Beam example, Solid, Shell or Beam?

← Back to tutorial overview

We model the same I-beam as a solid, a beam and a shell, and look at the main differences between the three modelling approaches.

🔩 The beam

	Value
Length	$L = 200$ along $x$
Clamp / tip	$x = 0$ / $x = 200$
Tip force	$F = 30$ N in $-y$
PMMA	$E = 2000$, $\nu = 0.4$
Abaqus I profile
$l,\ h$	10, 20
$b_1,\ b_2$	12, 12
$t_1,\ t_2,\ t_3$	1.5, 1.5, 1
$n_1$	$(0, 0, -1)$
Shell model
Flanges	$y = \pm 8.5$, $t = 1.5$, offset outward
Web	$z = 0$, $t = 1$

Table 1: Model data. Units mm, N, MPa.

Some quick hand calculations. The second moment of area of the I-section and the shear modulus are

\[I = \frac{b h^3 - (b - t_w)(h - 2 t_f)^3}{12} = 3496 \text{ mm}^4, \qquad G = \frac{E}{2(1+\nu)} = 714 \text{ MPa}.\]

We use the Timoshenko beam formulation, which adds the shear deformation of the web to the bending (Euler–Bernoulli) deflection. The shear is carried by the web, with area $(h - t_f)\, t_w = 18.5$ mm²:

\[\delta = \underbrace{\frac{F L^3}{3 E I}}_{\text{bending}} + \underbrace{\frac{F L}{G \,(h - t_f)\, t_w}}_{\text{shear}} = 11.44 + 0.45 = 11.90 \text{ mm}.\]

The shear term is 4 % of the deflection. Our B32 element inside ABAQUS is also a Timoshenko (shear-flexible) element, so the beam model includes it as well. The largest bending stress is at the clamp, in the top and bottom:

\[\sigma_{\max} = \frac{F L}{I}\,\frac{h}{2} = 17.2 \text{ MPa}.\]

🧱 Solid

The section, the C3D20R mesh and the Load step are already there.

Clamp the face at $x = 0$ with $U1 = U2 = U3 = 0$. ENCASTRE or PINNED give the same result here, because solid elements have no rotational degrees of freedom.
Create a reference point on the beam axis at the tip, $(200, 0, 0)$, by typing its coordinates. It does not need to lie on the mesh, so no partition is needed. Couple it to the tip face with a kinematic coupling.
Apply CF2 = -30 on the reference point and run.

Solid, $\sigma_{xx}$. Tip deflection 11.83 mm.

⚠️Which axis is the beam axis?

If you build the part from a sketch and extrude it, Abaqus by default extrudes along $z$. The beam axis is then $z$ and not $x$, so $\sigma_{xx}$ of the beam is S33 in Abaqus. You can rotate the instance in the Assembly to put the beam along $x$. If you leave it as it is, $\sigma_{xx}$ corresponds to S33.

📏 Beam

For the beam, the part is a 1D wire of length $L$ in 3D space.

I profile with $l = 10$, $h = 20$, $b_1 = b_2 = 12$, $t_1 = t_2 = 1.5$, $t_3 = 1$, and a beam section.
Beam orientation $n_1 = (0, 0, -1)$, check with Render beam profiles.
B32 mesh, Load step, clamp the vertex at $x = 0$, CF2 = -30 directly on the vertex at $x = 200$. No coupling is needed, because a beam node already represents the whole cross-section.
Add SF (section forces and moments) to the field output request, then run.

ℹ️Which stress does the beam show?

A beam only has stresses at its section points. By default Abaqus writes points 1, 5, 9 and 13, the flange tips (see plot below in the comparison section) for a I-profile. Different profiles have different section points (check the documentation for more). A contour of S11 paints the whole rendered profile with the value of one section point, chosen under Result → Section Points. With SF in the output, Abaqus can also plot BEAM_STRESS, which is computed from the section forces and varies over the height of the profile like in the solid.

Beam, S11 as the envelope (max) over the section points. Each element shows one value over the whole profile. Tip deflection 11.86 mm.

The same beam, BEAM_STRESS S11 computed from the section forces. The stress now changes over the height of the profile.

🧾 Shell

For the shell model, we are going to do this in 3 parts according to the sketch. The flanges are drawn at $y = \pm 8.5$, where they meet the web.

Shell sections Flange (1.5 mm) and Web (1 mm).
Offset the flange sections outwards and check with Render shell thickness.
S4R mesh with 1 mm seed, Load step, clamp the three edges at $x = 0$.
As for the solid, create a reference point at $(200, 0, 0)$ (if your model is centered with the coordinate system), couple it kinematically to the three tip shell edges, apply CF2 = -30 on it and run.

(a) Surfaces at the interface with outward offsets. (b) Mid-surfaces without offsets, 3 % too stiff.

Shell, $\sigma_{xx}$. Tip deflection 11.86 mm.

⚖️ Comparison

Model	$\delta$ (mm)	DOF	Memory
Hand	11.90	–	–
Solid C3D20R	11.83	242,340	1.4 GB
Beam B32	11.86	54	24 MB
Shell S4R	11.86	50,658	150 MB

Table 2: Comparison of the results between models.

All three models give the same tip deflection, within 0.6 % of each other and of the hand calculation. The beam gets there with 54 DOF, the solid needs more than 240,000.

(a) Where each model has a stress value at $x = 100$ mm. Solid at every node, shell at the bottom and top face of each wall (SNEG, SPOS), beam at 13 section points on the wall mid-lines. (b) What that gives in the top flange.

The stresses agree too, more or less. The 1D beam model has no section point at the top fibre (top part of the top flange), so its largest stress is read at the flange mid-line which is around 7 % lower.

Away from the ends, the three models give the same results. Only the solid and the shell see the clamp and the load introduction.

Deflection error against model size. Marker area is solver memory.

Refining the mesh does not change the deflection of any model, it only costs more memory and time.

💸 The RAM bill

What would happened if we had a model with 1000 I-beams?

(a) RAM for a structure of $n$ I-beams. (b) Price of a 32 GB DDR5 kit.

1000 I-beams	RAM	EUR, Jan 2026
Beam	1.6 GB	20
Shell	279 GB	3,519
Solid	5.9 TB	74,704

Table 3: RAM for a thousand I-beams and its price.

So what you should do? Always depends on the question and your goal. If the general behavior of the structure is the main goal, then using the 1D beam elements could be sufficient. However if you are really interested in specific details, interactions between beams or around bolts, then a Shell or a Solid model would be the most adequate.

it is up to you to figure out what is the best modelling techniques for your case while also considering the cost.

← Back to tutorial overview

	Value
Length	\(L = 200\) along \(x\)
Clamp / tip	\(x = 0\) / \(x = 200\)
Tip force	\(F = 30\) N in \(-y\)
PMMA	\(E = 2000\), \(\nu = 0.4\)
Abaqus I profile
\(l,\ h\)	10, 20
\(b_1,\ b_2\)	12, 12
\(t_1,\ t_2,\ t_3\)	1.5, 1.5, 1
\(n_1\)	\((0, 0, -1)\)
Shell model
Flanges	\(y = \pm 8.5\), \(t = 1.5\), offset outward
Web	\(z = 0\), \(t = 1\)