Reference: Abbott, Richard. Analysis and Design of Composite and Metallic Flight Vehicle Structures 3 Edition, 2019

These beam solutions are taken from  (NASA TM X-73305, 1975) Table B4.6.2

Where:

Note that these methods do not predict beam column failure, these methods only the internal loads and moments in the beam. To predict the stability failure of a beam column the method in section 15.3.6 should be used.