The number of pounds which concentrated at the centre will deflect a rectangular prismatic simple beam one inch may be found from the preceding formulæ by substituting D = 1" and solving for P'. The formulæ then becomes:
| 4 E b h3 | ||
| Necessary weight (P') | = | ---------- |
| l3 |
In this case the values for E are read from tables prepared from data obtained by experimentation on the given material.
Strength of Beams
The measure of the breaking strength of a beam is expressed in terms of unit stress by a modulus of rupture, which is a purely hypothetical expression for points beyond the elastic limit. The formulæ used in computing this modulus is as follows:
| 1.5 P l | ||
| R | = | --------- |
| b h2 | ||
| b, h, l | = | breadth, height, and span, respectively, as in preceding formulæ. |
| R | = | modulus of rupture, pounds per square inch. |
| P | = | maximum load, pounds. |
In calculating the fibre stress at the elastic limit the same formulæ is used except that the load at elastic limit (P1) is substituted for the maximum load (P).
From this formulæ it is evident that for rectangular prismatic beams of the same material, mode of support, and loading, the load which a given beam can support varies as follows:
(1) It is directly proportional to the breadth for beams of the same length and depth, as is the case with stiffness.
(2) It is directly proportional to the square of the height for beams of the same length and breadth, instead of as the cube of this dimension as in stiffness.