ON THE STRENGTH OF MATERIALS FOR IRON SHIPS. 213 



On the Strength of Materials considered in relation to the Construction 

 of Iron Ships. By William Fairbairn, LL.D., F.R.S., fyc, and 

 Thomas Tate, Esq.*. 



V. In the following investigation it will be assumed that, under the action of 

 equal forces, the extension of the fibres of a beam will be equal in amount to 

 their compression, and that the amount of the extension or compression, as 

 the case may be, is proportional to the magnitude of the force producing it ; 

 and in order to render this hypothesis more fully in accordance with the fact 

 that the ultimate resistances of the two forces of compression and extension 

 in a beam are in almost all cases different, it will be further assumed that the 

 material reaches its ultimate limit of resistance to the one force before it 

 reaches its ultimate limit of resistance to the other force. 



Section I. 

 On tlie Qualities of Iron hesl adapted for Iron Ships, especially Ships of War. 



2. The work expended in the elongation or compression of a bar is equal 

 to one-half the force multiplied hy the corresponding elongation. Moreover, 

 for bars of the same material, the work varies as the solid content of the bar ; 

 that is, 



U=mKL, (1) 



where TJ— the work of elongation, K= the section of the bar in square 

 inches, L= its length in feet, and u a constant for each class of material, 

 being the work done upon a bar .1 foot long and 1 square inch in section. 

 Hence 



u= mriKV (2) 



which determines the value of u from experimental data for different kinds 

 of material, where P is the strain in lbs., and I is the extension of the bar 

 corresponding to this strain. 



3. The value of u, determined for different kinds of material, gives us a 

 comparative measure of their powers of resistance to a strain of the nature of 

 impact, or of dynamic effect; hence the coefficient u may be called the 

 modulus of dynamic resistance, or, as Tredgold named it, the modulus of resi- 

 lience. It is presumed that the best kind of iron for resisting the impact of 

 shot or shell is that whose modulus of dynamic effect is greatest. 



4. The values of u, determined by Mr. Fairbairn's experiments for different 

 plates or bars of iron, show that the dynamic resistance of thick plates to 

 rupture is about twice and a half that of thin ones, that the resistance of 

 thick steel plates is about one-tenth greater than that of the Low Moor iron 

 plates A, and that the resistance of these latter plates is one-half greater than 

 that of the rolled plates D. 



5. Similarly the work expended in the deflection of a bar supported at its 

 extremities, by a force applied at its centre, is equal to one-half the pressure 

 multiplied by the corresponding deflection ; and, moreover, we also have 



U=mKL, (3) 



where u, the modulus of dynamic resistance, being constant for the same kind 

 of material, gives us a comparative measure of the resistance of different kinds 

 of material to a force of impact tending to produce transverse rupture. 



* In this inquiry Mr. Tate has deduced useful formulae from Mr. Fairbairn's experi- 

 ments — independent of other researches — on the strength of iron ships. 



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