ON STRESS DISTRIBUTION IN ENGINEERING MATERIALS. 



477 



This condition being once satisfied, equation (3) shows that the moduli 

 E'A', EA for the rod, as a whole, must be ir the ratio of dynamical 

 similarity f, i.e., in the ratio of the applied forces. 



Now Ic will usually have to be fixed beforehand ; h being known, the 

 radius of gyration K' in the model is fixed. 



The materials of the model are also usually not at our choice. Thus 

 E' is fixed. But A' can be varied within large limits, aud this without 

 altering k. An easy example of this is when the bars of the model are 

 rectangular in section. 



KVTZ 



■Zh 



2feutralAj3s 



Fig. 12. 



The height of the cross-section = K''v/r2 and is therefore fixed. But the 

 breadth 2h is at our disposal and can be varied, so that A' satisfies 

 equation (3). 



An important particular case occurs when certain rods or ties of the 

 full size are practically unyielding or inextensible, at any rate, in com- 

 parison with the others. In this case, B is infinitely great and E' must 

 also be infinitely great. All that is necessary then is to make the corre- 

 sponding bars of the model likewise unyielding or inextensible in com- 

 parison. Provided this is done, we need only trouble to satisfy the condi- 

 tions for the ' yielding ' or soft parts of the model and full size. 



If the model and full size are made up of two kinds of material only — a 

 ' yielding,' and an ' unyielding ' — it will usually be convenient to satisfy 

 equation (3) by adjusting p, the ratio of dynamical similarity, that is, 

 by applying suitable loads to the model instead of altering the cross-sections 

 to the right ratio. 



(3) Safety conditions for the model. 



The question of breaking stress on the model is one of fundamental 

 importance. For we have to be careful that the stresses imposed in con- 

 serving similarity shall not be so great as to cause the model to collapse. 



We have, y and y' being the distances from the neutral axes of the 

 outermost fibres in full size and model respectively, the greatest stresses 

 as follow : — 



Es + ^ (full size) ; 



Ws' -f ^y (model) ; 

 K 



(numerically positive values being taken for each quantity). 

 Now s' = s, R' = ^R ; but jf is not equal to ky in general. 



