## Classical Hand Calculations in Structural Analysis

You may have heard the term “Classical Hand Calculations in Structural Analysis”. What does it mean? And why should you care? This post is all about this very critical skill, an essential skill set for any good stress engineer in the aerospace industry. So without further delay, let us dive right into it.

In the stress analysis industries, especially in aerospace, classical hand calculations in structural analysis are pretty much a requirement to analyze even complex geometries. A few exceptions to this are the use of finite element analysis for loads models (FEM models built exclusively to extract internal and external loads), crack growth analysis for failure and damage tolerance (F&DT), some detailed FEM models for fatigue analysis where simple to use stress concentration factors are not available, among others.

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A stress engineer's ability to perform classical hand calculations in structural analysis is one of the most important skills highly regarded in the stress engineering circles. For example, if you build a detailed FEM to analyze a simple bracket, not only is it extremely inefficient but also considered as a lack of engineering judgement on your part.

You need to be able to do these quick back of the envelope calculations for your own sanity checks, and also for providing quick sizing of simple parts for the benefit of the designer or project engineer or management that comes to you with such simple requests. Beyond these simple classical hand calculations in structural analysis, there are obviously many more advanced methods that dive much deeper into that area.

You can see above in the figure, it is a simply supported beam. If you have a plate attached to seat track beams on either side and the plate is loaded in the middle, you know what the approximate load is, then a simple "Mc/I" calculation is all you need to size that plate.

It is a simple case of course, but even in complex cases good engineering judgement and proper assumptions of conservatism will provide you with a reasonable result to save you a lot of time in the long run. You do not have to be a stress engineer to do such calculations. Design engineers can do this as well to avoid potentially costly fixes later in the design release cycle. So what are some of the most common types of classical hand calculations in structural analysis?

### 1) Free Body Diagrams - Critical to understand the load path and checking your analysis

Free body diagrams (FBDs) are basically load and moment diagrams that you draw of the part as a free body by itself with the applied loads and moments balanced with reactive loads and moments, in other words, load and moment equilibrium checks. This type of analysis is typical for fastener checks, insert checks and section checks of structural joint components.

### 2) Euler Buckling - Compression member or column buckling

For example, if you have a tie rod assembly, you can determine the allowable load for the tube using simple Euler Buckling analysis, this is the preferred method, period.

### 3) 3D Rigid Body Analysis - Fastener Loads for a rigid joint

This is another commonly used method to determine the loads induced in the fasteners of a joint, another type of classical hand calculations in structural analysis.

The list can keep going such as lug analysis, bolt bending, plastic bending, crippling, etc. But I think you get the idea. Some of the most commonly used and widely accepted references for classical hand calculations in structural analysis are as follows:

• Formulas for Stress And Strain - Roarks
• Airframe Sress Analysis - Niu
• Analysis and Design of Flight Vehicle Structures - Bruhn
• Peterson's Stress Concentration Factors

If you master the above books, you will pretty much be the GOD of classical hand calculations in structural analysis. Don't worry, there are only a few and far in between of those special people, and I am definitely not one of those.

We simply need to learn the sections that are important to our own field to become an awesome stress engineer. One of the main goals of www.stressebook.com is to educate you, and provide you with the tools and skills needed to perform the classical hand calculations in structural analysis required to certify aircraft structures.

Videos - Classical Hand Calculations in Structural Analysis:

Here is an example video on Heel Toe or Prying Effect, another standard method of Classical Hand Calculations in Structural Analysis.

Here is the same example video on Heel Toe or Prying Effect with a horizontal load, another standard method of Classical Hand Calculations in Structural Analysis.

This video covers the same effect with the load Px acting in the opposite direction:

This video covers the solution with the combined loading of Py and Pz, Py acting in-plane of the vertical leg, and Pz acting Up:

So there you have it, I hope you learned something useful today. Please do share this post with your friends if you find value in it. And make sure you check out the courses as well..

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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.