Computing Combined Loads

Look at how to calculate a combination of loads on a composite laminate.

Can laminate loads simply be added together? Sure! For example, consider two loads on a laminate: one axial and one bending. In this case, all we need to do is add the axial strains to the bending strains.

The basic equations are given in the following matrix relation:

This can be calculated by hand, or you can use the fast and easy features within Helius Composite to efficiently perform the calculation.

Computing Combined Loads with Helius Composite

The Laminate module includes several analysis features that enable you to calculate the effects of different loading on a composite laminate. Two tabs within the Stress-Strain and Strength Analysis feature in the Laminate module will perform this particular calculation: Mid-Plane Strains/Curvatures and Global/Local Stress/Strain.

For this example, our first step is to construct our laminate and apply only the axial load (Nx).

  1. Navigate to Laminate > Stress-Strain and Strength Analysis.
  2. On the Laminate tab, name the laminate to be created Symmetric Laminate.
  3. Add the eight plies to the laminate as shown below.

  4. Navigate to the Laminate Loads tab and enter an Axial Load of 10,000 psi.
  5. Navigate to the Global/Local Stress/Strain tab and calculate the strain in the middle of the plies using the global coordinate system.
  6. Navigate to the Mid-Plane Strains/Curvatures tab and click Calculate.

    Note: the same result is obtained using either tool.

Next, we will add the strain due to the moment by replacing the axial load with the moment.
  1. Navigate to the Laminate Loads tab, remove the axial load and add a Transverse Moment of -1000 lb-in/in.
  2. Navigate to the Mid-Plane Strains/Curvatures tab and click Calculate.

  3. Record the mid-plane curvature Kx
  4. Navigate to the Global/Local Stress/Strain tab and calculate the strain on the top of the plies using the global coordinate system.

Quick hand calculation check:

In this case, our laminate is 0.04 inches thick, thus z=-0.02 inches at the top of the laminate. With that:

εx = vkx or εx= (-0.02 in)(7.81865/in) = -0.156 in/in as shown in Ply #1 above

Now, if we add the axial and bending strain, we get:

εTotal= 1.341E-3 + (-1.56E-1) = -0.155 in/in

Of course, Helius Composite allows you to apply both loads at once using the Laminate Loads input tab in each of the featured Laminate Analysis functions. In fact, you can apply eight different load factors at once.

Entering our axial and moment loads together, we get -1.55E-2 in/in, which is the same result obtained above by computing them separately and adding them together.

With the laminate analysis tools in Helius Composite, you can run this calculation over and over again with countless different layup and loading combinations without the time and potential error involved in hand calculations or spreadsheet tools. Additionally, you can plot or export your results for further analysis.

Parent topic: Tutorials