OF MATERIALS, NO.92., &C. Encyclopedia.) There fore, 4. The strain on the middle point, by a force ap plied there, is one-fourth of the strain which the same force would produce, if applied to one end of a beam of the same length, having the other end fixed.
5. The strain on any section C of a beam, rest ing on two props A and B, occasioned by a force applied perpendicularly to another point D, is pro portional to the rectangle of the exterior segments, xDB Therefore, is equal to to — AC • ore, An The strain at C occasioned by the pressure on D, is the same with the strain at D occasioned by the same pressure On C.
6. The strain on any section D, occasioned by a load uniformly diffused over any part EF, is the same as if the two parts ED, DF of the load were collected at their middle points e and f. Therefore, The strain on any part D, occasioned by a load uniformly distributed over the whole beam, is one half of the strain that is produced when the same load is laid on at D ; and The strain on the middle point C, occasioned by a load uniformly distributed over the whole beam, is the same which half that load would produce if laid on at C.
7. A beam supported at both ends on two props B and C (fig. 14.), will carry twice as much when the ends beyond the props are kept from rising, as it will carry when It rests loosely on the props.
8. Lastly, the transverse strain on any section, occasioned by a force applied obliquely, is diminish ed in the proportion of the sine of the angle which the direction of the force makes with the beam.
Thus, if it be inclined to it in an angle of thirty de grees, the strain is one half of the strain occasioned by the same force acting perpendicularly.
On the other hand, the . RELATIVE STRENGTH of a beam, or its power in any particular section tp resist any transverse strain, is proportional to the abr solute cohesion to the section directly, to the dia. tepee of its centre of effort from the axis of fricture directly, and to the distance from the strained point inversely.
Thus in angg section of the beam, of which 6 is the depth (that is, the di mension in the direction of the straining force), mea sured in inches, andf the number of pounds which one square inch will just support without being torn asunder, we must have/ x b x proportional to W X CB (fig. 15.) Or, x b x multiplied by some number m, depending on the nature of the ber, must be equal to to x CB. Or, in the case of the section C of fig. 16. that is strained. by the force so applied at D, we must have as x fie AC x DB to X B. Thus if the beam is of sound oak, ra is very nearly (see STRENGTH Or MATERIALS, fbds No. 116, EncycL) Therefore we have-- = to 9