## Structural Analysis

## Example - Bolted Joint Analysis

Written by Toshimi Taki

Prepared on May 6, 2007

**Introduction**

Energy method combined with MS-Excel gSolverh to solve bolted joints is presented as an example.

**Example Problem and Modelling**

Bolted joint is modeled as described in reference [1]. The plates or sheets are modeled as rods which are axial force elements. The bolts are modeled as springs which transfer shear force.

Single lap joints which are supported in out-of-plane direction are analyzed. See figure below.

The plates are made of aluminum alloy and the bolts are made of low alloy steel. All dimensions are in inches.

**Equivalent Joint Stiffeness**

The spring constant (or equivalent joint stiffness), K for bolted joint is calculated as follows (Reference [1]). Note that the definition of plate thickness is different from Reference [1].

The first term is bending compliance of the bolt, the second term is shear compliance of the bolt and the third term is bearing compliance of the plates.

Following table shows calculation of the equivalent joint stiffeness.

Click here to download MS-Excel template "bolted_joint_070506.xls" (1,666KB).

Calculated bold load distribution is shown in the figure below.

**Reference**

[1] M. B. Tate and S. J. Rosenfeld, gPreliminary Investigation of the Loads Carried by Individual Bolts in Bolted Joints,h NACA TN 1051, 1946.

(This paper can be downloaded from NASA report server.)