CHAPTER XXII

FRAMEWORK STRUCTURES-SIMPLE TRIANGULAR FRAMES

Simple

Nature of the Stress on the Bars of a Frame.

Triangular Frames. Derricks and Cranes. Sheer

PAGE

Flow of Water. Head. Discharge. Hydraulic Re-

PRELIMINARY CHAPTER

MENSURATION AND CURVE CONSTRUCTION

FOR the solution of many questions in Applied Mechanics,
it is necessary that the student should be able to find
the periphery or area of a plane figure of given dimen-
sions, or the surface or volume of a solid body.

Also the construction of certain curves is often neces-
sary; and a knowledge of a few simple properties of
these curves enables us to solve questions with greater
ease and rapidity than could otherwise be attained.
Hence we commence with the present chapter.

Most of the forms we meet with are of simple char-
acter, or else can be readily resolved into such simple
ones; we consider then these simple forms in order.
The Parallelogram.

RULE. The area of a parallelogram is obtained by

multiplying any side by

the perpendicular distance

between it and the opposite

side.

Thus in the figure we

have two parallelograms,

but the area of each is

Fig. 1.

axb square inches or feet, according as a and b are

inches or feet.

Or, if it be more convenient, the area of the right-

hand figure is cx d.

CHAPTER XXII

FRAMEWORK STRUCTURES-SIMPLE TRIANGULAR

Nature of the Stress on the Bars of a Frame. Si

Flow of Water. Head. Discharge. Hydraulic

sistance. Surface Friction

Pipes.

Loss of Head. Virtual Slope.
Discharge. Sudden Enlargements .

Form

Table of Coefficients of Hydraulic Resistance.

Flow of Gases

Examples

CHAPTER XXIV

HYDRAULIC MACHINES

Weight Machines. Overshot Wheel. Breast
Pressure Machines. Accumulators. Speed

Motion. Direct Acting Lifts. Hydra
Hydraulic Brakes

Pumps .

Examples

The Triangle.

RULE.-The area of a triangle is obtained by multi

cxd

2

Fig. 2.

plying any side by the perpendicular distance of the opposite corner from it, and dividing the result by 2.

The three triangles shown have then each the same axb

area, viz.

2

Or we can, as in the centre triangle, express it as

There are other rules which may be used, generally involving the trigonometrical functions of the angles, depending on what data are given. But the engineer should generally, in such cases, use the given dimensions to construct the figure to scale; and then measure the necessary dimensions required for the preceding rule.

EXAMPLE.—Find the area of a triangle, the sides of which are 7, 8, and 9 inches respectively.

If the triangle be constructed to scale, on the 8-inch side as base, and the perpendicular height is then measured, it will be found to be 6.7 inches.

The Trapezium.—This figure has one pair of sides parallel, but not the other.

RULE.-The area of a trapezium

is obtained by multiplying half the sum of the parallel sides by the perpendicular distance between them.

Hence area of figure

a+c

=

xb.

2

a

Fig. 3.

We can see how this rule is obtained if we divide the

figures into two triangles by the line BD.