20 



BULLETIN 77. U. S. DEPABTMENT OF AGBICULTUEE. 



The fiber stress at the elastic limit and the modulus of rupture 

 were computed for the diameter and moment of inertia obtaining 

 under the smaller loading point, the section being regarded as a 



true circle. The stiffness 



factor * 



was obtained 



from the moment of in- 

 ertia (I) and the deflec- 

 tion (d) at the center of 

 the beam. These values 

 for stiffness are compar- 

 able for pieces of the 

 same span only. The 

 true modulus of elasticity, 

 which is difficult to ob- 

 tain accurately for a beam 

 with a varying moment 

 of inertia, depends upon 

 the cube of the span. 

 This relation is not con- 

 sidered in the "stiffness 



P 

 factor" used, j^ } and this 



causes the values for the 

 7-foot span to be approxi- 

 mately ten times as large 

 as for the 15-foot span. 

 The work to maximum 

 load was calculated from 

 the area under the load- 

 deflection curve, and is 

 given in terms of unit 

 volume. In the calcula- 

 tions involving the unit 

 stresses of the props, the 

 top area of the prop was 

 used. 



The volume of the test 

 pieces was calculated by 

 multiplying the average 



Fig. 6.— Method used in testing mine props in compression. | ^ areas of the ton 



the butt, and the mean proportional between them, by the length. 

 The weight per cubic foot was obtained from this estimated vol- 

 ume, and is therefore given as "approximate." 



