410 



Mr. R. C. Nichols on the Resistances 



by the stress per inch at AB or CD will represent respectively 

 the total compressive and tensile stresses on the section, and 

 the sum of these multiplied by one third of the depth of the 

 section will be the moment of horizontal stress at that section. 

 But if the limits of elasticity have been exceeded at C D, 

 when C D is assumed to represent the stress per inch at that 

 line, it will no longer represent the amount of elongation or 

 the strain in units E times the length of those in which it 



B K 



measures the stress, but the line representing the strain in 

 such units will be longer than C D. Let this be represented 

 by EF (fig. 7). Let H now be the position of the neutral 

 axis. Draw EK, FI, straight lines through H, to meet AB 

 produced in K and I. Then as before, any horizontal lines 

 i k or ef drawn between these lines will represent the con- 

 traction or elongation at such lines. And if points cd be 

 taken upon all such lines ef, equidistant from the vertical line 

 through the centre of the section, so that the length of cd 

 may represent the stress due to the elongation ef, and lines 

 drawn through all such points from C and D to H, then the 

 area of the figure enclosed by these lines and the base C D 

 multiplied by the stress per inch at C D will be the total 

 amount of tensile stress. 



If the limit of elasticity has been also passed for compressive 

 strain, the same operation must be repeated at all lines ik. 

 But otherwise the area of the triangle IHK multiplied by the 

 stress per inch at C D will be the total amount of compressive 

 stress. And the sum of these areas each multiplied by the 

 stress per inch at C D, and by the distance of their respective 

 centres of gravity from H, will be the moment of horizontal 

 stress about the neutral axis. 



Inasmuch as the total amounts of tensile and compressive 

 stress must be equal to each other, it is manifest that H 

 and G will not under these circumstances coincide, but that 

 as the strain increases after the limit of elasticity has been 



