Cross-Sectional Area Calculator
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.
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) / 4Similarly, 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.
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) / 4AC = π * (102 - (10 - 2 * 1)2) / 4 = 28.274 mm2Applications 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:
- Subtract the squares of inner diameter from the outer diameter.
- Multiply the number with π.
- 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) × tHow 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) × tWhat 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.