In the Beams and frames pathway, we started with a simply supported beam: a 6 m UB 305 x 165 x 40 spanning between a pin and a roller, subject to a uniformly distributed load of 20 kN/m. We built it in the 2D canvas, solved it and checked the midspan moment, the reactions and the deflection against three formulas you already knew.
In this step, we'll look at exactly the same beam, built in the 3D canvas. We're deliberately starting with a structure you've already analysed, so that we can focus on the new environment rather than the engineering: how to move around in it, how to select things, and what a support and a load look like when every node has six degrees of freedom instead of three. Then we'll press Solve and confirm the same numbers as the 2D analysis.
The model for this step (The 6 m beam on a UB 305 x 165 x 40 under 20 kN/m, built in the 3D canvas and solved) isn't available yet.
1.0 The 3D canvas
The 3D canvas shows the model through a camera you can move, rather than flat on the page. The model sits in a space with three global axes, X, Y and Z. In the 3D canvas, the Z-axis is vertical (gravity direction). Gravity acts in the negative Z direction and the X-Y plane is the ground plane. Note that this is different to the 2D canvas, where Y is vertical. A load typed in the Y direction here acts sideways, not vertically.
1.1 Moving around
Drag in the viewport to orbit the camera around the model, right-drag to pan and scroll to zoom. You can find a minimal set of navigation instructions in the hint text below the viewport menu bar.
The viewport menu bar at the top of the 3D viewport contains a lot of helpful tools relating to how you view your model. If you lose the structure, the fit button (or F on the keyboard) centres it in the viewport again.
In the top-right corner of the viewport is the view cube, a small cube whose faces are labelled FRONT, BACK, LEFT, RIGHT, TOP and BOTTOM. Click a face and the camera snaps square-on to it. FRONT gives you the elevation you had in the 2D canvas, looking along Y with X to the right and Z up, and TOP gives you the plan. Click an edge or a corner of the cube for a three-quarter view.
The numpad does the same job. Keys 1, 3 and 7 give the front, side and top views, and 5 switches between a perspective and an orthographic camera.
1.2 The ground grid and snapping
The viewport menu also contains a grid checkbox which draws a lattice on the ground plane at a spacing you specify beside it. With the snap checkbox ticked, a coordinate you type into the Nodes table is rounded to that spacing, or to the fraction of it you pick, so nodes land on the lattice grid exactly. If a node is typed at 5.998 m instead of 6 m, the member won't quite meet its neighbour, and in a large model that kind of mistake can take a long time to track down. The best way to get familiar with the viewport menu is simply to click through the options and watch how the viewport responds.
1.3 Node mode and member mode
You will also find a vertical row of buttons along the left edge of the viewport. We'll highlight a few of them here, but again, it's best to open a library model and click around to really understand what each option does.
The 3D canvas can draw each member as its real cross-section, which is activated by the solid view button. Alternatively, you can draw each member as a line by clicking the wireframe button.
Probably the two most important buttons on this vertical strip are the node select and member select buttons. The nodes aren't drawn in solid view, so a click at a joint could mean either the node or the member. That's what the two selection modes are for. In member mode (the default), a click always picks the member under the pointer. Press 1 to switch to node mode, and a click at a joint picks the node, which shows as an orange dot through the member. Press 2 to go back to member select mode. Switch to wireframe view and the nodes are drawn as dots, so you can click a dot for the node or a line for the member in either mode.
1.4 The Build tab
The left panel beside the viewport has the same two tabs we saw when modelling in 2D, Build and Results. The toolbar runs through the same entities too: Select, then Member and Support, which draw on the canvas, and Nodes and Loads, which open tables. In the read-only view, all four buttons read Nodes, Members, Supports and Loads, and open tables, exactly as in 2D. The tables themselves have more columns, because of the additional degrees of freedom in 3D. A node now has three coordinates and a support has six tick-boxes, while a load has a direction (x, y or z) and a choice of axes. We'll meet each of these in the model below.
2.0 The model
The beam has a node at each end, n1 at the origin and n2 6 m along the X axis. The member between them, e1, is a frame member with a UB 305 x 165 x 40 from the catalogue and S355 steel from the materials table. In the 2D canvas, the catalogue needed to supply the section's area, 51.3 cm², and one second moment of area, 8,500 cm⁴. A 3D frame member can bend in two planes and twist, so the catalogue now supplies four properties: the area, the second moment of area about each axis, 8,500 cm⁴ and 764 cm⁴, and the torsion constant, 14.7 cm⁴. The steel's modulus is 210 GPa, as before, and the materials table also holds a Poisson's ratio, from which the shear modulus is derived.
Now, let's look at the supports, which is the first place where modelling in 3D differs from 2D. A node in a 3D frame has six degrees of freedom: three translations, ux, uy and uz, and three rotations, rx, ry and rz. The Supports table shows them as six tick-boxes, ux, uy, uz, rx, ry and rz. As with 2D, ticking one box restrains the corresponding degree of freedom. Two presets fill the boxes in for you: Pinned ticks the three translations, and Fixed ticks all six.
If you pressed Pinned at one end and ticked only uz at the other, you'd have the 2D pin and roller, but in three dimensions that isn't sufficient to restrain the beam. Think about what's holding the beam. Nothing stops it rotating about its own longitudinal axis: the beam could spin about the line between its two supports without any part of it straining, and there's no stiffness in the structure to resist that movement. A structure that can move without straining is a mechanism, and the stiffness method can't find a unique position for it.
So, as well as the translations, the pin end holds rx, the rotation about the beam's longitudinal axis. The roller end holds rx too, and uy as well as uz, because in three dimensions a roller must also restrain the out-of-plane degree of freedom. This leaves ux free, which allows the beam to move freely in the x-direction at that end. In other words, the left support ticks ux, uy, uz and rx, and the right support ticks uy, uz and rx. The two bending rotations, ry and rz, stay free at both ends, which is what makes the beam simply supported.
Finally, the Loads table's distributed load row has a column for the axes, global or local, and a column for the direction, x, y or z. Our 20 kN/m is in the global axes, in the z direction, with a negative magnitude so that it acts downwards, applied along the whole of e1 in a load case called Uniform load. There's a query position at 3 m, the midspan, so that the deflection there is a solver result in its own right. With that, the model is built and ready to be solved.
Things to try
Press Load the model. The beam is drawn as its real cross-section, with the load, the reactions and the deflected shape shown. The label reads δmax 18.91 mm @ 3 m (e1). Drag to orbit, right-drag to pan and scroll to zoom. Click FRONT on the view cube and you're looking at the elevation the 2D canvas gave you. Click RIGHT, or orbit until you're looking along the beam, and you'll see the I-shape of the section end-on, with its web vertical.
Switch on the Bending moment layer. This shows a parabola drawn on the tension side of the beam, labelled 90.0 kNm at its peak. Notice the two small chips beside the layer, Mz and My. Mz is active because the beam bends in one plane only. Switch on Shear force and you'll see a straight line from 60.0 kN at one support, through zero at midspan, to 60.0 kN at the far support. Again, only one of the two chips, Vy, is active.
Press 1 and click the joint at the left end. An orange dot appears, and the node n1 is selected. Press 2 and click the beam to select the member instead. Now, with Reactions on, hover over a support. The tooltip shows its reaction, 60.0 kN in Rz, acting upwards. Scroll down to the Reactions table and look at its six columns, Rx, Ry, Rz, Mx, My and Mz. At each support, Rz reads 60.00 kN and the other five read zero. The pin can resist a force along the beam and both supports can resist a twisting moment, but these reactions are not developed because we've only loaded the beam with a UDL in the z-direction.
Hover the beam at midspan (with Select activated from the main menu). The probe card mirrors the layers you have on, so with the bending moment, shear force and deformed shape shown it reads the moment there, 90.0 kNm, the shear, zero at midspan, and the deflection, 18.91 mm. The Displacements table has six columns, and shows that n1's ry is 10.084 mrad while n2's is -10.084. These are the end rotations, about the global Y-axis that the beam bends about. The Query stations table has a row e1 @ 3 m with the same moment and the same deflection.
If you're a member, press Copy to my projects: your copy opens in the editor. In the Nodes table, set n2's x to 8 and press Solve. The moment rises to 160.0 kNm (wL2/8), with the new span, and the deflection increases to 59.76 mm (remember, it grows with the fourth power of the span). This is exactly what the 2D canvas gave for the same edit.
Set n2's x back to 6. In the Loads table, change the distributed load's direction from z to y and solve again. The load now acts sideways, so the beam bends about its weak axis. The My chip lights instead of Mz, the peak moment is still 90.0 kNm, and the reactions have moved from the Rz column to Ry, 60.0 kN at each end. But the deflection, read under uy in the Displacements table, is 210.36 mm: eleven times the 18.91 mm. It has increased by the ratio of the two second moments of area the catalogue gave us, 8,500 cm⁴ to 764 cm⁴.
3.0 What you'll see
The simply supported beam, in 3D
The solver
By hand
Reaction at each support, Rz
60.0 kN
wL/2=20×6/2=60 kN
Moment at midspan, Mz
90.0 kNm
wL2/8=20×36/8=90 kNm
Shear at the supports, Vy
60.0 kN
wL/2
Deflection at midspan, δz
18.91 mm
5wL4/384EI=18.9 mm
Rotation at the supports, ry
10.084 mrad
wL3/24EI=10.08 mrad
Every other reaction component
0
nothing to resist
Every number in the table matches what the 2D canvas gave for this beam. The 2D Reactions table had three columns and the 3D one has six, and five of them read zero, as they should. There's no load along the beam, no load acting sideways and no torque, so the supports have nothing to resist in those directions. Reading the zeros is as much a part of checking a 3D model as confirming the non-zero values. A reaction that should be zero and isn't is usually the first sign of a load typed in the wrong direction.
Hand check: the three formulas again
The reactions. The beam and its load are symmetrical, so each support takes half of the total load,
R=2wL=220×6=60kN
which is the 60.0 kN in the Rz column at each node. The shear at each support is the reaction, 60 kN, falling to zero at midspan.
The moment. Cut the beam at midspan and look at the left half. The reaction pushes up 3 m from the cut, and the 60 kN of load on that half acts down at 1.5 m from it, so the moment at the cut is,
M=60×3−60×1.5=180−90=90kNm
which is wL2/8=20×36/8=90 kNm, the peak of the Mz diagram.
The deflection. With w=20 kN/m, L=6 m, E=210 GPa and I cm m, the deflection at midspan is,
δ=384EI5wL
or 18.91 mm, the δz the probe reads at midspan. Notice that the I we used is the 8,500 cm⁴ about the strong axis, because the load is in the plane of the web. The end rotation follows from the same curvature, θ=wL rad, the 10.084 mrad in the Displacements table.
Why the two solvers agree. The 2D and 3D solvers give the same numbers because it's the same beam in each. The additional degrees of freedom in the 3D case were never activated because the loading never induced any deformation outside the plane that was fully captured in the 2D analysis.
4.0 What the model assumes
Linear, elastic, first order, and restrained against twisting
The solution is linear, elastic and first order, exactly as it was in the 2D canvas: double the load and every number describing the response of the beam doubles, the material (steel in this case) never yields, and the load acts on the undeflected beam.
What's new is the tick in the rx box, which stops the beam rotating about its own axis. In reality, a simple bolted connection will usually provide this restraint. That said, by ticking the box we're assuming full restraint in our model. So, as with any modelling assumption, make sure the real-world details justify the model's restraints before you trust the results!
5.0 What to take from this step
All of the concepts that you're familiar with from the 2D canvas, and much of the interface, carry over to the 3D canvas. In this step we've proven that we can model the same structure in both. What's new is the ability to extend your model into a third dimension. With that comes a range of additional navigation features. You can orbit, pan and zoom, snap the camera to different views and switch between orthographic and perspective projections. We've really only mentioned a handful of the 3D environment's tools and options. This is a starting point, but as always, the best way to get comfortable in the 3D canvas is to spend some time working in it.
The other big change is the inclusion of additional degrees of freedom to capture behaviour in the third dimension. We solved a simply supported beam and read the same 60 kN, 90 kNm and 18.91 mm that the 2D canvas gave, again confirmed with some simple calculations. We also confirmed the zeros, since five of the six reaction components at each support are zero. So, when you move a model into 3D, the formulas you know still apply. You simply have more degrees of freedom to consider.
Here's one important rule of thumb that's worth following: if your analysis can be completed in 2D, stick with 2D. Only move a model to 3D if you must! Generally, taking a model into 3D significantly increases the scope for modelling errors.
Next, we'll put the same beam beside a copy of itself rolled through 90 degrees, and see what the local axes and the roll angle do to the deflection.