Releases, hinges and supports

So far in this pathway, every joint between members has been rigid, which is the default, and every support has been set up for us. In this step, we'll set both ourselves. We'll look at how a member end is released in 3D, where a release is made about one bending axis at a time, and at the hinge that releases every frame member arriving at a node. We'll also open the Supports table and see that in three dimensions a support has six tick-boxes and six spring boxes.

Our model is a small grillage. A primary beam spans 6 m between its supports, and a 4 m secondary beam frames into its midspan and carries a floor load. The secondary's end at the primary is released about both bending axes, which is how we model a simple beam-to-beam connection. The secondary's end reaction is applied to the primary only as a point load, so we can check the whole model by hand using statics alone. Then we'll make the connection rigid and see what changes.

The model for this step (A 6 m SHS 200 x 200 x 8 primary on pins, with a 4 m UB 305 x 165 x 40 secondary framing into its midspan under 15 kN/m) isn't available yet.

1.0 The idea

In the 2D canvas, a release at a member end is a single tick-box, which frees the one rotation a planar member has. A member in 3D bends in two planes, so a release in the 3D canvas is made per end and per axis. In the Members table, the releases column has four tick-boxes for each frame member. These are My and Mz at the start (node i), and My and Mz at the end (node j). Remember from step 2 that with the web vertical, local z is the strong axis, so a gravity load bends a beam about z and produces Mz, while a sideways load bends it about y and produces My. Releasing Mz at an end frees the rotation that a gravity load produces, and releasing My frees the rotation that a sideways load produces. Tick both, and the end carries no bending moment at all. This is how we model a simple connection, such as a fin plate or a pair of cleats that transmits shear but no moment worth counting.

A belongs to a node rather than a member end. Tick on a node in the Nodes table and every frame member arriving there is released about both bending axes at that end. It's the quickest way to model a joint where every member meeting there is pin-connected. The difference matters where some of the members through a node should stay continuous. In our grillage, the primary runs the node the secondary frames into, and we want the primary to stay continuous while only the secondary is released. So the release goes on the secondary's end, and the node is left alone.

	The solver	By hand
Secondary's far-end reaction, s2	30.0 kN	$wL/2 = 15 \times 4 / 2 = 30$ kN
Secondary's peak moment, at its midpoint	30.0 kNm	$wL^2/8 = 15 \times 16 / 8 = 30$ kNm
Secondary's end moment at the primary	0	a released end
Reaction at each end of the primary	15.0 kN	$P/2 = 30 / 2 = 15$ kN
Primary's midspan moment	45.0 kNm	$PL/4 = 30 \times 6 / 4 = 45$ kNm
Torque in the primary	0	nothing to twist against
Drop of the node where the beams meet	-17.33 mm	$PL^3/48EI = 17.3$ mm

Connection and primary	Hogging at the secondary's end	Torque in each half of the primary	Primary's midspan moment	Secondary's peak	Reactions at p1, p2, s2
Released, SHS (the model)	0	0	45.00 kNm	30.00 kNm at 2 m	15.0 kN, 15.0 kN, 30.0 kN
Rigid, SHS	4.84 kNm	2.42 kNm	43.19 kNm	32.47 kNm at 1.92 m	14.4 kN, 14.4 kN, 31.2 kN
Rigid, UB 356 x 171 x 51

Releases, hinges and supports

1.0 The idea

2.0 The model

3.0 What you'll see

4.0 What a release isn't

5.0 What to take from this step