## Beam and Bar Elements:

Beam and bar elements are the most commonly used elements in FEA. But often times, they are either poorly understood or not understood at all. In the hands of inexperienced users, this can lead to unexpected and probably negative consequences when beam and bar elements are interchangeably used for representing certain structural members under certain types of loading.

So without further due, let us dive in and dig a little deeper. We will look at the top level view of the most important aspects of beam and bar elements.

Beam and bar elements may sound like simple elements, but there is a lot of depth to those elements and I will only scratch the surface in this post, I myself have a lot more to learn. I am sharing what I do know in this post. ENJOY!

### Finite Element Analysis – BEAM and BAR Elements

A ‘BEAM’ element is one of the most capable and versatile elements in the finite element library. It is very commonly used in the aerospace stress analysis industry and also in many other industries such as marine, automotive, civil engineering structures etc. In aircraft cabin interiors however, in most cases a bar element is sufficient to get you the loads you need. To keep it simple to understand beam and bar elements, let us limit the discussion to symmetric and un-symmetric metallic beams, closed and open sections.

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So what is a ‘beam’ element and how is it different from a ‘bar’ element?

Beam and Bar Elements General Description:

A typical beam or a bar element is a 1D element. Meaning the element itself is defined in one dimension and modeled using two nodes, one at each end of the beam element, see Figure 1 above. Each node can have 6 degrees of freedom (DOF) – TX, TY, TZ (translations along X Y and Z), and RX, RY, RZ (rotations about X Y and Z) in a given coordinate system. Beams are capable of taking axial, bending, and shear loads, and also moments and torsional or twisting or torque loads.

There are three offset systems coupled with the orientation that work toward defining the behavior of a bar/beam element:

Neutral Axis (NA) – Defines the bending neutral planes, for a beam element this axis is offset from the shear center axis. For a bar element, all axes (including the ones below) are the same.

Shear Center (SC) – Defines the coupling of loading to twisting or bending or other effects if load is not applied along the shear center plane of ‘beam’ elements. It is recommended you refer to an undergraduate text book to learn about shear center and how it is calculated for different shapes and section types. In the practical world, the FEM software will automatically calculate this based on the property, orientation and shape definitions. Then the neutral axis is offset from the shear center axis for beam elements.

Nonstructural Mass (NSM) – Defines the effects of mass per unit length that does not contribute towards stiffness but adds nonstructural mass along a specified offset axis from the shear center axis.

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Element Orientation:

The element orientation is critical especially for noncircular, un-symmetric, or irregular sections. For circular cross sections, it does not matter for obvious reasons. Meaning it’s the same in any direction. But what exactly is element orientation? It is not that mysterious actually.

Let us use this I beam as an example as shown in Figure 3. You can see that the ‘I’ cross section is going along Zelem. So if this is how it is in the actual structure you are modeling, how will you define the orientation so it looks like this? I’ll tell you how, keep reading…

So in Figure 3, if you have one node at one end and the other end has the second node, then the element ‘X’ axis, or Xelem is always between these two nodes. No matter how many elements you use to define the I-Beam in the picture, the element X is always along the two nodes of every element. If it is not a straight beam then each elements X axis will be slightly angled to make up the approximate global curve of the curved I beam. There are also curved beam elements that allow you to specify a bend radius in the element property definition which makes a curved approximation more exact.

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The element orientation must be defined for bars and beams. In this case, you can use the global Y axis going to the right to define the element Y orientation vector, or you can also use a grid point or node to the right along the desired Yelem axis to define the element orientation. The third axis is automatically calculated by the FEM program. The axes are primarily used to define the elemental planes such as the neutral planes, shear center planes and they are parallel to each other or coincident in case of bar elements.

Similarities between BEAM and BAR elements: What is common?

• Both are 1D elements or line elements
• Element orientation definition methods (as discussed above) are the same
• Both elements follow the classical beam theory, meaning plane section remain plane
• Both elements are capable of including shear deflection using shear area coefficients (more important for short stubby beams or bars)
• Both elements are capable of including nonstructural mass per unit length effects
• Both elements have 4 data and stress recovery points on the cross section
• Both elements are capable of up to 10 data points along the element length

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Between the beam and bar elements, the beam element is capable of doing more as listed below:

• Beam elements can have tapered sections, meaning one end can be smaller/larger/wider/narrower/thinner/thicker than the other, but the shape cannot be totally different.
• Beam elements are capable of accounting for large deflections and differential stiffness due to large deflections
• Beam elements can have three different offsets. One for shear center, one for the neutral axis and one for the nonstructural mass axis. Whereas bar elements have only one axis, all three are the same neutral axis.
• For a bar element the grid points are located at the section centroidal neutral axis. For beam elements they are always at the shear center axis and the neutral axis is offset from the shear center axis. See figure 2 for more information.
• BAR elements are best for doubly symmetrical sections with load applied along centroidal planes, as they are not capable of accounting for bending or twisting or warping of the sections due to axial or transverse loads. This is only possible with BEAM elements.

When Beam and Bar elements are used properly in combination with offsets and plates and other element types, model sizes can be significantly reduced for large models. At the same time the structural behavior and load path can be captured accurately with confidence. This topic can be somebody's PhD thesis, it is that deep if you keep digging. But I think I covered the application side of it in this post. In the real world , it is very important to be aware of these technical aspects so you can be a better design engineer or a stress engineer.

http://www.stressebook.com/finite-element-analysis-course

http://www.stressebook.com/common-fem-element-types

Also check out this follow up post on the effect of the shear center offset on a stiffened plate. Click the image below.

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Surya Batchu

Surya Batchu is the founder of Stress Ebook LLC. A senior stress engineer specializing in aerospace stress analysis and finite element analysis, Surya has close to a decade and a half of real world industry experience. He shares his expertise with you on this blog and the website via paid courses, so you can benefit from it and get ahead in your own career.