User Manual Analysis3D v 3.01

Ever since 1992 Cuylaerts Engineering has been producing structural engineering software with special focus on a user-friendly interface. Due to this Analysis3D is being used in over 60 countries worldwide.

To assist you, there is already a large library of different sections included (Australia and New Zealand, China GB, Euro, India BIS, Japan JIS, Russia GOST, UK British Steel, US AISC, and Timber).

The software performs complex 3D analysis, such as analysis for flexure, torsion, axial, shear, and deflection. Users can input their desired loads and support conditions, choose or define any structural sections, produce 3D visualization and analysis text reports.

Analysis3D also includes Structural Steel Design that proposes the best section for each member. Each cross-section is tested for Plastic Tension or Compression, Bending moment (major and minor axis), Plastic Shear resistance, Reduced plastic shear resistance for the case of combined Torsion and Shear, Reduced moment resistance for the case of combined Bending and Shear, Reduced plastic moment resistance for the case of combined Bending and Axial force or bi-axial bending, Compression buckling, Lateral Torsional buckling, Combined bending and axial compression (Chen and Atsuta) and Maximum deflection.

Nonlinear or 2nd order Calculation takes into account the deformed structure and incrementally calculates the total effect on the structure.

Analysis3D has become what it is now, thanks to the comments and remarks of our users. We believe we can always improve Analysis3D, so we will be grateful to receive your remarks and observations.

Cuylaerts Engineering cannot be held responsible for possible errors in the software or the manual, nor for the consequences that arise from the faulty operation or calculation.

https://www.cuylaerts.net/

Please send your questions and remarks to frank@cuylaerts.net

1. General Overview - Getting started

Analysis3D calculates two- and three-dimensional Trusses and Frames. These structures consist of long slender Members that are supposed to behave linear elastic.

Below you can find a step-by-step approach to get started:

A: start from the Structure menu

1) Select the units and your region to determine which library of cross sections to use

2) Select the dimensions and type of structure: 2D or 3D, Truss (with hinges on the joints) or Frame

3) Add your joints and their coordinates

4) Connect the joints with members (beams) and specify the material and cross section of each beam

5) Specify all the support joints to give your structure the required stability

B: using the Loads menu

1) Specify the joint loads and/or member loads acting on the structure

2) Specify if the own weight of the structure needs to be calculated or not

3) Add your wind Loads

C: Calculate the structure and check the Results

Before entering a construction, be sure to determine whether the structure is a Frame or a Truss and whether the structure has 2 or 3 dimensions. You can also select your preferred Units and Region for the Cross Sections Library.

First enter the Joint coordinates using the Global Coordinate system.

Members can only be entered when the Joints are defined.

Joints, Members and all other structure data can be entered using the Menu Structure or interactively, by means of the mouse.

Entering the Data interactively has the following advantage:

1. The result of each minor change is visualized instantly and can be checked.

2. Selecting a Joint or a Member with the mouse is much handier than a search through the corresponding lists.

3. Support Joints and Joint Loads can be entered together with the corresponding Joint.

4. Member Loads can be entered together with the corresponding Member.

When all Structure data (Joints, Members, Support Joints, ) are entered, you can define the loads on the structure (Joint Loads, Member Loads, Wind Load,..)

A number of drawing buttons help you simplify the drawing control.

When the construction is fully described, you can Calculate the structure and view the Results.

The Joint Displacements are shown automatically. Members that fail the requirements for Member Stress or Buckling are indicated in red. The course of Axial Forces, Shear Forces, Torsion, Bending Moments and Deflection can be viewed with the Result Menu option Detail Member Forces.

All compressed members are tested for Buckling.

By using Member Design, you can improve and optimize the structure. Analysis3D will check the strength of each member and propose the minimal Cross Section for the loads applied.

Analysis for Windows calculates two- and three-dimensional Trusses and Frames. These structures consist of long slender Members that are supposed to behave linear elastic.

Before entering a construction, be sure to determine whether the structure is a FrameFrame or a TrussFrame and whether the structure has 2 or 3 dimensionsDDimension. You can enter your data in International or US UnitsUnits.

First enter the Joint coordinatesJoint. MembersMember can only be entered when the Joints are given.

Joints, Members and all other structure data can be entered with the Menu StructureStructure or interactively, by means of the mouse.

Entering the Data interactively has the following advantage:

1. The result of each minor change is visualized instantly and can be checked.

2. Selecting a JointJoint or a MemberMember with the mouse is much handier than a search through the corresponding lists.

3. Support JointsSupport and Joint LoadsJointLoad can be entered together with the corresponding Joint.

4. Member LoadsMemberLoad can be entered together with the corresponding Member.

A number of drawing shortcutsGraphicshortcut simplify the GraphicsGraphic control.

After defining Joints and Members, you can add Support Joints, Joint Loads and Member Loads.

When the construction is fully described, you can calculatecalculate the structure and view the ResultsResults.

The Joint DisplacementsDisplacement are shown automatically. Members that fail the requirements for Member StressMemberStress or BucklingBuckling are indicated in red. The course of Axial Forces, Shear Forces, Torsion, Bending Moments and Deflection can be viewed with the Result Menu option Detailed Member ForcesNTMForce.

All compressed members are tested for BucklingBuckling.

By using Member Design, you can improve and optimize the structure. Analysis3D will check the strength of each member and propose the minimal Cross Section for the loads applied.

2. The File Menu

The Files containing the structure data are saved by default with the extension ANA , but other extensions are possible.

New erases all structure data in order to enter a new construction from scratch.

Open loads an existing construction from disk into memory. The old structure data in memory will be overwritten and lost.

Save writes the structure data to disk with the given filename.

Combine loads the structure data from a given file into memory. The loaded data will be combined with the old structure in memory.

DXF-Files can be read and saved by this option. Thus, drawings from AutoCad or other drawing tools can be processed and edited. Reading and writing of DXF-files is restricted to straight lines. The name of the layer in the drawing will be used as the descriptor for the section used for each member.

Text File in/out retrieves or saves the structure in a text file with extension 'TXT'. When the structure has been calculated, the results will be added in the text file. In this way the results can be used for further processing or importing in other software like Excel. The layout is identical as the printer layout.

Library contains all Cross Section and Material data. The Library also contains your preferred Language, the color settings for drawing, your preferred Units used, the Region preference for the Cross Sections and safety factors for Buckling. At startup Analysis3D loads by default the Library file Analysis.lbr containing all settings that were last saved.

Exit stops Analysis3D. If some data have been changed since the last saving, the user will be prompted for a confirmation, after which the data can still be saved.

3. The Structure menu

3.1. Two or three-dimensional structures

With the Structure Menu option 2 or 3-Dimensional you can change the dimension of the construction. By selecting the menu option, the structure toggles between 2 and 3 dimensions.

The small coordinate system in the bottom left corner also indicates the actual dimensions selected.

When an existing 2-dimensional structure is converted into 3 dimensions, the resulting construction will be unstable due to a lack of restraints in the Z-direction. An adjustment of the support joints or joint restrictions is required.

3.2. Truss or Frame

With the Structure Menu option Truss or Frame the type of connections between the members is established. By clicking this option, the structure toggles between a Truss and a Frame.

When a structure only consists of members that are exclusively subjected to axial Forces, then the structure is called a Truss. When one or more Members are subjected to shear Forces or bending moments, then the structure should be considered as a Frame.

In case that the construction consists of both types of members, start with a Frame and indicate those members that act as a Truss. Use Hinges on both sides of the member for that purpose.

A circle in the origin of the small coordinate system in the bottom left corner indicates that the structure is a Truss. The circle symbolizes the Hinge.

3.3. Joints

A Joint is defined by a Joint Number and the corresponding coordinates given in American or International Units. The units are specified by the Structure Menu option Units. In International Units, Joint coordinates can be entered in meter or mm as indicated by the check box. The Global coordinate system for any structure is indicated by the small coordinate system in the bottom left corner of the screen.

The Joints can be entered either with the menu or interactively with the mouse.

3.3.1. Entering Joints from the Structure menu.

To add, change or remove Joints in the Joint list simply select the Joint option from the StructureStructure menu.

Adding new Joints: Enter the Joint Number and his coordinates to the left of the ADD button. When entering Joints in a 2-dimensional construction, Z-coordinates will not be accepted.

To add the Joint data to the list simply press ENTER in the last edit box, or press the ADD button. After each new added Joint, the Joint Number will automatically increase by one.

Removing Joints: Select the Joint(s) you want to remove and press the REMOVE button. The program requires that all Joint Number follow without a gap. The gap that is caused by the removal of the Joints will automatically be filled when the window is closed. All Joints after the gap will be moved forward.

Changing Joints: This can be done in 3 ways:

1) Type the Joint Number and press ENTER.

2) Double Click on the Joint Number with the mouse.

3) Select the Joint Number and click the Edit button.

In both cases the Joint will be removed from the list to the edit boxes, where you can edit the joint data. Don t forget to add the Joint to the list after editing. Editing the Joints directly in the list is not allowed.

The COPY button enables you to copy or moveCopy the selected Joints over a given distance in all directions.

3.3.2. Moving and Copying Joints

The selected Joints can be moved or copied over a given distance in the X, Y or Z direction with the COPY button from the Joint window.

All the intermediate Members will be copied also. This simplifies entering a large construction with identical substructures.

If the selected Joints only have to be moved instead of copied, select the MOVE button in the Copy Joints window.

3.3.3. Entering Joints interactively

To add a new Joint, double click the left mouse button on the screen. A new window will appear to enter the new Joint coordinates.

To change an existing Joint, double click with the left mouse button on the Joint you want to change. A new window will appear to allow editing of the selected joint and the selected Joint number will turn red.

To deselect a Joint, press the right mouse button.

From this window you can change the Joint coordinates directly. Use the arrow buttons to change the joint number you want to change. The +button enables you to add a new Joint. Using - will delete the current Joint.

The tabs SUPPORT and LOAD allow you change the Support JointsSupport and Joint LoadsJointLoad of the selected Joint.

This method allows you to view each change on the screen as soon as it is entered.

3.4. Members

A Member is defined by a begin JointJoint and an end Joint. The begin Joint is the Joint with the smallest x-coordinate according the local coordinate systemLocalSystem.

It is not necessary to apply this rule, since Analysis3D will automatically check begin and end Joint and makes these changes for you.

The names of the Cross SectionsCrossSection need to correspond to the ones defined in the library of Cross Sections.

The Material name must correspond to the Material name in the Material DataMaterial list.

The Members of a FrameFrame can have HingesHinges and can be rotated over a certain AngleAngle around its local x-axis.

Members can be entered either with the menu or interactively with the mouse.

3.4.1. Entering Members from the Structure Menu.

To add, change or remove Members in the Member list simply select the Members option from the StructureStructure menu.

Adding new Members: Enter the Member Number begin and end Joint, the name of the Cross Section and in case of a FrameFrame: the HingesHinge and the rotation AngleAngle.

To add the Member data to the list simply press ENTER in the last edit box, or press the ADD button. After each new added Member, the Member Number will automatically increase by one.

Removing Members: Select the Member(s) and press the REMOVE button. The program requires that all Member Number follow without a gap. The gap that is caused by the removal of Members will automatically be filled when the window is closed. The Member numbers after the gap will be moved forward.

Changing Members: This can be done in two ways:

1) Type the Member Number and press ENTER.

2) Select the Member with the mouse and press the right mouse button.

In both cases the Member will be moved from the list to the edit boxes, where you can edit the Member data. Don t forget to add the Member to the list after editing. Editing the Members directly in the list is not allowed.

The Cross Section button lets you change the Cross Section of all Members with a given Section. For instance, you can change all Members with Cross Section IPE200 into IPE240.

The Material button lets you change the material name of all Members of a given material. For instance, you can change all Members with Material FE360 to FE450.

With the Hinge button you can change the Hinges of the selected Members.

3.4.2. Entering Members interactively.

To enter a new Member select begin and end Joint Number with the left mouse button. A selected Joint Number turns Red. Use the right mouse button to deselect a Joint.

The new Member window will enable you to add the other properties of the Member. Analysis3D assumes that the new Member has the same properties as the last entered Member, but this can be overwritten.

The names of defined Cross Sections and Material Data can be selected from the drop-down list.

To change an existing Member select begin and end Joint Number with the left mouse button. A window in the top right of the screen will enable you to change the properties of the Member. At the same time the Local Coordinate System of the selected Member is displayed.

Once a Member has been selected, it can be removed, together with the Member Loads, by pressing the - button. To add a member, press the + button.

To enter the Member LoadsMemberLoad of the selected Member press the LOAD tab.

This method lets you view each change or new Member on the screen instantly.

3.4.3. Hinges

A FrameFrame can contain one or more MembersMember that have a Hinge on one or both sides. A Hinge indicates that the member is exclusively subjected to axial Forces on the side of the Hinge.

The following symbols are used to indicate the Hinges:

0 : The Member has no Hinges.

B : The Member has one Hinge at the Begin Joint.

E : The Member has one Hinge at the End Joint.

2 : The Member has two Hinges at the begin and end Joint.

A Truss by definition consists of members with Hinges on both sides. Hence Hinges cannot be defined in case of a Truss.

3.4.4. The Rotation Angle of a Member

A MemberMember can be rotated around his local x-axis over a certain angle during construction. For example, an I-beam can be used turned over 90 to bear large transverse Forces. An exact representation of the angle of rotation is important since the Moment of Inertia of the Member has to be recalculated. The angle is positive according the right-hand rotation rule along the positive local x-axis.

The resulting Rotation Angle can be represented graphically by selecting the Member with the mouse. The Local Coordinate SystemLocalSystem of the selected Member will be displayed. These coordinates will help you to determine the positive local x-axis. The local y-axis always coincides with the major Cross Section Moment of Inertia Ix.

Since Members in a TrussTruss are exclusively subjected to tension and compression, it has no influence whether the Members are rotated or not.

3.5. Coordinate Systems

3.5.1. The Global Coordinate System

All JointsJoint, Support JointsSupport, Joint LoadsJointLoad, Joint DisplacementsDisplacement and ReactionsReactions are referenced to the Global Coordinate System.

The Global Coordinate System consists of a set of right-hand orthogonal axes X, Y and Z which are oriented as shown in the left bottom corner of the screen.

The representation of the Global Coordinate System will follow the point of view. It will also indicate whether the Structure is a TrussFrame or a Frame, and whether the structure has two or three dimensionsDDimension.

The positive global Y-axis represents the vertical height of a structure. This means that the own-weight forces will work in the negative Y direction.

3.5.2. The Local Coordinate System

IN THEORY

The local x-axis runs parallel with the MemberMember through the middle of the Cross Section.

The JointJoint with the smallest global X coordinate is the begin Joint. This means that the local x-axis always points from the begin Joint to the end Joint of a Member.

In case that the global X coordinates are equal, the Joint with the smallest Y coordinate is the begin Joint. When both X and Y coordinates are equal, the smallest Z coordinate indicates the begin Joint.

The local z-axis will always be oriented parallel to the global XZ plane.

The local y-axis will be oriented so that its positive direction projects onto the positive global Y-axis.

In the special case that the local x axis is parallel to the global Y axis (e.g., a vertical Member), the local z-axis will have the additional restriction that it will be parallel to the global Z axis and extend in the positive Z direction.

IN PRACTICE

Put into practice, Analysis3D will take care that the Member Data coincides with the local coordinate system.

For your information the local coordinate system of the Member is shown additionally on the screen when a Member is selected with the mouse (by selecting both joint numbers of that member).

3.6. Support Joints

A Support Joint is defined by the JointJoint Number and the restrictions per axis.

To indicate the Restraints, we use the following agreement:

When there is no Restraint in the given direction, the corresponding direction will be left blank using a space.

R : any movement is Restrained in the given direction. Displacements will stay zero.

D : the support experiences a forced Displacement in the given direction. The magnitude of the displacement it given by Dx, Dy or Dz.

S : a Spring supports the joint in the given direction. Dx, Dy or Dz indicate the Spring constant.

Rx, Ry and Rz indicate a translation Restraint in the GlobalGlobalSystem X-, Y- and Z-direction. When for instance Rx = R, translation is restricted in the Global X-direction. As a result, a Reaction Force in the X-direction will act upon the structure from the Support Joint.

Mx, My and Mz indicate a rotation Restraint round the Global X-, Y- and Z-direction. When for instance Mx = R, rotation is restricted round the Global X-axis. As a result, a Reaction Moment round the X-axis will act upon the structure from the Support Joint.

Since the Members in a TrussFrame are connected with Hinges, Trusses cannot have rotation Restraints.

The Joints in a two-dimensional Frame can only have translation Restraints in the Global X- and Y-direction and a rotation Restraint round the Z-axis.

Dx, Dy and Dz indicate the magnitude of the forced displacements or spring constants. The meaning of the value depends on the contents of the corresponding translation Restraint.

Forced displacements can be entered in mm or inches depending on the Units option from the Structure Menu. Accordingly, Spring constants can be given in kN/cm or Kips/inch.

Examples:

Pinned support:

Rx = R Ry = R Mz =

Horizontal roller:

Rx = Ry = R Mz =

Fixed support:

Rx = R Ry = R Mz = R

The top left of the Support windows displays the most commonly used types of supports. Click on one of these images to choose your type of support.

Since the drawing of the support can only show the Restrictions in two dimensions, the drawing will change according to the point of view in a three-dimensional structure.

Support Joints can be entered both with the Menu and with the mouse.

3.6.1. Entering Support Joints from the Structure Menu

To add, change or remove Support Joints in the Restraints list simply select the Support Joint option from the StructureStructure menu.

Adding new Support Joints: Enter the Joint Number and the restrictions for each axis. FramesFrame can also have rotation Restraints besides the translation Restraints.

To add the Support Joints to the list simply press ENTER in the last edit box, or press the ADD button. After each new added Support, the Support Joints Number will automatically increase by one.

Removing Restraints: Select the Support(s) and press the DELETE button.

Changing Restraints: This can be done in 3 ways:

1) Type the Support Number and press ENTER.

2) Double click the Joint number with the left mouse button.

3) Select the Joint number and press the Edit button.

In both cases the Support Joint will be removed from the list to the edit boxes, where you can edit the Restraint data. Don t forget to add the Support Joints to the list after editing. Editing the Supports directly in the list is not allowed.

3.6.2. Entering Support Joints interactive

To add, change or remove Support Joints first select the JointJoint by double clicking the left mouse button. In the lower right corner of the screen appears a window to enter the Joint coordinates. The Support Joints can be edited by selecting the SUPPORT tab.

To clear a Support Joint clear all restraints. Pressing the - button will also delete the Joint displayed.

This method allows you to view each change on the screen as soon as it is entered.

3.7. Cross Sectional Data

Analysis3D has an extensive library of standard MemberMember Cross Sections. The list can be easily updated.

The Units and Region option from the Structure Menu allows you to select a different Library of Cross Sections. Also, the units are specified by the same Structure Menu selection.

You can also download or save a different file with Cross Sections using the File menu from the top left of the Cross Section window. Analysis3D offers a wide selection of Libraries from different regions to choose from. E.g., Euro, US AISC, UK British Steel, Russia GOST, China GB, India BIS, Japan JIS, Australia and New Zealand and Timber.

Each Cross Section has a unique Section Name:

Shape: Identifies the section out of the following choices: I-section, U-section or channel, L-section, T-section or half I-section, Rectangular box, Circular tube, Full section.

Fabric: How was the section made: Rolled or Welded

Ax : the Cross Sectional Area in [cm2] or [inch2]

h : total height of the section in [mm] or [inch]

d : total width of the section in [mm] or [inch]

tw : web thickness in [mm] or [inch]

tf : flange thickness in [mm] or [inch]

r : radius between flange and web in [mm] or [inch]

Ix : the Cross Section Moment of Inertia about the x axis in [cm4] or [inch4]

( as a result of a Load along the local y-axis )

Iy : the Cross Section Moment of Inertia about the y axis [cm4] or [inch4]

( as a result of a Load along the local z-axis )

It : the Cross Section Torsional Constant [cm4] or [inch4]

(as a result of a Moment round the local x-axis)

For a round section the Torsional Constant is equal to the polar Moment of Inertia.

Wx, Wy : Elastic Section Modulus in [cm3] or [inch3]

Zx, Zy : Plastic Section Modulus in [cm3] or [inch3]

ex : the distance from the neutral line of the Member to the outside of the Member along the main axis of that Member. In the case of asymmetrical Cross Sections this will usually be the longest distance.

ey : the distance from the neutral line of the Member to the outside of the Member along the secondary axis of that Member.

For both ex and ey it is important to use the longest distance to the outside of the member as shown in the figure below.

et : for closed sections et is the greater of ex or ey. In the case of open sections et is the thickness of the thickest part of the section. This usually is the maximum flange thickness of the beam cross section.

et for full rectangular beams: b (see Torsional Constant above)

et for full open sections: maximum thickness (of flange or body)

M : the Mass of the Member per meter [kg/m] or [kg/ft]

3.8. Material Data

Each Material is defined by:

Material: a unique name for the Material

E : the Modulus of Elasticity in [kN/cm ] or [Kips/inch ]

G : the Shear Modulus in [kN/cm ] or [Kips/inch ]

G = E / 2(1+v) with: v = Poisson constant;

for metals v = 1/3

Re : the Limit Stress of the material in [N/mm ] or [Kips/inch ] = 0.7 Yield Point or Tensile Strength.

The Linear Coefficient of Expansion in 10^-6 1/K.

The units are specified by the Structure Menu option UnitsUnits.

3.9. Units and Region

All data can be expressed in International SI units, in US Units or Continental Units. You can select your preferred Units from the drop-down list.

It is possible to enter the Joint coordinates in International SI Units, the Forces in American Units and view the results in both International and American Units. Toggling between Units can introduce a minor deviation due to rounding off.

Below are the most commonly used Units with the corresponding conversion factors.

	SI Units	US Units	Continental Units
Joint Coordinates:	meter [m]	foot [ft]	meter [m]
Forces:	kNewton [kN]	thousands of pounds [Kips]	kilogram [kg]
Moments:	[kNm]	[Kip-ft]	[kgm]
Distributed Load:	[kN/m]	[Kip/ft]	[kg/m]
Joint Displacements:	[mm]	Inch [in]	[mm]
Stresses:	[N/mm ]	[Kips/in ]	[kgf/mm ]

1 foot = 0.3048 meter

1 inch = 25.4 mm

1 pound [lbf] = 4.44822 Newton

1 kgf = 9.80665 Newton

1 N/mm = 1MPa

Region

You can select from the drop-down list the Region for which the Cross-Sectional Data will be selected.

The following Regions are available with Lists of Cross Sections:

Australia New Zealand

China GB

Euro

India BIS

Japan JIS

Russia GOST

UK British Steel

US AISC (available both in metric and in imperial units)

Other Sections

Timber

On request, this list can be easily expanded or amended to fit your needs.

Standard used

This selection allows you to choose which International or Local Standard will be used for optimizing the structure with the Member Design or Detailed Design options from the Result Menu.

Analysis3D offers the following Standards to choose from:

AISC ASD

AISC LRFD

BS 5950

CISC 94

Eurocode 3

Your selection of Units and Region needs to be stored in the Library file for this to remain active when you restart Analysis3D as your default selection.

4. The Loads Menu

4.1. Joint Loads

A Joint Load is defined by the Joint Number and the Forces and Moments acting on that JointJoint.

You can use up to 9 different Load Cases. Each Load Case is defined by the Load Case number from 1 to 9. The importance of each Load Case is determined with the Load CombinationsLoadCombination option from the structure menu.

The Forces in kN or Kips are parallel with the Global coordinate SystemGlobalSystem as drawn in the left bottom of the screen. Thus, a positive Force Fy points up. By default, Forces are represented in red.

Moments in kNm or Kips-ft are positive according the right-hand rule round the respective global coordinate axis. In two-dimensional Structures the Moments are drawn as an arc, in the case of three dimensions the moments are drawn as an arrow, by default painted purple.

The units are specified by the Structure Menu option Units and RegionUnits.

Since the Members in a TrussFrame are connected with Hinges, Trusses cannot have Moments as Joint Loads.

The Joints in a two-dimensional Frame can only have Forces in the Global X- and Y-direction and a Moment round the Z-axis.

Joint Loads can be entered from the Structure Menu or interactively.

To enter Joint Loads interactively, first select the desired Joint and press the LOAD tab.

4.2. Member Load

A Member Load is defined by the Member NumberMember and the Forces in kN or Kips and Moments in kNm or Kip-ft acting on that Member.

You can use up to 9 different Load Cases. Each Load Case is defined by the Load Case number from 1 to 9. The importance of each Load Case is determined with the Load CombinationsLoadCombination option from the structure menu.

There are five different basic Load Types for Member Loads. For simplicity these five Load Types get an arbitrary Load Type Number as indicated below. But you can also simply click at the bottom of the screen on the Load Type you want to use and Analysis3D will select the corresponding Load Type number for you:

1 : A Point Load F in [kN] or [Kips] along the x-, y- or z-axis, at a distance a in [m] or [ft] from the begin JointJoint.

2 : A Moment M in [kNm] or [Kip-ft] round the x-, y- or z-axis, at a distance a in [m] or [ft] from the start Joint.

3 : A Distributed Load q in [kN/m] or [Kips/ft] along the x-, y- or z-axis.

4 : A Symmetrical Trapezoidal Distributed Load q in [kN/m] or [Kips/ft] along the x-, y- or z-axis with transition a in [m] or [ft].

5 : a Non Symmetrical Trapezoidal Distributed Load along the x-, y- or z-axis that starts with a Load Q1 in [kN/m] or [Kips/ft] at a distance a in [m] or [ft] from the begin Joint and that is b [m] or [ft] long. Thus, the end Load Q2 in [kN/m] or [Kips/ft] is on a distance a+b from the begin Joint.

L/G: Forces and Moments can be entered according the GlobalGlobalSystem or the Local coordinate SystemLocalSystem. Entering L or G in the L/G field makes this choice. Forces that are parallel or perpendicular to a Member with a slope can easily be entered with the Local Coordinate System.

Member Loads can be entered from the Structure Menu or interactive with the mouse.

To enter Member Loads interactively, first select the Member with the mouse, and press the LOAD tab. Select the Load case and Load type by using the arrow buttons. To delete a load, all forces have to be cleared.

4.3. Wind Load

Wind Load is calculated according to Eurocode 1991-1-4 or according to ASCE 7-16. Analysis3D also provides a General option not restricted by a national code.

Wind Load according to Eurocode 1991-1-4 (EN 1991-1-4:2005+A1 April 2010)

For Wind Load calculations there are basically 2 options:

- for an open structure only the wind load on the beams is calculated

- for a closed structure the calculation assumes the walls are closed and the wind acts on the surface of the entire closed area.

Wind Load calculation according to Eurocode 1991-1-4 starts from the fundamental value of the basic wind velocity Vb0. This is the characteristic 10 minutes mean wind velocity, irrespective of wind direction and time of year, at 10 m above ground level, in open country terrain. It corresponds to a mean return period of 50 years.

The Basic wind velocity Vb = Cdir . Cseason . Cprob . Calt . Vb0.

Cprob is calculated with the input given using the formula:

The mean wind velocity Vm(z) at height z above the terrain is calculated as: Vm(z) = Cr(z).Co(z).Vb

The roughness factor Cr(z) is calculated based in the Terrain Category specified and the formula

Cr(z)= kr. ln(z/z0)

Peak velocity pressure is given by qp(z) = [1+7Iv(z)] .ρ. Vm²(z)

Where Iv(z) is the turbulence intensity which allows to take into account the contribution from short term fluctuations Iv(z) = k1 / [Co(z). ln(z/z0)].

The wind pressure acting on the external surface: We = qp(z).Cp

Where Cp is the pressure coefficient as indicated in the overview per zone.

For walls:

For duopitch roofs:

Please note that Eurocode requires to investigate the option with positive and with negative pressure coefficients. For duopitch roofs, 4 combinations are required for investigation, consisting on positive and negative pressure coefficients on each side of the roof.

Finally the forces on the structure are calculated using Fwe = CsCd.∑ We.Aref.

All calculated values are shown in grey cells, the values that require input are left white. However; most of the non-calculated cells are completed with default values already.

The button Calculate determines the pressure coefficients as per Eurocode. However, the user has the freedom to overwrite any number before applying the Wind Loads to the structure. When pressing the button Apply Wind Load, Analysis3D will use the numbers displayed for the final calculation.

To apply these forces, the user can select the Load Case the Wind Loads should be attributed to and they will be added to the list of Member Loads.

With the option Load Combination from the main menu, the user can choose the relative weight of the Wind Load for the combined calculation.

Wind Load according to ASCE 7-16

For Wind Load calculations there are basically 2 options:

- for an open structure only the wind load on the beams is calculated

- for enclosed or partially enclosed buildings, the calculation assumes the walls are closed and the wind acts on the surface of the entire area.

Wind Load calculation according to ASCE 7-16 starts from the basic wind speed Vb. This is the nominal design 3-second gust wind speed at 10m (33ft) above ground for Exposure C category. These correspond to approximately a 3% probability of exceedance in 50 years.

The velocity pressure q is calculated as q = 0.613 . Kz. Kzt. Kd. Vb

Where the Topographic Factor Kzt is determined by Kzt = (1 + K1 . K2 . K3) and derived from figure 26.8-1 below.

The velocity pressure exposure coefficient Kz = 2.01 . (z/zg)^2/alpha. For z < 15 ft (4.6m) : Kz = 2.01 . (15/zg)^2/alpha

The terrain exposure coefficients are derived from Table 26.11-1 below

K_d is the Wind Directionality factor and can be derived from table 26.6-1 below.

Design wind pressures for the MWFRS (Main Wind Force Resisting System in Directional Procedure) of buildings of all heights is determined by the following equation: p = q . G . Cp qi . GCpi (N/m2 )

External pressure coefficients are calculated by Analysis3D based on Figure 27.3-1 below

And the wind loads are applied according to :

All calculated values are shown in grey cells the values that require input are left white. However; most of the non-calculated cells are completed with default values.

To apply these forces, the user can select the Load Case the Wind Loads should be attributed to and they will be added to the list of Member Loads.

With the option Load Combination from the main menu, the user can choose the relative weight of the Wind Load for the combined calculation.

Wind Loads for General application

Since it is almost impossible to include each and every standard for each and every country, the General option minimizes the predetermined calculations and just allow the user to let Analysis3D apply the Wind Loads as specified by the user (according to the national standard applicable).

Based on the velocity pressure and the pressure coefficients specified by the user, Analysis3D will calculate the Wind Load for each wall and roof. For the coefficients, the following rule applies: positive pressure coefficients are pointing towards the building, negative coefficients are pointing away from the building.

For Open structures, Analysis3D will only calculate the wind on the surface of the steel structure, assuming no walls exist.

4.4. Snow Load

Analysis3D offers 3 options to calculate Snow Loads. Snow Loads can be defined according to ASCE/SEI 7-16, according to Eurocode 1 - Actions on structures - Part 1-3 or using a General method not restricted by any specific standards.

Snow Load according to ASCE/SEI 7-16

Before we can apply any snow loads to our structure, we need to know the ground snow load (p_g) at our location, which can be found using Figure 7.2-1 from ASCE 7-16.

Also, you can directly find the ground snow load for your location through online Hazards by Location tool, provided by ATC.

In some special cases, site-specific case studies are needed to determine ground snow loads and therefore cannot directly be found on the map provided.

The snow load that is applied to our structure is not the ground snow load, but in most cases, the flat roof snow load (roof slope ≤ 5 ).

The flat roof snow load is calculated using formula below:

pf = 0.7 C_e C_t I_s p_g

Where:

p_g = Ground Snow Load

C_e = Exposure Factor from table 7.3-1 below

Where the Surface Roughness Categories as defined as below:

Surface Roughness B: Urban and suburban areas, wooded areas, or other terrain with numerous, closely spaced obstructions that have the size of single-family dwellings or larger.

Surface Roughness C: Open terrain with scattered obstructions that have heights generally less than 30 ft (9.1 m). This category includes flat, open country and grasslands.

Surface Roughness D: Flat, unobstructed areas and water surfaces. This category includes smooth mud flats, salt flats, and unbroken ice

Ct = Thermal Factor from the Table 7.3-2 below

Is = Importance Factor: The value for Is shall be determined from Table 1.5-2 based on the Risk Category from Table 1.5-1 below.

Sloped Roof Snow Loads: p_s

The Snow loads acting on a sloping surface shall be assumed to act on the horizontal projection of that surface. The sloped roof snow load, p_s, shall be obtained by multiplying the flat roof snow load, pf , by the roof slope factor, Cs:

p_s = C_sp_f

The values of C_s for warm roofs and cold roofs are determined from Figure 7.4-1 below.

For roofs with an unobstructed slippery surface that allows snow to slide off the eaves, the roof slope factor Cs shall be determined using the dashed line in Fig. 7.4-1.

For all other roofs, the solid line in Fig. 7.4-1 shall be used to determine the roof slope factor Cs.

After Calculating the Snow Load, we can use the Apply Snow Load button to distribute the Snow Load accordingly over the roof.

Snow Load according to Eurocode 1 (EN 1991-1-3:2003)

In order to calculate the Characteristic Snow Load on the ground Sk, we first, need to select the climatic region from the drop-down box.

In each climatic region a given load-altitude correlation formula applies and this is given in Table C.1 below. Different zones are defined for each climatic region. Each zone is given a Zone number Z, which is used in the load altitude correction formula.

The National Annex specifies the characteristic values to be used. To cover unusual local conditions the National Annex may additionally allow the client and the relevant authority to agree upon a different characteristic value from that specified for an individual project.

Annex C of EN 1991-1-3:2003 gives the European ground snow load map. The National Annex may make reference to this map in order to eliminate, or to reduce, inconsistencies occurring at borderlines between countries.

Where:

S_k is the characteristic snow load on the ground [kN/m2]

A is the site altitude above Sea Level [m]

Z is the zone number given on the map.

The Snow Load on the Roof (s) is calculated usin the formula below:

s = C_t C_e μ_i s_k

Where the thermal coefficient C_t should be used to account for the reduction of snow loads on roofs with high thermal transmittance (> 1 W/m2 K), in particular for some glass covered roofs, because of melting caused by heat loss. For all other cases: C_t = 1,0

C_e = Exposure coefficient determined from the table below.

The snow load shape coefficient 1 that should be used for sloped roofs is given in Table 5.2 below. The values given in Table 5.2 apply when the snow is not prevented from sliding off the roof. Where snow fences or other obstructions exist or where the lower edge of the roof is terminated with a parapet, then the snow load shape coefficient should not be reduced below 0,8.

The values of 1 apply for undrafted load arrangements, 2 applies for drifted load arrangements,

The following 3 cases need to be investigated for a pitched roof/

After Calculating the Snow Load, we can use the Apply Snow Load button to distribute the Snow Load accordingly over the roof.

Snow Load for general application

Since it is almost impossible to include each and every standard of each and every country, the General option minimizes the predetermined calculations and just allow the user to let Analysis3D apply the Snow Load on the Roof as given by the user (according to the national standard applicable).

4.5. Seismic Loads

Analysis3D offers 3 options to calculate Seismic Loads. Seismic Loads can be defined according to Eurocode 8 (EN 1998: 2004) or according to ASCE/SEI 7-16 or using a General method not restricted by any specific standards.

Seismic Load according to ASCE/SEI 7-16

First, we identify the map data properties for our building. We can obtain the seismic map data from free tools such as the ASCE 7 Hazard Tool at https://asce7hazardtool.online.

Here we can find the values for:

SS: the Long-period transition period, the spectral response acceleration parameter at short periods:

S1: the spectral response acceleration parameter at a period of 1s:

R is the response modification factor from ASCE/SEI 7-16 Table 12.2-1

All fields that require input are white Edit boxes. The fields that are the result of a calculation are shaded. When all input values are entered, we can determine the results by pressing the Calculate button.

Site Class is a classification assigned to a site based on the types of soils present and their engineering properties, as defined in the table 20.3-1 below. The calculations in Analysis3D are limited to the Site classifications A to D.

The Risk Category is found in the table 1.5-1 below.

The structure type is determined from the table 12.8-2 below.

The Design earthquake spectral response acceleration parameters at short periods, S_DS, and at 1-s periods, S_D1, are determined from the equations:

SDS = 2/3 S_MS

SD1 = 2/3 S_M1

Where the MCER spectral response acceleration parameters for short periods (S_MS) and at 1 s (S_M1), adjusted for site class effects, are determined by equations

S_MS = F_a SS

S_M1 = F_v S1

With Fa and Fv from the tables 11.4-1 and 11.4-2 below

The Risk Category is calculated from the tables 11.6-1 and 11.6-2 below. But for Risk Category I, II, or III structures located where the mapped spectral response acceleration parameter at 1-s period, S1, is greater than or equal to 0.75 shall be assigned to Seismic Design Category E. Risk Category IV structures located where the mapped spectral response acceleration parameter at 1-s period, S1, is greater than or equal to 0.75 shall be assigned to Seismic Design Category F

The approximate fundamental period (T), in seconds, shall be determined from the following equation:

T =C_t h_n^x

where h_n is the structural height

and the coefficients Ct and x are determined from Table 12.8-2 below.

The effective seismic weight, W, of a structure shall include the dead load, above the base and other loads above the base as listed below:

1. In areas used for storage, a minimum of 25% of the floor live load shall be included.

EXCEPTIONS:

a. Where the inclusion of storage loads adds no more than 5% to the effective seismic weight at that level, it need not be included in the effective seismic weight.

b. Floor live load in public garages and open parking structures need not be included.

2. Where provision for partitions is required by Section 4.3.2 in the floor load design, the actual partition weight or a minimum weight of 10 psf (0.48 kN∕m2) of floor area, whichever is greater.

3. Total operating weight of permanent equipment.

4. Where the flat roof snow load, Pf , exceeds 30 psf (1.44 kN∕m2), 20% of the uniform design snow load, regardless of actual roof slope.

5. Weight of landscaping and other materials at roof gardens and similar areas

For Analysis3D to be able to calculate the effective weight, the input is required for each Load Case. We have the possibility to apply a combination coefficient to each Load Case (which is fully independent from existing Load case factors). As an example, we would apply a combination coefficient of 1.0 to Dead Loads and a combination coefficient of 0.25 to Live Loads.

The seismic base shear, V, in a given direction shall be determined in accordance with the following equation:

V = C_sW

where

C_s = the seismic response coefficient

W = the effective seismic weight.

The seismic response coefficient, C_s, is determined in accordance with equation

C_s = S_DS / (R/I_e)

where

I_e = the Importance Factor determined in accordance with Table 1.5-2 below.

R is the response modification factor from ASCE/SEI 7-16 Table 12.2-1

The value of Cs shall not exceed the following:

When the value of the seismic base shear is calculated. We can distribute the base shear over the different floors.

The lateral seismic force induced at any level is determined from the following equations:

Where

C_vx = vertical distribution factor;

V = total design lateral force or shear at the base of the structure

wi and wx = portion of the total effective seismic weight of the structure (W) located or assigned to level i or x; hi and

hx = height from the base to level i or x

k = an exponent related to the structure period as follows:

for structures that have a period of 0.5 s or less, k = 1;

for structures that have a period of 2.5 s or more, k = 2; and

for structures that have a period between 0.5 and 2.5 s, k shall be 2 or shall be determined by linear interpolation between 1 and 2

We can use the Apply Seismic Load button to distribute the Seismic base shear accordingly over the different levels of the structure. The factors Ex and Ez are the multipliers used for the Seismic Loads for each direction.

Seismic Load according to Eurocode EN 1998:2004

Analysis3D applies the Lateral force method of analysis. This type of analysis may be applied to buildings whose response is not significantly affected by contributions from modes of vibration higher than the fundamental mode in each principal direction. This requirement is deemed to be satisfied in buildings which fulfil both of the two following conditions:

a) they have fundamental periods of vibration T1 in the two main directions which are smaller than the following values

b) they meet the criteria for regularity in elevation given by EC8 section 4.2.3.3.

The ground type is determined from table 3.1 below.

The Shape of the elastic response spectrum: If deep geology is not accounted for, the recommended choice is the use of two of spectra: Type 1 and Type 2. If the earthquakes that contribute most to the seismic hazard defined for the site for the purpose of probabilistic hazard assessment have a surface-wave magnitude, Ms, not greater than 5,5, it is recommended that the Type 2 spectrum is adopted.

T₁ is the fundamental period of vibration of the building for lateral motion in the direction considered. For buildings with heights of up to 40 m the value of T₁ (in s) may be approximated by the following expression:

where C_t is 0,085 for moment resistant space steel frames, 0,075 for moment resistant space concrete frames and for eccentrically braced steel frames and 0,050 for all other structures; H is the height of the building, in m, from the foundation or from the top of a rigid basement.

q is the behaviour factor and is specified by the National Annex. The ranges are given by table 6.1 below.

Design ground acceleration on type A ground (ag = ϒ1 . agR); can be found from the National Annex.

agR is the reference peak ground acceleration on type A ground

ϒ1 is the importance factor. The value of ϒ1 for importance class II shall be, by definition, equal to 1.0. NOTE The values to be ascribed to ϒ1 for use in a country may be found in its National Annex. The values of ϒ1 may be different for the various seismic zones of the country, depending on the seismic hazard conditions and on public safety considerations. The recommended values of ϒ1 for importance classes I, III and IV are equal to 0,8, 1,2 and 1,4, respectively.

β is the lower bound factor for the horizontal design spectrum. NOTE The value to be ascribed to β for use in a country can be found in its National Annex. The recommended value for β is 0,2.

Mass of building: the masses to be used in a seismic analysis should be those associated with the load combination:

Where G equals the Dead load and Q the Imposed load. is the combination coefficient for a variable action i, to be used when determining the effects of the design seismic action. This can be set to 0.3 by default. Since Analysis3D cannot determine which Loads are Dead Loads and which are Imposed Loads to be taken as part of the Seismic Load, we need to clearly identify which Loads to account for.

Dead Loads need to be given a combination coefficient of 1 by the user and loads that don t need to be taken into account as Seismic action, need to be given a combination coefficient of 0.

For the horizontal components of the seismic action the design spectrum, Sd(T), is defined by the following expressions:

Where the values of S, T_B(S), T_C(S) and T_D(S) are found in the tables 3.2 and 3.3 below.

Base shear force: The seismic base shear force for each horizontal direction in which the building is analyzed, shall be determined using the following expression:

Distribution of the horizontal seismic forces:

The fundamental mode shapes in the horizontal directions of analysis of the building may be approximated by horizontal displacements increasing linearly along the height of the building.

The seismic action effects shall be determined by applying, to the two planar models, horizontal forces Fi to all storeys.

Where:

Fi is the horizontal force acting on storey i;

Fb is the seismic base shear;

zj, zj are the heights of masses mi mj above the level of application of the Seismic action (foundation or top of a rigid basement).

Mi,mj are the storey masses.

Seismic Load for general application

Since it is almost impossible to include each and every standard of each and every country, the General option minimizes the predetermined calculations and just allow the user to let Analysis3D calculate the Mass of the building depending on the input given by the user (according to the national standard applicable). The Mass of the building is calculated using the combination coefficients given for each Load Case.

Only 1 Correction factor is applied (as a combination of all factors from the national standard) to calculate the Seismic base shear.

The Apply Seismic Load button will distribute the Seismic base shear over the different levels of the building.

The seismic action effects shall be determined by applying, to the two planar models, horizontal forces Fi to all storeys.

Where:

Fi is the horizontal force acting on storey i;

Fb is the seismic base shear;

zj, zj are the heights of masses mi mj above the level of application of the Seismic action (foundation or top of a rigid basement).

Mi,mj are the storey masses.

4.6. Load Combinations

All Joint Loads and Member Loads have a Load Case number from 1 to 9. This number corresponds to a given Load Case Name and Load Factor. The only purpose of the name is to act as a reminder for the type of Load Case that is used.

Load Case number 0 is reserved for the self-weight of the structure.

The Load factor is used to calculate the actual importance of a given Load Case. A Load Factor of 2 will double all Loads on the construction with this Load Case number. The total Load that is applied to the structure can be a combination of 9 different load cases, each with a specific importance. A Load factor of 0 eliminates all Loads having that Load Case from the calculation.

In the example below, Load Case number 1 represents the Dead Load or Permanent Load, which is given a Load Factor of 1.35. Load Case 2 represents the Live or Imposed Load and is given a Load Factor of 1.5. The Wind Load is assigned to Load Case 3 with a Load Factor of 0.9.

The columns refer to the different possible Load Combinations (from 1 to 9). Each Load Combination column can have its unique set of Load Factors you want to evaluate. By default, all load factors from Load Combinations 2 to 9 are set to 0.

On top of the table, you can select which column (from 1 to 9), with the corresponding set of Load Factors, that will be used first for the visualization and calculation of the results.

4.7. Calculate or Neglect the Self Weight

When the Loads on the Structure are being calculated, the contribution of the Self Weight of the construction can be neglected or taken into account.

This choice is made by the option Calculate or Neglect Self Weight in the Structure Menu.

The own Weight is calculated starting from the Mass M per meter (or per foot) as indicated in the Cross-Sectional DataCrossSection.

4.8. Temperature

When the temperature of the Structure changes, there will be equivalent JointJoint displacements displacement. In case that Support JointsSupport restrict those displacements, the structure will experience a Load.

With the option Temperature from the Structure Menu, you can enter the temperature difference in Kelvin between the temperature at which the construction is build, and the temperature at which you want to calculate the structure.

The Linear coefficient of expansion is given in the material list in 10^-6 1/K.

5. The Drawing menu

Redraw

This Menu option redraws the screen. Clicking the Redraw button from the tool bar has the same result.

Drawing Options

Here you can change the options on the drawing: A shortcut key can also toggle most of these optionsGraphShortcut.

Drawing

By selecting these options, Forces, Moments, Support Joints, Joint Displacements and Detailed Member Forces and Stresses will be shown (when calculated). Forces and Moments are represented by default in Red, except for moments in 3D structures that are shown as purple arrows.

When the Detailed Member forces are drawn, it is possible to show or hide the different Detailed Member forces with the mouse. Click with the left mouse button on the name of the selected force in the top left corner of the screen. Click again to redraw.

The factor to magnify the Forces, Joint Displacements and Detailed Member Forces can be changed. By default, the Joint Displacements are ten times exaggerated.

Numbering

By selecting the Joint and/or Member check box, the Joint numbers and/or Member numbers will be shown in the drawing or the name of the cross sections will be displayed.

This option also allows you to visualize the values of the Utilization factor or ratio for each member, based on the Member Design or Detailed Design results. Values of the Utilization ratio >1 are displayed in red.

Viewing Angle

Here you can enter the horizontal and vertical viewing angle. This only makes sense with a 3-dimensional Structure. The horizontal Angle has to be between -360 and +360 , the vertical viewing Angle between -90 and +90 . The default setting is 20* horizontal and vertical.

5.1. Drawing Shortcut Keys

The keyboard

The arrow keys let you rotate the structure:

Ctrl arrow left / right : changes the horizontal angle of view by 30 .

Ctrl arrow up / down : changes the vertical angle of view by 30 .

Alt arrow left / right : changes the horizontal angle of view by 10 .

Alt arrow up / down : changes the vertical angle of view by 10 .

To view a certain aspect of the structure:

Ctrl-F : Front view

Ctrl-L : Left view

Ctrl-R : Right view

Ctrl-T : Top view

Display or hide features:

Ctrl-J : toggles the display of Joint numbers.

Ctrl-M : toggles the display of Member numbers or Section names.

Ctrl-S : toggles the display of the Structure or the Displacements.

Ctrl-N : toggles the display of Detailed Member Forces. Visualize the values of the Member Forces.

The Mouse

Zoom window: Press down the left mouse button and move to select the window to zoom.

Select a Joint with the mouse by clicking on the Joint Number:

Left mouse button: selects the Joint Number which turns red.

Right mouse button: deselects the Joint.

Double clicking the left mouse button on a Joint Number lets you change or remove the Joint. Double clicking on the blank screen, creates a new Joint.

Selecting two different Joints lets you change, create or remove the Member between those Joints.

6. Calculate

Before Analysis3D starts calculating, the structure is tested for stability and consistency. If the Structure is not stable, an error message is generated and the calculation stops.

In that case an error message will show The global construction is not stable . This means that there is a shortage of Support restraints.

This error message can also occur when the structure is not homogeneous. To demonstrate this with an example of a simple beam with 3 supports: to allow Analysis3D to acknowledge that all 3 supports are connected to the beam, the beam should be split in 2 beams. One beam from support 1 to support 2 and another beam from support 2 to support 3.

When you would only connect support 1 and support 3 with a beam (passing the location of support joint 2). Analysis3D will not know that support 2 is actually connected to that same beam. Analysis3D will see it as a loose support floating in the air at a point that happens to be next to the beam, but unconnected. To make support 2 connected to that same beam you need one beam to go from support 1 to support 2 and a 2nd beam from support 2 to support 3.

The same goes for any connection. Analysis3D requires that each connection is actually connecting all the joints you want to be connected.

Another typical error message could be The Structure is not consistent . This occurs when there are duplicate joints with (almost) the same joint coordinates. Please remove the duplicate joints to continue. The structure will also be not consistent when one or more joints is not connected to the rest of the structure.

Nonlinear or 2^nd order Calculation

In the standard Calculation Analysis3D assumes that the original geometry can be used throughout the analysis. This means that the loads are considered to be fixed in position so that all forces and moments are constant and acting in the same direction as the structure deforms. However, we know that this is actually not the case. When a load is applied to a joint in a real structure, that joint will move and the load will move with it. This movement of the load position can change both the direction at which the load acts with respect to the members connected to the joint, and the moment which the load causes about other points in the structure. If the displacements are large enough, the effect which the load have upon the structure can change significantly.

During Nonlinear or 2^nd order Calculation, Analysis3D takes into account the deformed structure and incrementally calculates the effect on the structure. Each increment uses the geometry of the structure due to the application of the previous increment. Because of the incremental approach, Nonlinear calculation takes somewhat longer to complete.

Sway structures require 2^nd order Calculations because of the magnitude of the sway. Analysis3D allows you to check if structures are classified as Sway or Non-Sway.

Very large structures can generate an error message, because there is not enough free memory. To solve this problem:

1. Close all other applications before starting the computation. In some cases, it can be useful to restart Windows.

2. Enlarge the virtual memory.

Analysis3D supports multitasking so that you can even start another copy of the program while the calculation is busy.

The Drawing will automatically be updated by showing the Joint Displacements (by default ten times exaggerated).

Finally, the Results can be consulted.

Stiffness Reduction Factor

Some standards require that the analysis of the structure to determine the required strengths of the components uses reduced stiffnesses. This reduction factor will be applied to all stiffnesses in the structure.

A stiffness reduction factor of 0.8 will reduce the stiffness with 20% and displacements will increase accordingly.

7. Results

7.1. Joint Displacements

The Joint Displacements are presented in a table, and made visible on the screen. The Displacements are by default ten times exaggerated in the drawing. Members that fail the requirements for Member Stress or Buckling are indicated in red. The resulting stresses are displayed in the corresponding list.

Displacements in [mm] or [inch] are expressed in the Global Coordinate System as indicated in the bottom left corner. Thus, a positive translation in the Y direction moves upwards.

The Rotations in [ ] are given according the right-hand rule in the Global Coordinate System.

At the bottom right, you can select from the drop-down list, which Load Combination you want to use for visualizing the results.

7.2. Member Forces

The Member Forces in [kN] or [Kips] and the Moments in [kNm] or [Kips-ft] are given according to the Local Coordinate System.

The units are specified by the Structure Menu option Units and Region.

With Trusses the Member Forces on both sides are equal and opposite. So only the Member Force at the end Joint is displayed. This conforms to the definition:

Positive Member Force = Tension

Negative Member Force = Compression

With Frames the Member Forces on both sides can be different. Thus, the Member Forces on both Joints are displayed.

The details of the selected member are displayed on the top of the page, including the weight of the member.

On the top right of the screen, you will find the total weight of the structure.

At the bottom right you can select from the drop-down list, which Load Combination you want to use for visualizing the results.

7.3. Member Stresses

The Member Stresses in [N/mm ] or [Kips/inch ] are presented according to the Local Coordinate System.

The units are specified by the Structure Menu option Units and Region.

With Trusses the Member Stresses on both sides are equal and opposite. So only the Member Stress at the end Joint is displayed. This conforms to the definition:

Positive Member Stress = Tension

Negative Member Stress = Compression

With Frames the Member Stresses on both sides can be different. Thus, the Member Stresses on both Joints are shown.

SAx : the axial stress or strain.

SFy, SFz : the Shear stresses along the local y- respectively z-direction.

The Shear stresses are calculated according SFy = Fy . Sx / (tw . Ix).

This formula is reflecting that the Shear Force is working on the area of the web of the section.

SBy, SBz : the Bending stresses along the local y- respectively z-direction.

Bending Stress is calculated with SBz = Mz ex / Ix

STx : the Torsional stress.

The Torsional Stress is calculated with STx = Mx et / It.

SRes : the Resulting Stress computed according Huber and Hencky (also referred to as Von Mises yield criterion)

SRes = sqrt( SAx + SBy + SBz - SAx SBy SBy SBz SBz SAx + 3SFy + 3SFz + 3STx )

In the case that the Structure is two-dimensional the equation becomes:

SRes = sqrt( SAx + SBz - SAx SBz + 3SFy )

So SRes is not the real composed Member Stress but the ideal comparative stress that can be compared with Yield Strength (Re) as defined in the material properties.

All members that are not meeting the requirements versus the Yield Strength Re, as given in the material

data, are highlighted in the list.

At the bottom right you can select from the drop-down list, which Load Combination you want to use for visualizing the results.

7.4. Sway and Natural Frequency

Sway Stability is considered to determine if a structure is sway or non-sway. This depends on the geometry and the load cases under consideration. It is determined and influenced by the of P-delta effect.

Non-sway structures:

Horizontal loads are carried by the bracing or by horizontal support

Change of geometry (2nd-order effect) is negligible

Sway structures:

Horizontal loads are carried by the frame

Change of geometry (2nd-order effect) is significant

Analysis3D calculates for each story if it is sway or non-sway. In the case the structure is classified as sway, 2^nd order analysis is required. Analysis3D allows you to calculate 2^nd order effects in the case of Sway structures.

In Eurocode 3 the critical Sway ratio is determined as:

While ACI 318-19 works with the invers stability index ratio:

The Natural Frequency of the given structure is calculated using the formula below:

Where: Ktot represents the total combined stiffness of the building and Mtot equals the total mass.

7.5. Buckling

The calculation of Buckling assumes that all Loads are entered with a Load Factor.

The Load Factor is the ratio between the Force used for the calculations and the real Force. This Load Factor is by default set to 1.5. If any other Load Factor has been used, the Load factor should be changed accordingly.

The Safety Factor depends upon the conditions. For steel constructions a default Safety Factor of 2.5 is used. Machine parts such as a piston rod need a Safety Factor of 4 to 10.

The resulting Maximum admissible Buckling Load depends on the given Load Factor and Safety Factor.

For each compressed Member, the slenderness and the Maximum admissible Buckling Load is calculated, taking into account the Support restraints.

A distinction has to be made dependent on the slenderness of the Member.

Slenderness = Member length / sqrt( I / Ax )

Eulers Limit Slenderness = 3,14 sqrt( E / 0,7 Re ) = 111 ( for FE360 )

Slenderness <= 20: In this area the maximum admissible strain will be reached long before Buckling takes place. A computation on train is sufficient. The maximum admissible Buckling Load will be: Ax . Re.

20 < Slenderness < Eulers Limit Slenderness: This is the plastic area, where the present Stress may not exceed the Yield Point of the material. The maximum admissible Buckling Load follows the straight line of Von Tetmayer.

Slenderness > Eulers Limit Slenderness: This is the elastic area and can be calculated with Euler.

The maximum admissible Buckling Load = 3,14 EI / (safety factor . buckling length )

At the bottom right you can select from the drop-down list, which Load Combination you want to use for visualizing the results.

Remarks:

In the calculation of the maximum admissible Buckling Load the smallest radius of inertia is used. The program will choose Ix or Iy. In Angle Cross Sections the smallest radius of inertia (along the diagonal) is not available, this will result in a minor aberration.

The maximum limit Stress is set at 0,7 Re. This Stress corresponds to Eulers limit Slenderness. Since this only applies to rolled Sections, the calculations for Buckling only apply to these Sections.

7.6. Reactions

The Reaction Forces are calculated by adding the Member ForcesMemberForce in the Support JointsSupport.

The Forces in [kN] or [Kips] are oriented along the Global Coordinate SystemGlobalSystem as indicated in the bottom left corner of the screen. Positive Reactions in the Y direction are pointed up.

Moments in [kNm] or [Kips-ft] are shown according the right-hand rule in the Global Coordinate System.

The units are specified by the Structure Menu option Units and RegionUnits.

At the bottom right you can select from the drop-down list, which Load Combination you want to use for visualizing the results.

7.7. Detailed Member Forces

The option Detail Member Forces calculates for one Member the values of:

Axial (Normal) Forces (N)

Shear Forces (Ty and Tz)

Torsion (Mx)

Bending Moments (My and Mz)

Deflection (fy and fz)

The sign definition for the member Forces is as follows:

A Normal Force is positive, when it induces Stress in the considered Section.

A Shear Force is positive, when it rotates the released part to the left.

A Bending Moment is positive, when she gives Stress in the part above the center of the Section.

Deflection is positive when it coincides with the positive Local Coordinate System.

Thus, all Forces and Moments in the following drawing are positive.

The number of divisions of the Member can be set.

The calculation shows the detailed member Forces in a table. The maximum values are highlighted.

All Members selected from the list to the right will be drawn together with their detailed member Forces.

At the bottom right you can select from the drop-down list, which Load Combination you want to use for visualizing the results.

7.8. Detailed member Stresses

The option Detail Member Stresses calculates for one Member the course of:

Normal (Axial) Stress (SAx),

Shear Stress (SFy en SFz),

Torsion Stress (STx)

Bending Stress (SBy en SBz),

Deflection (fy)

Resulting Comparative Stress (SRes)

SRes is not the real composed Member Stress but the Ideal Resulting Comparative Stress that can be compared with Re.

For the calculation of the Resulting Comparative Stress see Member Stresses

The sign definition is equal as for the Detail Member Forces:

The number of divisions of the Member can be changed.

The maximum value for each stress is highlighted, also any stresses that are not meeting the requirements versus the Yield Strength Re, as given in the material data, are highlighted in the list.

All Members selected from the list to the right will be drawn together with their detailed Stresses.

At the bottom right you can select from the drop-down list, which Load Combination you want to use for visualizing the results.

7.9. Member Design

This is a powerful tool to optimize your construction in 2 ways.

If a given member is not strong enough for the selected calculation method, Analysis3D will propose the smallest cross-section from the list with Cross-sections. These members are highlighted (selected) in the list with members.

If a given member is over designed, then Analysis3D will propose you the cross-section with minimum area Ax that is acceptable for the given load, to minimize cost.

Each cross-section can be checked in the following different ways as selected in the Units and Region menu option:

- using the AISC-ASD standard

- using the AISC-LRFD standard

- using the BS 5950 standard

- using the CISC 94 standard

- using the Eurocode 3 standard

The maximum utilization factor or utilization ratio is specified which should be ≤ 1. The utilization ratio is a measure for how close a section is to using its maximal section capacity and is obtained by the ratio between the applied loads and the loads at the design resistance.

You can choose to use all or just partly incorporate the proposed changes. After the changes are made, you need to recalculate the structure to see the effect. You will find that because of the changed sections, the forces in the structure are divided differently. This means that other sections are no longer ideally dimensioned. You will find that you may need a few iterations to come to the best solution.

Change button: Just change the one selected member after the button with the proposed Section. Before pressing this button, you can override the proposals by manually changing the section or angle.

Change All button: Change all members with the proposed sections.

Only Selected button: Change the Section of the selected (highlighted) members. These members are already selected for you and contain only those members that are not strong enough. Of course, you can always change any selection you want.

Based on our experience this is the best process to come to a structure with optimal sections.

1. Start with the first Load case you have to evaluate. In this process you can use the Change All button to find the smallest sections to minimize cost.

2. As you will move on by checking the other Load cases for the same construction, you then can only change those sections that are not strong enough. (Press the Only Selected button).

Each change of a cross-section will affect the distribution of the forces in the total structure. This means that the total structure needs to be recalculated for validation of the final result.

At the bottom right you can select from the drop-down list, which Load Combination you want to use for calculating the results.

7.10. Detailed Member Design

Each cross-section can be checked in the following different ways as selected in the Units and Region menu option:

- using the AISC ASD standard

- using the AISC LRFD standard

- using the BS 5950 standard

- using the CISC 94 standard

- using the Eurocode 3 standard

For each method, Analysis3D will not only test the given Cross-sections, but will also calculate optimized sections for the defined loads.

At the bottom right you can select from the drop-down list, which Load Combination you want to use for visualizing the results.

Detailed Design.JPG

7.11. AISC-ASD

Design for Strength Using Allowable Strength Design according to ANSI/AISC 360-16

Reference: Specification for Structural Steel Buildings, July 7, 2016 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

Design according to the provisions for allowable strength design (ASD) satisfies the requirements of this Specification when the allowable strength of each structural component equals or exceeds the required strength determined on the basis of the ASD load combinations.

Design shall be performed in accordance with the equation Ra ≤ Rn Ω

Where:

Ra = required strength using ASD load combinations

Rn = nominal strength

Ω = safety factor

Rn/Ω = allowable strength

The nominal strength, Rn, and the safety factor, Ω, for the applicable limit states are specified below:

TENSILE STRENGTH: Ω_t = 1.67

COMPRESSION: Ω_c = 1.67

FLEXURE: Ω_b = 1.67

SHEAR: Ω_v = 1.67

TORSION: Ω_T = 1.67

Allowable Strength Design (ASD) requires 2nd order effects (P-Δ effect) to be included. This is achieved by performing 2^nd order analysis or by using a Moment magnification factor. Analysis3D assumes ASD is performed on the results of a Nonlinear or 2nd order Calculation before the ASD analysis is done

All formulas and calculations are detailed in the LRFD design.

7.12. AISC-LRFD

Design for Strength Using Load and Resistance Factor Design (LRFD) according ANSI/AISC 360-16.

Reference: Specification for Structural Steel Buildings, July 7, 2016 AMERICAN INSTITUTE OF STEEL CONSTRUCTION

Design according to the provisions for load and resistance factor design (LRFD) satisfies the requirements of this Specification when the design strength of each structural component equals or exceeds the required strength determined on the basis of the LRFD load combinations.

LRFD requires 2nd order effects (P-Δ effect) to be included. Analysis3D assumes LRFD will by calculated using 2nd order Analysis results and that the second-order analysis be carried out under LRFD load combinations.

Classification of Sections for Local Buckling

For members subject to axial compression, sections are classified as nonslender-element or slender-element sections. For a nonslender-element section, the width-to-thickness ratios of its compression elements shall not exceed λr from Table B4.1a. If the width-to-thickness ratio of any compression element exceeds λr, the section is a slender-element section. For members subject to flexure, sections are classified as compact, noncompact or slender-element sections. For a section to qualify as compact, its flanges must be continuously connected to the web or webs, and the width-to-thickness ratios of its compression elements shall not exceed the limiting width-to-thickness ratios, λp, from Table B4.1b. If the width-to-thickness ratio of one or more compression elements exceeds λp, but does not exceed λr from Table B4.1b, the section is noncompact. If the width-to-thickness ratio of any compression element exceeds λr, the section is a slender-element section

Design shall be performed in accordance with: R_u ≤ φR_n

where R_u = required strength using LRFD load combinations

R_n = nominal strength

φ = resistance factor

φR_n = design strength

Tension

For members designed on the basis of tension, the slenderness ratio, L/r, preferably should not exceed 300.

The design tensile strength of tension members is obtained according to the limit states of tensile yielding in the gross section: P_n = F_y A_g

The resistance factor φt = 0.90

Compression

For members designed on the basis of compression, the effective slenderness ratio, Lc /r, preferably should not exceed 200.

The resistance factor φc = 0.90

FLEXURAL BUCKLING OF MEMBERS WITHOUT SLENDER ELEMENTS

The nominal compressive strength, P_n, shall be determined based on the limit state of flexural buckling: P_n = F_cr A_g

The critical stress, F_cr, is determined as follows:

TORSIONAL AND FLEXURAL-TORSIONAL BUCKLING OF SINGLE ANGLES AND MEMBERS WITHOUT SLENDER ELEMENTS

The nominal compressive strength, P_n, shall be determined based on the limit states of torsional and flexural-torsional buckling: P_n = F_cr A_g

The critical stress, F_cr, is determined as above.

For doubly symmetric members twisting about the shear center:

For singly symmetric members twisting about the shear center where y is the axis of symmetry:

For unsymmetric members twisting about the shear center, Fe is the lowest root of the cubic equation:

MEMBERS WITH SLENDER ELEMENTS

The nominal compressive strength, P_n, shall be the lowest value based on the applicable limit states of flexural buckling, torsional buckling, and flexural-torsional buckling in interaction with local buckling.

P_n = F_crA_e

Slender Element Members Excluding Round HSS: The effective width, be, (for tees, this is de; for webs, this is he) for slender elements is determined as follows:

and

Round HSS:

The effective area, A_e, is determined as follows:

DESIGN OF MEMBERS FOR FLEXURE

For guidance in determining the appropriate sections of this chapter to apply the table below is used.

The design flexural strength, φ_bM_n shall be determined using φ_b = 0.90

DOUBLY SYMMETRIC COMPACT I-SHAPED MEMBERS AND CHANNELS BENT ABOUT THEIR MAJOR AXIS

The nominal flexural strength, Mn, shall be the lower value obtained according to the limit states of yielding (plastic moment) and lateral-torsional buckling.

Yielding: M_n = M_p = F_y Z_x

Lateral-Torsional Buckling:

- When L_b ≤ L_p, the limit state of lateral-torsional buckling does not apply.

- When L_p < L_b ≤ L_r :

with and

_-When L_b > L_r : M_n = F_crS_x ≤ M_p

with and

DOUBLY SYMMETRIC I-SHAPED MEMBERS WITH COMPACT WEBS AND NONCOMPACT OR SLENDER FLANGES BENT ABOUT THEIR MAJOR AXIS

The nominal flexural strength, M_n, shall be the lower value obtained according to the limit states of lateral-torsional buckling and compression flange local buckling.

For lateral-torsional buckling: the provisions of the previous paragraph shall apply.

Compression Flange Local Buckling:

(a) For sections with noncompact flanges:

(b) For sections with slender flanges:

OTHER I-SHAPED MEMBERS WITH COMPACT OR NONCOMPACT WEBS BENT ABOUT THEIR MAJOR AXIS

The nominal flexural strength, Mn, shall be the lowest value obtained according to the limit states of compression flange yielding, lateral-torsional buckling, compression flange local buckling, and tension flange yield.

Compression Flange Yielding: M_n = R_pcM_yc

with M_yc = F_yS_xc = yield moment in the compression flange

and

Lateral-Torsional Buckling:

When L_b ≤ L_p, the limit state of lateral-torsional buckling does not apply.

When L_p < L_b ≤ L_r :

When L_b > L_r : M_n = F_crS_xc ≤ R_pcM_yc

With and

where

and

Compression Flange Local Buckling:

For sections with compact flanges, the limit state of local buckling does not apply.

For sections with noncompact flanges:

For sections with slender flanges:

DOUBLY SYMMETRIC AND SINGLY SYMMETRIC I-SHAPED MEMBERS WITH SLENDER WEBS BENT ABOUT THEIR MAJOR AXIS

Compression Flange Yielding: M_n = R_pgF_yS_xc

where

Lateral-Torsional Buckling: M_n = R_pgF_crS_xc

When L_b ≤ L_p, the limit state of lateral-torsional buckling does not apply.

When L_p < L_b ≤ L_r:

When L_b > L_r:

Compression Flange Local Buckling: M_n = R_pg F_crS_xc

For sections with compact flanges, the limit state of compression flange local buckling does not apply.

For sections with noncompact flanges:

For sections with slender flanges:

I-SHAPED MEMBERS AND CHANNELS BENT ABOUT THEIR MINOR AXIS

Yielding: M_n = M_p = F_y Z_y ≤ 1.6 F_y S_y

Flange Local Buckling:

For sections with compact flanges, the limit state of flange local buckling does not apply.

For sections with noncompact flanges:

For sections with slender flanges: M_n = F_cr S_y where

SQUARE AND RECTANGULAR HSS AND BOX SECTIONS

Yielding: M_n = M_p = F_y Z

Flange Local Buckling:

For compact sections, the limit state of flange local buckling does not apply.

For sections with noncompact flanges:

For sections with slender flanges: M_n = F_y S_e

Web Local Buckling

For compact sections, the limit state of web local buckling does not apply.

For sections with noncompact webs:

For sections with slender webs:

Compression flange yielding: M_n = R_pg F_y S

Compression flange local buckling: M_n = R_pg F_crS_xc

and

Lateral-Torsional Buckling

When Lb ≤ Lp, the limit state of lateral-torsional buckling does not apply.

When Lp < Lb ≤ Lr:

When Lb > Lr:

with and

ROUND HSS

Yielding: M_n = M_p = F_y Z

Local Buckling:

For compact sections, the limit state of flange local buckling does not apply.

For noncompact sections:

For sections with slender walls: M_n = F_cr S with

TEES AND DOUBLE ANGLES LOADED IN THE PLANE OF SYMMETRY

Yielding:

For tee stems and web legs in tension M_p = F_yZ_x ≤ 1.6 F_y S_x

For tee stems in compression Mp = F_y S_x

Lateral-Torsional Buckling

For stems and web legs in tension

When Lb ≤ Lp, the limit state of lateral-torsional buckling does not apply.

When Lp < Lb ≤ Lr:

When Lb > Lr: M_n = M_cr with

where

For stems and web legs in compression anywhere along the unbraced length: M_n = M_cr ≤ F_y S_x

with

Flange Local Buckling

For sections with a compact flange in flexural compression, the limit state of flange local buckling does not apply.

For sections with a noncompact flange in flexural compression:

For sections with a slender flange in flexural compression:

Local Buckling of Tee Stems in Flexural Compression: M_n = F_cr S_x

SINGLE ANGLES

Yielding: M_n = 1.5 M_y

Lateral-Torsional Buckling:

For equal-leg angles with no axial compression:

For other angles:

Leg Local Buckling:

For compact sections, the limit state of leg local buckling does not apply.

For sections with noncompact legs:

For sections with slender legs: M_n = F_cr S_c with

RECTANGULAR BARS AND ROUNDS

Yielding: for rounds and for rectangular bars with : M_n = M_p = F_yZ ≤ 1.6 F_y S_x

Lateral-Torsional Buckling:

For rectangular bars with bent about their major axis, the limit state of lateral-torsional buckling does not apply.

For rectangular bars with :

For rectangular bars with : Mn = F_cr S_x ≤ M_p where

DESIGN OF MEMBERS FOR SHEAR

The design shear strength, φ_v V_n shall be determined using φ_v = 0.90 and the nominal shear strength, V_n, shall be determined according to the sections below.

I-SHAPED MEMBERS AND CHANNELS

Shear Strength of Webs without Tension Field Action:

The nominal shear strength: V_n = 0.6 F_y A_w C_v1

For webs of rolled I-shaped members with C_v1 = 1.0

For all other I-shaped members and channels:

when : C_v1 = 1.0

when :

with k_v = 5.34

SINGLE ANGLES AND TEES

The nominal shear strength of a single-angle leg or a tee stem is: V_n = 0.6 F_y b t C_v2

RECTANGULAR HSS, BOX SECTIONS, AND OTHER SINGLY AND DOUBLY SYMMETRIC MEMBERS

The nominal shear strength V_n = 0.6 F_y A_w C_v2

ROUND HSS

V_n = F_cr A_g / 2

WEAK-AXIS SHEAR IN DOUBLY SYMMETRIC AND SINGLY SYMMETRIC SHAPES

For doubly and singly symmetric shapes loaded in the weak axis without torsion, the nominal shear strength for each shear resisting element is: V_n = 0.6 F_y b_f t_f C_v2

DESIGN OF MEMBERS FOR COMBINED FORCES AND TORSION

DOUBLY AND SINGLY SYMMETRIC MEMBERS SUBJECT TO FLEXURE AND AXIAL FORCE

Doubly and Singly Symmetric Members Subject to Flexure and Compression or Tension:

The interaction of flexure and compression or tension in doubly symmetric members and singly symmetric members constrained to bend about a geometric axis (x and/or y) shall be limited by the Equations:

Doubly Symmetric Rolled Compact Members Subject to Single-Axis Flexure and Compression

If M_ry/M_cy <= 0.05 :

For the limit state of in-plane instability, the previous Equations shall be used with Pc taken as the available compressive strength in the plane of bending and Mcx taken as the available flexural strength based on the limit state of yielding.

For the limit state of out-of-plane buckling and lateral-torsional buckling:

UNSYMMETRIC AND OTHER MEMBERS SUBJECT TO FLEXURE AND AXIAL FORCE

MEMBERS SUBJECT TO TORSION AND COMBINED TORSION, FLEXURE, SHEAR, AND/OR AXIAL FORCE

Round and Rectangular HSS Subject to Torsion

The design torsional strength, φ_T T_n for round and rectangular HSS according to the limit states of torsional yielding and torsional buckling shall be determined as follows: T_n = F_cr C and φ_T = 0.90

For round HSS, F_cr shall be the larger of: and but shall not exceed 0.6 F_y

For rectangular HSS:

HSS Subject to Combined Torsion, Shear, Flexure and Axial Force

When Tr exceeds 20% of Tc, the interaction of torsion, shear, flexure and/or axial force shall be limited by

To summarize the maximum utilization ratio is specified which should be ≤ 1.

The utilization ratio is a measure for how close a section is to using its maximal section capacity and is obtained by the ratio between the applied loads and the loads at the design resistance.

7.13. BS 5950

BS 5950 starts from the classification of sections into 4 categories: Plastic, Compact, Semi-compact or Slender. The classification of the cross-section will determine the way the allowable stress is determined.

Analysis3D will evaluate Plastic, Compact, Semi-compact sections. Slender sections are beyond the scope of Analysis3D.

When using the BS 5950 code, Analysis3D design assumes that a 2^nd order analysis has already been performed, so that moment magnification factors for the moments causing side-sway can be taken as unity.

Each cross-section is tested for:

- Compression Resistance

- Tension Capacity

- Shear Capacity

- Moment capacity

- Lateral-Torsional Buckling Moment Capacity

- Local Capacity Check

- Overall Buckling Check

7.14. CISC 94

CISC 94 starts for the determination of the nominal strengths for axial compression and flexure, the sections are classified as either Class 1 (Plastic), Class 2 (Compact), Class 3 (Noncompact), or Class 4 (Slender). If a section fails to satisfy the limits for Class 3 sections, the section is classified as Class 4. Currently Analysis3D does not check stresses for Class 4 sections.

When using the CISC 94 code, Analysis3D assumes that a P- analysis has been performed so that moment magnification factors for moments causing sidesway can be taken as unity.

The strength reduction factor is taken as 0.9 (CISC 13.1)

Each cross-section is tested for:

- Compression Strength

- Tension Strength

- Bending Strength

- Shear Strength

- Capacity Ratio for Compressive Axial and Bending Stresses

- Capacity Ratio for Tensile Axial and Bending Stresses

7.15. Eurocode 3

The Eurocode 3 (EN 1993-1-1: 2005) standard first evaluates the section and defines a section class depending on the cross-section properties and the section load combination. The section class will determine the method of analysis.

- Class 1 cross-sections are those which can form a plastic hinge with the rotation capacity required from plastic analysis without reduction of the resistance.

- Class 2 cross-sections arc those which can develop their plastic moment resistance, but have limited rotation capacity because of local buckling.

- Class 3 cross-sections are those in which the stress in the extreme compression fiber of the steel member assuming an elastic distribution of stresses can reach the yield strength, but local buckling is liable to prevent development of the plastic moment resistance.

- Class 4 cross-sections are those in which local buckling will occur before the attainment of yield stress in one or more parts of the cross-section.

Classification of Sections:

A cross-section is classified according to the highest (least favorable) class of its compression parts.

Class 4 cross-sections are beyond the scope of Analysis3D.

When using Eurocode 3, Analysis3D design assumes that a P- analysis or 2^nd order analysis has been performed so that moment magnification factors for moments causing sidesway can be taken as unity.

No allowance is made for fastener holes. This is outside of the scope of Analysis3D and requires separate investigation.

The nominal strengths in compression, tension, bending, and shear are computed for Class 1, 2, and 3 sections according to the following subsections. The material partial safety factors used by the program are:

Tension: The design value of the tension force N_Ed at each cross section shall satisfy:

and the design expression for yielding of the gross cross-section (plastic resistance) is given as:

Compression: The design value of the compression force N_Ed at each cross-section shall satisfy:

and

Bending moment: The design value of the bending moment M_Ed at each cross-section shall satisfy:

with

Shear: The design value of the shear force V_Ed at each cross section shall satisfy:

For plastic design is the design plastic shear resistance V_pLRd is given as:

then additional shear buckling check is required by

where and

Combined bending and shear:

Where the shear force is less than half the plastic shear resistance its effect on the moment resistance may be neglected. Otherwise, the reduced moment resistance should be taken as the design resistance of the cross-section, calculated using a reduced yield strength

where

Combined bending and axial force:

For class 1 and 2 cross sections, the following criterion shall be satisfied:

For a rectangular solid sections:

For I sections:

For bi-axial bending the following criterion may be used:

For Class 3 cross-sections the maximum longitudinal stress shall satisfy the criterion:

Combined bending, shear and axial force:

Where V_Ed exceeds 50% of V_pl,Rd the design resistance of the cross-section to combinations of moment and axial force should be calculated using a reduced yield strength

for the shear area

where

Buckling resistance:

The design compression force N_Edshall satisfy:

where

and

The non-dimensional s1enden1ess is given by

with

Torsional and torsional-flexural buckling:

For torsional and torsional-flexural buckling the slenderness is calculated as:

where N_cr = N_cr,_TF but N_cr < N_cr,T

N_cr,TF is the elastic critical torsional flexural buckling force

N_cr,T is the elastic critical torsional buckling force

and

Buckling resistance in bending:

Laterally unrestrained members subject to major axis bending are verified against lateral- torsional buckling as follows:

where

The Lateral torsional buckling curves General case

The Lateral torsional buckling curves for rolled sections or equivalent welded sections

For rolled or equivalent welded sections in bending the values of XLT for the appropriate nondimensional slenderness may be determined as:

and

Uniform members in bending and axial compression:

Members which are subjected to combined bending and axial compression should satisfy:

The values of the interaction factors are give below:

To summarize the maximum utilization factor is specified which should be ≤ 1.

The utilization factor is a measure for how close a section is to using its maximal section capacity and is obtained by the ratio between the applied loads and the loads at the design resistance.

8. The Print Menu

Print Heading

The five lines enable you to enter a Heading, for your printed output. Since the Heading is saved with the configuration file, it will stay unchanged after rebooting.

Structural Data:

-Joints and Support Joints

-Members

-Joint Loads

-Member Loads

-Cross Section Data

-Material Data

If the construction is calculated, Analysis3D will also print the results:

-Joint Displacements

-Member Forces

-Member Stresses

-Buckling

-Reactions

-Detailed Member Forces

Detailed Design

This option will send the results of the detailed design calculations to the printer.

Drawing

The presented drawing is copied to the printer as shown on the screen.

Printer Setup

This option allows you select your printer and paper together with changing your printing properties.

9. End-User License Agreement ("Agreement")

Please read this End-User License Agreement carefully before downloading or using Analysis3D.

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You agree to indemnify and hold the Company and its parents, subsidiaries, affiliates, officers, employees, agents, partners and licensors (if any) harmless from any claim or demand, including reasonable attorneys' fees, due to or arising out of your: (a) use of the Application; (b) violation of this Agreement or any law or regulation; or (c) violation of any right of a third party.

No Warranties

The Application is provided to You "AS IS" and "AS AVAILABLE" and with all faults and defects without warranty of any kind. To the maximum extent permitted under applicable law, the Company, on its own behalf and on behalf of its affiliates and its and their respective licensors and service providers, expressly disclaims all warranties, whether express, implied, statutory or otherwise, with respect to the Application, including all implied warranties of merchantability, fitness for a particular purpose, title and non-infringement, and warranties that may arise out of course of dealing, course of performance, usage or trade practice. Without limitation to the foregoing, the Company provides no warranty or undertaking, and makes no representation of any kind that the Application will meet your requirements, achieve any intended results, be compatible or work with any other software, applications, systems or services, operate without interruption, meet any performance or reliability standards or be error free or that any errors or defects can or will be corrected.

Without limiting the foregoing, neither the Company nor any of the company's provider makes any representation or warranty of any kind, express or implied: (i) as to the operation or availability of the Application, or the information, content, and materials or products included thereon; (ii) that the Application will be uninterrupted or error-free; (iii) as to the accuracy, reliability, or currency of any information or content provided through the Application; or (iv) that the Application, its servers, the content, or e-mails sent from or on behalf of the Company are free of viruses, scripts, trojan horses, worms, malware, timebombs or other harmful components.

Some jurisdictions do not allow the exclusion of certain types of warranties or limitations on applicable statutory rights of a consumer, so some or all of the above exclusions and limitations may not apply to You. But in such a case the exclusions and limitations set forth in this section shall be applied to the greatest extent enforceable under applicable law. To the extent any warranty exists under law that cannot be disclaimed, the Company shall be solely responsible for such warranty.

Limitation of Liability

Notwithstanding any damages that You might incur, the entire liability of the Company and any of its suppliers under any provision of this Agreement and your exclusive remedy for all of the foregoing shall be limited to the amount actually paid by You for the Application or through the Application or 100 USD if You haven't purchased anything through the Application.

To the maximum extent permitted by applicable law, in no event shall the Company or its suppliers be liable for any special, incidental, indirect, or consequential damages whatsoever (including, but not limited to, damages for loss of profits, loss of data or other information, for business interruption, for personal injury, loss of privacy arising out of or in any way related to the use of or inability to use the Application, third-party software and/or third-party hardware used with the Application, or otherwise in connection with any provision of this Agreement), even if the Company or any supplier has been advised of the possibility of such damages and even if the remedy fails of its essential purpose.

Some states/jurisdictions do not allow the exclusion or limitation of incidental or consequential damages, so the above limitation or exclusion may not apply to You.

Severability and Waiver

Severability

If any provision of this Agreement is held to be unenforceable or invalid, such provision will be changed and interpreted to accomplish the objectives of such provision to the greatest extent possible under applicable law and the remaining provisions will continue in full force and effect.

Waiver

Except as provided herein, the failure to exercise a right or to require performance of an obligation under this Agreement shall not affect a party's ability to exercise such right or require such performance at any time thereafter nor shall be the waiver of a breach constitute a waiver of any subsequent breach.

Product Claims

The Company does not make any warranties concerning the Application.

United States Legal Compliance

You represent and warrant that (i) You are not located in a country that is subject to the United States government embargo, or that has been designated by the United States government as a "terrorist supporting" country, and (ii) You are not listed on any United States government list of prohibited or restricted parties.

Changes to this Agreement

The Company reserves the right, at its sole discretion, to modify or replace this Agreement at any time. If a revision is material, we will provide at least 30 days' notice prior to any new terms taking effect. What constitutes a material change will be determined at the sole discretion of the Company.

By continuing to access or use the Application after any revisions become effective, You agree to be bound by the revised terms. If You do not agree to the new terms, You are no longer authorized to use the Application.

Governing Law

The laws of the Country, excluding its conflicts of law rules, shall govern this Agreement and your use of the Application. Your use of the Application may also be subject to other local, state, national, or international laws.

Entire Agreement

The Agreement constitutes the entire agreement between You and the Company regarding your use of the Application and supersedes all prior and contemporaneous written or oral agreements between You and the Company.

You may be subject to additional terms and conditions that apply when You use or purchase other Company's services, which the Company will provide to You at the time of such use or purchase.

Contact Us

If you have any questions about this Agreement, please contact Us:

By email: frank@cuylaerts.net