Design Procedure for Statically Loaded Bolt

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3. Design Procedures for Statically Loaded Bolted Joints

Design Flow Chart for Statically Loaded Bolted Joints

Figure 3.1 sets out the principal steps in selecting a threaded fastener to sustain a steady loading. Like any design procedure, it cannot cover every case and eventuality; nor can it be followed blindly, and the user must exercise thought and judgement during the process. It may be necessary to iterate some of the steps before a satisfactory solution is obtained.

of 14Bolted Joints and Threaded Fasteners

09/02/2009http://www.co-design.co.uk/dpg/bol/bol3.html

Table 3.1 Bolt Loads & Torques

THREAD SIZE (MM)

Maximum Axial force (kN) For Bolts/Screws of Grade * 8.8 10.9 12.9 See Note 1

Torque to Produce this Force (Nm) 8.8 10.9 12.9 See Note 2

M3 2.3 3.25 3.9 1.3 1.8 2.1

M4 4.0 5.65 6.75 2.7 3.8 4.6

M5 6.55 9.2 11.1 5.5 8.0 9.5

M6 9.25 13.0 15.6 9.5 13.0 16.0

M8 17.0 23.9 28.7 23.0 32.0 39.0

M10 27.1 38.0 45.7 46.0 64.0 77.0

M12 39.5 55.5 66.7 80.0 110 135



Note 1 The Maximum Axial Force is based on not exceeding a combined stress of 90% of the yield stress (or 0.2% proof stress for materials which do not exhibit a yield point) acting on the previously defined stress area.

Note 2 The torque to create the maximum axial force is based on a coefficient of friction of 0.125 at the thread and the bolt head (or nut face). The value for friction can vary widely in practice. (See table 5.1) Equation 5.1 or 5.2 enable torques for other frictional values to be calculated.

* For an explanation of the material grading system, see Section 6

Figure 3.1 Flowchart for statistically loaded bolted joints

3.1 Having ascertained the maximum load that the joint is required to carry, it is necessary to apply a factor of safety to this load to ensure that the constituent parts of the joint remain in contact with each other when the load is applied. If the bolts are considerably less stiff in the axial direction than the remainder of the joint (which is normal) and if the bolts were to be tightened only to the value of the load to be carried, then there will be little residual contact pressure when the joint is loaded. Section 3.6 explains this situation mathematically and in greater detail. Consequently, it is usual to apply a factor of safety to the calculated load at the joint. A factor of safety of 2 is recommended. This load is considered to be the "minimum preload at the joint".

3.2 The method of achieving the desired bolt load must be chosen next. Table 3.2 (page 15) describes various methods and their associated accuracies. By choosing a method and considering the associated tolerances, a "maximum preload at the joint" can be calculated.

3.3 Configuring of the joint in terms of the number of bolts, their style, their size and their disposition is an iterative process which may require a number of attempts before a satisfactory solution emerges. One approach is to develop a spreadsheet which considers one or more styles and creates a combination of numbers of bolts versus their diameter. If pressed, the user may include a revision of the tightening method into the iteration loop as well in order to reduce the maximum bolt load. Reductions in the factor of safety

M14 54.0 76.0 91.3 125 180 215

M16 75 105 126 195 275 330

M20 117 164 197 385 540 650

M24 169 237 284 60 930 1100

M27 221 311 374 980 1740 1650

M30 269 379 454 1350 1850 2250

M36 393 553 664 2280 3210 3850



should be avoided unless of a trivial nature (say 5%).

In terms of bolt pattern/disposition, the user is advised to study the issues discussed in Section 3.5.2 and shown in Figure 3.4. The main issue here is that the fasteners need to be as close to the line of action of the load as possible and the more flexible the joint components are the more important this issue becomes. Similarly, if the joint components are comparatively flexible then the proximity of fasteners to one another needs to be decreased. Section 3.5.2 and Figure 3.5 explain this issue in more detail.

3.4 For most initial design purposes, the decision can be made to conclude the bolt selection at this intermediate "finish" point on the flowchart, where reference is made to this section. For final design work the next steps of the flowchart should be completed taking the user to the second '"finish" point. Experience with use of the method will enable the designer to make better informed judgements concerning the need to proceed. In many instances, where the joint is stiffer than the bolts by a considerable margin, the remaining steps may serve to confirm the previous design and no revision will be necessary. However, until the designer has acquired that level of experience, caution should be exercised and the full procedure undertaken.

3.5 Estimation of Stiffness of the Bolt and Joint Members The stiffness (k) of any axially loaded member is given by the equation:

where: A = loaded cross sectional area; E = Young's modulus; l = loaded length

Thus, in order to achieve the desired high ratio of joint stiffness to bolt stiffness the following ratios should be maximised:

3.5.1 Length Ratio In the case of through-drilled joints clamped by a nut and bolt, the clamped length of the joint and the grip length of the bolt are clearly identical. However, since the tensile stress in the bolt does not fall immediately from its full value to zero at the loaded faces of the bolt head and nut, it is usual to consider the effective length of the bolt to be slightly greater than the actual grip length. This has the beneficial effect of slightly reducing the bolt stiffness. An addition of 0.4 times the local shank diameter at each end is suitable - see Figure 3.2



Where the bolt is screwed into a tapped hole in one of the joint members, the latter is clearly not wholly in compression. This tends to reduce the stiffness of the joint compared to the bolts. The following effective lengths are suggested:

Here, the effective joint length, lje is greater than the effective bolt length, resulting in a less favourable stiffness ratio than for the case of a bolt in a through-drilled hole.

3.5.2 Area Ratio

The designer often has considerable freedom in selecting the cross sectional areas of the bolt and joint members.

The bolt area will be determined by strength considerations. With a standard bolt, the critical section is usually the thread root diameter, which is less than the nominal bolt diameter, and is also subject to stress concentrations. The bolt shank may therefore be waisted down or drilled axially to give a cross sectional area somewhat below the thread root area, without loss of strength. A small length of the full shank diameter may have to be retained near the joint interfaces for lateral location purpose, but the resulting bolt will



be more resilient than a standard one, and will therefore attract a smaller proportion of any load applied to the joint. With a waisted bolt, it is also possible to increase the underhead radius and thus relieve the stress concentration in this region. Both measures increase the effective fatigue strength of the bolt which is important when the joint load has a dynamic component.

The joint area should always be as large as possible, provided the joint members can be made stiff enough to ensure reasonable parity of pressure over the whole joint interface. It is pointless to employ large, thin flanges which will distort under the clamping load and result in a concentration of load around the bolts, but little elsewhere. (See Fig 3.4)

For design purposes, we must try to estimate an effective area for use in calculating the joint stiffness. If the diameter of the joint faces Dj, does not exceed the bolt head or washer diameter DH, the compressive load in the joint may be assumed uniform, so that:



For irregular shaped joints, the joint diameter Dj may be estimated by drawing lines, at 452 to the bolt axis from the collar diameter of the bolt or nut to the joint interface, (see Fig 3.5)

In order to ensure effective clamping of the joint by the bolts in a high duty connection, the size and number of bolts should be chosen so that the joint diameters of adjacent bolts touch or overlap slightly.

3.5.3 Modulus Ratio



It is therefore desirable in the interests of overall joint stiffness to employ confined gaskets or '0' rings for sealing and allow the jointed components to abut directly, in preference to using interposed gaskets (see Figure 3.6). (a) Confined gasket, giving stiff joint. b) Interposed gasket, giving low joint stiffness .

3.6 Preloading of Bolted Joints

3.6.1 Behaviour of a Bolted Joint under a Varying Axial Load

The three diagrams of Figure 3.7 show a bolted joint: firstly when the nut has been hand tightened so that the components are snug but before significant load is applied, secondly when the nut has been tightened to produce a pre-load or pre-tension P in the bolt, and thirdly under the subsequent influence of an external load W applied to the joint.

When the pre-load is applied, the bolt stretches and the joint members compress under the influence of forces applied at the nut and bolt faces. The compressive load applied to the joint is clearly equal to the bolt tension P, so that the extension of the bolt relative to the amount by which the joint members compress will be in inverse proportion to their relative stiffnesses. Since the joint members are usually stiffer than the bolt, the amount of joint compression, �

j, is usually less than bolt stretch, �

b.



The result can be plotted on a load/extension diagram as shown in Figure 3.8. It can be seen from this diagram that the external load W is shared between an additional load on the bolt and a reduction in compression of the joint, in proportion to their stiffnesses.

Thus by designing the joint members to be very stiff and the bolt to be resilient, and applying a high preload to the bolt so that the joint faces do not separate when an external load is applied, a large external load can be seen to cause a small increase in the bolt load but a much larger decrease in the joint load. This has important implications later when fatigue is considered on joints with fluctuating loads but, in the context of steady loads applied and removed relatively infrequently, it is important to note the need for a preload to prevent joint faces separating and also that the increase in the bolt load is likely to be very small.



Figure 3.8 Load/extension diagram for a pre-loaded joint with an extension applied load

3.6.2 Choice of Preload Having established that it is desirable to preload a bolted joint that is subsequently subjected to a tensile load, we must now decide how much preload to apply. On the one hand, we must ensure that the joint faces will not separate under the application of an external load to the joint, and on the other we must not apply such a high preload that the bolt will fail when we tighten it up. Let us define the minimum preload to avoid separation of the joint members as P

min and the maximum preload which can be applied

without causing failure of the bolt in service as Pmax

From Figure 3.8, it can be seen that the safety factor on separation of the joint faces is equal to:

In order to ensure that the joint members do not separate, it is prudent to apply a high safety factor to the condition of joint parting. A figure of at least 2 is suggested:

In practice, Wj is not usually known at the initial design stage, so a first assumption of

Pmin „ 2W can be used. We have now therefore specified a lower limit for the preload,

Pmin. The upper limit of preload must be such that the bolt will not fail, either during tightening or under subsequent external load application. It is suggested that a maximum value of preload, P

max, is made equivalent to a nominal tensile stress at the minimum bolt

cross section of 85-90% of the bolt material yield strength is a good initial choice.

METHOD ACCURACY REMARKS

Yield Control ±5%Yield is detected during tightening by continuous



Table 3.2 Methods to achieve a specified preload in threaded fasteners

3.6.3 Control of Preload

A permissible range of preload, Pmin to P

max has now been established, based on criteria of

joint parting and bolt strength. The tightening of the nut must be controlled and monitored to an accuracy which will result in a preload somewhere within this safe range. If a preload equal to the mean of P

max and Pmin is specified, the permissible error in

preload control is ± (Pmax - P

min)/(P

max + P

min). The choice of the method used to control the

tightening of the nut therefore influences the required strength of the bolt, and indeed the design of the complete bolted assembly.

monitoring of torque (T) and angle of turn of the nut (0) and noting the reduction in dT/d0 which occurs at yield. Complex equipment is required. A similar accuracy may be achieved using a proprietary load-indicating bolt, known as the 'Rotabolt'

Angle Control (Turn-of-the-nut)

±10% at best The nut is tightened hand-tight and then turned through a further specified angle, calculated to produce the required strain in the bolt. The hand-tight condition is difficult to control accurately unless the joint members are stiff and flat.

Direct Measurement of Bolt Stretch

±10% at best The extension of the bolt on tightening is measured and compared to a specified value. Both ends of bolt must be accessible for measurement, which must be accurately carried out since extension is normally small. (Typical strain ª 0. 1 %).

Torque Wrench:

Strain Calibrated

Torque Calibrated

Uncalibrated

± 10-15%

± 15-25%

± 25-50%

The nut is tightened to a specified torque. The resulting tension produced in the bolt varies considerably with thread and collar friction. A torque wrench setting is therefore worthless unless Strain accompanied by an indication of whether assembly should be dry or lubricated. Additional errors will result from lack of consistency of the wrench and any inaccuracy in calibration.

Air-stall Power Wrenches

Calibrated

Uncalibrated

± 25-40%

± 30-100%

Air operated power wrenches in which the spanner : socket carrier is designed to stall at a pre-set torque. Used for automated assembly in mass production. Maintenance of accuracy depends upon frequent recalibration against a known standard.



Table 3.2 gives a guide to the accuracy of preload control offered by a range of commercially available methods, together with comments on their limitations. In selecting the method to be employed, the designer should be sure that his intentions are within the capabilities of the service environment, as well as his assembly shop, if the fasteners concerned will require periodic re-tightening in service.

3.6.4 Loss of Preload

The initial preload applied to the bolt tends to be degraded by subsequent application and removal of the external load on the joint. This is due to embedding of the contacting surfaces and flattening of surface roughness, and tends to occur rapidly with the first few load applications, and more slowly thereafter. The effect is most pronounced with soft materials and poorly finished surfaces.For design purposes, the amounts of embedding shown in Table 3.3 may be taken as representative for pairs of steel surfaces.

Table 3.3 Typical embedding at interfaces of a bolted joint (steel)

For aluminium surfaces, the figures quoted should be trebled. For soft gasket materials (which may also bed down due to heat) the amount of embedding may be much larger.

Type of surfaceMachined Thread

Formed Thread

Machined Surface

Ground Surface

Amount of embedding at each interface (mm)

.005 -003 .004 .002



Design Procedure for Statically Loaded Bolt

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