Spherical Shells Subjected to Internal Pressure.

D = internal diameter of shell in inches;

P = internal pressure in pounds per square inch;
S = safe tensile stress per square inch;

Let:

t = the thickness of metal in the shell in inches. Then:

This formula also applies to hemi-spherical shells, such as the hemi-spherical head of a cylindrical container subjected to internal pressure, etc.

Example:- Find the thickness of metal required in the hemi-spherical end of a cylindrical vessel, 2 feet in diameter, subjected to an internal pressure of 500 pounds per square inch. The material is mild steel and a tensile stress of 10,000 pounds per square inch is allowable.

If the radius of curvature of the dome head of a boiler or container subjected to internal pressure is made equal to the diameter of the boiler, the thickness of the cylindrical shell and of the spherical head should be made the same. For example, if a boiler is 3 feet in diameter, the radius of curvature of its head should be made 3 feet, if material of the same thickness is to be used and the stresses are to be equal in both the head and cylindrical portion.

Collapsing Pressures of Cylinders and Tubes Subjected to External Pressures. The following formulas may be used for finding the collapsing pressures of modern lap-welded Bessemer steel tubes:

in which P = collapsing pressure in pounds per square inch; D = outside diameter of tube or cylinder in inches; t = thickness of wall in inches.

Formula (1) is for values of P greater than 580 pounds per square inch, and Formula (2) is for values of P less than 580 pounds per square inch. These formulas are substantially correct for all lengths of pipe greater than six diameters between transverse joints that tend to hold the pipe to a circular form. The pressure P found is the actual collapsing pressure, and a suitable factor of safety must be used. Ordinarily, a factor of safety of 5 is sufficient. In cases where there are repeated fluctuations of the pressure, vibration, shocks and other stresses, a factor of safety of from 6 to 12 should be used.

The table "Tubes Subjected to Externa! Pressure" is based upon the requirements of the Steam Boat Inspection Service of the Department of Commerce and Labor and gives the permissible working pressures and corresponding minimum thickness of wall for long, plain, lap-welded and seamless steel flues subjected to external pressure only. The thicknesses in the table have been calculated from the formula:

in which D outside diameter of flue or tube in inches; T = thickness of wall in inches; P= working pressure in pounds per square inch; F = factor of safety. The formula is applicable to working pressures greater than 100 pounds per square inch, to outside diameters from 7 to 18 inches, and to temperatures less than 650° F.

A full

The Formulas (1) and (2) given on the preceding page were determined by Prof. R. T. Stewart, Dean of the Mechanical Engineering Department of the University of Pittsburg, in a series of experiments carried out at the plant of the National Tube Co., McKeesport, Pa. These tests occupied a period of four years. report of the details of these experiments will be found in a paper presented by Prof. Stewart before the American Society of Mechanical Engineers in May, 1906. The principal conclusions to be drawn from the results of this research may be briefly stated as follows:

The length of tube, between transverse joints tending to hold it to a circular form, has no practical influence upon the collapsing pressure of a commercial lapwelded steel tube, so long as this length is not less than about six times the diameter of the tube.

The apparent fiber stress under which the different tubes failed varied from about 7000 pounds per square inch for the relatively thinnest to 35,000 pounds per square inch for the relatively thickest walls. Since the average yield point of the material tested was 37,000 pounds and the tensile strength 58,000 pounds per square inch, it is evident that the strength of a tube subjected to external fluid collapsing pressure is not dependent alone upon the elastic limit or ultimate strength of the material from which it is made.

16

0.385

17

18

0.344 0.366
0.366
0.389 0.409 0.429 0.448 0.468
0.387 0.412 0.433 0.454 0.475 0.496 0.516

Dimensions and Maximum Allowable Pressure of Tubes Subjected to External

0.404 0.422

0.440

0.459

0.488

RIVETING AND RIVETED JOINTS

Classes of Riveted Joints. When the plates to be joined by riveting overlap each other and are held together by one or more rows of rivets, a lap-joint is formed. In a butt-joint the plates are in the same plane and are united by a cover plate or butt strap, which is riveted to each plate. A combination lap-joint consists of a cover plate inside or outside the lap, and three rows of rivets, the central row passing through the two plates and the cover, and having twice as many rivets as the other two rows. The term single riveting means one row of rivets in a lap-joint or one row on each side of a butt-joint; double riveting means two rows of rivets in a lapjoint or two rows on each side of the joint in butt riveting. Joints are also triple and quadruple riveted.

Pitch of Rivets. The pitch is the distance from center to center of adjacent rivets. The pitch of rivets should be as large as possible without impairing the tightness of the joint when under pressure. For single-riveted lap-joints in the circular seams of boilers which have double-riveted longitudinal lap-joints:

in which d= the actual diameter of rivet (in parallel hole); = thickness of plate. For double-riveted lap-joints:

pitch = 8t

The following formulas for determining the pitch are given by Unwin:
For single-riveted joints in single shear (mild steel):

For triple-riveted joints with rivets in single shear (mild steel):

In the foregoing formulas, d= diameter of the driven rivet.

To secure a joint of maximum strength, the breadth of lap must be such as to prevent it from breaking zigzag. Tests have demonstrated that rupture is equally probable through a diagonal as through a transverse line, unless the net diagonal

d
3

section exceeds the net section along the transverse line by 30 to 35 per cent. This corresponds to a diagonal pitch of P+ in which P is the straight pitch, and d, the diameter of the rivet hole. A general rule for the pitch between rows in staggered riveting is as follows: The pitch between rows should equal one-half the pitch of the rivets in a row, plus 4 of the diameter of the rivet holes. The distance from the edge of the rivet hole to the edge of the plate should never be less than the rivet diameter.

Rivet Diameter. - Rivet diameters for plates of given thickness range in practice from d= 1.2Vt to d = 1.4 V1, in which d = diameter of the rivet and t = thickness of plate. The larger size is preferable for steel and single-riveted joints, and the smaller for iron and multiple-riveted joints.

Length and Proportions of Rivets. In order to form the head and fill the clearance space in the rivet hole, the rivet should have a length in excess of the thickness of the plate equal to about three-fourths the diameter for countersunk head, and from 1.3 to 1.7 times the diameter for ordinary riveting. (See table, "Rivet Lengths for Forming Round and Countersunk Heads.") The proportions of rivet heads are given in the accompanying illustration (Unwin). The dimensions are given in terms of the diameter and represent the average conditions, the sizes varying more or less in different shops.