9.3Bearing Joints

9.3.1.1 Overview

A “bearing” joint is one which has slipped until the fasteners “bear” on the holes as illustrated by Figure 9-10. A joint is also considered to be a bearing joint when a tight tolerance shaft (or plug gauge) is used.

Bearing type joints are mostly used where the necessary clamping force to prevent slip exceeds the clamped material’s under-head crushing strength (see Section 7.11). Such joints are therefore preloaded to a level below the flange’s crushing strength, but sufficiently high to lock the fastener under transverse vibration. The joint is then allowed to slip into bearing, where the shear load is transmitted via the fasteners into the flanges via bearing stress within holes.

Figure description:

• Entities: Four hex-head bolts, four nuts, and three overlapping horizontal plates.
• Force: Lateral shear force vectors labeled "$F_Q$" acting in opposite directions on the central plate.
• Configuration: A cross-sectional view of a bolted joint assembly where the central plate is positioned between two outer plates.
• Details: Cross-hatching indicates material sections; the central plate appears segmented or jointed between the second and third bolts.

Figure 9-10 - Shear Joint in Bearing

Figure 9-11 shows a lap joint with a large number of fasteners. In such joints some of the fasteners, due to their position at the end of the fastener row, take a higher load than others. When the external shear load is applied, some load redistribution invariably takes place due to local line contact yielding. However, after this redistribution the outer fasteners can still experience shear loads some 15 % above average.

Note that this type of joints are not recommended. A preferred design is to have the joint transferring the shear loads by friction.

Figure description:

• Text: E CSS
• Layout: Parallelogram with a blue border divided into two sections.
• Left section: White background containing a blue, italicized letter "E".
• Right section: Blue background containing the letters "CSS" in white.

Figure description:

Fastener Shear Stress Distribution in a Lap Joint

Fastener Shear Stress τ vs. Fastener Number

Figure 9-11 - Long Bearing Shear Stress Distribution

9.3.1.2 Thread Within the Hole

An important design feature of any bearing joint is the number of disengaged threads in the load path within the joint. This is illustrated by Figure 9-10, in which the threaded regions of the fasteners extend partially into the hole, proportionately increasing the hole bearing stress. In the extreme case where the interface plane passes through a threaded part of the fastener, its shear area is reduced from the shank cross-sectional area, Asha , to the thread’s stress area, AS . For these reasons, it is recommended that the thread be carefully dimensioned to minimise the length of disengaged thread in the joint, while also ensuring that there is sufficient thread to account for manufacturing tolerances.

9.3.1.3 Pivoting Bearing Joint

Another type of bearing joint that is commonly found in mechanisms where relative rotation of the flanges about a single fastener pivot (scissors action) is a design requirement. In this case the nut needs a locking mechanism and the fastener preload is negligibly low. The fastener is therefore predominantly subject to transverse shear and bearing loads between fastener and hole. Also, depending on the degree of eccentricity of the applied load, the bending stresses within the fastener can be significant.

9.3.1.4 Strength Analysis of Bearing Joints

The strength of a bearing designed shear joint depends on its resistance in three failure modes; fastener shear, hole bearing and flange shear-out failure. The strength calculation methods for each of these failure modes are given in the following Sections.

9.3.2.1 Overview

For the calculation of the shear resistance of the fastener’s cross-section at the joint’s shearing plane has to be used. If the thread is lying in the shear plane, the fastener’s stress cross-sectional area to be used is AS . Otherwise, the fastener’s shank is in the shear plane and it is important to use its cross-sectional area Asha .

9.3.2.2 Pure Shear

The MoS for shear failure of the fastener are as follows:

where $\tau_{y}$ and $\tau_{ult}$ are the yield and ultimate shear stresses for the fastener, and $A_{s}$ is the cross-sectional area at the shear plane (either $A_{sha}$ or $A_{s}$).

9.3.2.3 Combined Shear and Axial Loads

In a bearing design the preload is chosen to ensure that the assembled joint can slip into bearing at the first external shear load application. It is therefore necessary to calculate the slip load and preload the fasteners to a level below that the one to prevent slip.

The joint’s strength depends not only on the shear and tension interaction in the fastener but also on the dimensions and material properties of the clamped parts. The relative magnitude of the axial and shear components of the combined loading can make it necessary to reduce the axial preload in order to allow more of the fastener’s strength to be used in shear. It is therefore necessary, when designing a bearing joint experiencing both tension and shear loads, to work backwards to a remaining clamping force rather than size the fastener by the preload requirements.

The fastener’s shear capacity depends not only on the bolt size and its material shear strength, but also on the levels of axial and torsional stress in the triaxial stress system in its shearing planes.

The equations [9.3.3], [9.3.4], [9.3.5] and [9.3.6] assume that all torsional stresses (due to torque tightening) are removed by embedding, and bending stresses are small. Under these assumptions only the interaction between axial and shear stress are considered within the fastener.

In cases where it cannot be assumed that bearing joints have negligible fastener bending, it is important to apply more comprehensive fastener failure theories.

Thus, the verification of the combined loaded bearing joint uses stress interaction relations. If the thread is in the shear plane (not a recommended design practice), it is important to satisfy the following combined stress interaction relations:

If the shank is in the shear plane, the following stress interaction relations can be used:

The above equations [9.3.3] to [9.3.6] use the following ratios for the fastener’s strength utilisation ratios:

If gapping is tolerable, the stress interaction relations is also to be checked with Equations [9.3.7] and [9.3.8] replaced by the following (overall axial load) equations respectively:

The margins of safety for combined axial and shear forces acting on the fastener are,

The calculation of the margin of safety on combined loads for equation [9.3.3&4] is graphically depicted in Figure 9-12. Point A represents a loading case that results in a combined margin of safety below the critical level. Point B represents the margin of safety for a higher loading case at the critical level but with the same ratio between the combined loads. This graphical interpretation cannot be used for the cubic terms in equations [9.3.5&6].

Figure description:

Relationship between R_A and R_Q

Annotations

• A (text_label - position: R_Q ≈ 0.30, R_A ≈ 0.60)
• B (text_label - position: R_Q ≈ 0.45, R_A ≈ 0.89)
• Vector (arrow - position: Starts at (0,0, passes through point A, and ends at point B on the curve))
• Boundary Curve (line - position: Quarter-circle arc defined by R_Q^2 + R_A^2 = 1)

Figure 9-12 - Graphical Determination of the Margin of Safety on Combined Loads

9.3.2.4 Shear Strength of Fastener Group with Hole Tolerance

When a joint has more than one fastener, hole tolerances cannot be perfect and thus a clearance between hole and fastener. This clearance requires extra deformations to bring the full set of fasteners into bearing, and creates a reduction in the strength of the joint.

The theory in Reference 9.1 can be used to calculate the total bearing strength of a fastener group with hole clearances at their maximum tolerance bounds. The theory makes the following limiting assumptions:

Steel fasteners in aluminium flanges Fastener shanks are in bearing (i.e. no thread in holes)

The theory use a conservative approach whereby the first fastener to fail is in the hole at the maximum tolerance bound, whereas as all other holes are at the centre of their tolerance bounds. This situation is shown in Figure 9-13.

Figure description:

• Row of four fasteners (black circles within holes (white circles.
• Three fasteners are centered within their holes.
• One fastener (far right is in contact with the edge of its hole.
• Label: "Fastener in contact with hole" pointing to the rightmost fastener.
• Dimension: "CL / 2" indicating the clearance gap between a centered fastener and its hole edge.

Figure 9-13 - Fastener Group with hole clearance

The combined strength of the fastener group is the ideal strength assuming perfect tolerances (i.e. the total shear strength of all fastener shanks), minus the force capable to bring all fastener shanks into bearing, i.e.

where n is the number of fasteners in the bearing joint and FCL is the shear force capable to move the fastener shank by a distance equal to the hole clearance.

Where F CL * is a parameter given by the empirical relation,

The variable, $CL$, is the hole clearance, which is defined as $D_{h} - d$.

Equation [9.3.17] is graphically presented in Figure 9-14.

Figure description:

Figure 9-14 - Shear load parameter versus hole clearance

Figure description:

• Text: ECSS
• Visual elements:
  • Letter "E": Italicized, white font on a blue rectangular background.
  • Letters "CSS": Blue, serif font on a white background.
  • Border: Entire logo is enclosed in a blue-outlined parallelogram.

9.3.3.1 Overview

The method for evaluating net tension section failure is taken from Reference 9.2. By this theory, the net tension section is defined as the smallest area that is obtained by deducting the summed area of all holes lying in any potential failure path (straight or zig-zag) across a flange from the gross cross-sectional sectional area. It is important to consider t his failure mode considered for both friction grip joints and bearing joints.

In order to obtain a sufficiently large net tension section area to transmit the tension load through the flange, it is necessary to meet the following condition:

where $\sigma_{ult}$ is the yield strength of the respective flange, and $K_{R}$ is a reduction factor for the flange material's ultimate strength (see Section 9.3.3.2 below), and $A_{net,min}$ is the smallest net tension section area calculated by,

where $A_{gross}$ is the flange area ignoring the presence of the holes, and $A_{holes,i}$ is the summation of the hole areas along the $i$'th potential path across the flange.

The summation of the holes’ areas, Aholes , considers the full area of the first hole but then only fractional parts of each succeeding hole, and is calculated by,

where pi and si are the lateral and longitudinal distances between the centres of the i'th and (i -1)’th holes (see Figure 9-15), and t is the thickness of the flange, and it is important that the expression inside the angled brackets is replaced with zero if it evaluates to a negative value.

Figure 9-15 shows the nomenclature used to define the net tension section.

Figure description:

• Rectangular flange subject to tension (indicated by outward-pointing arrows on left and right.
• Staggered pattern of ten circular holes.
• p: Lateral distance between the centers of two adjacent holes.
• s: Longitudinal distance between the centers of two adjacent holes.
• d: Diameter of a hole.

Figure 9-15 - Nomenclature for Net Tension Section Calculation

The margin of safety on net tension section failure is therefore given by,

9.3.3.2 Net Section Data for Some Aluminium Alloys

Aluminium alloys develop a net ultimate stress that varies according to the proportion of area lost through holes. The curves in Figure 9-16 give reduction factors to be applied in Equation [9.3.20]. The curves correspond to the following general groups of alloys:

• • Al-Cu solution treated and naturally aged sheet and plate (e.g. L163 2014 A CLAD 105OA-T3)
• • Al-CuAl-Zn solution treated and artificially aged sheet or plate (e.g. L165 2014 A CLAD 105OA- T6, L88 7075 CLAD 7072-T6)
• • Al-Cu solution treated and naturally aged extruded bar (e.g. L102 2014 A T4),
• • Al-Cu solution treated and artificially aged extruded bar (e.g. L168 2014 A - T6510, DTD 5124 Al- Zn, 7075-T6)

With the exception of curve 3, the data in Figure 9-16 is applicable to loadings that are either longitudinal or transverse to the grain (or final direction of rolling). There is also some limited evidence that curve 1 can be applicable to naturally aged extruded bar loaded in the transverse direction.

Figure description:

Effect of Number of Bolts and Σd/w on Reduction Factor KR NUMBER OF BOLTS IN JOINT

REDUCTION FACTOR KR

Legend

• 1 Bolt — color: black; symbol: Line 1
• 2 Bolts — color: black; symbol: Line 2
• 3 Bolts — color: black; symbol: Line 3
• 4 Bolts — color: black; symbol: Line 4

Annotations

• Axis break on Y-axis (vertical_line - position: y between 0 and 0.8)
• Solid lines indicate measured or primary data region (text_label - position: left side of chart)
• Dashed lines indicate extrapolated data region (text_label - position: right side of chart)

Figure 9-16 - Ultimate Strength Reduction Factors for Net Tension Section Failure

The curves in Figure 9-16 are based on data from tests on specimens with unfilled holes, however spot checks have shown that they can be applied to loaded holes. The data was derived from specimens where the edge distance of the holes was 4d. From the general shape of the curves it can be assumed that they are applicable at lower edge distances, say to 2d.