## The Effective Area for a Built-Up Section.

This post will check a practice problem for a built-up section, problem no.3-19 quoted from Prof. Mccormack’s book, fifth edition. It is required to compute the effective net area of the built-up section shown in Fig 3-19. The holes are punched for 3/4 inches. The U factor is given as equal to 0.90.

### The gross area for a Built-Up Section.

The built-up section consists of two channels of C10x25 and two plates that have a dimension of 1/2×11 inches. The thickness of each plate is 1/2 inch and the length is 11 inches.

We will estimate these four elements, since we have two channels we can estimate the gross area for one channel and multiply by two. Similarly, we can find the area of one plate and then multiply it by 2.

From the table of areas for channels Table 1-5, we can find that for section C10x25 its area is equal to 7.35 inch^2.

For a plate, it is easy to estimate, the area of a rectangle of (1/2″x11″), the area of one plate is equal to the product of (1/2×11) the result is 5.50 inch^2.

The areas of the two channels are equal to (2×7.35)=14.70 inch^2.

While the area of the two plates equals (2*5.50)=11.0 inch^2.

The sum of areas will give us a total area of 14.70 inch^2, please refer to the next image for more details.

The bolts used are of diameter 3/4 inches, to get the hole diameter we add 1/8 inch to the bolt diameter so the diameter of the hole will be equal to 7/8 inches.

### The net area for a Built-Up Section.

For the Effective Area for a Built-Up Section, we need to find the net areas for the two channels and the net area for the two plates.

1-for the net area for plates use section (1-1). We have 4 bolts, and the area of these four bolts is equal to the hole diameter by the number of bolts multiplied by the thickness of the plate, this value will be deducted from the gross area of the plates.

The same section 1-1, we can use to get the net area of the two channels, again we have four bolts connecting the flanges of the two channels to the upper and lower plates.

We estimate the area of the holes by multiplying 4x the diameter of the holes by the thickness of the flange of the C channel.

The final net area of the built-up section equals 22.42 square inches. The net area for channels is 13.74 square inches. The net area for the two plates is 9.25 square inches. Please refer to the next slide image for more details.

### The Effective Area for a Built-Up Section.

The final value for the effective area for a built-up section will be equal to U*An, U is given as equal to 0.90, then the effective area of a built-up section will be equal to the product of (UxAn) or 0.9x(13.174+9.25)=20.18 inch^2.

For staggered connection, please refer to posts 16 and 17 for the details of a solved problem Problem 3-4-3 for MC section-staggered bolts.

For more information about block shear for beams, please refer to Block Shear-Coped Beam Problems.

This post is included within the list of tension members’ posts-part 3.

A useful external link –**Tensile yielding and tensile rupture**. **A Beginner’s Guide to the Steel Construction Manual, 14 ^{th} ed.**