ON STRESS DISTRIBUTIONS IN ENGINEERING MATERIALS. 205 
ments of T,is to use a test-piece under pure flexure (without shear) in its 
own plane. This can be readily produced in a straining frame as in the 
accompanying diagram. The stress will then vary linearly from P to Q 
and may be read off along a scale PQ, which can be previously calibrated 
against a specimen under known tension. 
A little sideways shift of the test-plate is then all that is required to 
compensate the stress-difference at any given point, provided that the 
direction of principal stress had been found previously. 
Coker has used a calibration tension member to determine the distribu- 
tion of stress in plates of various shapes—for example, in tension specimens 
pierced with circular holes, decks of ships with various openings, cement 
briquettes, &c. (17). He has also (18) investigated Andrade’s problem 
of the block whose opposite faces slide with regard to one another re- 
maining undistorted, and he obtains by this optical method a distribution 
of shear very similar to that obtained by Andrade from direct measure- 
ments of the slide. Mr. Scoble and he have also applied this method to 
determine the distribution of stress due to a rivet in a plate (19). 
The photo-elastic determination of stress carried out in this way does 
not, however, determine the stress in the plate completely. It will be 
noticed that all the method gives is the principal stress-difference at any 
point. If each principal stress at a given point be increased by any 
arbitrary quantity, the appearances are in no wise altered. To obviate 
this, Coker has used the stretch-squeeze effect in the plate to measure 
the sum P—Q of the principal stresses, a suggestion due originally to 
Mesnager (20). For clearly, if r be the thickness of the plate, 1 Poisson’s 
ratio, the plate, at the point where the principal stresses are P, Q, will 
become thinner by an amount 77(P+Q) an amount which is small, 
but with delicate instruments not impossible to measure. 
It will be noticed that this provides yet a third method for exploring 
the field of stress in a plate. 
There is, however, no necessity for doing this, as the information 
derived from the known values of the stress-difference and the direction 
of the lines of principal stress can be readily applied to find the complete 
system of stresses. 
Let the axes of x and y be taken in the plane of the plate. Let P and 
Q now denote the normal stresses across elements dy and dz respectively, 
S the shearing stress across either of the above elements. Then, if the 
