CHAPTER III
STRUCTURAL BOLTS
This chapter provides an in depth discussion of structural bolts including the materials from which they are made, manufacturing processes, design requirements, strength, stiffness and ductility considerations and behavior of instrumented bolts.
Since the scope of the research was limited to high-strength
structural bolts, discussion of bolt types other than A325 and A490 will be limited to providing background information. First, a background of standard bolt grades and material properties for high strength structural bolts will be presented, including a brief discussion of foreign bolt specifications. Next, the dimensions and manufacturing techniques of bolts will be discussed. This will be followed a discussion of common installation and fabrication techniques. An evaluation of current models for predicting the strength and stiffness characteristics of bolts is given next, followed by a brief discussion of ductility. Finally, the results of a comprehensive testing program will be presented followed by a discussion and conclusions.
3.1 Standard Bolt Grades Bolts typically used for structural joining applications can be classified based on three ASTM specifications: A307, A325, and A490. A307 bolts, or black bolts, are available in diameters ranging from 1/4” to 4” and in Grades A, B, and C. Grade A bolts are intended for general applications and have a specified minimum
30
tensile strength of 60 ksi. Grade B bolts are intended for flange joints in piping systems and have a tensile strength of 60 - 100 ksi. Grade C bolts are available as anchor bolts or studs manufactured from A36 steel with a tensile strength of 58 - 80 ksi (ASTM A307-94). A325 bolts are available standard diameters ranging from 1/2” to 1-1/2”. Bolts with diameters up to and including 1” have a minimum tensile strength of 120 ksi and bolts with larger diameters have a minimum tensile strength of 105 ksi. A325 are available in two types. Type 1 bolts are manufactured from medium carbon, carbon boron, or medium carbon alloy steel. A325 Type 3 bolts are made from corrosion resistant steel with weathering characteristics comparable to A588 steel. The A325 Type 2 bolt specification was withdrawn in November of 1991, but consisted of bolts made from low carbon martensite steel (ASTM A325-97; Kulak et al., 1987). A490 bolts have a specified minimum tensile strength of 150 ksi and are available in three types. A490 Type 1 bolts are available in diameters from 1/2” to 1-1/2” and are manufactured from alloy steel. A490 Type 2 bolts are available in diameters of 1/2” to 1” and made from low carbon martensite steel. A490 Type 3 bolts are available in diameters from 1/2” to 1-1/2” and are made from corrosion resistant steel with weathering characteristics comparable to A588 steel (ASTM A490-97). 3.1.1 Other Bolt Types Structural bolts other than those described above are also available. Both the A325 and A490 specifications have metric companions designated A325M and A490M, respectively. The bolts are designated M16, M20, M22, M24, M27,
31
M30, and M36. The ‘M’ indicates that bolt is metric and the following number is the nominal diameter in millimeters (CISC, 1997; ISO 7411). The International for Organization Standards (ISO) has introduced a set of specifications for bolts, nuts and washers that is very similar to the ASTM standards. ISO 7411 governs high strength structural bolts with large widths across the flats and ISO 7412 govern high strength structural bolts with short thread lengths. ISO 898 governs the properties of the material from which bolts are manufactured. Property classes 8.8 and 10.9 correspond closely to ASTM material specifications for A325 and A490 bolts, respectively. In addition to defining minimum tensile strengths for the materials, the ISO specifies minimum elongations after fracture that the bolt material must be able to sustain, thus providing minimum ductilities in the specification. Designations for ISO bolts consist of the specification number followed by the bolt size and property class. An ISO 7411 M16 x 80 - 8.8 bolt, for example, is a high strength structural bolt with a diameter of 16 mm and a length of 80 mm made from material conforming to the 8.8 property class. The ISO bolts are available in the same sizes as the A325M and A490M bolts. A 12 mm diameter bolt is also available but is not recommended for use (ISO 7411). The Deutsches Institut für Normung, or the German Specification, has a bolt specification very similar to the ISO specification. DIN 6914 is the specification that governs structural bolts. Like the ISO bolts, they are available in grades 8.8 and 10.9 which are similar to ASTM A325 and A490 bolts, respectively (Steurer, 1996).
32
3.2 Bolt Materials The behavior of any structural component is highly dependent on the properties of material from which it is produced; bolts are no exception. The variations in the characteristics of different grades and types of bolts is almost entirely due to the variation of material properties. 3.2.1 Steel Composition Because steel is invariably the material from which structural bolts are made, a discussion of its composition is warranted. Typical carbon steel is made up of iron, carbon, manganese, silicon, copper, phosphorus, sulfur, and other residual elements. The properties of a heat of steel are largely dependent on the amount of carbon present. Low carbon steel is typically classified as steel containing between 0.02% and 0.30% carbon, medium carbon steel is typically classified as steel with carbon levels from 0.30% to 0.70%, and steel with carbon levels greater than 0.70% is classified as high carbon steel (Pollack, 1988). Carbon is the principal hardening element in steel. Increasing the level of carbon increases the steel’s strength and hardness but at the cost of reduced ductility (AISI, 1986). A steel is classified as an alloy if certain elements are present in levels greater than specified limits. Typical alloying elements include manganese, phosphorous, sulfur, silicon, nickel, chromium, molybdenum, vanadium, copper, and boron (AISI, 1986). More desirable hardening and ductility characteristics can be achieved by using an alloy steel instead of standard carbon steel. Table 3-1 lists chemical requirements for A325 Type 1, A490 Type 1 and A490 Type 2 bolts (ASTM A325-97; ASTM A490-97).
33
Table 3-1: Chemical Requirements for A325 and A490 Bolts. A325 Type 1
A490
Element
Carbon
C Boron
C Alloy
Type 1*
Type 2
C
0.30-0.52%
0.30-0.52%
0.30-0.52%
0.30-0.48%
0.15-0.34%
Mn, min
0.60%
0.60%
0.60%
---
0.70%
P, max
0.040%
0.040%
0.035%
0.040%
0.040%
S
0.050%
0.050%
0.040%
0.040%
0.050%
Si
0.15-0.30%
0.10-0.30%
0.15-0.35%
‡
---
B
†
0.0005-0.003%
†
‡
0.0005% min
* 1-1/2” diameter A490 Type 1 bolts require a carbon content of 0.35-0.53%. † Boron shall not be added intentionally. ‡ Sufficient elements must be present so as to classify the steel as an alloy by the AISI.
3.2.2 Heat Treatment and Hardness Characteristics To help increase strength and hardness while maintaining acceptable ductility levels, high-strength structural bolts must be quenched and tempered. A325 and A490 bolts are heated to a temperature above their transformation temperature, quenched, and then tempered to a temperature of at least 800° F except for A490 Type 2 bolts which are tempered at a temperature of at least 650° F (ASTM A325-97; ASTM A490-97). A325 bolts are typically tempered at 800° F and A490 bolts are typically tempered at 1200° F (Baumsta, 1998). The range of hardnesses for structural bolts is shown Table 3-2.
34
Table 3-2: Hardness Requirements for Structural Bolts. Brinell Type
Diameter, dB
A307 Grade A
1/2” to 4”
1/2” to 1” A325 1-1/8” to 1-1/2”
A490
1/2” to 1-1/2”
Rockwell
Length
Min
Max
Min
Max
< 3dB
121
241
69 RB
100 RB
> 3dB
---
241
---
100 RB
< 3dB
253
319
25 RC
34 RC
> 3dB
---
319
---
34 RC
< 3dB
223
286
19 RC
30 RC
> 3dB
---
286
---
30 RC
< 3dB
311
352
33 RC
38 RC
> 3dB
---
352
---
38 RC
3.3 Dimensions of High-Strength Fasteners Figure 3-1 shows standard dimensioning nomenclature for high-strength fasteners. Heavy-hex, high-strength bolts are specially sized so that the same size wrench will fit both the nut and the head of the bolt. Additionally, the thread length, Lt, of high-strength bolts is shorter than for conventional bolts to allow the threads to be easily excluded from the shear plane when used in shear. Because of this, connection designers must take care when specifying the lengths of bolts to provide enough threads to avoid jamming the nut into the thread runout when pretensioning the bolt.
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A325
Ls F
Lth
Hb
Lb
ID T
Hn
OD
W
Figure 3-1: Nomenclature for Heavy-Hex Fastener Dimensions
3.4 Manufacturing Techniques Bolts are manufactured in one of two basic ways; by forming or threading. Each of these two manufacturing techniques can be broken down further into subcategories. Forming methods include cold heading, warm heading, hot forging or forming, and turning or screw machining. Threading methods include roll threading, cut threading, and ground threading (Phebus et al., 1998). ASTM specifications require that A325 and A490 bolts be either rolled or cut while A307 bolts may either cold or hot forged, or machined from bar stock (ASTM A307-94; ASTM A325-97; ASTM A490-97).
36
3.5 Nuts and Washers Nuts conforming to the A194/A194M or A563 specifications must be used with A325 and A490 bolts. When washers are used with A325 bolts, they must conform to either the F436 or F959 specification. When washers are used with A490 bolts, they must conform to the F436 specification. The use of washers is discussed further in Section 3.6.2 (ASTM A325-97; ASTM A490-97).
3.6 Bolt Installation The installation of high-strength fasteners in structural systems must be closely monitored to ensure that the proper pretension is applied to each bolt. Variables that influence the installation of bolts include the type of tension control system used, the type and size of bolts used, and the amount of lubrication present on the bolts. Although they are permitted to be used as snug tight fasteners, high-strength bolts are usually fully tensioned. To provide adequate pretension, the bolt is tightened until the tension in the bolt approaches or slightly exceeds the yield point of the bolt, typically 70% of the tensile strength. Table 3-3 shows the required pretensions by bolt type and size (AISC, 1994). The required pretensions for bolts above 1” in diameter can be difficult to attain. For this reason, fully tensioned bolts larger than 1” in diameter are not often used.
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Table 3-3: Required Pretension for High-Strength Bolts (kips) (AISC, 1994) Diameter
A325
A490
1/2”
12
15
5/8”
19
24
3/4”
28
35
7/8”
39
49
1”
51
64
1-1/8”
56
80
1-1/4”
71
102
1-3/8”
85
121
1-1/2”
103
148
3.6.1 Pretensioning Methods Several methods of pretensioning are available. They include the turn-ofthe-nut method, calibrated wrench method, and use of direct tension indicators or tension control bolts. The turn-of-the-nut method consists of calculating the amount of nut rotation, past the snug tight condition, that is necessary to induce the required tension in the bolt. Rotations of 120° to 240° are typical. The calibrated wrench method consists of using a torque wrench, either manual, electric, or pneumatic, that is calibrated with a torque-tension tester. The Skidmoore-Wilhelm torque-tension tester, shown in Figure 3-2, provides an accurate measure of the bolt tension relative to the torque applied by the wrench. The tester is a doughnut shaped hydraulic load cell that has been calibrated in some unit of force, usually kips. A cross section of the tester is shown in Figure 3-3. It is made up of an inner piston that slides inside an outer housing. interchangeable bushings and face plates allow a wide range of bolt sizes to be tested. As the a bolt is tightened in the tester, forces are exerted on the face plate
38
and bushing which, in turn, create a hydraulic pressure that can be measured and converted back into a force. The full stroke of the piston is approximately 0.25”.
Figure 3-2: Skidmoore-Wilhelm Type Torque-Tension Tester
Direct tension indicators or load indicator washers, shown in Figure 3-4(a), are washers that have raised dimples on their face that flatten out against the base material as the nut is tightened. When the gap between the flat part of the washer and the base material reaches a set limit, the bolt has reached its full pretension. Different washers are required for A325 and A490 of the same diameter because of the different pretensioning requirements.
39
Hydraulic Oil
Outer Housing
Interchangable Face Plate Interchangable Bushing
Hydraulic Piston
Retaining Ring
Figure 3-3: Cross section of Skidemoore-Wilhelm Torque-Tension Tester
Tension control or twist-off bolts, shown in Figure 3-4(b), are bolts that have a spine attached to the threaded end. A special wrench holds the spine and the nut and turns them relative to each other until the spine shears off. The bolt manufacturer calibrates the bolts so that the spines twist off when the bolt pretension has reached the specified level.
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(a)
(b)
Figure 3-4: DTI Washers (a) and Tension Control Bolts (b)
When using the calibrated wrench method or tension control bolts, great care must be taken to prevent the nut from running up onto the thread runout portion of the bolt. If this happens, either the torque measurements will be erroneous, or the spine will twist-off of the tension control bolt without inducing the desired pretension. Bolts designed for shear in the ‘threads excluded’ configuration are particularly susceptible to this problem. The problem can be avoided by using additional washers.1 3.6.2 Bolt Friction When a high-strength bolt is tensioned by torquing, approximately 40 to 50% of the applied torque is lost in friction between the bearing faces of the bolt and the base material and 30 to 40% is lost due to friction between the nut and bolt threads. This leaves only 10 to 30% of the applied torque to induce the axial pre1. The 1994 LRFD, on page 8-8, states that “additional washers are permitted to be used under the nut or under the head when circumstances permit.” It is recommended by the author, however, that shim plates be used when more than four washers are required.
41
tension (Barron et al., 1998a). Reducing the amount of friction in the bolt system allows the same pretension to be applied with a lower torque. The torque-tension relationship of bolts can be expressed in its simplest form as (Novak et al., 1998)
T
Kd b F .
EQ 3-1
where: T = the applied torque (k-in) K = the nut factor db = the bolt diameter (in) F = the bolt pretension (kip) The nut factor is a measure of the friction present in the bolt, nut, and washer system. The average nut factor for a 1” diameter A490 bolt as received from the supplier is 0.179, the average nut factor for the same bolt preserved with Johnson stick wax is 0.275, and the average nut factor for a rusty 1” diameter A490 bolt is 0.389 (Novak et al., 1998). Two of the easiest ways to reduce bolt friction are to use washers and lubricants. Washers help to reduce the friction between the bearing surfaces of the nut face and base material by providing a clean, smooth surface, free of mill scale and rust. The use of washers under the turned element is required by the RCSC specification when high-strength bolts in standards holes are tensioned by the calibrated wrench method, or when the yield strength of the base metal is less than 40 ksi (RCSC, 1996). When tension control bolts are used, the nut and washer
42
that are supplied with the bolt must be used. ASTM F436 hardened washers are typically used with high-strength bolts. By using commercially available lubricants, the nut factor can be reduced to values of 0.050 to 0.100 (Novak et al., 1998). When using lubricants, it is important to lubricate both the threads and the bearing faces of the bolt head, nut face, washers and base material.
3.7 Strength Of the many characteristics of bolts, strength is the most important. The possible failure modes of bolts are tensile failure, shear failure, and combined tensile and shear failure. 3.7.1 Tensile Strength Tensile loading is the most fundamental mode of loading of bolts. The possible failure mechanisms under axial loading are tension failure of the bolt, stripping of the bolt threads, and stripping of the nut threads. High-strength fasteners are designed so that tension failure of the bolt will occur before stripping of the threads. As a result, the design engineer need only be concerned with tensile strength of the bolt. The axial strength of a bolt can be calculated as the ultimate strength of the bolt material multiplied by the cross sectional area of the bolt. Considering a failure in the shank of the bolt, the cross sectional area is calculated as shown in Equation 3-2 (Barron et al., 1998a).
Ab
π d 2b 4
43
EQ 3-2
where Ab = cross sectional area of the bolt shank (in2) db = nominal diameter of the bolt (in) Bolts subjected to tension rarely fracture through the shank, though, and using the area of the shank in capacity calculations can result in an overestimate of the bolt’s actual strength. Another alternative is to use the root area of the threads in capacity calculations, as shown in Equation 3-3 (Barron et al., 1998a).
A br
2 π d b ± 1.3 4 n th
EQ 3-3
where Abr = cross sectional area of the bolt’s root (in2) nth = number of threads per inch of the bolt Tests conducted on fasteners show that using the root area for strength calculations yields conservative results. Equation 3-4 is an empirical equation that returns an area that is midway between the root and shank area (ASTM A490-97; Barron et al., 1998a).
A be
2 π d b ± 0.9743 4 n th
44
EQ 3-4
where Abe = effective cross sectional area of the bolt It should be noted that Equations 3-3 and 3-4 are not valid for metric bolts. Equations 3-5 and 3-6 should be used for metric bolts (Barron et al., 1998a).
A br
A be
π ( d b ± 1.3p b )2 4
EQ 3-5
π ( d b ± 0.9382p b ) 2 4
EQ 3-6
where pb = thread pitch of a bolt (mm) The number of threads included in the grip of the bolt has an effect on the bolt’s capacity. ASTM F606 requires that heavy hex bolts be tensile tested with four complete threads exposed within the grip. This is in contrast to the six exposed threads required for standard bolts (ASTM A490-97). It has been noted in the literature that the tensile strength of a bolt is, to a small degree, a dependent on the length of threads present in the bolt’s grip, Ltg. Testing has demonstrated that the ultimate capacity of bolts with fewer threads in the grip is slightly larger than the capacity of bolts with many threads present in the grip. The increase in capacity is not generally regarded as being sufficient to require a certain number of threads be included or excluded from the grip. The only requirement is that the end of the bolt be at least flush with the face of the nut so that all of the threads within the nut are engaged. A general rule of thumb that
45
is often used is to require that two threads of the bolt stick out beyond the face of the nut. 3.7.1.1 LRFD An alternative method for the determination of the tensile strength of bolts is used by the LRFD (AISC, 1994). The capacity is computed as
Bn
Ft Ab
EQ 3-7
where Bn = the nominal tensile resistance of the bolt Ft = the effective tensile strength of the bolt material, F t ≅ 0.75F u Ab = the nominal area of the bolt’s shank Ft is taken as 90 ksi for A325 bolts and 113 ksi for A490 bolts. Table 3-4 shows the ratios of the effective tensile area of a bolt to its gross area. Since Abe / Ab is approximately equal to 0.75, Equation 3-7 provides a reasonable estimate of the bolt strength for the range of bolt sizes typically used for bolted connections. For design, the nominal tensile resistance of the bolt, Bn, is multiplied by a resistance factor, φbf, of 0.75.
46
Dia. 1/2" 5/8" 3/4" 7/8" 1" 1-1/8" 1-1/4" 1-3/8" 1-1/2"
Table 3-4: Nominal and Effective Bolt Areas Ab Abe Abr Abe / Ab nth
Abr / Ab
13 11 10 9 8 7 7 6 6
0.6400 0.6576 0.6834 0.6971 0.7014 0.6971 0.7249 0.7097 0.7320
0.1963 0.3068 0.4418 0.6013 0.7854 0.9940 1.2272 1.4849 1.7671
0.1419 0.2260 0.3345 0.4617 0.6057 0.7633 0.9691 1.1549 1.4052
0.1257 0.2017 0.3019 0.4192 0.5509 0.6929 0.8896 1.0538 1.2935
0.7227 0.7367 0.7571 0.7679 0.7713 0.7679 0.7897 0.7778 0.7952
3.7.1.2 Eurocode The Eurocode (1993) predicts the tensile strength of a bolt as
Bn
0.9F u A be
EQ 3-8
where Bn = the nominal tensile resistance of the bolt Fu = the tensile strength of the bolt material Abe = the effective tensile area of the bolt The ultimate strength of the bolt material is taken as 800 N/mm2 (116 ksi) for grade 8.8 bolts and 1000 N/mm2 (145 ksi) for grade 10.9 bolts. For design, the nominal resistance of the bolt is divided by a partial safety factor, γMb, of 1.25. This results in a design resistance, φBn, of 0.72AbeFu. 3.7.2 Shear Strength In its simplest form, the shear strength of a bolt is calculated by multiplying the bolt material’s ultimate strength, reduced by 40% for shear stress instead of tensile stress, by the bolt’s cross sectional area.
47
The cross sectional area
depends on whether the shear plane passes through the shank of the bolt or through its threads. When the shear plane passes through the bolt’s shank, Ag should be used and when it passes through the threaded portion, Ar should be used. The advantage of designing a connection with the threads excluded from the shear plane becomes obvious upon examination of Equations 3-2 and 3-3. Bolts subjected to shear through their threads have strengths ranging from 64% to 73% of the same bolts subjected to shear through their shanks. The reduced thread length of heavy hex bolts allows the threads to be more easily excluded from the shear plane than for standard bolts. 3.7.2.1 LRFD The LRFD (AISC, 1994) uses a design approach for the shear resistance of a bolt that is similar to the approach used for the tensile strength. The nominal shear resistance is calculated as
Bv
Fv Ab
EQ 3-9
where Bv = the nominal shear resistance of the bolt Fv = the effective shear strength of the bolt material Ab = the gross area of the bolt’s shank When the threads of the bolt are excluded from the shear plane, Fv is calculated as (AISC, 1994)
48
Fv
0.5F u .
EQ 3-10
When the threads are not excluded from the shear plane, Fv is calculated as
Fv
0.4F u .
EQ 3-11
Table 3-4 shows the ratio of the root area of the bolt’s threaded portion to the gross area of the bolt shank. Using the reduction factor of 0.67 results in a reasonable approximation of the bolt’s root area. As with the tensile strength, the nominal shear strength is multiplied by a resistance factor, φbf, of 0.75 to obtain the design resistance. 3.7.2.2 Eurocode The Eurocode (1993) uses the follow equations to calculate the shear resistance of bolts. For bolts with the threads excluded from the shear plane
Bv
0.6F u A b ,
EQ 3-12
for grade 8.8 bolts with the threads not excluded from the shear plane,
Bv
0.6F u A be ,
49
EQ 3-13
and for grade 10.9 bolts with the threads not excluded from the shear plane,
0.5F u A be
Bv
EQ 3-14
where Bv = the nominal shear resistance of the bolt Fu = the ultimate strength of the bolt material Ab = the gross area of the bolt’s shank Abe = the effective tensile area of the bolt As with the tensile strength, the nominal shear strength is divided by a partial safety factor, γMb, of 1.25 to obtain the design resistance. 3.7.3 Torsional Strength The shear stress of a bolt subjected to torsion is described by Equation 3-15 below.
τ
Tρ J
where: τ = shear stress (ksi) T = applied torque (k-in) ρ = radius of the point of stress (in) J = polar moment of inertia (in4)
50
EQ 3-15
Substituting the bolt’s polar moment of inertia and the outer radius into Equation 3-15 yields the maximum shear stress in the bolt (Barron et al., 1998a).
τ max
16T πd r
EQ 3-16
where: dr = the diameter of the root of the threads (in) The importance of the torsional strength of fasteners becomes obvious when using fully tensioned, high-strength bolts.
A typical 7/8” diameter A490 bolt
requires 600 to 640 ft-lbs of torque to provide adequate pretension. Assuming that 50% of that torque is applied directly to the bolt (the other 50% being attributed to friction and axial tension) shear stresses of up 50 ksi can be generated. 3.7.4 Bending Although bolts aren’t typically designed for bending, bending stresses are often present due to misalignment, non-perpendicular holes, joint prying and other causes. The stress in a bolt due to bending is the same as for any other typical member and is written as
σ
Mc . I
51
EQ 3-17
where: σ = bending stress (ksi) M = applied bending moment (k-in) c = distance from the neutral axis of the point of stress (in) I = the moment of inertia of the bolt (in4) Coupled with the pretension and tension due to loading, the bending stresses can be critical. The commentary to the LRFD addresses the bending of fasteners by using a relatively low resistance factor of 0.75 for strength calculations (AISC, 1994). 3.7.5 Combined Loading So far, four individual modes of loading have been discussed. In connections, though, fasteners are often subjected to a combination of loadings. A combination of shear and tension, for example, is often present in connections between diagonal bracing and beam and columns. The simple act of pretensioning a bolt induces both shear stress from the applied torque and axial stress from the resulting pretension. In fact, tests show that the tensile capacity of a bolt is reduced by as much as 15-20% during pretensioning (Barron et al., 1998a). For these reasons, it is clear that combined loading conditions deserve special attention. Tests conducted at the University of Illinois indicate that the interaction between shear and tension in bolts can be accurately predicted by using the elliptical relationship (Kulak et al., 1987)
2
x y2 2 ( 0.62 )
1.0 .
52
EQ 3-18
where: x = ratio of shear stress to tensile strength y = ratio of tensile stress to tensile strength This relationship can be reduced to a circular one if the ratio of shear stress to shear strength that is shown in Equation 3-19 is used.
2
RT RV
2
1.0
EQ 3-19
where: RT = ratio of tensile stress to tensile strength RV = ratio of shear stress of shear strength The LRFD recommends a simplified, tri-linear version of the circular relationship. Both relationships are shown in Figure 3-5. The relationship between torsion and tension in bolts is critical because high-strength bolts are nearly always fully tensioned by torquing.
Figure 3-6
shows the load-elongation curves for two bolts. The upper curve represents a bolt that was loaded from the snug tight condition until failure and the lower curve represents a bolt that was fully tensioned before being loaded to failure. The fully tensioned bolt yields at a lower tension than the snug tight bolt because of the interaction between the axial and torsional stresses. After being fully tensioned, though, the torsion is relieved and the bolt is able to reach the full tensile strength of the snug tight bolt. The dashed portion of the lower curve represents the behavior of a bolt that is loaded to failure by torquing.
53
1 2
2
RT RV
1.0
RT
R T RV
1.3
0 RV
0
1
Figure 3-5: Tension-Shear Interaction Relationship for Bolts
Bolt Load
Snug Tight
Fully Tensioned
Elongation Figure 3-6: Fully Tension vs. Snug Tight P-∆ Curves for Bolts
54
It should be noted that well lubricated twist-off or tension control bolts don’t exhibit the behavior shown in Figure 3-6 because torsion only exists in the portion of the bolt between the twist-off spine and the nut. When a standard bolt is tightened, a torque is applied to the shank of the bolt. It is this torsion that, combined the applied tension, affects the behavior of the bolt. When a tension control bolt is tightened, the torque is applied to the portion of the bolt between the twist of spline and the nut. Any residual torsion present in the shank of a tension control bolt is left as a result of friction between the nut or bolt head and the washers. Because of this, the tension control bolts will tend to follow the path of the snug tight bolts in Figure 3-6, even when they are fully tensioned.
3.8 Stiffness The stiffness of structural joints using bolts in tension depends greatly on the stiffness of the individual bolts. Because of this, accurate predictions of the stiffness of the individual bolts are essential to accurate models of the overall connection stiffness. The stiffness of an axially loaded member can be expressed in the familiar form shown in Equation 3-20.
k
AE L
55
EQ 3-20
where: k = local axial stiffness (kip/in) A = the cross sectional area of the member (in2) E = the modulus of elasticity (ksi) L = the member length (in) The stiffness of a bolt is complicated, though, by the fact that it has a changing cross section. As shown in Figure 3-1 and Section 3.7.1, the cross sectional area of the bolt’s shank is larger than that of its threaded portion. This difference in area can be represented by considering a component spring with different stiffnesses in series. The stiffnesses are calculated by using Equation 3-20 for each section separately. The overall stiffness is then calculated as shown in Equations 3-21(a) and 3-21(b) (Barron et al., 1998b).
1 Kb
1 Kb
1 1 ks kt
EQ 3-21(a)
Ls L tg A b E A be E
EQ 3-21(b)
where: Kb = the overall stiffness of the bolt (kip/in) ks = the stiffness of the bolt shank (kip/in) kt = the stiffness of the bolt’s threaded portion (kip/in) Ls = the length of the shank (in)
56
Ltg = the length of threads included in the bolt’s grip (in) Ab = the cross sectional area of the bolt’s shank (in2) Abe = the effective area of the bolt’s threaded portion (in2) Tests indicate that Equation 3-21(b) overestimates the stiffness of bolts. To slightly reduce the predicted stiffness, it has been proposed by Barron and Bickford (1998b) that part of the bolt head stiffness and part of the nut stiffness be included in the overall stiffness calculation. This adjustment is included as shown in Equation 3-22.
1 Kb
fd b Ls L tg fd b A b E A b E A be E A be E
EQ 3-22
where: f = a correlation factor db = the nominal diameter of the bolt (in) Recommendations for the value of the factor, f, in Equation 3-22 range from 0.3 to 0.6 (Barron et al., 1998b).
3.9 Ductility The ductility of fasteners is important because fasteners are often the weakest link in a bolted connection. Generally, steel loses ductility as it is hardened. Consequently, A490 bolts are generally considered to possess less ductility than A325 bolts because they are harder.
57
The length of the threaded portion of the bolt that is present in its grip, Ltg, is significant when considering ductility. This is true because nearly all of the yielding in the bolt takes place in its threaded portion.
When more threads are
included within the grip, more material is available for yielding and the overall elongation capacity, or ductility, of the bolt is greater.
3.10 Individual Bolt Testing Program The objectives of the individual bolt testing were to 1) determine the preload of the bolts when the spline of the bolts twisted off, 2) verify the manufacture’s certification for strength, 3) provide information about the stiffness and ductility of the bolts as a function of the length, and 4) provide benchmark strain-bolt force relationships for the instrumented bolts. Several bolts were selected for testing from the lots of bolts used in the component and full scale tests. Because the strength, stiffness, and ductility of bolts is dependent on the diameter, grade, and length, two lengths of bolts were selected from the 7/8 in and 1 in diameter A325 and A490 lots. Several types of individual bolt tests were performed. The first type of tests conducted were calibration tests to determine the preload in the tension control bolts when the spline twisted off. The second type of tests conducted were direct tension tests to determine the bolts’ initial stiffness, yield point, ultimate strength and ductility. The Skidmore-Wilhelm torque tension tester was used for both types of tests. The third type of test conducted was an in-situ test to determine the relationship between the bolt force and externally applied load. Finally, benchmark tests of instrumented bolts were performed to provide a relationship between the strain in a bolt’s shank and the bolt force.
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It should be noted that the results of the tests documented here can only be rigorously applied to button head bolts. Although the behavior of hex head bolts will, in most respects, be nearly identical, differences in stiffness and strength may arise due to the different configuration. A comprehensive investigation of hex head bolt characteristics that is very similar to that documented here for button head bolts was conducted by Steurer (1996). 3.10.1 Pretension Calibration Tests For the first type of test, the pretension calibration test, the Skidmore-Wilhelm torque tension tester was used alone as shown in Figure 3-2. The torque tension tester is essentially a hydraulic load cell with a hole in the center to allow a bolt to pass through. It consists of an inner piston with a 0.25 in stroke operating inside of an outer housing. The force of the bolt being tightened causes an increase in the internal hydraulic pressure which is then converted to force using a calibrated pressure transducer. An analog pressure gage calibrated to read bolt force in kips was supplied with the tester but an electronic pressure transducer was later added to facilitate automatic data acquisition. After adding the pressure transducer, the tester was recalibrated to its full scale capacity in a universal testing machine. 3.10.1.1 Test Method For the pretension calibration tests, the bolt being tested was inserted though the center of the tester from behind and the spacer plates, washers, and nuts were installed on the bolt from the front. No more than four washers were used together on either side of the bolt (i.e. under the head or nut). When more washers were required for longer bolts, 1/2 in shim plates were used. After ensuring that enough washers and spacer plates were used to avoid running the nut
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onto the shank of the bolt during tightening, the nut was tightened finger tight, and the data acquisition system was balanced. Next the bolt was tightened using one of two LeJeune wrenches until the spine of the bolt twisted off and the bolt’s pretension was recorded. The load reading from the pressure transducer dropped slightly (~3-5%) after the spine of the bolt twisted off but reached a constant value within 30 to 45 seconds. This constant value was the value recorded as the pretension in the bolt. 3.10.1.2 Results The results of 109 tests of LeJeune tension control bolts were used to verify the pretension induced when tightening. A significant difference in pretension was noticed between the bolts tightened using an electric wrench and the bolts tightened using a manual ratcheting wrench. On average, the pretension in bolts tightened with the manual wrench was 81.5% of the pretension required by the LRFD while electric wrench induced an average of 96.1% of the required pretension. Table 3-5 shows the results grouped by type and size of bolt. The pretension achieved was highly dependent on the condition of threads of the bolts. After sitting the kegs for several months, the bolts tended to dry out and lose the lubrication that was applied by the manufacturer. Informal tests of bolts in this condition resulted in very low pretensions. As a result, all bolts tested individually and in the component and full scale tests were well lubricated. This is a violation of ASTM F1852-98 which states that “no lubrication shall be permitted other than that applied by the manufacturer.” The author views this requirement as impractical. The bolts used in this investigation were kept in a well controlled environment, presumably in a much more desirable environment than would be
60
experienced on a typical job site, and the threads of the bolts still dried out resulting in increased thread friction, larger nut factors, and lower induced pretensions. The potential drawbacks of adding additional lubrication are more than overshadowed by the consequences of not adding lubrication.
Table 3-5: Pretension Calibration Test Results Wrench:
7/8" A325 Elect Man
Average: 38.3 kip St Dev: 6.5 kip Samples:
18
Required: 39.0 kip Ratio:
98.1%
1" A325 Elect Man
7/8" A490 Elect Man
1" A490 Elect Man
37.5 kip 12.3 kip
53.8 kip 4.6 kip
42.0 kip 2.2 kip
44.3 kip 7.1 kip
36.2 kip 8.5 kip
57.8 kip 5.2 kip
47.1 kip 4.2 kip
6
12
4
28
16
15
10
39.0 kip
51.0 kip
51.0 kip
49.0 kip
49.0 kip
64.0 kip
64.0 kip
96.2%
105.6%
82.4%
90.3%
73.9%
90.2%
73.7%
3.10.1.3 DTI Washer Tests A small number of direct tension indicator washers were obtained and an informal investigation was conducted using standard hex head bolts. Five, 7/8” diameter and two, 1” diameter A325 bolts were calibrated using the washers. The average preloads achieved were 44.6 kip and 58.3 kip, respectively. All of the pretensions exceeded the required pretensions of the LRFD (AISC, 1994). 3.10.2 Direct Tension Testing Direct tension testing was conducted to obtain reliable load-elongation data for the bolt which included the elastic stiffness, plastic stiffness, yield point, ultimate strength and ultimate elongation.
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3.10.2.1 Test Method The Skidmore-Wilhelm torque tension tester was again used for the tension testing but was attached to a hydraulic pump and placed into the test apparatus as shown in Figure 3-7. Attaching the tester to the hydraulic pump allowed a load to be applied to the bolt in pure tension instead of as a torqued tension. The tester was recalibrated after attaching the pump. The test apparatus allowed the elongation of the bolt to be measured as the force was applied to provide a forceelongation relationship for the bolt. LVDTs measured the displacement of the bolt head and the end of the bolt. The difference in the readings from the measured displacements provided the elongation. To avoid damaging the LVDTs with the bolts as they fractured, the LVDTs were attached to the bolts with fishing line that was strung over rods as shown in the figure. This allowed the LVDTs to be placed vertically and behind plexiglass, out of harm’s way. Two different procedures were used for the tension testing. Test method #1 was used for tests 1-20 while method #2 was used for tests 21-73. 3.10.2.1.1 Tension Test Method #1: The piston of the torque-tension tester was positioned very close to its fully contracted position. The bolt was then inserted, the spacer plates and washers were added and the nut was snugged tight. The LVDTs were then attached to the ends of the bolt, the data acquisition system was balanced and the bolt was loaded using the hydraulic pump to a point slightly above its expected pretension level. This provided data points for the elastic portion of the bolt’s force-elongation relationship.
Next, the load was
released from the bolt, the LVDT was detached from the nut end of the bolt, the bolt was pretensioned using one of the LeJeune wrenches and the pretension
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was recorded. Finally, the LVDT was reattached to the nut end of the bolt and the bolt was loaded to failure with the hydraulic pump.
Figure 3-7: Direct Bolt Tension Test Setup
Using this method created several problems. First, positioning the piston of the tester near its fully contracted position was a problem because if the piston actually bottomed out while the bolt was being tightened with the wrench, the load readings obtained were erroneous. This happened a few times. The second
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problem with this method is that the full range of the tester couldn’t be used for the actual tension test and many of the bolts tested didn’t actually fracture. Finally, the data reduction was difficult because the force-elongation relationship was obtained in two separate parts that had to be reconnected. This test method was abandoned in favor of method #2 after bolt test #20. 3.10.2.1.2 Tension Test Method #2: For method #2, the piston of the tester was position at its fully extended position, the bolt was inserted, the washers and spacer plates were installed and the nut was snugged tight. The acquisition system was then balanced and the bolt was pretensioned with one of the LeJeune wrenches. After recording the pretension, the load was released and the piston was repositioned at its fully contracted position. Additional plates and washers were added to the same bolt as needed and the nut was again snugged tight. Finally, the LVDTs were attached to the ends of the bolt, the data acquisition was balanced and the bolt was loaded to failure using the hydraulic pump. Method #2 offered several advantages over method #1. First there was no danger of bottoming out the piston of the tester while pretensioning the bolt. Second, the full range of the tester was available for the tension testing. Finally, the reduction of data obtained using method number #2 was much easier than that obtained from method #1. 3.10.2.2 Data Reduction The methods used to reduce the data varied depending on the type of test conducted and the method used. Some aspects of the data reduction were common to all of the tests. These will be discussed here while those aspects specific to individual methods will be discussed under separate headings.
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Because of the limited stroke of the tester, all of the bolts didn’t actually fracture. All bolts which are included in this dissertation did at least reach a peak load level and were relaxing before the limit of the tester was reached. The force-elongation data presented for those that didn’t fracture include a portion of apparent hardening at the end of the curves. This is due to the piston reaching the end of its stroke which caused an increase in internal hydraulic pressure without actually increasing the load on the bolt. The hydraulic pump that was used to load the bolts was a manual pump. As a result, the unrefined force-elongation curves contain divots that are due to a relaxation in the system when the handle of the pump is being raised between strokes. Although these divots may provide useful information, they have been removed from the data. Figure 3-8 shows a plot of the unrefined data with the smoothed data superimposed. 3.10.2.2.1 Tension Test Method #1: The reduction of the data obtained from tension test method #1 required several steps. The elastic portion of the curve was obtained separately from the inelastic portion. As a result, an offset was present in the raw data. This offset was removed by examining points of common force between both data sets. Next, the initial portion of the elastic data was examined for linearity. Some data showed a lack of linearity in the first 5 to 10 kips, apparently due to slack in the system. This nonlinear region, if present, was removed to avoid skewing the stiffness values obtained from the elastic portion of the curve. After eliminating any erroneous data points, an apparent yield point was identified and a best linear fit was made through the data up to this point. The slope of this linear fit was recorded as the elastic stiffness of the bolt. Next, the entire force-elongation curve was shifted to ensure that the linear fit passed
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though the point of zero force and elongation. Finally, the data was smoothed by removing any divots from the inelastic region.
80 70
Bolt Force (kip)
60 50 40 30 20 10 0 0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
Elongation (in)
Figure 3-8: Divots Caused by the Manual Hydraulic Pump
3.10.2.2.2 Tension Test Method #2:
The reduction of data obtained from
tension test method #2 was the same as that for data obtained from tension test method #1 with the exception that the was no offset between the elastic and inelastic parts of the force-elongation curve to be removed.
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3.10.2.3 Results The complete results of the individual bolt testing are presented along with the bolt certifications in Appendix C. A discussion of the results and selected data are presented in this section. Fifty-five bolts were tested to failure under direct tension as described earlier. Several different quantities were examined. These include elastic stiffness, elastic limit, ultimate strength, and ductility. 3.10.2.3.1 Elastic Stiffness: The elastic stiffness prediction shown in Equation 3-22 includes a factor for the contribution of the bolt head and nut to the bolt’s overall stiffness. If the elastic stiffness of the bolt, Kb is known, the correlation factor, f, can be determined explicitly as shown in Equation 3-23 (Barron et al., 1998b).
f
L s L tg E ± K b A b A be 1 1 d b A b A be
EQ 3-23
The average value of f found from the tension tests is 0.73 with a standard deviation of 0.54. Several of the tests exhibited stiffnesses that were substantially lower than expected. Values of f obtained from these tests are as large as 2.86. The reason for the lack of stiffness in these tests is unknown. These tests are undoubtedly the source of the large standard deviation in the factor, f. When the results of seven tests which yielded values for f above 1.00 are discarded, the
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average of the remaining tests was found to be 0.55 with a standard deviation of 0.16. 3.10.2.3.2 Elastic Limit: When considering the nonlinear behavior of bolts or bolted connections, it is necessary to know when the elastic limit has been reached. Manufacturer certifications and standard codes do specify an elastic limit. They simply report or specify a minimum ultimate strength which leads to an elastic-perfectly plastic material model.
Depending on the level of accuracy
required, this may or may not suffice. By dividing the measured elastic limit by the bolt’s ultimate strength, a ratio can be defined and used to predict the onset of inelastic behavior. For the purposes of this dissertation, the elastic limit is defined as the load at the last data point lying with a strain less than a 0.5% offset. The average ratio obtained from the tension tests was 0.83 with a standard deviation of 0.04. For the sake of simplicity, a ratio of 0.85 is recommended.1 3.10.2.3.3 Ultimate Strength: Ultimate strength is the single most important characteristic of a bolt. A goal of the tension testing was to verify the manufacturer’s certified values of ultimate strength. The ultimate strength is defined as the largest load achieved during a tension test, divided by the effective area of the bolt. Two variations of the tests performed as part of this research from the ASTM standard are noted. First, ASTM F606 section 3.4.1 states that 4 threads shall be exposed between the fixture and thread runout portion of the bolt. The number threads included in the bolt’s grip was a variable in our test series. Therefore, this requirement was waived. Second, the manufacturer’s certification for the bolts
1. The Eurocode (1993) recommends ratios of 0.80 for grade 8.8 bolts and 0.90 for grade 10.9 bolts for Fy / Fu.
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used in the test series indicate that a wedge tension test was used to determine the ultimate strength. ASTM F606 section 3.5.1 states that in a wedge tension test, a 10° wedge shall be used under the head of the bolt. No such wedge was used in the tests. ASTM F606 section 3.4.1 permits the used of a “suitable fixture” for tensile testing. On average, the ultimate strength determined from the tension tests was 8% higher than that reported on the manufacturer’s certification with a standard deviation of 4%. An examination of the manufacturers certifications for the bolts showed that the average ultimate strength of the A325 bolts was 140.0 ksi with a standard deviation of 3.4 ksi and the average ultimate strength of the A490 bolts was 162.7 ksi with a standard deviation of 2.7 ksi. These values represent an average strength that is 16.7% higher than that specified for the A325 bolts and 8.5% higher for that specified the A490 bolts. 3.10.2.3.4 Elongation: The elongation at failure of a bolt is a direct indicator of the bolt’s ductility. Of the fifty-five bolts tested under direct tension, thirteen A325 and twenty-four A490 bolts actually fractured. The other tests were stopped because the stroke of the Skidmore-Wilhelm tester was exhausted. The percent elongation of the fractured bolts was calculated as shown in Equation 3-24.
Lg ∆ Lg
EQ 3-24
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where: Lg = the grip length of the bolt ∆ = the elongation at fracture measured by the acquisition system The elongation at failure determined from the tests was 5.2% with a standard deviation of 1.6% for the A325 bolts and was 3.6% with a standard deviation 1.1% for the A490 bolts. 3.10.3 in-situ Tension Testing A third type of test was performed on two bolts, bolts #9A and 44A. This test was designed to obtain a relationship between the applied force and bolt force for pretensioned bolts. It is generally accepted that the force present in bolts remains relatively constant at the pretension load until the clamping force of the bolts is overcome by the external loads. At that point, the force in the bolts increases at a rate that is at least proportional to the applied load, depending on the level of prying present. 3.10.3.1 Test Method To replicate the in-situ condition, the valve restricting oil flow from the tester into the reservoir of the hydraulic pump was opened to allow free flow. The bolt was then inserted into the tester, the washers and spacer plates were added and the nut was fully tensioned using one of the LeJeune wrenches. By allowing the oil to flow freely from the tester into the reservoir of the hydraulic pump, the piston of the tester bottomed out as the bolt was fully tensioned. After the bolt was tensioned, the LVDTs were attached to the ends of the bolt, the acquisition system was balanced, the valve on the hydraulic pump was closed and the bolt was loaded to failure.
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3.10.3.2 Data Reduction When subjecting bolts to direct tension, there is no way to measure the force in the bolt directly; only the force applied to the bolt can be measured. The very nature of the in-situ test is to find a relationship between the applied load and the bolt force. Therefore, it is recognized that the two are not equal and an indirect method of determining the bolt force must be employed. Two approximations must be made concerning the actual bolt force in these tests. First, because the valve controlling the flow oil between the tester and the reservoir of the hydraulic pump was left open while the bolt was tightened, no direct measure of the bolts’ preload was possible. As a result, the average preload of six other bolts from the same lots were used as the preload of the bolts tested. Second, the force-elongation relationship of the bolts tested in the in-situ condition were approximated as the multi-linear representation of an identical bolt tested under the standard tension test method. The multi-linear force-elongation relation of bolt #9 was used for #9A and #44 was used for #44A. The data reduction for each bolt consisted of two steps. First, the bolt’s estimated preload was used to calculate the initial elongation. Second, the initial elongation was added to the actual elongation from the in-situ test. This sum was then used to calculate the bolt force based on the approximated multi-linear loadelongation relation for each of the data points recorded. 3.10.3.3 Results The relationship between the bolt force and the external applied load for bolt #44A is shown in Figure 3-9. The dashed line represents the one-to-one relationship expected from a bolt with no preload. If the material clamped by a bolt is considered rigid, then there should be no increase in the bolt force until the externally
71
applied load reaches and exceeds the bolt’s preload. If it recognized however, that the material clamped by a bolt is elastic, then a small increase in bolt force is expected before the externally applied load overcomes the bolt’s preload1. An examination of Figure 3-9 shows that a portion of the line representing the bolt force actually lies below the idealized dashed line. It is recognized that this is theoretically impossible and violates equilibrium. The problem is attributed to experimental error arising from the aforementioned approximations.
100
90
80
Bolt Force (kip)
70
60
50
40
30
20
10
0 0
10
20
30
40
50
60
70
80
90
Applied Load (kip)
Figure 3-9: Bolt Force and External Load Relationship for Test 44A
1. A complete treatment of the problem is given by Kulak, Fisher, and Struik (1987).
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100
3.10.3.4 Instrumented Bolt Tension Testing Bolts instrumented with strain gages were used in the component tests. Each of these bolts was calibrated in the elastic range to obtain a relationship between the strain in the bolt and load present in the bolt. Because they were only calibrated in the elastic range, these relationships are not representative of the entire force range of the bolts. For this reason, five instrumented bolts were tested to failure in the tension test setup shown in Figure 3-7. The method used in testing the instrumented bolts was very similar to tension test method #2. The piston of the tester was positioned in the fully extended position, the bolt was inserted, the spacer plates and washers were added and the nut was snugged tight. Next the data acquisition system was balanced and the nut was tightened using a spud wrench to a level near the expected pretension of the bolt while the acquisition system recorded the internal strain and applied load. This was the method used to calibrate the instrumented bolts used in the component tests. Next, the load was released and the bolt was tensioned using one of the LeJeune wrenches. The load was then released again, the piston of tester positioned at its fully contracted position, and additional spacer plates and washers were added as needed. Finally, the LVDTs were attached to the ends of the bolt, the acquisition system was balanced and the bolt was loaded to failure while recording the internal strain, applied load, and bolt elongation.
3.11 Discussion Several observations can be made from the examination of the design codes and experimental results presented in the chapter.
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•
The models employed by the LRFD for bolt strengths result in values that are approximately equal to those based on more rigorous models but require less computation.
•
The conservative resistance factors used by the LRFD and Eurocode combined with the overstrength of the bolt material properties yield conservative design values for the tensile resistance, as Table 3-6 shows.
Table 3-6: Design vs Actual Tensile Capacities for the 7/8” and 1” Bolts Used Actual Eurocode LRFD φBn φBn / Bactual φBn φBn / Bactual Bolt Strength
7/8" A325 1" A325 7/8" A490 1" A490
•
64.6 kip 84.8 kip 75.1 kip 98.6 kip
38.6 kip 50.6 kip 48.2 kip 63.3 kip
0.60 0.60 0.64 0.64
40.6 kip 53.0 kip 51.0 kip 66.6 kip
0.63 0.63 0.68 0.68
The model proposed by Barron and Bickford (1998b) provides reasonable estimates of the axial stiffness of the bolts tested.
•
Under tensile loading, A325 bolts demonstrated 44% higher elongation at failure than A490 bolts.
•
The levels of pretension achieved were somewhat lower than LRFD requirements when an electric wrench was used for tightening and were significantly lower than code requirements when a manual wrench was used for tightening.
•
The level of pretension achieved is largely dependent on the condition of the threads of the bolt and nut.
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