membrane then gives the torsional modulus. The maximum torsional shear stress can be obtained by dividing the torsional moment with the torsional modulus Zt.

Warping torsion is evaluated by using the relationship between shear and axial deformation from classical elastic theory. The shear deformation is obtained from the pure torsion analysis. The warping constant, Cw, is then determined from the longitudinal displacements.


Calcsheet

The section property calculations can be grouped on a calcsheet for printing or sending to Calcpad. Various settings can be made with regards to the inclusion of design results and pictures.

Tip: You can embed the Data File in the calcsheet for easy recalling from Calcpad.

Recalling a data file If you enable the Data File option before sending a calcsheet to Calcpad, you can later recall it 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 analysis module as well.

Wind Pressure Analysis 8-17

Wind Pressure Analysis

The Wind Pressure Analysis module is a simple utility for the calculation of free stream velocity pressure on building structures.


Theory and Application

A brief summary is given below with respect to the supported design codes and symbols used.

Design codes The following codes of practice are supported:

• CP3 - 1972.

• SABS 0160 - 1989.

List of symbols The code symbols are used as far as possible:

k : Pressure coefficient that depends on altitude.

Qz : Free stream velocity pressure (kPa).

V : Regional wind speed (m/s).

vz : Characteristic wind speed at a height z (m/s)

zg : Gradient height that depends on the terrain category and class of structure (m).

α : Height exponent that depends on the terrain category and class of structure.


Input

The following structural and environmental parameters are required:

• Height of building: The total height exposed to wind loading.

• Height above sea level: Altitude to use for calculating the design wind speed.

• Wind speed: Regional design wind speed for a fifty-year return period. Refer to the relevant design code for regional values.

• Terrain category: This value indicates the likely exposure of the structure to wind loading. A higher value denotes increased shielding and lower wind pressures:

Terrain Category Description

1 Open terrain

2 Outskirts of towns

3 Built-up and residential areas

4 City centres

• Class: The class of structure quantifies the importance of the analysis:

Class Description

A Structural component

B Structure as a whole

C For checking structural stability


• Return period: Enter a return period to indicate the importance of the structure:

Return Period Description

100 High risk buildings, e.g. hospitals and communication centres

25 Low risk structures, e.g. farm outbuildings

5 Temporary structures

50 Most other structures


Calcsheet

Press Analyse to calculate and display the wind pressure distribution. Use the Calcsheets page to print the results or send the displayed information to Calcpad.

Recalling a data file The Data File is automatically included when sending a calcsheet to Calcpad. You can later recall the data file 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 Wind Pressure Analysis module as well.


Gutter and Down pipe Design 8-23

Gutter and Down pipe Design

The Gutter Design Module is used to design gutters and down pipes to drain roofs of typical building structures.


Theory and application

Below is a brief summary of the application of the theory.

Scope The program can evaluate roof drainage systems subjected to intense short duration rains. It takes into account the shape of the gutter, the outlet into which the gutter discharges and the pipe-work that conveys the flow to below.

Design code The program is based on the requirements of BS 6367 - 1983.

Units of measurement The program supports both Metric and Imperial units of measurement.

Assumptions The same assumptions used in the code are applicable. These include:

• The gutter slope does not exceed 1:350.

• The gutter has a uniform cross-sectional shape.

Note: Reference should be made to the code for guidance on the positioning and sizing of gutter outlets and other requirements.


Input

Define the drainage system and storm to be drained:

• Storm characteristics

• Gutter geometry

• Outlet and down pipe definition.

Storm characteristics The following parameters should be entered to define the storm:

• Return period (years): This parameter is used as a measure of the security of an acceptable degree of damage. A return period of between five and fifty years is normally used for typical situations. For higher risk scenarios, a value of one and a half times the expected life of the building and higher should be used. Refer to the code for detail.

• Two minute M5 rainfall (mm): This quantity is defined as the expected rainfall in a two minute period during a one in five year storm. Press 2 Minute M5 Rainfall Constants to display regional data for the United Kingdom and South Africa. Refer to the code or other relevant hydrological data for regions not listed.

• Design duration (1 to 10 minutes): Adjust the default two-minute design duration if necessary. The M5 rainfall is then adjusted in accordance with Table 10 of the code.

• Effective drainage area: Roof area to be drained, taking into account any adverse effect of wind on sloping roofs and vertical surfaces and other factors.

Note: Gutters and down pipes may normally be omitted for roofs with area of 6 m2 or less.


Gutter geometry Rectangular and trapezium shaped gutters can be defined:

• Top width (mm): Width at the top of the gutter.

• Base width (mm): The bottom width of the gutter. Set the base width equal to the top width for rectangular gutters.

• Sloping depth (mm): For a trapezium shaped gutter, enter the depth in which the gutter slopes outward from the base.

Note: You are not required to enter the total depth of the gutter. The program calculates the depth required for proper draining.


Outlet and down pipe parameters The type of outlet influences the flow collected from the gutter. The following types of outlets can be specified:

• Type 1: Outlet with sharp corners.

• Type 2: Outlet with rounded corners.

• Type 3: Outlet with tapered edges not exceeding 45° with the vertical.

The down pipe dimensions are defined using the following values:

• Aspect ratio: The ratio of the larger to smaller down pipe dimensions. Use a unity value for square and circular down pipes.

• Larger dimension: Enter the larger dimension of the down pipe. Use the diameter in the case of a circular down pipe.


Calcsheets

The Calcsheets page displays the design calculations. The program evaluates the following three components of the drainage system:

• The gutter or channel that collects the flow from the roof.

• The outlet into which the flow from the gutter discharges.

• The pipe-work that conveys the flow from the outlet to a lower drainage system.

The three parts of the system can be designed separately if the outlet and down pipe is made large enough for flow to freely discharge from the gutter. The actual down pipe and outlet may however be smaller than that required for this method, prompting the program to perform a more detailed analysis.


Free-flow design In the phase of the analysis, the gutter and down pipe sizes for free flow are determined:

• Flow in the gutter is evaluated to establish whether free flow is possible.

• The upstream and downstream free flow depths are determined and the required gutter depth calculated.

• The flow through the outlet is check to see if orifice or weir-type flow is present.

• The required free-flow sizes are determined for circular and rectangular down pipes.

Evaluation of the entered system The second phase of the analysis involves the evaluation of the entered down pipe and gutter sizes:

• The specified down pipe and outlet are evaluated to determine their flow capacity.

• If the down pipe is smaller than that required for free flow in the gutter, the restricted flow characteristics of the gutter are determined and a gutter depth suggested.

• The checking procedure is performed for both rectangular and circular down pipes.

• Finally, the design flow volume is calculated.

Recalling a data file The Data File is automatically included when sending a calcsheet to Calcpad. You can later recall the data file 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 Gutter and Downpipe Design module as well.


Documents

Chapter General Applications - Ahmed Mansourahm531.com/Prokon and EQ course/Prokon Manual/Chap-08.pdf · Chapter General Applications The ... • The section is then sub-divided into