A steel plate is 300 mm wide and 10 mm thick. It has one rivet of nominal diameter 18 mm. The net sectional area of the plate is
2805 mm2
Calculating Net Sectional Area of Steel Plate with Rivet Hole
The question asks us to determine the net sectional area of a steel plate that has a rivet hole. The net area is the area of the cross-section of the plate remaining after deducting the area of the hole(s). This area is crucial in structural design as it determines the plate's capacity to resist tension forces without tearing at the hole locations.
Given Parameters of the Steel Plate and Rivet
- Width of the steel plate: 300 mm
- Thickness of the steel plate: 10 mm
- Nominal diameter of the rivet: 18 mm
- Number of rivets: 1
Steps to Calculate Net Sectional Area
To find the net sectional area, we first calculate the gross area of the plate and then subtract the area of the hole made for the rivet.
1. Calculate the Gross Area
The gross area is the total cross-sectional area of the plate without considering any holes.
Gross Area = Width $\times$ Thickness
Gross Area = $300 \, \text{mm} \times 10 \, \text{mm} = 3000 \, \text{mm}^2$
2. Determine the Effective Hole Diameter
For calculating the net area in tension, the diameter of the hole is taken as the nominal diameter of the rivet plus a standard clearance. As per design codes like IS 800:2007, for rivets up to 24 mm nominal diameter, a clearance of 1.5 mm is added.
Effective Hole Diameter = Nominal Rivet Diameter + Clearance
Effective Hole Diameter = $18 \, \text{mm} + 1.5 \, \text{mm} = 19.5 \, \text{mm}$
3. Calculate the Area of the Hole to be Deducted
The area of the hole that weakens the section is the effective hole diameter multiplied by the thickness of the plate.
Area of Hole = Effective Hole Diameter $\times$ Thickness
Area of Hole = $19.5 \, \text{mm} \times 10 \, \text{mm} = 195 \, \text{mm}^2$
4. Calculate the Net Sectional Area
The net sectional area is the gross area minus the area of the hole(s) on the critical section.
Net Sectional Area = Gross Area - Area of Hole
Net Sectional Area = $3000 \, \text{mm}^2 - 195 \, \text{mm}^2 = 2805 \, \text{mm}^2$
Summary of Calculations
| Parameter | Value |
|---|---|
| Plate Width | 300 mm |
| Plate Thickness | 10 mm |
| Nominal Rivet Diameter | 18 mm |
| Gross Area | 3000 mm2 |
| Effective Hole Diameter | 19.5 mm |
| Area of Hole | 195 mm2 |
| Net Sectional Area | 2805 mm2 |
Based on the calculations, the net sectional area of the steel plate is 2805 mm2.
Revision Table: Steel Plate Net Area Calculation
| Concept | Description | Formula/Calculation |
|---|---|---|
| Gross Area | Total area of the plate cross-section without holes. | Width $\times$ Thickness |
| Effective Hole Diameter | Diameter used for calculating area reduction due to holes (includes clearance). | Nominal Diameter + Clearance (e.g., 1.5 mm for $\le$ 24mm rivets) |
| Area of Hole | Area deducted from gross area due to the hole. | Effective Hole Diameter $\times$ Thickness |
| Net Area | Area remaining after deducting holes. Critical for tension strength. | Gross Area - Sum of Hole Areas |
Additional Information: Steel Connection Concepts
Calculating the net sectional area is a fundamental step in designing tension members in steel structures, especially those connected using bolts or rivets. Here are some related concepts:
- Tension Members: Structural elements designed to carry tensile forces. Their strength is often limited by yielding of the gross section or rupture of the net section.
- Bolted Connections: Similar to riveted connections, holes are made for bolts. The net area calculation principle is the same, using the bolt hole diameter (bolt diameter + clearance).
- Critical Section: This is the cross-section along which rupture is most likely to occur. In a plate with holes, it's usually the section passing through the line of holes that results in the smallest net area. For a single rivet/bolt, it's the section perpendicular to the load passing through the hole.
- Block Shear Failure: A potential failure mode in bolted/riveted connections where a block of material shears along one plane and tears along another. Design checks involve calculating resistance against yielding and rupture in both shear and tension areas.
- Gross Section Yielding: The capacity of the member based on the yield strength of the steel across the entire gross area.
- Net Section Rupture: The capacity of the member based on the ultimate tensile strength of the steel across the net area. Design ensures that the member is safe against both yielding and rupture.
Understanding the difference between gross and net area and how to calculate them correctly is vital for designing safe and efficient steel structures.
Important Questions from Tension Member
A single angle in tension is connected by one leg only. If the areas of connecting and outstanding legs are respectively a and b, then what is the net effective area of the angle?
A) \(a-\frac{b}{1+0.35\times\frac{b}{a}}\)
B) \(a+\frac{b}{1+0.35\times\frac{b}{a}}\)
C) \(a-\frac{b}{1+0.20\times\frac{b}{a}}\)
D) \(a+\frac{b}{1+0.20\times\frac{b}{a}}\)
The net area of round bars to resist the tension, is the area of the cross-section at
The following are the statements about lug angle used to connect heavily loaded tension member to gusset plates.
(i) The length of end connection is reduced
(ii) By using lug angles there will be saving in the gusset plate
(iii) Cost of connection increases due to additional fasteners and angle required.
The best tension member section will be as:
Which of the following failure is not a type of failure in tension members in steel structures?
