A simply supported beam

Let's start with a simply supported beam: the steel beam spans 6 m between a pin and a roller and is subject to a uniformly distributed load along its full length. The cross-section is a catalogue UB 305 x 165 x 40. In this step, we'll see how the beam is built in the editor - two nodes, one member, a section, two supports and a load. Then we'll take a look at the results our Solve returns, compared against three formulas.

The model for this step: A 6 m beam on a UB 305 x 165 x 40 under 20 kN/m — A 6 m beam on a UB 305 x 165 x 40 under 20 kN/m. Orbit, read the results and hover the members; nothing you do here changes the model.

1.0 The idea

A simple structural model only has a few entities. Nodes are points with coordinates. Members run between nodes, carry a section (the shape, with its area and second moment of area) and a material, e.g. steel (with its modulus of elasticity and various other properties). Supports restrain nodes by restricting translations and/or rotations. Actions or loads push, twist or rotate members or nodes, essentially placing a demand on the structure. The modelling editor's main toolbar runs through these fundamental components of a structural model: Select, then Node, Member, Support and Load. In the read-only view, the same buttons read Nodes, Members, Supports and Loads, and open tables.

A solve takes those building blocks, builds the stiffness matrix for the structure, and finds the displacements that balance the loads.

Dive deeper into exactly how this is done:

	The solver	By hand
Reaction at each support	60.0 kN	$wL/2 = 20 \times 6 / 2 = 60$ kN
Moment at midspan	90.0 kN·m	$wL^2/8 = 20 \times 36 / 8 = 90$ kN m
Shear at the supports	60.0 kN	$wL/2$
Sag at midspan	18.91 mm	$5wL^4/384EI = 18.9$ mm
Rotation at the supports	10.084 mrad	$wL^3/24EI = 10.08$ mrad

A simply supported beam

1.0 The idea

2.0 The model

3.0 Reading the results

4.0 What you'll see

5.0 Baked-in assumptions

6.0 What to take from this step