—_— a a 
SIMPLE STRAINS AND STRESSES 65 
PP to pull the bar asunder at C. This system of internal forces is called 
tensile stress. 
Since stress is a distributed force, its intensity is measured in the 
same way as that of fluid pressure, viz. by the number of units of force 
on a unit of area, such as pounds per square inch, tons per square inch, 
or tons per square foot. 
If the stress at the section C be uniformly distributed over the section, 
and its intensity be denoted by f (say in lbs. per square inch), and if 
a denote the area of the section (say in square inches), and P denote the 
load (say in lbs.), then it is obvious that P= af. 
79. Compressive Strain and Compressive Stress.—If the external 
forces acting on the bar AB (Fig. 77) be reversed in direction, the bar 
becomes shorter by an amount x, and a compressive strain is produced 
whose amount is z//. At any cross section C there is compressive stress 
which resists the tendency of the forces PP to crush the bar at C. 
As in the case of tension, if the stress is uniformly distributed over 
the cross section, P=af, but f now denotes compressive stress. 
It should be mentioned here that unless a bar which is subjected to 
compression by a load acting in the direction of its length is short com- 
pared with its transverse dimensions, it has a tendency to bend, and the 
compressive stress at a transverse section is not uniform, hence the formula 
P=af only applies to short pieces, or to long pieces if special means are 
adopted to prevent the bending of the latter. Long pieces in compression 
are considered in Chapter X. 
80. Shearing Strain and Shearing Stress.—Suppose a rectangular 
block of india-rubber ABCD (Fig. 78) to have its face BC cemented to 
a vertical wall, and that it has a rigid plate cemented to its opposite face 
AD. The face ABCD being vertical, let a 
vertical force P be applied at the middle point 
of the lower edge of the plate. The force P ° 
will evidently tend to make the plate slide on- 
the face AD of the rubber. The force P will 
also tend to make the face BC of the rubber 
slide on the wall, and it is also evident that if 
any vertical transverse section XX be taken 
dividing the block into two parts, the force 
P will tend to make the part AXXD slide on 
the part BXXC along the interface XX, as 
shown to the right of Fig. 78. In each case 
the tendency to slide is resisted by a tangential or shearing stress acting 
along the face. 
The load P will cause the block ABCD to become distorted so that 
the rectangle ABCD will become a parallelogram aBCd, and the shearing 
strain produced is measured by the fraction Aa/AB or 2/1. 
If the area of a transverse section XX is denoted by a, and if the 
shearing stress is uniformly distributed over the section and is denoted 
by /, then as in the case of tension P=a/. 
81. Volume Strain.—If a body be subjected to pressure all over its 
surface, as when immersed in water under pressure, it will suffer a change 
of volume, and if V is the original volume of the body, and v the altera- 
tion of volume due to the pressure, then v/V is called the volume strain, 
E . 
