The resistance to Compression, or crushing-stress,

The resistance to Tension, or pulling-stress,

The resistance to Shearing, or sliding-stress, and

The resistance to Transverse strains, or cross-breaking stress.

Materials yield to Compression in three different ways: 1. By direct crushing or crumbling of the material, or

2. By gradual bending of the piece sideways and ultimate rupture, or

3. By buckling or wrinkling (corrugating) of the material lengthwise.

Materials yield to Tension,

1. By gradually elongating (stretching), thereby reducing the size of the cross-section, and then,

2. By direct tearing apart.

Materials yield to Shearing by the fibres sliding past each other in two different ways, either

1. Across the grain, or

2. Lengthwise of the grain. Materials yield to Transverse strains,

1. By deflecting or bending down under the load, and (when this passes beyond the limit of elasticity),

2. By breaking across transversely.

In calculating strains and stresses, there are certain rules, expressions, and formulae which it is necessary for the student to understand or know, and which will be here given without attempting elaborate explanations or proofs. For the sake of clearness and simplicity, it is essential that in all formulas the same letters should always represent the same value or meaning; this will enable the student to read every formula off-hand, without the necessity of an explanatory key to each one. The writer has further made it a habit to express, in all cases, his formulae in pounds and inches (rarely using tons or feet); this will frequently make the calculation a little more elaborate, but it will be found to greatly simplify the formulae, and to make their understanding and retention more easy.

In the following articles, then, a capital letter, if it were used, would invariably express a quantity (respectively), either in tons or feet, while a small letter invariably expresses a quantity (respectively), either in pounds or inches.

The following letters, in all cases, will be found to express the same meaning, unless distinctly otherwise stated, viz.: -

a

signifies area, in square inches.

b

,,

breadth, in inches.

c

,,

constant for ultimate resistance to compression, in pounds, per square inch. (See Tables IV and V.)

d

signifies depth, in inches.

e

,,

constant for modulus of elasticity, in pounds-inch, that is, pounds per square inch. (See Table IV.)

f

,,

factor of safety.

g

,,

constant for ultimate resistance to shearing, per square inch, across the grain. (See Tables IV and V.)

g1

,,

constant for ultimate resistance to shearing, per square inch, lengthwise of the grain. (See Table IV.)

h

,,

height, in inches.

i

,,

moment of inertia, in inches. (See Table I.)

k

,,

ultimate modulus of rupture, in pounds, per square inch. (See Tables IV and V.)

l

,,

length, in inches.

m

,,

moment or bending moment, in pounds-inch. (See Table IX.)

n

,,

constant in Rankine's formula for compression of long pillars. (See Table II.)

o

,,

the centre.

P

,,

the amount of the left-hand re-action (or support) of beams. in pounds.

q

,,

the amount of the right-hand re-action (or support) of beams, in pounds.

r

,,

moment of resistance, in inches. (See Table I.)

s

,,

strain, in pounds.

t

,,

constant for ultimate resistance to tension, in pounds, per square inch. (See Tables IV and V.)

u

,,

uniform load, in pounds.

V

,,

stress, in pounds.

w

,,

load at centre, in pounds.

x, y, and z signify unknown quantities, cither in pounds or inches.

δ

signifies total deflection, in inches.

P2

,,

square of the radius of gyration, in inches.

Stresses 1001

,,

diameter, in inches.

Stresses 1002

,,

radius, in inches.

π

= 3.14159, or, say, 3.1-7 signifies the ratio of the circumference and diameter of a circle.

If there are more than one of each kind, the second, third, etc., are indicated with Roman numerals, as for instance, a, a1,a11, a111, etc., or b, b1, b11, b111, etc.

In taking moments, or bending moments, strains, stresses, etc., to signify at what point the}' are taken, the letter signifying that point is added, as for instance: -

m

signifies moment or bending moment at centre.

mA

,,

,,

,,

,,

Point A.

mB

,,

,,

,,

,,

point B.

mx

,,

,,

,,

,,

point X.

s

,

strain at centre.

SB

,,

,,

Point B.

SX

,,

,

" X

V

,,

stress at centre.

vD

,,

,,

point D.

vX

,,

,,

X.

w

signifies load at centre.

wA

,,

,,

,,

point A.