Cross section
Hollow rectangle
Hollow rectangles with sides - H and W having thickness t









Width (W)
in
Height (H)
in
Thickness (t)
in
Area (A)
in²

The cross-sectional area calculator determines the area for different types of beams. A beam is a very crucial element in construction. The load bearing member of bridges, roofs and floors in buildings are available in different cross-sections. Read on to understand how to calculate cross-sectional area of I section, T section, C beam, L beam, round bar, tube, and beams with rectangular and triangular cross-sections.

What is a cross-section and how to calculate a cross-sectional area?

A cross-section is defined as the common region obtained from the intersection of a plane with a 3D object. For instance, consider a long circular tube cut (intersect) with a plane. You'll see a couple of concentric circles. The concentric circles are the cross-section of a tube. Similarly, the beams — L, I, C, and T — are named based on the cross-section shape.

A Tube with section view
Section view of a Tube

In order to calculate the area of a cross-section, you need to look at them as basic shapes. For instance, a tube is a concentric circle. Therefore, for a tube with inner and outer diameter (d and D) having thickness t, the area of cross-section can be written as:

AC = π * (D2 - d2) / 4

We also know that the inner diameter d is related to thickness t and outer diameter D as:

d = D - 2 * t

Therefore, the area of cross-section becomes:

AC = π * (D2 - (D - 2 * t)2) / 4

Similarly, the area of cross-section for all other shapes having width W, height H, and thicknesses t1 and t2 are given in the table below.

Different cross sections
Cross-sections
Section
Area
Hollow Rectangle
(H * W) - ((W - 2t1) * (W - 2t2))
Rectangle
W * H
I
2 * W * t1 + (H - 2 * t1) * t2
C
2 * W * t1 + (H - 2 * t1) * t2
T
W * t1 + (H - t1) * t2
L
W * t + (H - t) * t
Isosceles Triangle
0.5 * B * H
Equilateral Triangle
0.4330 * L2
Circle
0.25 * π * D2
Tube
0.25 * π *(D2 - (D - 2 * t)2)

How to find cross-sectional area?

Follow the steps below to find the cross-sectional area.

  • Step 1: Select the shape of cross-section from the list, say, Hollow rectangle. An illustration of the cross-section and the related fields will now be visible.
  • Step 2: Enter the width of the hollow rectangle, W.
  • Step 3: Fill in the height of the cross-section, H.
  • Step 4: Insert the thickness of the hollow rectangle, t.
  • Step 5: The calculator will return the area of the cross-section.

Example: Using the cross-sectional area calculator.

Find the cross-sectional area of tube having outer diameter of 10 mm and a thickness of 1 mm.

  • Step 1: Select the shape of cross-section from the list, i.e., Tube.
  • Step 2: Enter the outer diameter of tube, D = 10 mm.
  • Step 3: Insert the thickness of the tube, t = 1 mm.
  • Step 4: The area of cross-section is :
AC = π * (D2 - (D - 2 * t)2) / 4
AC = π * (102 - (10 - 2 * 1)2) / 4 = 28.274 mm2

Applications of cross-section shapes

Did you know?

  • An I or H beam is used extensively in railway tracks.
  • T beams are found in use in early bridges and is used to reinforce structures to withstand large loads on floors of bridges and piers.

FAQ

How to calculate cross-sectional area of a pipe ?

To calculate cross-section of a pipe:

  1. Subtract the squares of inner diameter from the outer diameter.
  2. Multiply the number with π.
  3. Divide the product by 4.

How to calculate area of an I section?

The area of I section with total width W, height H and having thickness t can be calculated as:

Area = 2 × W × t + (H - 2 × t) × t

How to calculate area of an T section?

The area of a T section with total width W, height H and having thickness t can be calculated as:

Area = W × t + (H - 2 × t) × t

What is the cross section of a cube?

The cross-section of a cube is a square. Similarly, for a cuboid, it is either a square or a rectangle.

Rahul Dhari
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