# Shear Clip Freebody Diagram (FBD)

We touched on a typical shear clip in other blog posts listed below:

**http://www.stressebook.com/stress-engineering-interview-questions-part-3/****http://www.stressebook.com/classical-hand-calculations-in-structural-analysis/**

Click here to access pdf versions of the latest blog posts…

However, in this post we will look at a relatively more interesting shear clip. Although it may seem like a small insignificant part, a shear clip is a highly effective part along various shear dominant joints, mainly riveted joints.

In summary, a shear clip primarily transfers shear loading efficiently from one part to another. It is never intended to transfer any tension loads.

Additionally, you can read more about these clips in Chapter D3.1 of this book: **Analysis And Design Of Flight Vehicles Structures.pdf**

Figure 1 shows the general loading and attachments of the shear clip. It may look like a machined part in the figure above, however that is almost never the case. They are primarily bent sheet metal parts due to their relatively small thickness, usually thinner than a tenth of an inch. Typically, rivets are used to secure them to back up structure.

In this post, our main focus will be on the following tricks of the trade:

**Classical Hand Calculations****Freebody Diagrams****Fundamental Principles of Static Equilibrium****Determine Resultant shear/bearing loads at the fasteners**

## Left Leg Freebody Diagram (FBD):

First, let us start with the left side free body diagram of this clip. We cut the right portion out and imagine the left leg as a free-standing leg. We then draw out the applied loads/moments and reaction loads/moments required to balance the left leg. The goal is static equilibrium of this free body. Figure 2 also shows the local coordinate system used in the analysis.

### Left Leg Static Equilibrium:

In Figure 2 below, we see a half red arrow at the top right pointing up. In other words, this is the internal load applied to the left leg of the clip. This load is reacted equally by the two fasteners vertically along the Y axis (Ry arrows shown in Red pointing down, with cross lines on them).

In addition, we also have the applied moment due to the internal load about the fastener CG (counterclockwise moment applied about the midpoint between the two fasteners).

However, an equal and opposite clockwise moment, formed by the force couple Rx, reacts this moment, shown in blue pointing along the X axis with cross lines on them. The figure below also shows the reaction moment in blue about the fastener centroid.

### Force Balance:

Applied Load:

Py = -300 lb

Reactions Along Y (split equally between the two rivet holes and opposite to the applied load):

Ry = +Py/2 = 300 lb/2 = 150 lb

Equilibrium Check:

Sigma Fy = 0

Py + Ry_top + Ry_bot = 0

-300 lb + 150 lb + 150 lb = 0 (Check Verified)

### Moment Balance:

Applied Moment (about the Z axis at the fastener centroid):

Mz = Py*X = 300 lb * 0.5 in = 150 in-lb

Force Couple Reactions Along X:

Rx_top = Rx_bot = 150 in-lb/1.0 in = 150 lb

Equilibrium Check:

Sigma Fx = 0

Rx_top + Rx_bot = 0

-150 lb +150 lb = 0 (Check Verified)

Resultant Shear/Bearing Loads:

The resultant shear or bearing load at each fastener of the left leg is as calculated below.

Rs = sqrt (150^2 + 150^2) = 212.13 lb

## Right Leg Freebody Diagram (FBD):

Similarly, let us now examine the right-side free body diagram of this clip. We cut the left portion out and imagine the right leg as a freestanding leg. We then draw out the applied loads/moments and reaction loads/moments required to balance the right leg. The goal is static equilibrium of this free body. Figure 3 also shows the local coordinate system used in the analysis.

In Figure 3 below, we see a half arrow at the top left pointing up. In other words, this is the internal load applied to the right leg of the clip.

### Right Leg Static Equilibrium:

The applied load is reacted equally by the two fasteners vertically along the Y axis (Ry1 arrows shown in Red, pointing up, with cross lines on them).

In addition, we also have the applied moment due to the internal load about the fastener CG (clockwise moment applied about the midpoint between the two fasteners).

However, an equal and opposite counterclockwise moment, formed by the force couple Ry2, reacts this moment. This force couple is shown in light orange pointing along the Y axis with cross lines on them. The figure also shows the reaction moment in light orange about the fastener centroid.

### Force Balance:

Applied Load:

Py = 300 lb

Reactions Along Y (split equally between the two rivet holes and opposite to the applied load):

Ry1_inner = Ry1_outer = -Py/2 = -300 lb/2 = -150 lb

### Moment Balance:

Applied Moment (about the Z axis at the fastener centroid):

Mz = Py*X = 300 lb * 0.5 in = 150 in-lb

Force Couple Reactions Along Y:

Ry2_inner = -150 in-lb/1.0 = -150 lb

Ry2_outer = 150 in-lb/1.0 = 150 lb

Equilibrium Check:

Signa Fy = 0

Py + Ry1_inner + Ry1_outer + Ry2_inner + Ry2_outer = 0

300 lb – 150 lb – 150 lb – 150 lb + 150 lb = 0 (Check Verified)

Resultant Shear/Bearing Loads:

The resultant shear or bearing load at each fastener of the right leg is as calculated below.

Rs_inner = -150 lb – 150 lb = -300 lb

But:

Rs_outer = -150 lb + 150 lb = 0 lb

## Conclusions:

In conclusion, for this unique shear clip we learnt how to properly balance freebody diagrams, calculate reaction loads as well as how to verify static equilibrium.

Above all, the final revelation of the ‘zero’ net reaction load at the right leg outer rivet pretty much takes the cherry in my opinion.

I hope you enjoyed reading through this blog post and learnt from it. Feel free to leave your comments below.

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