I have been often asked questions to what does those numbers in top bottom and membrane stresses mean in shell analysis. How do I quantify these numbers? There has been some confusion on the bending stress result values.

I ran a couple of studies to understand this better. There are four options available for you to look up your results. Top / Bottom / Bending / Membrane.

Here is a plate (4 x 2 x 0.1 in) fixed at one end and loads at the other end.

The following formulas are used for calculating Bending and membrane stresses.

Bending Stress = +/- Mc/I Membrane Stress = F/A

Top. Total (membrane + bending) stresses on the top face

Bottom. Total (membrane + bending) stresses on the bottom face

We will take a look at results near the loaded edge.

Case #1 One end fixed and a moment of 100 lb-in at the other end.

Membrane stress is 0 psi here.
Top stresses are purely due to tension in the top most layer.
Bottom stresses are purely due to compression in the bottom most layer.

Membrane stress 0 psi	Top stress

Bottom Stress	Bending Stress

Case #2 One end fixed and a 5000 lb force at free end

Membrane stress here is 25000 psi
Bending stress 0 psi

Membrane stress 25000 psi	Top 0 psi

Bottom 0 psi	Bending stress 0 psi

Case #3 Load in case 1 and case 2 applied together.

Top Stress = -30,000 + 25,000 = -5,000 psi
Bottom Stress = +30,000 + 25,000 = +55,000 psi
Membrane Stress = +25,000 psi
Bending Stress = -30,000 psi

Top stress 5000 psi	Bottom stress 5000 psi
Membrane stress 25000 psi	Bending stress 5000 psi

Top stress 5000 psi Bottom stress 5000 psi

Membrane stress 25000 psi Bending stress 5000 psi
Conclusion The top / bottom and membrane stress calculations are accurate but the bending stress reported is always the top stress. This could result in misinterpretation of results; if not well understood.