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Research Papers

# An Improved Stiffness Model for Bolted Joints

[+] Author and Article Information
Sayed A. Nassar, Antoine Abboud

Department of Mechanical Engineering, Fastening and Joining Research Institute, Oakland University, Rochester, MI 48309

J. Mech. Des 131(12), 121001 (Nov 03, 2009) (11 pages) doi:10.1115/1.4000212 History: Received July 10, 2008; Revised August 26, 2009; Published November 03, 2009; Online November 03, 2009

## Abstract

An improved stiffness model is proposed for bolted joints made of similar and dissimilar plates. A novel approach is used to obtain an expression for the effective area used for determining the joint stiffness. More accurate estimate of the joint stiffness provides a more reliable prediction of the joint behavior both during its initial assembly, as well as under subsequently applied tensile loads in service. The effect of the grip length-to-diameter ratio, joint sizes, underhead contact radii ratio, hole clearance, and plate material/thickness ratio are investigated. Experimental data are used for determining the envelope angle $α$ in the proposed analytical model. Finite element modeling is used for evaluating the accuracy of the proposed stiffness model.

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## Figures

Figure 1

(a) Typical model of a bolted joint and (b) approximate model of a bolted joint

Figure 2

Conical and spherical pressure distribution envelope

Figure 3

Half model of bolted joint for Do≥L tan α+γd

Figure 4

Stress distribution on element dz of the joint

Figure 5

Equivalent elastic model of the joint

Figure 6

Half model of bolted joint for γd<Do<L tan α+γd

Figure 7

Two plates with dissimilar materials for Do≥L tan α+γd

Figure 8

Sample cylindrical test joints with different sizes and grip lengths

Figure 9

Experimental setup for joint compression test

Figure 10

Experimental data on effective area Ac

Figure 11

FEA modeling for joint of similar material

Figure 12

Effect of the joint diameter on the effective area Ac

Figure 13

Effect of the joint diameter on the effective area Ac

Figure 14

Effect of the joint diameter on the effective area Ac

Figure 15

Effect of the contact radii ratio on Ac for Do≥(L tan α+γd)

Figure 16

Effect of the contact radii ratio on Ac for γd<Do<(L tan α+γd)

Figure 17

Effect of the hole clearance on Ac

Figure 18

Effect of the hole clearance on Ac

Figure 19

Effect of the thickness ratio on the joint stiffness kc for Do≥(L tan α+γd)

Figure 20

Effect of the thickness ratio on the joint stiffness kc for Do≥(L tan α+γd)

Figure 21

Effect of the thickness ratio on the joint stiffness kc for γd<Do<(L tan α+γd)

Figure 22

Effect of the thickness ratio on the joint stiffness kc for γd<Do<(L tan α+γd)

Figure 23

Eccentric bolt holes in cylindrical and square joints

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