#### Stress Engineering Interview Questions Part 2: Technical

Stress Engineering Interview Questions Part 2: Technical

In Part 1 of this series, we discussed:

1. What is a Free Body Diagram
2. What are SFD and BMD for Beams, and
3. A tricky twist to the SFD and BMD of a simply supported center loaded beam

In this Stress Engineering Interview Questions Part 2, we will cover two more very important questions, ready? Alright then.

#### Q: What is a statically determinate structure?

Answer: A statically determinate structure is a structure that has at least as many equations of static equilibrium as the number of unknown forces acting on the structure.

In other words, given the total number of applied loads, we should be able to determine all the reaction loads simply by using the equations of static equilibrium alone.

The equations of static equilibrium available to us based on Newton’s Laws are:

• Sigma Fh = 0 –> Sum of all horizontal applied forces and reactions is zero.
• Sigma Fv =0 –> Sum of all vertical applied forces and reactions is zero.
• Sigma M = 0 –> Sum of moments about any point (including direct moments and moments due to all forces) is zero.

All the examples that were shown in Part 1 were statically determinate problems.

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#### Q: What is a statically indeterminate structure?

Answer: A statically indeterminate structure is a structure that is loaded and constrained in such a way that the equations of static equilibrium are not sufficient to solve for all the unknown forces acting on the structure.

In other words, the total number of unknown forces is greater than the total number of static equilibrium equations available. In most real world aircraft structures, this is the case. Therefore, the final static equilibrium of the structure is dependent on the stiffness of the structure along the load path.

So how can we solve a problem like this? Additional compatibility equations must be employed to solve for all the unknowns. The more complex the structure is, the more difficult it is to determine the reactions using simple statics. And therefore FINITE ELEMENT ANALYSIS comes to our rescue to solve these types of problems. Surface contact, bending of panels, twisting of the structure, members of different stiffness along the load path etc. all contribute to the structure’s indeterminacy and FEM can handle all of this using its internal system of equations.

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For example, the structure shown below is a statically indeterminate structure. Why? Because a lot is happening here, the reaction loads are stiffness dependent and there will be a shear center effect (lies somewhere outside on the other side of the structure). We can see that the center of gravity (CG) of this structure (it lies somewhere inside), along which the FWD inertia load is applied, does not coincide with the shear center.

Although this structure is not exactly a C channel, a pure inertia load at the center of gravity will result in a twisting of this structure due to the moment arm between the CG and the shear center. This twisting would have to be balanced by the floor fittings (top attachment is pinned) in multiple planes. These reaction force couples will be influenced by the bending stiffness of the sandwich panels and their proximity to the overall CG.

Finite Element Analysis is one of the best and most widely used approximation tools to solve for unknowns using the compatibility equations of complex structures.

So what are compatibility equations? An example is displacement compatibility. The video below (courtesy ECUSW) demonstrates the concept on a simple axial beam system.

In the NEXT PART, we will dig into some more cool questions and answers.

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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.