Grasshopper for structural engineers

1Install Rhino and meet the canvas

By the end you have Rhino 8 running, the Grasshopper window open, and one red point on screen that you made with a component.

Idea

Rhino is a 3D modeller: you draw points, curves and surfaces at real size. Grasshopper is a second window that comes with Rhino. In it you do not draw. You place components and connect them with wires, and the result appears in Rhino as a red preview. Change a number and everything downstream updates. That chain of components is called a definition.

Two files hold your work: the Rhino model (.3dm) and the Grasshopper definition (.gh). For structural work the definition is the valuable one. It is the rule that makes the geometry, so one definition can produce a hundred variants of a roof.

Example: install on your Mac

1. Download Rhino 8 for Mac. The evaluation is the full version and runs for 90 days. After that, saving and plug-ins stop until you buy a licence.
2. A student licence costs ¥39,600 in Japan and is the same program as the commercial one. One licence covers both Mac and Windows, so it moves with you to a Windows PC later. You need proof of student status.
3. Open Rhino and start a new model from the template Large Objects - Meters. This course works in metres because the analysis plug-in reads coordinates as metres.
4. Click in the command line, type Grasshopper and press Enter. The canvas opens in its own window.

In Rhino: your first component

1. Double-click an empty spot on the canvas. A search box appears. Type Construct Point and press Enter.
2. Look at the Rhino Perspective viewport. A small red point sits at the origin. Red means it is a Grasshopper preview, not a real Rhino object yet.
3. Double-click the canvas again, type Number Slider, press Enter. Drag from the slider's right edge to the X input of the point.
4. Drag the slider. The point moves along the red X axis.

Checklist

• Rhino 8 is installed and opens a model in metres
• I can open Grasshopper with the Grasshopper command
• I can place a component by double-clicking the canvas and typing its name
• I moved a red preview point with a slider

2Move around and draw in 3D

By the end you can orbit, pan and zoom without thinking, and draw a line by typing coordinates.

Idea

Rhino shows four viewports: Top, Front, Right and Perspective. Top looks down the Z axis, so it is your plan (伏図). Front looks along Y, so it is your elevation or frame view (軸組図). Z is up. Double-click a viewport's name to make it fill the window, and again to go back.

You work by typing command names. Type Line, press Enter, then answer the prompts. A point is typed as x,y,z. A point relative to the last one starts with r, so r0,0,3.5 means 3.5 m straight up from where you were.

If two-finger drag does nothing on your trackpad, open Rhino's settings, go to Trackpad, and turn on Use two fingers to pan and rotate views.

Coming from Jw_cad

In Rhino: a column grid by hand

1. Maximise the Top viewport. Type Point and enter 0,0,0. Repeat for 6,0,0, 12,0,0, then the same three at Y = 8: 0,8,0, 6,8,0, 12,8,0. That is a grid of 2 bays by 1 bay, 6 m by 8 m.
2. Type Line, start at 0,0,0, end at r0,0,3.5. You have one column (柱), 3.5 m tall.
3. Select the line, type Copy, and copy it to the other five points.
4. Switch to Perspective, orbit around it, then type ZE.

Notice how slow that was for six columns. In Session 8 Grasshopper makes the same grid for any number of bays with five components.

Checklist

• I can orbit, pan and zoom in Perspective without looking it up
• I know which viewport is the plan and which is the elevation
• I drew a line by typing absolute and relative coordinates
• I built the six-column grid by hand

3Objects, units, snaps and layers

By the end you can name the five kinds of geometry Grasshopper passes around, and you know why two nodes half a millimetre apart are a problem.

Idea

Everything Grasshopper makes is one of a few Rhino object types. Each has a structural meaning.

A structural model is mostly points and lines. Two members are connected only when their end points are at the same place. Rhino decides "the same place" with the document tolerance, which you see with the Units command. With metres, a tolerance of 0.001 means 1 mm.

In Rhino

1. Type Units. Confirm the model units are metres and read the absolute tolerance.
2. Turn on Osnap at the bottom of the window and tick End, Mid and Int. Draw a line (Line) from the top of one column to the top of the next. The cursor should jump to the end point. That is a girder (大梁).
3. Open the Layers panel (Layer). Make three layers named C, G and Grid, each with its own colour. Select the columns and move them to C, the girders to G, the points to Grid.
4. Select a girder and turn on the Gumball. Drag the blue arrow to move it in Z. Undo it.

Checklist

• I can say what a point, curve, surface, brep and mesh stand for in a structure
• I checked the units and tolerance of my model
• I drew a girder that snaps exactly to two column tops
• My columns and girders are on separate named layers

4Components, wires and sliders

By the end you can read any small definition from left to right and say what each box does.

Idea

A component takes data in on the left, does one job, and gives data out on the right. A Number Slider makes a number. A Panel, the yellow note, shows whatever you wire into it. Use panels constantly: when you are not sure what a wire carries, plug it into a panel and read it.

The colour of a component is its status, and this page uses the same code.

Example: a point and a line

Two sliders set the X and Z of point B. Point A has nothing wired in, so it stays at the origin. Line joins them, Length measures the result, and a panel shows the number.

Try it here

In Rhino

1. Build the definition above. Find each component by double-clicking the canvas and typing its name.
2. Double-click the name of a slider to open its settings. Set the range to 0 to 10 and the rounding to one decimal.
3. Shortcut: double-click the canvas and type 0<6<12. You get a slider from 0 to 12 already set to 6.
4. To unplug a wire, right-click the input and choose Disconnect. To plug a second wire into the same input, hold Shift while you drag.

Checklist

• I predicted the 3, 4, 5 result before dragging the sliders
• I can say what grey, orange, red and green mean on a component
• I built the point and line definition in Grasshopper
• I can set a slider's range and I know the 0<6<12 shortcut

5A parametric portal frame

By the end you have a portal frame (門形ラーメン) driven by a span slider and a height slider.

Idea

One slider can feed many inputs. That is the whole point of a parametric model: the span is stored once, and every point that depends on it follows. Here the span L goes to the X of two points and the height H goes to the Z of two points.

Build frames in the XZ plane, which is the Front view. Z is up, and the analysis plug-in applies gravity along Z.

Example

Four points: A at the left base, B at the left top, C at the right top, D at the right base. Polyline joins them in the order you wire them. Explode breaks the polyline back into three separate members, because an analysis needs one line per member. Length then returns three numbers, one per segment.

Try it here

In Rhino

1. Place four Construct Point components and two sliders. Wire L and H as in the figure. Leave Y empty on all four.
2. Place Polyline. Wire A into V, then hold Shift and wire B, C and D into the same input, in that order.
3. Add Explode and Length, and read the lengths in a panel.
4. Select everything, press Cmd + G to group it, and type a name on the group: Portal frame geometry.

Checklist

• I can explain why L is wired to two points and H to two points
• I can tell a single-item wire from a list wire by how it is drawn
• I built the portal frame and it follows both sliders
• My definition is grouped and named

6Rhino geometry in, baked geometry out

By the end you can bring a curve you drew in Rhino into a definition, and send Grasshopper's result back to Rhino on a layer.

Idea

Data crosses between the two windows in both directions. Going in, a Curve or Point parameter can reference an object in the Rhino model: move the object and the definition updates. Going out, Bake turns the red preview into real Rhino objects. Baked objects are a copy. They do not update when you move a slider afterwards.

At an office the usual pattern is: the architect's roof line or surface comes in by reference, your definition generates the structure on it, and you bake the result when a version is agreed.

Example

In Rhino

1. In the Front viewport, draw a gentle roof line about 24 m long with Curve.
2. In Grasshopper place a Curve parameter (Params, Geometry). Right-click it, choose Set one Curve, and click your roof line.
3. Wire it into Divide Curve (Curve, Division) with a slider on N. Red points appear along the line.
4. In Rhino, drag a control point of the roof line (turn them on with PointsOn). The points follow.
5. Right-click Divide Curve, choose Bake, pick a layer, and confirm. The points are now real Rhino points.
6. Right-click the Curve parameter and choose Internalise data. The curve now lives inside the .gh file and no longer needs the Rhino object.

Keep definitions readable from the first day: inputs on the left, logic in the middle, results on the right, every stage in a named group. Double-click a wire to add a Relay when a long wire needs a bend. A colleague should be able to follow it without you.

Checklist

• I referenced a Rhino curve and saw the definition follow when I edited it
• I baked a result to a chosen layer
• I can explain the difference between referenced, internalised and baked geometry

7Making and reading lists

By the end you can generate a row of evenly spaced points and pick any one of them by its index.

Idea

A list is an ordered set of items, numbered from 0. Most components do not care whether they receive one item or fifty. Give Construct Point a list of four X values and it makes four points. You never write a loop.

Series is the list maker you will use most: a start value S, a step N and a count C. For column lines at 6 m centres, that is start 0, step 6, count 4, which gives 0, 6, 12, 18.

Try it here

Example: components for working on a list

In Rhino

1. Build Series into Construct Point as in the figure, and read the points in a panel.
2. Add List Item. Wire the points into L and a slider into i. One point turns up as its output. Select List Item to see it highlighted green in Rhino.
3. Set i to 5 with only 4 points. List Item quietly returns index 1, the second point, because its Wrap input W is True by default and the index wraps round. Wire a Boolean Toggle set to False into W and set i to 5 again: now List Item returns nothing, which is easier to notice.
4. Add Cull Pattern with a panel containing True and False on two lines wired into P. Every second point disappears.

Checklist

• I know that list indices start at 0
• I can make evenly spaced points with Series
• I can pick one item with List Item
• I can explain the difference between Series and Range

8Data matching

By the end you can predict what a component does when its inputs are lists of different lengths. This one rule explains most surprises in Grasshopper.

Idea

Suppose X receives 4 values and Y receives 3. Which X goes with which Y? Grasshopper has three answers.

Longest List is built into every component. For the other two you place a Shortest List or Cross Reference component (both under Sets, List) in front of the inputs.

Example: the column grid

You want a column at every crossing of 4 grid lines in X and 3 in Y (通り芯). Wire the two Series straight into Construct Point and you get 4 points on a diagonal, because of Longest List. Put Cross Reference in between and you get the 12 you wanted.

Try it here

In Rhino

1. Make two Series: step 6 with count 4, and step 8 with count 3.
2. Wire them straight into X and Y of Construct Point. Count the points.
3. Insert Cross Reference between them. Count again.
4. Add a third Series for Z with step 3.5 and count 2, then zoom in on Cross Reference until a small plus sign appears, and click it to add a third input. You now have the node grid of a one-storey frame.

Checklist

• I can predict the number of results for each of the three rules
• I know Longest List is the default and that it reuses the last item
• I built a column grid with Cross Reference

9A truss from two lists

By the end you have a parallel-chord truss (平行弦トラス) built from lists, and you know the trick that connects node i to node i + 1.

Idea

A truss is two rows of nodes and four sets of lines between them: bottom chord (下弦材), top chord (上弦材), verticals (束材) and diagonals (斜材). Each set is one Line component fed with two lists.

• Verticals: bottom node i to top node i. Same index, so wire the two lists straight in.
• Chords: node i to node i + 1 in the same row.
• Diagonals: bottom node i to top node i + 1.

"i + 1" is what Shift List does. It slides a list along by S places, so item 1 moves to position 0, item 2 to position 1, and so on. Pair the original list with the shifted one and each node meets its neighbour.

Try it here

Example: the full truss

1. Bottom nodes: Series (start 0, step L / n, count n + 1) into the X of Construct Point.
2. Top nodes: Move the bottom nodes by a Unit Z vector with the depth H as its factor.
3. Verticals: Line with A = bottom, B = top.
4. Bottom chord: Line with A = bottom, B = bottom through Shift List (S = 1, Wrap = False), with Shortest List in front.
5. Top chord: the same with the top nodes.
6. Diagonals: Line with A = bottom, B = top through Shift List, again with Shortest List.

That gives diagonals that all lean the same way. For a Pratt truss they must run down towards midspan in both halves, mirrored at the centre. Split the node lists at midspan with Split List, build each half, and shift the bottom list in one half and the top list in the other.

In Rhino

1. Build the six steps above with three sliders: span L, depth H and panels n. Use Division for L / n and Addition for n + 1.
2. Check the member count in a panel. A truss with n panels has 4n + 1 members.
3. Group each member set and name it. You will need them separately when you assign sections.

Checklist

• I can explain how Shift List connects node i to node i + 1
• I found the stray line caused by Wrap and the one caused by Longest List
• I built a truss with span, depth and panel sliders
• My truss has exactly 4n + 1 members

10What a tree is

By the end you can read a tree's structure in a Param Viewer and say how many branches it has and how long each one is.

Idea

A data tree (データツリー) is a set of lists. Each list is a branch, and each branch has an address called a path, written in curly brackets: {0}, {1}, {0;2}. A plain list is a tree with one branch, {0}.

Trees appear on their own. Give Divide Curve three curves and ask for 4 segments each. It returns 15 points, and it keeps them in three branches of 5 so you still know which point belongs to which curve.

Example

{0;0}   N = 5     points on curve 0
  0  point
  1  point
  2  point
  3  point
  4  point
{0;1}   N = 5     points on curve 1
{0;2}   N = 5     points on curve 2

Read a path from the right. The last number is the newest level: here it is the index of the curve. The 0 in front is left over from the input list. Simplify Tree removes the part all paths share, which turns these into {0}, {1}, {2}. The live examples on this page show simplified paths.

The rule that makes trees useful: a component runs once per branch. Polyline given this tree draws three polylines, one through each branch.

In Rhino

1. Draw three separate lines in Rhino. Reference all three in one Curve parameter with Set Multiple Curves.
2. Wire it into Divide Curve with N = 4, then wire the P output into a Param Viewer (Params, Util) and into a panel.
3. Read the paths. Then right-click the P output, choose Simplify, and read them again.
4. Wire P into Polyline. Count the polylines.

Checklist

• I can say what a branch and a path are
• I can read branch count and branch length from a Param Viewer
• I can recognise a tree by its dashed wire
• I know that a component runs once per branch

11Flatten, Graft and Flip Matrix

By the end you can reshape a tree on purpose, and recognise the two classic mistakes when you see them.

Idea

All four exist as components under Sets, Tree. Flatten, Graft and Simplify are also one right-click away on any input or output, and a small icon appears on the port when one is active.

Try it here

In Rhino

1. Build a grid of points with one branch per floor. The quickest way is in the next session. For now, use your three divided curves from Session 10 as the three floors.
2. Wire the points into Polyline four times, each through a different operation, and compare.
3. With Flip Matrix, check the Param Viewer before and after: the number of branches and the length of each branch swap places.

Checklist

• I can predict the Param Viewer result of Flatten, Graft and Flip Matrix
• I can explain why a flattened tree gives one zigzag polyline
• I can explain why Polyline turns orange after Graft
• I used the right-click Flatten, Graft and Simplify on a port

12A multi-storey frame, organised by floor

By the end you have a frame for any number of storeys and bays, with beams stored by floor and columns stored by grid line.

Idea

Grafting one input is how you build a tree deliberately. Give Construct Point a plain list of X values and a grafted list of Z values. Each Z sits alone in its own branch, so the component runs once per level, and each run pairs that one Z with the whole X list. Out comes one branch of nodes per level.

Example

1. Nodes by level: as in the figure.
2. Beams (梁): within each branch, Line from the nodes to the same nodes through Shift List, with Shortest List. Because a component runs once per branch, one Line component draws the beams of every floor. Remove the ground branch first with Tree Branch or by starting the Z series at the first floor.
3. Columns (柱): Flip Matrix on the nodes, so each branch is one grid line from bottom to top. Then the same Shift List trick draws every column.

The output is two trees. Beams are grouped by floor, columns by grid line. That grouping is what lets you say "floors 1 to 3 get H-400, floors 4 to 6 get H-350" later.

Try it here

In Rhino

1. Build the frame with four sliders: storeys, bays, storey height (階高) and bay width (スパン).
2. Put a Param Viewer on the beams and on the columns. Confirm the branch counts match the live example.
3. Use Tree Branch with path {0} to isolate the first-floor beams, and give them a different preview colour with Custom Preview.

Checklist

• I can explain why grafting Z gives one branch of nodes per level
• I built a frame that follows storey and bay sliders
• My beams are grouped by floor and my columns by grid line
• I pulled out one floor with Tree Branch

13Curves and how to divide them

By the end you can place nodes along any curve and you know what "equal division" really means.

Idea

Every curve has a parameter, t, that runs from its start to its end, a little like a kilometre post along a road. Evaluate Curve returns the point at a given t. Right-click a curve input and choose Reparameterize to make t run from 0 to 1, so 0.5 is roughly the middle.

For structures the workhorse is Divide Curve. It cuts a curve into N pieces of equal length along the curve and returns N + 1 points. On a straight chord that means equal spacing. On an arch it does not: the points are evenly spaced along the arc, so their spacing on plan is uneven.

Try it here

In Rhino: a parabolic arch

A parabola carries uniform load in pure compression, which is why arch bridges use it. Its shape is z = 4 f x (L − x) / L².

1. Make the x values with Range: domain 0 to L, 20 steps.
2. Place Expression. Zoom in on it to add inputs and name them x, L and f. Double-click it and type 4*f*x*(L-x)/L^2.
3. Send x and the result into the X and Z of Construct Point, then the points into Interpolate.
4. Divide the arch with Divide Curve. For hangers at equal spacing on the deck instead, divide the deck line and send those x values through the same Expression.

Checklist

• I can explain what the parameter t of a curve is
• I know Divide Curve gives equal lengths along the curve, not equal spacing on plan
• I built a parabolic arch from an Expression

14Vectors and moving things

By the end you can copy a truss along a building to make a roof, with every truss kept in its own branch.

Idea

A vector is a direction with a length. Unit X, Unit Y and Unit Z make a vector along an axis, and their input F sets its length. Move shifts geometry by a vector. Loads are vectors too: a 10 kN load downwards is the vector (0, 0, −10).

Move with one truss and a list of vectors is where lists and trees meet. The truss is a list of lines. The vectors are a list as well. Wire them in plainly and Longest List pairs line 0 with vector 0, line 1 with vector 1, and tears the truss apart. Graft the vectors and each one runs separately against the whole truss.

Try it here

In Rhino

1. Take your truss from Session 9 and merge its four member sets into one list with Merge.
2. Build Series into Unit Y into the T input of Move, as in the figure. Right-click T and choose Graft.
3. Check with a Param Viewer: one branch per truss.
4. Add purlins (母屋). Move the top chord nodes the same way, then use Flip Matrix so each branch holds the same node on every truss, and run Polyline.

Checklist

• I can make a vector of a given length along an axis
• I can explain why the vectors must be grafted before Move
• I copied my truss into a row with one branch per truss
• I added purlins with Flip Matrix

15Surfaces and grids on them

By the end you can turn a roof surface into a grid of members, including a diagrid.

Idea

A surface has two directions, called U and V, the way a curve has one parameter t. Divide Surface returns a grid of points on it as a tree: one branch per U position, each holding the points along V. From there it is the list work you already know.

• Lines along V: within each branch, node j to node j + 1.
• Lines along U: Flip Matrix first, then the same.
• Diagrid: connect node (i, j) to node (i + 1, j + 1), and node (i + 1, j) to node (i, j + 1). That is one branch shifted against the next.

Try it here

In Rhino

1. Build the arc from Session 13 and extrude it with Extrude (Surface, Freeform) along a Unit Y vector.
2. Add Divide Surface (Surface, Util) with sliders on U and V. Put a Param Viewer on P.
3. Draw the V lines and the U lines as two separate groups.
4. For the diagrid, pair each branch with the next one. Shift Paths or Relative Item (both under Sets, Tree) can do it. The simpler route to start with is Flip Matrix, then Shift List inside each branch.

When the surface comes from an architect it will not be a neat extrusion. Reference it from Rhino as in Session 6 and the rest of the definition stays the same.

Checklist

• I can explain what U and V are on a surface
• I can read the tree that Divide Surface returns
• I drew grid members in both directions on a barrel roof

16Domains, Remap and Graph Mapper

By the end you can turn any list of numbers into the range you need, and shape how a value changes from bottom to top with a curve.

Idea

A domain is a range of numbers, written 0 To 24 in Grasshopper. Bounds finds the domain of a list: the smallest and the largest value. Remap Numbers moves values from one domain to another and keeps their proportions. A value 30% of the way through the source domain lands 30% of the way through the target.

Graph Mapper bends numbers between 0 and 1 along a curve that you choose and can edit by dragging its grips. Put the three together and you get the most common pattern in design work:

1. Take an index, such as the floor number: 0, 1, 2 and up.
2. Remap it to 0 To 1 with Bounds as the source.
3. Shape it with Graph Mapper.
4. Remap it again to the real design range, such as a plate scale from 0.7 to 1.2.

The same pattern sets a beam's depth along its span, the camber of a truss (キャンバー), or the size of members up a tower.

Try it here

In Rhino

1. Series with step 1 and count 20 for the floor numbers. Multiplication by 4 gives the floor heights.
2. Bounds (Maths, Domain) on the floor numbers, into the S input of Remap Numbers (Maths, Domain). Leave T at its default, 0 To 1.
3. Graph Mapper (Params, Input). Right-click it and pick a graph type. Wire the remapped values in.
4. Construct Domain (Maths, Domain) from two sliders, 0.7 and 1.2, into the T input of a second Remap Numbers.
5. Floor plates: XY Plane (Vector, Plane) with origins at (0, 0, height), then Rectangle (Curve, Primitive) on each plane with its X and Y inputs set to the domain -15 To 15, so each 30 m square is centred on its plane.
6. Scale (Transform, Affine) each rectangle about its plane origin by the factor. Then Loft (Surface, Freeform) through all of them for the skin.

Checklist

• I can work out a Remap Numbers result by hand
• I built the tower plates with Graph Mapper and two Remaps
• I can predict the shape a graph type gives before I switch to it

17An attractor point on a facade

By the end you can drive a facade pattern from a point, and cut the number of different panels without losing the pattern.

Idea

An attractor is a point that changes things according to their distance from it. Measure the distance from every panel centre to the point, remap those distances, and use the result as the opening size. Openings grow towards a view or shrink towards a neighbour.

The design question that follows always reaches the engineer and the contractor: if every panel is different, every panel is a separate drawing and a separate mould. Rationalising means rounding the sizes into a few types (パネルの種類). Five types can keep the look of a smooth pattern at a fraction of the cost.

Example

1. Panels: a facade surface into Divide Domain² (Maths, Domain) and Isotrim (Surface, Util). Each panel is a small surface.
2. Centres: Area (Surface, Analysis) returns the centroid of each panel.
3. Distance (Vector, Point) from each centroid to the attractor.
4. Bounds and Remap Numbers turn the distances into opening factors, for example from 0.85 near the point to 0.15 far away.
5. Scale each panel about its centroid by its factor. That scaled panel is the opening.

Try it here

In Rhino

1. Draw a 30 m by 12 m rectangle in the Front view and make a surface from it with PlanarSrf. Reference it in a Surface parameter.
2. Build the five steps above. Reference a Rhino point as the attractor, so you can drag it with the Gumball.
3. To rationalise, insert four components between the two Remaps: remap to 0 To 1, multiply by (types − 1), Round (Maths, Util), divide by (types − 1), then remap to your real range.
4. Count the different sizes: Create Set (Sets, Sets) keeps one copy of each value; List Length counts them.

Checklist

• My facade openings follow an attractor point I can drag in Rhino
• I rounded the openings into a set number of panel types
• I can explain to an architect why five panel types are cheaper than two hundred

18A twisting tower and its diagrid

By the end you can build a twisting, tapering tower, wrap it in a diagrid, and say what the twist does to its columns.

Idea

A tower is a list of floor plates. Give each floor an angle and a scale and the whole form follows. Graph Mapper decides how the twist is shared: evenly, mostly at the top, or slowly at both ends.

For the engineer, a twist means that a column following the corners leans, and a leaning column pushes sideways at every floor. A diagrid (ダイアグリッド) avoids that: diagonal members in a triangulated net carry both gravity and wind or earthquake load. Towers such as 30 St Mary Axe in London, engineered by Arup, use one.

Try it here

In Rhino

1. Floor plates as in Session 16: planes at each floor height and a 30 m square on each.
2. Angles: remap the floor numbers to 0 To 1, Graph Mapper, then multiply by the total twist in degrees.
3. Rotate (Transform, Euclidean) each plate about its own plane. Its A input expects radians: convert with Radians (Maths, Trigonometry), or right-click A and choose Degrees.
4. Taper: Scale each plate about its centre with a factor that runs from 1 at the base to your top scale.
5. Diagrid: Divide Curve on every second plate gives the nodes, one branch per level. Connect node j on one level to nodes j and j + 1 on the next with Shift List. On every second level, shift the division by half a spacing so the diagonals cross between floors.

Checklist

• My tower twists and tapers from sliders, with the twist shaped by Graph Mapper
• I built a diagrid on the tower
• I can explain why twisted corner columns push sideways and how a diagrid helps

19Panels on a curved roof

By the end you can measure how far each panel of a curved roof is from flat, and choose a geometry that gives flat panels.

Idea

Glass and metal panels are cheapest when they are flat. On most curved surfaces, the four corners of a panel do not lie in one plane. The panel is warped, and the amount is called its deviation from flat. Plane Fit (Vector, Plane) finds the plane closest to a set of points and reports how far they are from it.

Three ways out, each with a cost:

• Triangles are always flat, but you get twice the panels and more joints.
• Smaller panels warp less, but there are more of them.
• A translation surface, made by sliding one curve along another, gives flat four-sided panels on a doubly curved roof. Engineers such as Jörg Schlaich and Hans Schober used this for glass grid shells.

Try it here

In Rhino

1. A hypar from four corner points: 4Point Surface (Surface, Freeform) with two high and two low corners.
2. Divide Domain² and Isotrim for the panels.
3. Deconstruct Brep (Surface, Analysis): its V output gives the corner points of each panel, one branch per panel.
4. Plane Fit on those points. Its dx output is the deviation. Multiply by 1000 for millimetres.
5. Compare with a tolerance using Larger Than (Maths, Operators), and colour the panels with Custom Preview.

Checklist

• I measured panel deviation with Plane Fit and coloured the panels by it
• I can name three ways to get flat panels and the cost of each
• I can explain why a translation surface gives flat quads

20Install Karamba3D and analyse one beam

By the end Karamba3D runs on your Mac and its deflection for a simple beam agrees with 5wL⁴/384EI.

Idea

Every Karamba model is assembled from the same parts, in the same order: elements, supports, loads, then Assemble Model, then Analyze, then a view. If you give no cross section or material, Karamba uses a default for each, so always set them yourself.

Example: install on your Mac

1. Quit Rhino. In Finder open Applications, select Rhino 8, choose File, Get Info, and tick Open using Rosetta.
2. Open Rhino, type PackageManager, search for Karamba3D, choose version 2.2 and install it. Restart Rhino.
3. Open Grasshopper. A Karamba3D tab is now in the component bar.

Without a licence Karamba runs in one of two modes. The free mode has no element limit but leaves out some components. The manual marks those with a blue diamond, and Utilization of Elements is one of them. The full-feature trial has everything but stops at 20 beams and 50 shells. A student licence costs €30 plus VAT and removes both limits.

Example: the chain for one beam

1. Line from (0, 0, 0) to (6, 0, 0), then Line to Beam.
2. Cross Sections, set to I-Profile in its drop-down: height 30, flange width 15, flange thickness 0.9, web thickness 0.65. Karamba takes section sizes in centimetres. That is H-300×150×6.5×9.
3. Support at the start point with Tx, Ty, Tz and Rx switched on, and a second Support at the end point with Ty and Tz. A button is on when it is black. Six restraints is the minimum for anything in 3D, and Rx stops the beam spinning about its own axis.
4. Loads: a uniform line load on the beam with the vector (0, 0, −10), which is 10 kN/m downwards. In 2.2 line loads are in the Beam Loads component as the Block type. Leave its start and end at 0 and 1 so the load covers the whole span.
5. Assemble Model, then Analyze. Hover over the outputs of Analyze to find the maximum displacement, and put a panel on it.
6. ModelView to scale the deformation, and BeamView to draw the bending moment.

Try it here

Checklist

• Karamba3D 2.2 is installed and its tab shows in Grasshopper
• I can name the parts of a Karamba model in order
• I can explain why this beam needs six restraints and which six I chose
• My Karamba deflection is within a few percent of the hand value

21Analyse the truss

By the end your truss from Session 9 shows tension and compression in colour, and the chord force agrees with M / H.

Idea

A truss member carries axial force (軸力) only. In Karamba, Line to Beam has a Bending input. Set it to False and the beams lose their bending stiffness and become truss members.

A plane truss in 3D space can also move sideways out of its plane. Nothing pushes it that way, but the manual is clear that what counts is whether a displacement is possible, not whether a force acts. So besides the two bearings, restrain Ty at every node.

Example

1. Merge all truss lines into one list and wire them into Line to Beam with Bending = False.
2. Supports: Tx, Ty, Tz at the left bottom node (a pin, ピン支点). Ty and Tz at the right bottom node (a roller, ローラー支点). One more Support fed with all the nodes and only Ty on.
3. Loads: Point-Load at the top nodes. With a line load w, each inner node takes P = w L / n and the two end nodes take half. The force vector is (0, 0, −P).
4. Assemble, Analyze, then Beam Forces. Its N output is the axial force of each member.
5. In BeamView switch on Axial Stress. Karamba draws compression in red and tension in blue, the same colours this page uses.

Try it here

Checklist

• I predicted which members are in tension before looking
• I can explain why a plane truss needs out-of-plane restraints
• My truss runs in Karamba and shows red and blue members
• The chord force in Karamba agrees with M / H

22Analyse the portal frame

By the end you can read a bending moment diagram from Karamba and check a laterally loaded frame by hand.

Idea

A rigid frame (ラーメン) resists load by bending, so keep Bending on. The results you care about are the bending moment (曲げモーメント), the shear force (せん断力), the axial force, and the sway at beam level, which gives the storey drift angle (層間変形角). In Japan that angle is normally limited to 1/200 in the first-stage seismic check.

Load cases keep different actions apart. A point load goes into load case 0 unless you feed a number into its LCase input. A common split is vertical load in case 0 and lateral load in case 1, so you can read the long-term (長期) results alone and then the results with seismic load added (短期).

Example

1. Take the three exploded segments from Session 5 into Line to Beam.
2. Supports at A and D. Fixed (固定) means all six buttons on. Pinned means Tx, Ty and Tz only.
3. Loads: a Point-Load at B with the vector (P, 0, 0), and a line load on the beam.
4. Assemble, Analyze, then Beam Forces for N, V and M. In BeamView open Section Forces and switch on the bending moment.

Try it here

Checklist

• I can explain what changes between pinned and fixed bases
• I checked a column-top moment against P·H/2
• My frame runs in Karamba with a bending moment diagram on screen
• I put vertical and lateral load into separate load cases

23Sections, utilisation and Japanese practice

By the end you can give different sections to different member groups, and you know what Karamba's utilisation number does and does not mean in Japan.

Idea

Members get a section through their name. Feed a text such as top, bottom or diag into the Id input of Line to Beam. Then wire a cross section into Assemble Model and tell it which Id it belongs to. This is why you kept the member sets in separate groups and trees.

Karamba reports utilisation, the ratio of stress to strength. Two things to know before you trust it. BeamView's utilisation uses normal stress only, without shear or buckling. The Utilization of Elements component does consider buckling, but follows Eurocode 3. Neither is the Japanese check.

So treat Karamba's utilisation as a quick way to compare options, and compute the 検定比 yourself. It is two components: divide N by the area, or M by the section modulus (断面係数), then divide by f. The allowable stress for compression and for bending is lower than F / 1.5 when buckling governs, and that part stays a hand or office-tool check.

Example: JIS H-sections used on this page

Where Grasshopper sits in an office

Grasshopper and Karamba are used most in the early stages: generating geometry for a complex roof, comparing ten structural options in an afternoon, finding where the forces go. The calculation submitted for building confirmation (確認申請) is normally produced in the office's own analysis software. Your definition's job is to get a good scheme to that point quickly, and to hand over clean centre lines.

In Rhino

1. Give your truss members the Ids top, bottom, vert and diag.
2. Assign a heavier section to the chords than to the web members through Assemble Model.
3. From Beam Forces, compute your own 検定比 for the tension members with Division components and show the largest one in a panel.

Checklist

• I assigned sections to member groups by Id
• I can explain why Karamba's utilisation is not the Japanese 検定比
• I computed a 検定比 for a tension member inside my definition

24Column buckling

By the end you can work out a column's allowable compressive stress fc from its slenderness, and find the lightest section that carries a load.

Idea

A slender member in compression fails by buckling (座屈) sideways long before the steel yields. How slender it is depends on two things:

• The buckling length lk (座屈長さ) = K × L, where K depends on how the ends are held. In theory K is 0.5 with both ends fixed, 0.7 with one fixed and one pinned, 1.0 with both pinned, and 2.0 for a cantilever.
• The radius of gyration i (断面二次半径) of the section. An H-section has a large ix and a small iy, so unless it is braced it buckles about its weak axis.

The slenderness ratio (細長比) is λ = lk / i. Japanese practice for steel with F = 235 N/mm² then gives the long-term allowable compressive stress fc:

Example

An H-250×250×9×14 column, 4 m tall, pinned at both ends, carries N = 600 kN long-term. iy = 6.32 cm and A = 91.43 cm².

1. λ = 400 / 6.32 = 63.3, below Λ.
2. λ/Λ = 0.528, so ν = 1.5 + 0.667 × 0.279 = 1.686.
3. fc = (1 − 0.4 × 0.279) × 235 / 1.686 = 123.8 N/mm².
4. σc = 600,000 / 9,143 = 65.6 N/mm², so the 検定比 is 65.6 / 123.8 = 0.53.

Try it here

In Rhino

1. Keep a small section table in a panel or a CSV file read with Read File: name, A, ix, iy, Zx. Pick a row with List Item and split it into numbers with Text Split (Sets, Text).
2. Buckling length: Multiplication of L and K. Slenderness: Division by iy (and by ix), then Maximum (Maths, Util) of the two.
3. Two Expressions, one for each fc formula, with inputs λ, Λ and F.
4. Larger Than compares λ with Λ. Pick'n'Choose (Sets, List) uses that result to pick the right formula: 0 picks the first stream, 1 the second.
5. σc = N / A, then the ratio σc / fc. Show it in a panel, and colour the column with Custom Preview when it is over 1.

Checklist

• I can work out fc by hand for a given λ
• My definition picks the right fc formula automatically
• I can explain why the weak axis usually governs

25Bending plus axial force

By the end you can check a column that carries both axial force and bending, and say what the check assumes.

Idea

A frame column carries axial force from the floors above and bending from the frame action. The two stresses add up, so the check adds the two ratios (組合せ応力):

fb, the allowable bending stress, equals ft = F / 1.5 only when the compression flange cannot buckle sideways. An unbraced H-section can twist and buckle sideways under bending (横座屈), and the code then gives a smaller fb. Square hollow sections (角形鋼管) do not suffer this, and they are equally stiff in both directions. That is one reason Japanese moment-frame columns are usually square tubes.

Try it here

In Rhino

1. Take the column forces from Karamba's Beam Forces: N and the moment M about the strong axis, at both ends of each element.
2. σc = N / A and σb = M / Z with Division. Watch the units: kN and cm² give kN/cm²; multiply by 10 for N/mm².
3. Reuse your fc from the last session. fb = 156 for a braced member.
4. Add the two ratios and take the largest along the member with Sort List or Bounds.

Checklist

• I can check a beam-column by hand
• I can say when fb = F / 1.5 is allowed and when it is not
• My definition computes the combined ratio from Karamba's forces

26Load combinations and the check report

By the end your definition checks long-term and short-term combinations, drift and deflection, and writes a one-panel report.

Idea

Allowable stress design checks combinations of loads (荷重の組合せ), each against its own allowable stress:

K appears with both signs because an earthquake can come from either side. Snow rules differ in heavy-snow areas (多雪区域), so check the rules for your site. On top of the stress checks come the stiffness checks: storey drift angle under K, normally 1/200 or less, and beam deflection under long-term load, where many offices aim for span / 300.

A linear analysis can be added up. Put G in load case 0 and K in load case 1, and the result of G + K is the sum of the two cases. You do not need to run the analysis again for each combination.

Try it here

In Rhino

1. Give the vertical loads LCase 0 and the lateral loads LCase 1.
2. Beam Forces once with LCase 0 and once with LCase 1. Combine them with Addition and Subtraction: G + K and G − K.
3. Ratios for each combination. Divide the short-term ones by 1.5, or multiply the allowables.
4. Drift: Nodal Displacements for LCase 1 at beam level, divided by the storey height.
5. Report: Format (Sets, Text) builds a line such as Left column 0.71 0.93 OK. Merge the lines into one panel.

Checklist

• My definition checks G, G + K and G − K with the right allowables
• It checks drift and beam deflection too
• All the results appear in one readable panel

27Galapagos: the lightest roof truss

By the end you can set up Galapagos with a genome, a fitness and a penalty, and judge whether its answer is any good.

Idea

Galapagos (Params, Util) is an evolutionary solver. You give it two things:

• A genome: the sliders it is allowed to move. Here they are the depth, the number of panels, and a 0, 1, 2 slider for the truss type.
• A fitness: one number to make as small or as large as possible. Here it is the steel weight of one truss, in kilograms.

It tries a population of random designs, keeps the fittest, breeds new designs by mixing and mutating their sliders, and repeats for many generations. It cannot read your checks, so you build them into the fitness: if a design breaks the deflection limit, add a large penalty to its weight so it can never win.

Galapagos does not promise the best possible answer. When the search space is small, as here with 435 combinations, you can check its answer by trying them all (brute force).

Example

1. The truss from Session 9 with sliders for depth H (1.2 to 4.0 m), panels n (4 to 12, step 2) and type (0 to 2).
2. Sizing: for each member group, the lightest steel pipe (鋼管, STK400) from a list that passes its check. Tension: σ ≤ 156 N/mm². Compression: σ ≤ fc from Session 24, with the member length as buckling length. Every member: λ ≤ 250.
3. Fitness: total weight, plus 10 × weight × the amount by which the deflection exceeds span / 300.

Try it here

In Rhino

1. Place Galapagos. Drag from its Genome input to each slider you want it to move. Galapagos only accepts sliders and gene pools as genes.
2. Wire one number into Fitness: your weight plus penalty.
3. Double-click Galapagos to open its editor. On the Options tab, set Fitness to Minimize.
4. On the Solvers tab, press Start Solver. When it stops, pick the best design in the list and press Reinstate to set the sliders to it.
5. Sizing inside Grasshopper is easiest if the section of each group is also a gene: a slider that picks a row from your section table. Add a penalty when any 検定比 is over 1. With a full Karamba licence, Optimize Cross Section can do the sizing instead, but it checks to Eurocode, not the Japanese rules.

Checklist

• I set up Galapagos with a genome, a fitness and a penalty
• I compared its answer with a brute-force or second run
• I can explain what a flat optimum means for the decision

28Trade-offs and the Pareto front

By the end you can show a client the trade-off between two goals and explain which designs are worth discussing.

Idea

Real decisions have more than one goal. A deeper truss is lighter, but it costs ceiling height and cladding. A stiffer truss is heavier. A design is Pareto optimal when no other design is better on both goals at once. Those designs form the Pareto front; every design off the front can be beaten on both goals.

The engineer's job is to show the front and say where the good choices are. The client or architect then picks a point on it. Galapagos searches for one number only. Plug-ins such as Wallacei and Octopus search for several at once, but they run on Windows, so try them on a lab or office PC.

Try it here

In Rhino

1. Data Recorder (Params, Util) records every value that passes through it. Record weight and depth while Galapagos runs, or while you step a slider.
2. Plot the results in Rhino: Construct Point with x = weight / 1000 and y = depth. Scale the axes so the cloud is readable.
3. Mark the front: sort by weight, then keep each point whose depth is lower than every lighter point's. A short GhPython script does this neatly; by eye on the plot is fine to start.

Checklist

• I can explain what a Pareto front is with an example
• I can say what a depth limit costs in steel
• I plotted a trade-off chart from recorded designs

29From a hanging chain to an arch

By the end you can form-find an arch with Kangaroo and show, with Karamba, why it carries its load almost without bending.

Idea

Robert Hooke published the idea as a Latin anagram in 1676: as hangs the flexible line, so but inverted will stand the rigid arch. A chain can only pull, so the shape it hangs in is the line of its forces. Flip it, and every link pushes instead of pulls, still along the line. Gaudí designed the church at Colònia Güell this way, with weighted strings.

• Under its own weight, spread evenly along its length, a chain hangs as a catenary.
• Under a load spread evenly along the horizontal, like a deck hung from it, it hangs as a parabola. That is why the parabolic arch in Session 13 suits a bridge.

Kangaroo works with goals. Length (Line) holds a link at a length, Anchor holds a point still, Load pushes a point. The Solver moves all the points until every goal is balanced as well as it can be.

Try it here

In Rhino

1. A 20 m line, divided into links: Divide Curve, then Polyline and Explode, gives the link lines.
2. On the Kangaroo2 tab, Length (Line) with the links and a length of 1.12 × the link length, so the chain is 12% longer than the span.
3. End Points of the original line into two Anchor goals.
4. Load on every point with the vector (0, 0, −1).
5. Entwine or Merge all the goals into the Solver's GoalObjects input. Its output points form the hanging chain.
6. Flip: Scale NU (Transform, Affine) with a Z factor of −1. Then Line to Beam in Karamba, pinned supports at both ends, and the same loads pointing down.

Checklist

• I form-found a hanging chain with Length, Anchor and Load goals
• I flipped it and showed in Karamba that its bending is close to zero
• I can explain the difference between a catenary and a parabola

30From a hanging net to a gridshell

By the end you can form-find a gridshell roof, check it in Karamba, and say how its supports change its shape.

Idea

The same idea works in 3D. Hang a net from its corners or edges and it takes a shape in pure tension; flip it and you have a gridshell (グリッドシェル) in compression. The Mannheim Multihalle, a timber gridshell by Carlfried Mutschler and Frei Otto with Ove Arup & Partners as engineers, completed in 1975, took its form from a hanging model.

Which points you anchor changes everything. A net held at its corners sags along its free edges; held on all four edges it forms a dome. Link lengths matter too: equal-length laths are easy to build, so a good gridshell keeps its member lengths close to each other.

Try it here

In Rhino

1. A flat grid: Mesh Plane (Mesh, Primitive), 20 by 20 m with 10 by 10 faces.
2. Mesh Edges (Mesh, Analysis) gives the links. Length (Line) with 1.1 × their length.
3. Anchors: the end points of the boundary edges, which Mesh Edges returns from its first output, or the four corner vertices only.
4. Load on every vertex with (0, 0, −1). Solver, then Scale NU with Z = −1 to flip.
5. In Karamba: Line to Beam on the flipped edges, pinned supports at the anchored points, and the same loads pointing down. Check that the members are in compression.

Checklist

• I form-found a gridshell from a flat mesh
• I checked in Karamba that its members are in compression
• I can explain how the anchors change the shape

31Truss roof: the geometry

By the end you have a truss roof over a hall, controlled by five sliders and organised so that someone else can read it.

The brief

A hall 24 m wide and 36 m long, the size of a school gymnasium (体育館). Steel trusses span the 24 m and stand 6 m apart. Start with a depth of span / 10 and 6 panels.

In Rhino

1. One truss: reuse Session 9. Keep top chord, bottom chord, verticals and diagonals as four separate outputs.
2. Make it a Pratt truss, with the diagonals running down towards midspan in both halves.
3. The row: reuse Session 14. Graft the vectors, one branch per truss.
4. Purlins and a bottom chord tie between trusses: Flip Matrix, as in Session 14.
5. Lay the canvas out in named groups from left to right: Inputs, One truss, Roof, Analysis, Results.
6. Bake one version to layers named by member type.

Checklist

• My roof follows all five sliders without breaking
• Each member type is a separate output, and each truss its own branch
• Every group on my canvas has a name

32Truss roof: analyse, check and present

By the end you have analysed one roof truss, checked it three ways, and written down what you found.

Idea

A roof load is an area load q in kN/m². One inner truss collects a strip as wide as the truss spacing, so its line load is w = q × s, and each top node takes P = w L / n. Analyse one truss in its plane before you try the whole roof. It is quicker to check and tells you nearly everything.

Try it here

In Rhino

1. Add Karamba to the truss as in Session 21. Compute P from q, s, L and n with Multiplication and Division, so the load follows the sliders.
2. Check 1, statics: the chord force against M / H.
3. Check 2, stress: your own 検定比 for the most loaded tension member.
4. Check 3, stiffness: midspan deflection against your limit. A common office target for steel roof members is span / 300. Confirm the one your project uses.
5. Move the depth slider from 1.6 m to 3.2 m in steps and note the chord force and deflection each time. Which depth would you propose, and why?
6. Write half a page: the brief, a screenshot of the definition, a screenshot of the result, the three checks, your proposed depth.

Take it further

• Add the buckling check from Session 24 to the compression members, and let Galapagos from Session 27 choose the depth.
• Fill the comparison table below with three depths you tried, to practise for the projects that follow.

Checklist

• I can turn an area load into node loads on a truss
• My roof truss passes the statics, stress and stiffness checks, or I know why not
• I compared at least four truss depths and chose one
• I wrote the half-page summary

33Footbridge: three options

By the end you have one definition that draws three structural options for a park footbridge, switchable with one value list.

Steps

1. Start from your truss definition (Session 9) and your tied arch (Session 13 challenge). Put each in a named group.
2. One Value List (Params, Input) with Pratt, Warren and Tied arch. Stream Filter picks which option's lines go on to the analysis.
3. Deck: the bottom chord or tie carries cross beams every panel; the load on one main structure is 5 × 3 / 2 = 7.5 kN/m.
4. Give every option the same inputs: span, depth or rise, and number of panels or hangers.

Try it here

Checklist

• One value list switches between the three options
• Every option shares the same span and load inputs
• No part stands more than 2.5 m above the deck

34Footbridge: analyse and compare

By the end you have analysed all three options and written a one-page recommendation backed by numbers.

Steps

1. Karamba for each option: pinned at one end, roller at the other, out-of-plane restraints as in Session 21, the 7.5 kN/m load at the nodes.
2. Check members with your report from Session 26: tension, buckling for compression, and the deflection limit.
3. Record steel weight, deflection, the largest 検定比, depth or rise, and the number of different member sizes for each option.
4. Fill in the comparison table. Set the weights to what this client cares about, and be ready to defend them.
5. Write half a page: the brief in one line, a picture of each option, the table, your recommendation, and one risk to check next.

Comparison table

Checklist

• All three options run in Karamba and pass, or I know why one cannot
• The comparison table is filled in from my own results
• I wrote the half-page recommendation

35Atrium gridshell: form and panels

By the end you have three roof forms for a glazed courtyard, each with its panel flatness measured.

Steps

1. Build all three forms over the same 20 m square with the same 10 by 10 grid and the same rise.
2. Measure every panel's warp with Plane Fit, and count the panels over 5 mm.
3. For option A, use Galapagos from the Session 30 challenge to hit the rise exactly.

Checklist

• Three forms over the same plan, grid and rise
• Panel warp measured and counted for each

36Atrium gridshell: analyse and compare

By the end you have analysed the three forms and can explain why the form-found one works hardest for its weight.

Steps

1. Karamba for each form: the grid as beams with one pipe size, pinned along all four edges, 1.5 kN/m² turned into node loads (load × the plan area around each node).
2. Read the largest deflection, the largest 検定比 and how many members go into tension.
3. Size the pipe so the worst member passes, and record the steel weight.
4. Fill in the table and write your recommendation, including what the glass supplier needs to hear.

Comparison table

Checklist

• All three forms analysed with the same section and load
• The table is filled in and I wrote the recommendation

37Diagrid tower: form and facade

By the end you have a parametric tower with three twist options, a diagrid and an attractor facade on one side.

Steps

1. Tower and diagrid from Session 18, with the twist on a Value List of 0, 45 and 90.
2. Facade panels between the diagrid nodes on the south face, openings from the attractor in Session 17, rationalised to 6 types.
3. Count the different diagrid member lengths for each option, rounded to 10 mm. Fewer lengths mean simpler fabrication.

Checklist

• One value list switches the three twist options
• The south facade follows the attractor with at most 6 panel types

38Diagrid tower: analyse and compare

By the end you know how the twist changes the tower's lateral stiffness and its steel, with numbers for each option.

Steps

1. Karamba: the diagrid members as beams with one pipe size, fixed at the base, floor plates as rigid rings (stiff beams around each node level).
2. Lateral load: a horizontal point load at every node level. Use 100 kN per level as a placeholder for this exercise.
3. Read the top sway and the storey drift angles; compare with 1/200.
4. Record steel weight, top sway, member lengths and facade panel types for each option, then fill in the table.

Comparison table

Checklist

• All three options analysed under the same lateral load
• The table is filled in and I can explain the effect of the twist

39A one-page portfolio sheet

By the end you have one A3 sheet that shows how you think, ready for an Arup or KKE application or interview.

Idea

An interviewer looks at a portfolio page for less than a minute. The page should show a question, a method, options, a comparison and a decision, in that order. Pick your strongest project, usually the footbridge or the gridshell.

Steps

1. Clean the definition: inputs on the left, results on the right, every group named, no loose wires. Add a short Scribble (Params, Util) title to each group.
2. Capture the canvas with File, Export Quick Image, and the Rhino views with ViewCaptureToFile, all at the same size.
3. Lay out the sheet in the order above. Keep text short: a reviewer reads the headings and the numbers.
4. Practise saying the page out loud in two minutes, in English and in Japanese.

Checklist

• My definition is clean enough to screenshot
• The A3 sheet follows the five-part layout
• I can present it in two minutes in English and in Japanese