Fixity, releases and hinges

So far, our model's supports have been a pin and a roller, which restrain the node's position (or translation more precisely) but don't provide any rotational restraint. In this step, we'll add the third common support model, the fixed support, which restrains all translation and rotation. We'll also see what happens inside a member when a rotational release is introduced through a hinge.

This time our modelling canvas has three independent models, one above the other:

a cantilever,
a propped cantilever,
a beam fixed at both ends with a hinge in the middle.

All are subject to a 20 kN/m uniformly distributed load (UDL).

The model for this step: A cantilever, a propped cantilever and a hinged beam, each under 20 kN/m — A cantilever, a propped cantilever and a hinged beam, each under 20 kN/m. Orbit, read the results and hover the members; nothing you do here changes the model.

1.0 The idea

A support model restrains some or all of a node's three degrees of freedom: translations $u_x$ , and rotation . For each restricted degree of freedom, we obtain a support reaction. A pin restrains and ; a roller restrains , and a fixed support restrains all three, so it reports a moment reaction as well as two orthogonal force reactions. In the Supports table, the degrees of freedom that can be restrained for each node are represented by check boxes: , and .

	The solver	By hand
Cantilever: moment at the wall	-160.0 kN·m	$wL^2/2 = 20 \times 16 / 2 = 160$ kN m
Cantilever: tip deflection	-35.85 mm	$wL^4/8EI = 35.9$ mm
Propped cantilever: prop reaction	45.0 kN	$3wL/8 = 45$ kN
Propped cantilever: moment at the wall	-90.0 kN·m	$wL^2/8 = 90$ kN m
Propped cantilever: sagging peak	50.6 kN·m at 2.25 m from the prop	$9wL^2/128 = 50.6$ kN m at $3L/8$
Hinged beam: moment at each wall	-360.0 kN·m	$w(L/2)^2/2 = 20 \times 36 / 2 = 360$ kN m
Hinged beam: sag at the hinge	-181.51 mm	$w(L/2)^4/8EI = 181.5$ mm

Fixity, releases and hinges

1.0 The idea

2.0 The models

3.0 What you'll see

4.0 What a release isn't

5.0 What to take from this step