This section is from the book "Safe Building", by Louis De Coppet Berg. Also available from Amazon: Code Check: An Illustrated Guide to Building a Safe House.

Where r = the moment of resistance in inches of the fibres at said point.

Where (t/f) = the safe resistance to tension of the material, per square inch.

The same formulae apply to cantilevers as well as beams. The moment of resistance r of any fibre is equal to the moment of inertia of the whole cross-section, divided by the distance of the fibre from the neutral axis of the cross-section.

The greatest strains are along the upper and lower edges of the beam (the extreme fibres); we, therefore, only need to calculate their resistances, as all the intermediate fibres are nearer to the neutral axis, and, consequently, less strained. The distance of fibres chosen in calculating the moment of resistance is, therefore, the distance from the neutral axis of either the upper or lower edges, as the case may be. The moments of resistance given in the fourth column, of Table I, are for the upper and lower edges (the extreme fibres), and should be inserted in place of r, in all the above formulae.

To find at what point of a beam the greatest bending moment takes place (and, consequently, the greatest fibre strains, also), begin at either support and move along the beam towards the other support, passing by load after load, until the amount of loads that have been passed is equal to the amount of the reaction of the support (point of start); the point of the beam where this amount is reached is the point of greatest bending moment.

In cantilevers (beams built in solidly at one end and free at the other end), the point of greatest bending moment is always at the point of the support (where the beam is built in).

In light beams and short spans the weight of the beam itself can be neglected, but in heavv or long beams the weight of the beam should be considered as an independent uniform load.

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