r3.08.03 Calculation of the characteristics of a beam of any cross section

Summary:

The principle of calculating the various characteristic quantities of beam sections is presented. These are established from the geometric characteristics of the cross section of the beam.

These values are to be provided to operand SECTION: “GENERALE” of operator AFFE_CARA_ELEM [U4.42.01]. To determine them, numerical methods are presented, and implemented in command MACR_CARA_POUTRE.

In the case of sections” RECTANGLE “and” CERCLE “, the characteristics are calculated directly in AFFE_CARA_ELEM using simplified formulas that are explained here.

• 1. Geometric characteristics
  • 1.1. Any section
  • 1.2. Special case of rectangular and circular sections
• 2. Shear coefficients and the shear center
  • 2.1. Analytical methods
  • 2.2. Special case of rectangular and circular sections
  • 2.3. Numerical method for calculating shear coefficients and shear center
  • 2.4. Calculation of the shear coefficients of a network
• 3. The constants related to twisting
  • 3.1. Calculation of C in the case of any sections
  • 3.2. Calculating the torsional constant in MACR_CARA_POUTRE
  • 3.3. Calculation of the radius of torsion in any section
  • 3.4. Torsion constant for circular and rectangular sections
  • 3.5. The effective torsional radius
• 4. Calculation of the warping constant
• 5. Bibliography