Strength and elasticity of structural members

STRENGTH AND ELASTICITY OF STRUCTURAL MEMBERS

BY R. J. WOODS,
FELLOW AND ASSISTANT PROFESSOR OF ENGINEERING, R.I.E. COLLEGE, COOPER'S HILL.

LONDON; EDWARD ARNOLD; 1903

Strength and elasticity of structural members

PREFACE.

These chapters were originally written as a series of lectures for students at the Royal Indian Engineering College, Cooper's Hill; so that the book may be looked upon as one mainly for students of Engineering.

The aim has been to make the work as practical as possible; and to keep the methods simple and concise, involving only a fair knowledge of elementary mathematics. Numerous diagrams and illustrations have been introduced, so as to enable the student to obtain as clear an insight into the methods as possible.

Many of the proofs are of course similar to those ordinarily used in other published works, and I have especially to acknowledge the following books of reference :

-    Strength and Elasticity of Materials. Professor EWING.
-    Theory of Structures and Strength of Materials. Professor BOVEY.
-    Elements of Machine Design. Professor UNWIN.
-    Notes on Engineering Construction. Professor REILLY.

I have to thank Professor Minchin, F.R.S., for much advice and assistance, and I am also indebted to Dr Brightmore, D.Sc., for his help.

A large number of Examples have been added as exercises for the student on the application of the principles explained in each chapter.

CONTENTS.

- GRAPHIC STATICS.
- STRESS AND STRAIN.
- STRESS-STRAIN DIAGRAMS, WORKING STRESS, RESILIENCE.
- COMPOUND STRESSES.
- BENDING MOMENTS AND SHEARING FORCES.
- MOMENTS OF INERTIA.
- GIRDERS.
- DEFLECTION OF BEAMS.
- DEFLECTION.
- BENDING AND DIEECT STRESS. NON-AXIAL LOADS. STRESS AT A PLANE JOINT. MASONRY STRUCTURES.
- COLUMNS AND STRUTS.
- RIVETED JOINTS.
- CONTINUOUS GIRDERS.
- CANTILEVER BRIDGES. SUSPENSION BRIDGES. ARCHED RIBS.
- TORSION.
- RIVETED JOINTS

Definitions. Lap and butt joints.

In a lap joint one plate overlaps the other, and they are connected by one or more rows of rivets.

In a butt joint the plates are kept in the same plane, and the joint is covered on one or both sides by a cover plate, and riveted to each.

The lap joint is objectionable, owing to the straining forces on the two plates not being in the same line, thus forming a couple, which weakens the joint by bending (Fig. 247).

The butt joint is the one generally used, and is the more effective joint, owing to its symmetry and the absence of eccentric stresses.

Single riveting is when there is only one line of rivets in a lap joint, or one line on each side of the joint in a butt joint.

Double riveting, when there are two lines of rivets in the lap, or two lines on each side of the joint in a butt joint.

Fig. 245 shows a single-riveted lap joint; Fig. 246 a single-riveted butt joint; Figs. 248 to 251 show double-riveted lap and butt joints.

In chain riveting the rivets in the several rows are opposite to one another (Figs. 248 and 250).

In zig-zag riveting the rivets in one row alternate with the spaces in next row (Figs. 249 and 251).

The pitch is the distance from centre to centre of the rivets in one row.

The lap is the distance at right angles to the joint, between the edges of two overlapping plates ; or, in the case of a butt joint, the distance between the joint and the end of the cover plate.

A rivet is in single shear when shearing can take place only on one cross section of the rivet, as in lap joints and in butt joints with one cover plate (Figs. 245 and 246).

A rivet is in double shear when shearing can take place on two cross sections, as in butt joints with two cover plates.

Rules to be observed in designing joints.

Diameter of Rivets for given Plates.

Let t = thickness of plate in inches.
d diameter of rivet in inches.

The following rule is sometimes used: d = 2t for plates under 1/2";
D = 1 ½ t for plates of 1/2" and over.

In girder-work the rivets ought, if possible, to be of one size throughout, or at most two sizes. -In structural iron-work of this class rivets 3/4" and 7/8" are most generally used. Field rivets, which have to be riveted up by hand when the girder is in position, should never exceed 3/4" diameter, on account of the difficulty of driving tight rivets of larger size by hand.

Minimum pitch. The pitch of the rivets, as will be seen presently, is found by equating the shearing strength of the rivets to the tensile strength of the net area of the plate, but the distance between the edges of the rivet holes should never be less than the diameter of the rivet. This gives the minimum pitch 2d.

In boiler-work the pitch of the rivets is necessarily close, but in girder-work the pitch is practically never less than three diameters.

A maximum pitch of 6" should not be exceeded, as it is advisable to keep the plates close to prevent the entrance of water.

The distance from the centre of rivet hole to the edge of a plate should not be less than l 1/2d. This leaves a clear diameter of rivet between the edge of hole and edge of plate. This minimum distance is, in practice, increased to 1 1/2d + 1/16, and in girder- work is often 2d. It should be noted that the diameter of the hole is usually 1/16 of an inch larger than the diameter of the rivet, to allow the latter to enter when hot.

The grip of a rivet that is, the distance between its heads is the thickness of the plates to be joined by it, plus 1/32 of an inch for each joint between the plates to allow for uneven surfaces, which prevents very close contact. The maximum grip of a rivet should not exceed four times the diameter of the rivet.

Strength of riveted joints.

Take, for simplicity, the case of a single-riveted lap joint. Consider a strip of such a joint of width equal to the pitch (Fig. 252). As each rivet supports such a strip, the results obtained may be applied to the joint as a whole.