Steel Plate Net Section Area Calculation

This explanation details how to calculate the net section area of a steel plate, which is a crucial concept in structural engineering. The net section area represents the effective area of a plate after accounting for material removed by bolt holes or other perforations. Understanding this calculation is key for determining the load-carrying capacity of steel components.

Given Steel Plate Dimensions

We are provided with the following dimensions for the steel plate:

• Plate Width ($b$): 25 cm
• Plate Thickness ($t$): 10 mm
• Bolt Hole Diameter ($d_{hole}$): 15 mm

Understanding Net Section Area Concept

The net section area is calculated by subtracting the area of the holes from the gross cross-sectional area of the plate. This calculation is essential for determining the load-carrying capacity of a steel member, ensuring safety and efficiency in design. A larger bolt hole reduces the effective strength of the plate.

Steel Plate Calculation Steps

Follow these steps to determine the net section area:

Step 1: Convert Units for Calculation

First, ensure all units are consistent. We will convert millimeters (mm) to centimeters (cm) because the width is given in cm, facilitating easier calculation.

• Plate Thickness ($t$): Convert $10 \text{ mm}$ to cm. $t = 10 \text{ mm} = \frac{10}{10} \text{ cm} = 1 \text{ cm}$
• Bolt Hole Diameter ($d_{hole}$): Convert $15 \text{ mm}$ to cm. $d_{hole} = 15 \text{ mm} = \frac{15}{10} \text{ cm} = 1.5 \text{ cm}

Step 2: Calculate Gross Section Area

The gross section area ($A_g$) is the total area of the plate without considering any holes. It is calculated as the product of the plate's width and thickness.

The formula is: $A_g = \text{Width} \times \text{Thickness}$ $A_g = b \times t$

Substituting the values:

$A_g = 25 \text{ cm} \times 1 \text{ cm}$

$A_g = 25 \text{ cm}^2$

Step 3: Calculate Bolt Hole Area Deduction

The area that needs to be deducted from the gross area is the area occupied by the bolt hole. This is calculated by multiplying the diameter of the bolt hole by the thickness of the plate.

The formula is: $A_{hole} = \text{Bolt Hole Diameter} \times \text{Thickness}$ $A_{hole} = d_{hole} \times t$

Substituting the values:

$A_{hole} = 1.5 \text{ cm} \times 1 \text{ cm} = 1.5 \text{ cm}^2$

Note: Standard engineering practice sometimes involves adding a small clearance (typically 2 mm) to the bolt hole diameter before calculating the area to be deducted. However, based on the options provided in the question, the calculation uses the specified bolt hole diameter directly.

Step 4: Compute Final Net Section Area

The net section area ($A_n$) is obtained by subtracting the area of the bolt hole from the gross section area.

The formula is: $A_n = A_g - A_{hole}$

Substituting the calculated values:

$A_n = 25 \text{ cm}^2 - 1.5 \text{ cm}^2

$A_n = 23.5 \text{ cm}^2

Verification of Steel Plate Area Calculation

The calculated net section area is 23.5 cm². This result matches one of the provided options, confirming the calculation method.