# Matplotlib compatibility patch for Pyodide
import matplotlib
if not hasattr(matplotlib.RcParams, "_get"):
    matplotlib.RcParams._get = dict.get

Stresses and displacements

This chapter includes the following topics:

• Model
  • Normal stress-strain relations
  • Shear stress-strain diagram
  • Fibre model
  • Small rotations bar element
• Cross-sectional properties
  • Static moment, centroid and normal force centre
  • Second moment of area and Section modulus
  • Polar moment of inertia
  • Torsional moment of inertia thin-walled tubes
  • Shear force centre
  • Core of a cross-section
• Strain diagram
  • … for extension
  • … for bending
  • … for torsion
• Kinematic relations
  • … for extension
  • … for bending
  • … for torsion in circular cross-sections and thin-walled tubes
• Constitutive relations
  • … for extension
  • … for bending
  • … for torsion
  • … for temperature influences
• Solve stresses in an extension element
  • Normal stresses
• Solve stresses in a bending element
  • Normal stresses
  • Shear stresses
• Solve stresses in a torsional element
  • … in a thin-walled circular cross-section
  • … in solid circular bars and thick-walled circular tubes
  • … in a closed thin-walled non-circular cross-section
  • … in open thin-walled cross-sections
  • … for various cross-sections in combination with shear force
• Solve displacements truss structures
  • … using constitutive equation
  • … using differential equations
  • … using Williot
• Solve displacements frame structures
  • … using differential equations
  • … using forget-me-nots
• Solve displacements circular and thin-walled tubes for structures in torsion
  • … using constitutive equation
  • … using differential equations
• Solve displacements statically determinate structures subjected to temperature influences