Surface-Loading on the Flexure of Beams. 495 



Experiment 6 was made to establish Proposition III. with 

 greater certainty. 



Beam 128 millim. x 19 millim. x 5*5 millim. was placed 

 on the base of the straining-frame, on a piece of thin paper, 

 and loaded with shot until the first blue fringe came down to 

 a point 1*7 millim. from the top. The load was 65 lb. 



The same beam was then supported on two steel rollers 

 2 millim. in diameter and 120 millim. apart, and centrally 

 loaded over a similar roller until the same blue fringe appeared 

 at the bottom of the beam. The load was 55 lb. 



An hyperbola has been drawn (see fig. 1, Plate II.) of con- 

 venient proportions, cutting the horizontal through the above- 

 mentioned point at 28*5 divisions from the normal ; the shear 

 corresponding to the blue fringe is thus represented by 28*5 

 divisions, and there is that shear at the point with a load of 

 651b. 



Now the stress due to bending, at the extreme bottom fibre 

 of a beam 19 millim. deep, 120 millim. span, and 5*5 millim. 

 thick, with a load of 55 lb., is 1*436 tons per square inch. 



The vertical compressive stress at this point, due to the 

 load of 55 lb., is, as is shown later on, 0*121 ton per square 

 inch ; but we are not justified in superposing the shears pro- 

 duced by these two stresses, being tensile and compressive at 

 right angles, and the former as much as twelve times the 

 latter, so I shall take the stress at the blue fringe as 1*436 

 tons per square inch. 



Hence the compressive stress produced by 65 lb. over a 

 span of 120 millim., at the top fibre, is 



1-436 x m 



and the corresponding value in scale-divisions is 



1*436 x ■=-? x ., , , = 33*7 divisions. 

 55 1-436 



This distance is set off along the top surface in the figure, 

 and the point so found joined to the centre of the middle 

 section : where it cuts the hyperbola we should get darkness 

 on the normal with a span of 120 millim. We can also 

 draw lines representing the bending-stresses for other spans 

 for the same load of 65 lb. 



The position of the black bands on the normal, as found by 

 experiment for spans of 120 and 100 millim., are indicated on 

 the normal, and will be found to agree very closely with those 

 points found independently by the intersection of the two 

 curves. 



