1. Introduction
  2. Rivets
  3. Connection Design
  4. Working Stresses
  5. Bolts and Friction Joints
  6. References


Connections between metal parts are required in most applications, and are a critical part of every design. The joining of parts by cylindrical fasteners passing through holes has a long history. More recently, fusion welding has provided another very flexible means of connection. For the connection of relatively thin members in steel construction, rivets were traditionally used. These are cylinders of mild steel with forged heads, one formed in the factory and one formed in the field on the hot rivet. Such connections proved very reliable, giving excellent service.

Today, in heavy steel fabrication, welding has almost completely replaced riveting as a means of making connections. At one time, welding was only reliable with low-carbon steel, but intensive study and testing and development of techniques has made it satisfactory for joining most alloys. Welds require less preparation of the metal, do not reduce the effective cross-section, and take a minimum of space. On the other hand, welds must be made in suitable orientations, and must be carefully inspected by advanced non-destructive means to ensure that they have the necessary strength. The fusion may change the metallurgical properties of the metal, or make the weld brittle. Welding must be very carefully done with the proper materials to avoid these fatal difficulties.

Rivets require that holes be made to receive them, which reduces the net cross section, and these holes must be very accurately aligned. Although rivets can be used in any orientation, enough clearance must exist to set them properly. A riveted joint is quickly made, and is easy to inspect. A visual inspection and a few taps with a hammer are all that is necessary. Reliability considerations mandated riveted connections for boilers, and for joining all but low-carbon steel, until relatively recently. Rivet holes are not all bad, however: they are very effective crack-stoppers, while a welded connection can crack completely through. Where possible, rivet holes were usually punched rather than drilled, since this was much quicker and easier. However, it left residual stresses around the hole that were usually alleviated by reaming a punched hole to a slightly larger diameter.

Holes made in the shop sometimes did not line up properly when the members were assembled in the field. Workmen then might use the much-deprecated practice of hammering in a drift (a tapered, hardened pin) to squeeze the holes so the rivet (or bolt) could be inserted. This usually made an inferior joint, susceptible to cracking or other problems. Welds always line up, of course, and this is one of the advantages of welding.

All the strength considerations with respect to riveted connections also apply to bolted connections. A bolt is, indeed, no more than an inferior rivet that is easy to apply, and can be removed easily if required. While welds and rivets require skilled work, bolts can be applied by anyone, and this is often an important consideration. Special high-strength bolts can be used in a new way, and this is discussed below.

The design of riveted and bolted joints is an excellent illustration of the "strength of materials" approach. It was once the first thing presented to the student after the basic definitions of stress and the strength of steel. However, it now seems to have been dropped from texts, which is a pity. This article may help to show what a good aid rivets are to learning, besides being an essential part of engineering design.

In this article, I shall speak mainly of rivets, but it all applies to bolts as well. We will be concerned with large rivets and bolts, those larger than 1/2" or 12 mm in diameter, and subjected to serious forces. Smaller rivets and bolts are, of course, very important, but strength is not such a prominent matter in their design. Because of the nature of my reference materials, U.S. engineering standards will be used, though metric standards are now available in all cases.

In a riveted connection, we are permanently joining two plate-like members or rolled shape flanges. The connection may be subjected to tension tending to pull the members apart, or to shear the members either axially or transversely. The connection may also resist moments, perhaps created by eccentric loads. Torsional, twisting or tearing forces may also be applied. It is essential to determine the forces that act on a connection, both under normal loads and in extraordinary circumstances, and to ponder the types of failures they may cause. In most introductory treatments, riveted connections are assumed to be under simple tension. In many cases, this is what is required.

A riveted connection subjected to general forces is not a simple thing, and does not fail in a simple way. Nevertheless, strength of materials methods, combined with rigorous testing, has led to a very effective and simple theory of design.


A rivet comes as a circular steel rod with a forged head, the manufactured head, on one end. For use, it is placed red-hot into a hole conventionally 1/16" greater in diameter. The length of a rivet is the distance from the underside of the head to the end of the fresh rivet. The thickness of the material to be joined is called the grip of the rivet. The length of the rivet to be used for a certain grip is given in tables. The rivet is then set by forging a field head onto it.

At one time hot rivets were thrown to a riveter by a rivet boy who heated them at his portable rivet forge. The rivets were inserted into the hole, and a heavy set held against the manufactured head. A set was held against the end of the rivet on the other side, and was hammered vigorously, forging the field head in short order. This was hand riveting. The work could be lightened by pneumatic or hydraulic hammers, but most satisfactory was machine riveting, in which high pressure was applied, usually hydraulically, to form the field head. This was quiet and fast, but required access to both sides of the work for the anvil against which the pressure could work.

Rivets were heated to 950°F - 1050°F, handbooks say. This is not hot enough for an austenitic transition, so it must only have been for causing thermal expansion, not for softening the metal. By the time the field head was formed, the temperature was much lower. Carbon steel expands at about 6.5 ppm per degree F, so the cooling rivet contracted and pressed the plates very strongly. This is no trivial effect, since cooling through 500°F will produce a stress of (6.5 x 10-6)(500)(30 x 106) = 97,500 psi if there is no change in length. The tension in the shank will not actually get this high, since the steel will yield long before this takes place. When the field head is forged, the rivet shank also expands to fill the hole, which is also desirable.

This shrinkage puts considerable stress on the rivet head, but rivet heads can apparently resist a tension at least up to their yield strength. The sharp corner beneath the head is a definite stress-raiser, and a head would fail by a crack starting from this corner. The end of the rivet hole is sometimes rounded in preparation, which would guarantee a fillet at this point. If the head should be weak, one presumes that it would pop off when the rivet cooled, so the defective rivet could be replaced.

Rivet steel was originally dead mild steel with less than 0.10% C, whose softness would be an aid in forming the field head. The old ASTM A141 rivet steel had an ultimate strength of 52-62 ksi, and a yield strength of 28 ksi or greater. A coupon of rivet steel could be bent over on itself without cracking in a test of its ductility. This meant that the rivet was a little softer than the plates joined, and was relatively easy to forge. Modern rivet alloys, such as ASTM A502, seem to be somewhat stronger. Bolts can be mild steel, but also of heat-treated high strength steel, much stronger than the materials to be joined.

Connection Design

The usual tension connection fails by tearing between the rivet holes, by shearing of a rivet, or by crushing of either the rivet or the material joined. Tearing between rivet holes is a failure of the material joined, not the rivet. Shearing of a rivet is a failure of the rivet itself. Crushing can be a failure of either the material joined or the rivet. Ideally, a joint should fail as often by any of the three methods. In practice, tearing between rivet holes seems to be the prevalent mode of failure in most connections.

The distance between two rivets in a row of rivets is called the pitch of the rivets, while the distance of the row from the edge of the plate (or another row of rivets) is called the gauge. The traditional rule for spacing of rivets is that they may be no less than 3 diameters apart. The AISC specifies a gauge of 1.5 + 4t inches, where t is the thickness of the plate joined. A gauge of 1.5 diameters is also reasonable. Rivets cannot be closer together, since then there would be no room for the riveting tools. Rivets cannot be spaced too widely, which would allow thin plates to gap and not close together firmly. Rivets in two parallel rows may be opposite one another, chained, or else may be staggered, or alternate. Rows of rivets are generally at right angles to the direction of the force to be resisted.

It is generally assumed that all the rivets in a connection share the load equally. This requires that the material be ductile and have a yield point, conditions well satisfied by structural steel. The AISC allows a working stress of 15 ksi for A502 rivets in shear. The AREA specifications for steel railway bridges allowed 13.5 ksi for power-driven rivets of A141 steel. The ASME boiler code assumed an ultimate shear strength of 44 ksi. With a factor of safety of 5, the working stress was 8.8 ksi. This illustrates the wide variety of working stresses allowed in different codes. I have not seen any correlation of shear strength with tensile strength, though there should be some connection. To find the force resisted by a single rivet in shear, just multiply these working stresses by the actual cross-sectional area of the rivet.

The total tensile force that can be supported by the connection will be the working stress in tension times the net area of the member. If there is a single row of rivets perpendicular to the direction of the stress, then the net area is the thickness of the plate times the width less the actual diameters of the holes. For example, suppose we have a lap connection with four 1" rivets in a single row. Allowing a shear strength of 13.5 ksi, a load of 10.6 kip per rivet, or 42.4 kip in all, can be supported. Let's suppose the member is 12" wide, which will allow a pitch of 3". The four rivet holes of 1-1/16" diameter will amount to 4.24", leaving 7.76" net. If the tensile strength of the plate is 18 ksi, a total area of 2.36 in2 will be required, or a thickness of 0.304". Therefore, a 3/8" plate will be ample.

The bearing stress must now be checked. Bearing stress is calculated on projected area, in this case 4" x 3/8", or 1.5 in2. The actual diameter of the rivet filling the hole, 1.0625" could just as well be used, but the nominal diameter is conservative. All the rivets are considered to share the bearing stress, as they share the shear stress. The bearing stress is 42.4/1.5 = 28.3 ksi, just in excess of the recommended 27 ksi. The easiest way to get a larger bearing area is to use a thicker plate. For a 7/16" plate, the bearing area will be 1.75 in2, and the stress will be 24.2 ksi, which is satisfactory. The joint is illustrated at the right. In the cross-section, the shaded area is the tension area, while the white areas are the bearing area.

In practice, we would probably start with the tension in the member. Selecting a rivet size, we would then divide the tension by the shear resistance per rivet to find the total number of rivets necessary (rounding up to the nearest integer). An arrangment of the rivets would be decided upon, and the member would be proportioned so that the tensile stress on the net area was permissible. Finally, the bearing stress would be checked, and adjustments made if necessary.

The efficiency of a connection is the ratio of the net tensile area to the gross area. In the above example, the gross area is 12 x 7/16 = 5.25 in2 and the net area is 7.76 x 7/16 = 3.40 in2, so the efficiency is 64.7%. More efficient connections can be made by using multiple rows of rivets or using splice plates, up to over 85%. The tensile member can be enlarged near the connection to allow for the connection efficiency.

We have neglected the eccentricity of the loads on a simple lap joint, and this is normally permissible. Connections carrying heavier loads would naturally be designed to be more symmetrical. Note that the strength of the connection is aided by the friction between the members that are clamped together by the rivets. This is usually a very significant contribution to the strength of the joint, but American and British practice is to neglect it, because it is difficult to estimate accurately. On the other hand, German and French engineers design connections on the basis of the frictional resistance, and consider rivet shear a bonus.

The calculation of net tensile area is more difficult in connections with more than one row of rivets. If the rows are far enough apart, they may be considered separately in the calculation of net tension area. As they come closer, there is the possibility of a tear moving from row to row that must be considered. This is generally done in a curious way that seems to work well in practice. The designer imagines routes of tearing across the member passing through certain holes. For each route, an effective net section is calculated, and the smallest net section that exists wins the contest. The net section is found by deducting the actual diameter of each hole along the path, diminished by a quantity s2/4g for each path between holes, where s is the difference in location parallel to the stress ("pitch") and g is the difference in location at right angles to this ("gauge"). If the rivets are in one row, as in the example, then s = 0 in each case, and the net section is found by deducting the holes, as in the example.

An example is shown at the left, with s and g illustrated. Let's assume the width w of the member is 9", and g = s = 3". If we consider a route straight across the member passing through the two holes at the left, the net section will be 9 - (2)(1) = 7.00 times the thickness. The net section on a route passing through all three holes will be 9 - [3 - 2(3/4)] = 9 - 1.5 = 7.50 times the thickness. 3/4 is the deduction 32/(4)(3). This is a larger area, so the first route governs.

If we reduce s from 3.0 to 1.5, then the deduction is 3/16 for each diagonal, so that the net area will be 9 - (3 - 3/8) = 6.375 times t. This is a smaller area than that through the two leftmost holes, so it will govern. Finally, if the three rivets were in line, then the net area would be 9 - 3 = 6 times t.

Working Stresses

Three working stresses were used in the design of a tension joint: the tensile strength of the plates joined; the shear strength of the rivets; and the bearing strength of the rivets. The values we used--18 ksi, 13.5 ksi and 27 ksi are typical. These must bear some relation to the strength of the steel in a tension test, which gives us the ultimate strength, the yield point and the elongation in a 2" gauge length. All mild steels behave in the same way, so it is only a matter of scaling the figures.

Pure iron is all bcc ferrite, with an ultimate tensile strength of about 50 ksi, a yield strength of about 25 ksi, and an elongation of 36%. Steel with 0.83% C has an ultimate tensile strength of about 130 ksi, an elongation of only 2% or so, and no definite yield point. These properties vary about linearly with carbon concentration between these limits. Structural uses demand a definite yield point, and considerable plastic deformation without loss of strength. The best compromise seems to be at about 0.2% C, where the ultimate strength is about 72 ksi, the yield point 36 ksi and elongation about 25%. Such steel has a Brinell hardness of 100, and is about 2/3 ferrite and 1/3 pearlite.

Working stresses are tied to the yield point in the AISC specifications. The working tensile strength is taken as 0.66 of the yield stress, or 24 ksi for A36 steel. A36 is a low-carbon steel with no more than 0.25% C, a tensile strength of 58-60 ksi, and a guaranteed yield point of 36 ksi. Since the ultimate strength is about twice the yield stress, this implies a factor of safety of 3. On the other hand, the ASME boiler code specifies a factor of safety of 5, which would make the working stress 14.4 ksi. Good practice seems to take a factor of safety between these limits. Our figure of 18 ksi from the AREA bridge code would correspond to a factor of safety of 4.

The working shear stress for the rivets is a different matter, since it is not measured directly in the tensile test. If a tensile specimen failed by shear at 45°, then this shear stress would be equal to the tensile stress. However, this does not appear to be the case. Instead, the working shear stress seems to be about 75% of the working tensile stress. One must assume that on test, this makes a joint equally strong against tearing and rivet shear.

The AISC code takes the strength in bearing between two parallel surfaces at 0.90 of the yield strength. This is reasonable if it is assumed that a material crushes at the yield strength in tension, which may or may not be valid. The bearing on rivets is referred to the projected section, not to the circumferential section, which will be π/2 = 1.57 times greater. The working stress in bearing is 1.5 times the working tensile stress in the AREA bridge code, so this may well be the reasoning involved. In the AISC code, the working stress in bearing on rivets is taken as 1.35 times the yield stress, or twice the working tensile stress. At least, connections seem to fail only rarely in bearing, so these specifications are probably satisfactory.

Therefore, as a rule of thumb, the working shear stress can be taken as 75% of the working tensile stress of the rivet steel, and the working bearing stress as 150% of the working tensile stress of the rivet steel or of the material joined, whichever is the smaller. These are relatively conservative estimates that should give safe results. Nevertheless, the requirements of any appliable code of practice should govern where safety is an issue.

The yielding property of mild steel that gives it such safety and reliability depends on the free motion of dislocations in the crystal structure. If the temperature is lowered, dislocations can move less and less freely. At about 0°C for carbon steel, the dislocations build up at pinning points and the metal becomes locally brittle, allowing cracks to form. This was discovered with the welded Liberty ships of the Second World War. In the cold North Atlantic, cracks formed in the hulls as the ships labored in the weather. Without rivet holes to stop them, cracks could propagate around the circumference of the hull, and the ships would break in two.

The transition from ductile to brittle failure is relatively sharp, and occurs only in BCC ferrite. An austenitic (FCC) steel does not behave in this way. The addition of a little extra manganese, about 1.3%, lowers the embrittlement temperature sufficiently for normal use. Low-nickel steels (3% -5% Ni) also resist embrittlement, because nickel favors austenitic crystal structure.

Bolts and Friction Joints

Carbon steel bolts, ASTM A307, are made in sizes from 1/4" to 4" for general purposes. The size of a bolt is its major diameter, with rolled or cut threads penetrating to a smaller root diameter. The net tensile area of a bolt of major diameter D inches is 0.7854(D - 0.9743/n)2 in2, where n is the number of threads per inch. The ultimate tensile strength of A307 bolts is 60 ksi, so with a factor of safety of 3, their working stress is 20 ksi. In shear, they are allowed only 10 ksi, so they are not quite the equivalent of a rivet of the same diameter. The thread length on a bolt is 2D + 1/2 inches, up to 6" long, with an extra half inch for longer bolts. Sizes of the head and matching nuts are given in tables. For example, the head of a 1" bolt is 1-1/2" over flats. A bolt is specified by its major diameter and threads per inch, plus a symbol for its thread series, as 1-8 UNC for a 1" bolt with 8 threads per inch in the Unified National Coarse series. The minimum number of threads per inch is 4.

Special high-strength steel bolts, ASTM A325, are made specifically for structural connections. There are other similar bolts, such as A449 and A490 bolts, but we'll discuss only the A325 bolts as a good example of the general type. These bolts are made from medium-carbon steel with 0.30% to 0.52% C. The bolts are heated to austenitize them, liquid quenched, and then tempered at 800°F (427°C). They are made in sizes from 1/2" to 1-1/2". Bolts 1" and less have an ultimate tensile strength of 120 ksi, while the larger ones have 105 ksi. Therefore, they are very much stronger than A307 bolts, and this extra strength is necessary for the way they are used. They are also considerably more expensive than A307 bolts, so one must be on the lookout for counterfeits. A325 bolts are marked thus on the heads, usually together with three radial lines at 120°.

In use, all the bolts in a connection are first brought to the "snug tight" state, which is as tight as a man with a wrench can manage. Then each nut or bolt head is given an extra half turn, or three-quarters of a turn for bolts over 8" long, by appropriate machinery. This is intended to create a tension in the bolt of 70% of its ultimate strength. For a 1" bolt, this is 51 kip. The tightening is very carefully inspected in practice, to make sure the desired tension is created. This clamping tension is very much greater than is usually allowed in rivets and bolts on the basis of working stresses. Originally, hardened washers were required under the part that was turned, either the nut or the bolt-head, but this is no longer necessary.

With bolts so tightened, the parts of the connection are so tightly pressed together that they cannot move, so long as the applied force is less than the frictional resistance. The AISC has adopted a slip factor of 0.35 as an equivalent to the static coefficient of friction. This means that a 1" bolt can resisist (0.35)(51) = 17.85 kip before the connection slips. The shear strength of the bolt calculated the usual way is (0.7485)(15) = 11.23 kip. There is a factor of safety here of 17.85/11.23 = 1.6. The bolt is considered as able to take 11.23 kip in the design, so if the joint fails by slipping, the shear will prevent failure. The joint is considered not to slip in practice, and so bearing and shear never come into play. In such a friction joint, bearing strength need not be checked at all.

This recalls the familiar property of Coulombic friction, that the frictional force is proportional to the normal force and independent of area. Bolts, of course, depend on friction to hold the nuts tight on the bolts. If there were no friction, the nuts would just unwind and fly off spinning!

A325 bolts can substitute for rivets of the same diameter one for one, even if a friction joint is not intended, and the bolts are never stressed as for a friction joint. The AISC now requires a friction joint in cases of reversed or varying stresses, so that the bad effects of motion and fatigue are minimized. Friction joints have been used much more extensively in German and French engineering, even with rivets. The AISC does not consider that the necessary tension can be established reliably with hot rivets, a caution that may well be excessive. Friction joints finally have a place in American engineering, however.


American Institute of Steel Construction, Manual of Steel Construction, latest edition (New York: AISC, 101 Park Avenue, New York NY 10017). Part 4, Connections.

C. Carmichael, ed., Kent's Mechanical Engineer's Handbook, 12th ed. (New York: John Wiley & Sons, 1950). Design and Production volume, Section 10.

American Railway Engineering Association, Specifications for Steel Railway Bridges (Chicago: AREA, 59 E. Van Buren St., 1950).

Annual Book of ASTM Standards 2000 (West Conshohocken, PA: ASTM, 2000). The A502 standard for rivets was withdrawn in 1999. The American National Standards Institute standard B18.1.2 for rivets is still available. The ANSI website is difficult to use and unfriendly, and it is not possible even to access a list of standards on the web, apparently. ANSI seems to be a typical arrogant American organization unwilling to provide public and educational services.

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Composed by J. B. Calvert
Created 7 October 2003
Last revised