Do you know if there is a formula for the maximum load that can be supported by a beam? The beam could be a simply supported beam, cantilevered, or fixed on both ends. By the way, is finding the equations for share and bending moment diagrams an undetermined problem?
Yes there are. Are you talking horizontal or vertical orientation of the principal axis? There are load-deflection formulae for any number of beams, load and load distributions, and end-point or boundary conditions. There are already standard formulas.
Thank you for your answer. Do you recommend any book or website where I could look for further info regarding this topic?
"Roarks Equations for Stress and Strain" is the most comprehensive book you'll ever find for stress and strain equations, but the information you seek can be found in any Mechanics & Strengths of Materials textbook. Solve for static equilibrium and find the maximum moment in the beam in terms of force. Plug it into your stress bending equation stress=M*y/I, and solve for force with stress = to yield strength or UTS (depending on which is defined as failure). y=furthest distance from neutral axis of the beam, M is your maximum moment, and I is the moment of inertia of the beam cross section about the neutral axis. It's slightly more difficult if the beam cross section is not uniform throughout but not by much.
Roark's is one possiblity. Then many textbooks and on-line resources have forumulas. For example - buckling of a column (efunda has a limited number of samples, then one has to register, but there is a lot of valuable information there) http://www.efunda.com/formulae/solid_mechanics/columns/columns.cfm http://www.tech.plym.ac.uk/sme/desnotes/buckling.htm http://www.diracdelta.co.uk/science/source/b/u/buckling load/source.html Then there are more complicated systems - http://www.ce.washington.edu/em03/proceedings/papers/84.pdf And of course, for horizontal beams and distributed load, there are formulas for maximum deflection and corresponding stresses in various types of beams and cross-sections. The peak load would be such that some location in the beam would exceed UTS and the beam would progress to failure. However, in practice, given various uncertainties in dimensions and material properties, and tolerances, one normally designs to some safety margin in order to avoid inadvertent failure.