Basics of Structural Analysis

Introduction

Structural analysis using about high school level physics and maths.

Aim to calculate fiberglass cansat structure

Basic theory

Principle of superposition: linearity. Displacement at location $B$ from forces $P_{1}$ and </math>P_2</math> located at different positions is calculated as $\Delta _{B}=\Delta _{BP_{1}}+\Delta _{BP_{2}}$

The energy principle: $dW=Fd\Delta$ giving the total energy as $W=\int _{0}^{\Delta }Fd\Delta$ which is called strain energy. For linear deformation this gives $U={\tfrac {1}{2}}F\Delta$.

Virtual work principle.

Dead loads, live loads, impact loads (impact factor), wind loads.

Equilibrium.

Forces:

• Normal force and axial force (out-of-plane forces, in-plane forces)
• Shearing force ${\frac {V(x)}{x}}=-w(x)$. Thus we have $\Delta V=\int w(x)dx$. $w(x)$ is the intensity of applied (normal?) force.
• Bending moment ${\frac {dM}{dx}}=V(x)$ and thus ${\frac {d^{2}M}{dx^{2}}}=-w(x)$.
• Torsion (of a plate)

Beam

Forces:

• Normal force and axial force
• Shearing force ${\frac {V(x)}{x}}=-w(x)$. Thus we have $\Delta V=\int w(x)dx$. $w(x)$ is the intensity of applied (normal?) force.
• Bending moment ${\frac {dM}{dx}}=V(x)$ and thus ${\frac {d^{2}M}{dx^{2}}}=-w(x)$.

Deflection of beams

The strain $\epsilon$ in the filament is due to the different lengths of filaments in bended beam. $\epsilon =$

Radius of curvature Failed to parse (unknown function "\doo"): {\displaystyle \frac1R = \frac{\doo v^2}{\doo x^2}} , and Failed to parse (unknown function "\doo"): {\displaystyle \epsilon_{xx} = -y \frac{\doo^2 v}{\doo x^2}} .

Column

Column is a vertical beam.

References

https://scholarshare.temple.edu/bitstream/handle/20.500.12613/7150/Udoeyo-Textbook-2020.pdf?sequence=1