In some materials the neutral axis changes its place while the bar is at work; thus wrought iron, after being a little compressed, will bear a great deal more compression than when in its original state; also the lower fibres, after being extended, will resist less than at first; the effect of which two actions is to move the neutral axis up.
146. The following table shows the relative resisting powers of wood, wrought and cast-iron; with the corresponding positions of the axis, with sufficient accuracy for practice.
| Material. | Resistance to extension. | Resistance to compression. | Ratio. | Distance of axis from top, in fractions of the depth. | |
|---|---|---|---|---|---|
| Wrought iron, | 90 | 66 | 90 66 | 90 156 | or 0.58 |
| Cast-iron, | 20 | 111 | 20 111 | 20 131 | or 0.15 |
| Wood, | 2 | 1 | 2 1 | ⅔ | or 0.66 |
Thus in beams subjected to a cross strain, as well as to a direct extensile or compressive one, the resistance is effected by the incompressibility and inextensibility of the material.
147. The formula for dimensioning any beam to support a given weight transversely is
S = 4bd2
e,
Where S represents the ultimate strength in lbs.
b represents the breadth in inches,
d represents the depth in inches,
e represents the length in inches,