Using Mastan

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Using Mastan

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Introduction

• Mastan is an engineering analysis tool used to
  analyze how different structures will react under
  specific loading conditions.
• Because Mastan uses the Matlab engine to do its
  calculations, it can do a wide range of analyses
  that are cumbersome or impossible on paper.

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Outline

• Structure Definition
• Example problem Truss
• Example problem Frame
• Miscellaneous options

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Before you begin, you must know

• Geometry nodes and elements
• Connections (fixed/pinned, frame/truss)
• Fixities (physical restraints on the structure)
• Sectional Properties
• A cross-sectional area of each beam
• I second moment of area
• J torsion constant
• Material Properties
• E modulus of elasticity
• ? Poissons ratio
• Yield stress

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Definition Nodes and Elements

• Elements (also called members) are the actual
  beams and columns your structure is made from.
• Nodes are the joints between elements.
• Nodes must be placed first, and then connected by
  elements in Mastan

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Definition Connections

• The kind of joints you are using is crucial to
  your structure.
• Use pins as joints for a truss, and fixed joints
  (such as welds) for a frame.
• It is usually not necessary to tell Mastan what
  kind of connections you are using until analysis
  time.

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Definition Fixities

• These are the physical restraints on the
  structure, for example, the way your structure is
  fixed to the ground.

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Definition Physical Properties(Properties
dependent upon shape rather than material)

• A cross-sectional area of beam
• I (second moment of area) I describes how
  difficult it is to spin the object in question
  about a certain axis.
• J the torsional constant, which describes how
  difficult it is to twist the object. (optional
  for Mastan)

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Material Properties (Properties dependent on
material)

• E Youngs modulus, or modulus of elasticity E
  is a measure of how much you have to pull on
  something to make it stretch a certain amount.
• ? Poissons ratio the ratio of axial stretch to
  lateral shrink for different materials.

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Material Properties, contd

• Yield stress Stress is force applied over a
  given area. Yield stress is that point where the
  ratio of the force applied on the object to its
  area has reached the point where the object will
  fail.

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Working with Mastan In order to analyze a
structure, you must input it into the program.
The relevant components are

• Nodes
• Elements
• Connections
• Sections (Define and Attach)
• Materials (Define and Attach)
• Fixities
• Loads (also, Moments and Distributed Loads)

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Example Problem Truss
200 kN
300 kN
300 kN
500 kN
400 kN

• Objectives
• Deflected shape diagram
• Axial Force diagram
• Node displacements
• Reactions
• Element results

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Example Problem Truss (contd)

• This truss, is made of two kinds of elements.
• The vertical members are wide flange W203X60
  beams (A7550mm2, Izz60.8106 mm4, Iyy20.4106
  mm4) made of Structural Steel (E200GPa,
  ?max250MPa.
• All other members are wide flange W203X36 beams
  (A4570m2, Izz34.5106 mm4, Iyy7.61106 mm4)
  made of annealed stainless steel (18-8)
  (E190GPa, ?max250MPa)

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Adding Nodes (rectangular frame)

• Go to Geometry/Define Frame and enter the number
  and width of the bays, the number and height of
  the stories, and (for 3D frames) the number and
  depth of the frames in each box respectively. Hit
  Apply.
• You may need to move some of the nodes to do so,
  go to Geometry/Move Node, select the node(s) you
  need to move by clicking on them, and enter the
  amount you want to move them (NOT their new
  coordinates) in the boxes at the bottom of the
  screen.

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Mastan will work with any consistent set of
units. We are using kN-mm-MPa.
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Adding Nodes (manual layouts)

• If you are building anything other than a
  rectangular frame, you will need to enter each
  node manually. Go to Geometry/Define Node, and
  enter the (x,y,z) coordinates of each node in the
  boxes at the bottom of the screen, pressing
  Apply after each one.

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Coordinates shown for second node added (node 12)
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Adding Elements

• Go to Geometry/Define Element. For each element,
  click on each of its end nodes to select them,
  and press Apply.

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Add enough elements to connect all nodes as
shown, including this last one.
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Subdividing Elements

• If necessary, it is possible to subdivide
  elements into as many equally-sized pieces as
  desired.
• This option is found under the Geometry menu.
• As an added note, the Geometry menu gives the
  options to move or duplicate nodes and reorient
  elements, should the need arise.

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After hitting Apply for one set, selecting the
next.
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Fill in with elements, as shown
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Notes on Material and Sectional Property Sets

• Note that elements do not become deselected after
  you attach the property set to them you must
  deselect them yourself.
• If you attach a second section or material
  property set to an element, it will replace the
  first.
• Properties/Remove Section or Remove Material
  deletes the section or material definition,
  rather than giving you the option to unattach it
  from one or more elements
• As you attach a section or material property set
  to an element, that element goes from being
  represented by a dotted line to a dashed one, and
  then to a solid line once both property sets are
  attached

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Defining Sectional Properties

• Go to Properties/Define Section, and enter your
  values of A and I (use Izz if the element is
  expected to bend around the z-axis, Iyy if the
  bending will occur around the y-axis) in the
  boxes at the bottom of the screen, then click
  Apply.
• If your structure will be made up of parts with
  different cross sections, continue to define
  sections for each one.

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Defined the first section, hit Apply to define
the second section.
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Applying Sectional Properties to Individual
Elements

• Go to Properties/Attach Section
• Select all of the elements that have the first
  cross section
• Make sure the first section is selected in the
  boxes at the bottom of the screen
• Hit Apply
• Continue in this manner until all of your
  elements have sectional property sets attached

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Attach Section 2 to vertical members after
attaching Section 1 to all others
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Defining Material Properties

• Go to Properties /Define Material, and enter your
  value of E in the box at the bottom of the
  screen.
• Also enter ? if you have it. Yield stress will be
  represented as Fy, which can be left as infinity.
• Hit Apply and continue in this manner until you
  have defined all of the materials that you will
  be using.

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Hit Apply to define Material 2, after defining
Material 1.
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Applying Material Properties to Individual
Elements

• Go to Properties/Attach Material
• Select all of the elements that will be made from
  that material
• Make sure the first section is selected in the
  boxes at the bottom of the screen
• Hit Apply.
• Continue in this manner until all of your
  elements have material property sets attached.

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Attach Material 2 to vertical members after
attaching Material 1 to all others.
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Defining Conditions

• Next, define the conditions under which the
  structure will be placed, including
• Fixities
• Loads
• Moments
• Distributed Loads

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Defining Fixities

• Go to Conditions/Fixities.
• Select one of the nodes that will be attached to
  the ground
• Check the boxes that correspond to the degrees of
  freedom that will be restrained.
• For example, if your structure is simply
  supported (meaning one end is held in place with
  a pin joint, the other using a roller along the
  x-axis), you will check x, y, and z motion (but
  no rotation boxes) for the first joint, but only
  y and z motion (again, no rotation) for the
  second joint.
• Hit Apply.

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The structure is simply supported (pin on left,
roller on right)
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Applying Point Loads and Moments

• Under the Conditions menu, select the kind of
  effect you want to apply.
• Select the node to which you will apply it.
• Enter the x, y, and z components of the effect
  into the boxes at the bottom of the screen.
• Hit Apply.

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Applying several point loads
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Example Problem Frame

• Objectives
• Shear force diagram
• Moment diagram
• Element results

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Set up the problem as previously described
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Applying Distributed Loads

• Under Conditions menu, select Distributed Loads
• Select the element(s) to which you want to apply
  the load
• Enter the x, y, and z components into the boxes
  at the bottom of the screen
• Hit Apply

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Applying the distributed load
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Analysis

• Mastan is capable of many different types of
  analyses
• The data resultant from these analyses can be
  displayed as
• Diagrams, or
• Numeric results

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Definition Elastic and Inelastic Behavior

• Elastic behavior When a loaded object is
  stretched and then the load is removed, the
  object returns to its original size and shape,
  much like an elastic band would.
• Inelastic behavior When the load permanently
  deforms the object, even after it is removed.

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1st and 2nd Order Elastic Analyses

• Go to the Analysis menu and pick the type of
  analysis you would like to perform.
• Choose Space frame, space truss, plane frame
  (x,y), or plane truss (x,y), depending on how
  your structure is put together and supported.

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1st Order Elastic Analysis of Planar Truss (x-y)
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Diagrams

• Diagrams can be made by selecting the desired
  diagram from under the Results/Diagrams menu
  from
• Deflected shape
• Axial force
• Shear, Y and Z
• Torque
• Moment, Y and Z

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Deflected shape, 1st Order Elastic Truss analysis
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Axial Force, 1st Order Elastic Truss analysis
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Y-axis Shear Stress, 1st Order Elastic Frame
analysis
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Moment about Z-axis, 1st Order Elastic Frame
analysis
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Numeric Results

• Pure numeric results can be found by selecting
  the node or element for which the results are
  needed, after choosing from the Results menu
• Node Displacements
• Node Reactions
• Element Results

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Viewing displacements at top center node
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Viewing reactions at far left node
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Viewing element results for selected element
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Miscellaneous Options

• Other options can be found under
• The View menu
• Geometry/Information/(Node or Element)

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View Options

• Pan/Zoom
• Rotate
• Zoom Box
• Center
• Fit
• Defined Views
• Labels
• Display Settings

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View/Pan/Zoom

• This option moves the display window or adjusts
  the size of the object on the display using a row
  of well labeled buttons at the bottom of the
  screen.

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Rotate

• This option rotates the angle of the display
  window in three dimensions using another row of
  well-labeled buttons at the bottom of the screen.

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Zoom Box, Center, and Fit

• Zoom Box select a box with the curser which
  will become the center of the new view
• Center select the center point of the new view
• Fit automatically re-zoom and center to fit the
  whole structure (with diagrams if applicable) on
  the screen

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Defined Views

• The predefined views are quite handy when
  dealing with 3-dimensional structures.
• The available ones are
• Front (x-y)
• Side (y-z)
• Top (x-z)
• Isometric (x-y-z)

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Labels

• In this menu, you may turn on or off the labeling
  of all of the various parts of structures and
  diagrams.
• This is useful when you would like to know more
  information, or when your display is getting
  cluttered.

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Display Settings

• Using the same menu system as before (the 2-3
  bottom lines of the screen), you can set the
  defaults for
• Font size, for menus or figure labels
• Pan amount
• Zoom factor
• Rotate amount
• Symbol

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Geometry/Information

• You can view the position, orientation, and
  loading condition of any node or element by
  selecting it after selecting the appropriate
  option from under the Geometry/Information menu.

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Viewing info for selected element
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Good Luck!

• Hopefully this tutorial has helped you learn to
  use Mastan.

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Connections

• If your structure is neither a pure truss nor
  frame (some of your joints are fixed and others
  are free to rotate), you will need to tell the
  program that by going to Geometry/Connections,
  selecting a member that is connected to the node
  in question, and checking the appropriate boxes
  at the bottom of the screen. Then deselect that
  member and do the same for the rest of the
  elements connected to the node, in turn.

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Types of Analyses

• You can do several different data analyses with
  Mastan
• 1st and 2nd order elastic
• 1st and 2nd order inelastic
• Critical load, elastic and inelastic
• User-defined analyses
• Definition of elastic and inelastic behavior

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1st and 2nd Order Inelastic Analyses

• Again, both kinds of analyses can be found under
  the Analysis menu.
• 1st Order Inelastic asks for the same information
  that 2nd Order Elastic did Solution type,
  increment size, number of increments, analysis
  type, and the option to start a new analysis or
  continue a previously started one.
• 2nd Order Inelastic also asks whether to use E or
  Et for the modulus

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1st Order Inelastic Analysis Frame
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Elastic and Inelastic Critical Load Analyses

• As in the previous options, you must select the
  type of structure you will be analyzing under
  Analysis Type.
• For Elastic Critical Load Analysis, you can
  specify the maximum number of buckling modes to
  use.
• For Inelastic, the maximum number of buckling
  modes is 1

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Elastic Critical Load Analysis with 1 mode of
failure
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Elastic Critical Load Mode 1 Deflected Shape
diagram
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User-defined Analyses

• For those who can program for Matlab, there is
  the possibility of creating your own specialized
  analysis procedures, but for the most part, the
  pre-programmed analyses should suffice.

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Results/MSAPlot

• This option opens a separate application to
  analyze and model response curves.

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Conditions/Define Settlement

• A linear settlement of any node can be defined
  using the Define Settlement option under the
  Conditions menu
• A rotational settlement of any node can be
  defined using the Define Rot Settlement option,
  again under the Conditions menu

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Example truss with linear settlement of 10mm y
applied to far right node