## Spring Element Forces

In this post, we will look at some sample models to dig a little deeper into spring element forces.

In the Spring Elements in Nastran post, we looked at the different types of spring elements and their capabilities. In the featured image above, we can see the FEM model has three spring element types with relatively stiff BAR elements (to avoid stiffness matrix singular errors in the enforced displacement load cases) attached at one end of the springs. All the left side nodes are fixed, while all the right side nodes can only move along ‘X’. The top element is a DOF Spring, the middle one is a CBUSH, and the bottom one is an axial spring.

Click here for a nice pdf if you want to dig a little more into spring element forces.

So, when we measure or query the load induced in a spring element:

Is a positive load always tension and a negative load always compression? Not really.

### Spring Element Forces – CASE 1:

In this case, we apply a compressive load of 100 lbf along -X, FX = -100lbf.

but as you can see in the table below, two types of element connectivity or nodal order are used. See figure below.

### Spring Element Forces – CASE 2:

In this case, we apply a displacement load of +0.1″ along X at the left node, and a +0.2″ displacement load at the right node.

Again, as you can see in the table below, two different types of element connectivity or nodal order are used.

This load case may be similar to a contact spring element situation, both nodes are moving and the relative displacement of the nodes is important. See figure below.

Consider the table shown below:

### Spring Element Forces – Force Results

OK, let us talk about the table above. The first column indicates the element type, and the last column is the secondary index indicating other variables.

We can see three different types of spring elements, and two different types of loading scenarios we discussed above, the orange row indicates the load case.

The yellow row indicates the connectivity, or the order of the nodes used to define each spring element. Node 1 for each element is the one that is completely fixed.

The 3rd thru 5th rows indicate the spring element forces induced in the different spring elements along with their signs.

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### Spring Element Forces: DOF Spring

The third row in the table shows that the load in a DOF spring is alternating between positive and negative depending on the load type and connectivity.

This means that you cannot rely on the sign of the induced load in this type of an element to indicate tension or compression by simply looking at the induced load.

### Spring Element Forces: CBUSH Spring

The fourth row in the table shows that the load in a DOF spring is also alternating between positive and negative depending on the load type and connectivity. However, it has opposite signs compared to the DOF spring element.

This again means that you cannot rely on the sign of the induced load in this type of an element to indicate tension or compression just by looking at the induced load.

### Spring Element Forces: Axial Spring

Finally, in the axial spring element, it seems like the induced load is consistent with positive tension and negative compression. This is interesting as the connectivity does not seem to influence the sign of the induced load.

However, it is important to note that this element provides stiffness in all three directions with a single stiffness value as it is axial in nature. No rotational stiffness is available with an axial element, you must use a torsional spring in that case.

In some cases, this is probably not what we want. For example a slotted fitting will allow movement in the direction of the slot, and in such cases this element is not a good choice. But if you know there will be no significant loading in the direction of the slots, then you may be OK.

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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.