## Solved problems for net area estimation.

## Brief description of the video.

Two solved problems will be introduced, the first solved problem is from Prof. McCormac’s handbook, for which it is required to estimate the net area for a given plate 3/8″x8″.

In the second solved problem- it is required to estimate the critical net area for a given plate with several routes. All calculations are discussed. This is a part of the video, which has a subtitle and closed caption in English.

You can click on any picture to enlarge then press the small arrow to review all the other images as a slide show.

## How to estimate the net area for plates?

### Solved Problem 3-1.

In the solved problem Example 3-1, we have a plate of 3/8 inch thick and 8 inches wide.

Determine the net area of the 3/8 inch x 8-inch plate, the plate is connected at its end with two lines of 3/4 inch bolts.

This is the original plate of 8 inches by 3/8 inch connected with two plates, thin plates each one has the same width of 8 inches and thickness is 1/4 inch.

This is the first gauge line in the direction of the longitudinal tension, which is in the direction of the applied force and this is the second gauge line.

As discussed earlier the distance between the two center lines at the longitudinal direction represents the gage distance, while the perpendicular distance is the pitch.

Now we don’t have a zigzag line, we will deal with the vertical section as we can see in the next slide image.

The next image shows what is the difference between the s distance and the g distance for bolted connection.

The area net, while selecting a vertical line AB= Ag – the area of bolts.

1-Our bolt diameter as given =3/4 inch, we will **refer to Prof. McCormac’s remark, while considering the diameter of the bolts, by adding 1/8 inch to the given diameter of the bolt. **

While drilling for the bolts, damage to the material will cause an extra dia of 1/16 inch, plus the 1/16 inch so the total added will be 1/8 inch.

2- After drawing section A-B, as shown, the width is 8 inches, the thickness is 3/8-inch, and two bolts.

We estimate the final diameter of the bolt as= (3/4+1/8)=7/8″ inch. The no. of bolts=2.

3-The A gross=3/8*8=3.00 inch2, for the Anet we deduct the area of the 2 holes, then Anet=Ag-sum(d)*t=3.00-2*(3/8)*(7/8)=2.34 inch2. for U=1, then A eff=1*2.34=2.34 inch2.

This is a list of the equations used to estimate the limit state of Yielding and limit state of fracture for tension members.

## A solved Problem 3-2-determine the critical net area for a plate.

This is the second problem 3-2, it is required to estimate the critical net area of 1/2 inch thick plate, for bolts dia =3/4 inch.

We have two paths for failure, the first path is path ABCD, in this path, we are going to deduct two holes, there is no zigzag line.

1-The area gross Ag=11*1/2=5.50 inch2, for Anet=Ag-sum(d)*t=5.50-2*(1/2)*(3/4+1/8)

=5.5-(7/8)=4.63 inch2.

For the second path, which is *path ABEF*, in this path, we are going to deduct Two holes, also consider the zigzag line BE for which S=3″ and g=6″.

2a-The area gross Ag=11*1/2=5.50 inch2.

2b- for Anet=Ag-sum(d)*t+tpl*S^2/4g=5.50-2*(1/2)*(3/4+1/8)+1/2*(3^2)/(4*6)=5.5-1/2*(7/8)+0.1875=4.81 inch2.

For the third path, which is path ABCEF, in this path, we are going to deduct three holes, also consider the zigzag line CF for which S=3″ and g=3″.

3a-the area gross Ag=11*1/2=5.50 inch2.

3b- for Anet=Ag-sum(d)*t+tpl*S^2/4g=5.50-3*(1/2)*(3/4+1/8)+1/2*(3^2)/(4*3)=5.5-1.3125+0.375=4.56 inch2.

Finally, the least net area will be=4.56 inch2, which is ABEF.

That is the end of a solved problem- 3-2.

This is the pdf used for the illustration of this post.

For more problems, please refer to the following external link.

For the next post, Solved problem 3-1, for the nominal strength.