In Newmark’s influence chart for stress distribution, there are ten concentric circles and ten radial lines. The influence factor of the chart is
0.01
Understanding Newmark's Influence Chart for Stress Distribution
Newmark's influence chart is a graphical method used in soil mechanics to determine the increase in vertical stress at any point below an area subjected to a uniform load. This method simplifies complex stress distribution calculations beneath arbitrarily shaped loaded areas.
The chart consists of a series of concentric circles and radial lines. The area under consideration is drawn to scale and placed on the chart such that the point where the stress is required is at the center of the chart. The loaded area is then divided into small units (areas) by the grid formed by the circles and radial lines.
Components of Newmark's Chart
- Concentric Circles: These represent lines of equal influence value from a point load.
- Radial Lines: These divide the area into sectors, helping to delineate the loaded region on the chart.
Each unit area on the chart (bounded by two consecutive circles and two consecutive radial lines) is considered to have a specific influence on the stress at the center. This influence is represented by the chart's influence factor.
Calculating the Influence Factor of Newmark's Chart
The influence factor of Newmark's chart is a constant value for a given chart. It is defined as the influence contributed by one unit area (one segment) of the chart at the center. The formula for the influence factor ($\text{I}_{\text{F}}$) is:
$$\text{I}_{\text{F}} = \frac{1}{\text{Number of radial lines} \times \text{Number of concentric circles}}$$
In this specific Newmark's influence chart, we are given:
- Number of concentric circles = 10
- Number of radial lines = 10
Now, we can calculate the influence factor using the formula:
$$\text{I}_{\text{F}} = \frac{1}{10 \times 10} = \frac{1}{100}$$
$$ \text{I}_{\text{F}} = 0.01 $$
Significance of the Influence Factor
The influence factor is crucial because it allows us to calculate the total increase in vertical stress ($\Delta\sigma_z$) at the center point due to the loaded area. If $N$ is the number of unit areas covered by the loaded area on the chart, and $q$ is the uniform pressure applied over the loaded area, the increase in vertical stress is given by:
$$\Delta\sigma_z = q \times N \times \text{I}_{\text{F}}$$
So, for this chart with an influence factor of 0.01, each unit area covered by the loaded region contributes $0.01 \times q$ to the total stress increase at the center.
Based on the calculation, the influence factor for a Newmark's chart with ten concentric circles and ten radial lines is 0.01.
| Parameter | Value |
|---|---|
| Number of Concentric Circles | 10 |
| Number of Radial Lines | 10 |
| Influence Factor Formula | <!-- $\frac{1}{\text{N}_{\text{circles}} \times \text{N}_{\text{radial lines}}}$ --> $$\frac{1}{\text{Number of concentric circles} \times \text{Number of radial lines}}$$ |
| Calculated Influence Factor | <!-- $\frac{1}{10 \times 10} = 0.01$ --> $$\frac{1}{10 \times 10} = 0.01$$ |
Revision Table: Newmark's Influence Chart Key Points
| Concept | Description |
|---|---|
| Purpose | Calculate vertical stress increase below loaded areas. |
| Components | Concentric circles, radial lines. |
| Influence Factor (IF) | Influence of one unit area at the center. |
| Formula for IF | <!-- $\frac{1}{\text{No. of circles} \times \text{No. of radial lines}}$ --> $$\frac{1}{\text{Number of circles} \times \text{Number of radial lines}}$$ |
| Stress Increase ($\Delta\sigma_z$) | <!-- $q \times N \times I_F$ --> $$q \times N \times I_F$$ (where $q$ is pressure, $N$ is number of covered units) |
Additional Information: Applying Newmark's Chart
To use Newmark's influence chart, the loaded area must first be drawn to scale on a transparent paper. The scale is determined by the distance $z$ below the loaded area where the stress is to be calculated. The radius of the first circle on the chart typically represents this depth $z$. Therefore, if a loaded area has a dimension $L$ and the point is at depth $z$, the dimension $L$ on the drawing should be $L/z$ times the radius of the first circle.
Once the loaded area is drawn to scale and placed on the chart with the point of interest at the center, the number of unit areas ($N$) completely within the loaded boundary and the number of unit areas partially within the boundary are counted. The partially covered areas are estimated (e.g., half area, quarter area) and summed up to get the total effective number of units $N$. This value $N$ is then multiplied by the uniform pressure $q$ and the chart's influence factor $\text{I}_{\text{F}}$ to get the vertical stress increase $\Delta\sigma_z$ at the point.
Important Questions from Vertical Stress Distribution
Vertical point load (Q) on the surface is 500 kN, σz (pressure increment) at 10 m depth (Z = 10 m,) directly under the axis of load will be
The time-dependent deformation on soil is known as?
Contact pressure in soil body is also called _______.
______ is a curve or cont our connecting all points below the ground surface of equal vertical pressure.
The intensity of vertical stress (σz) of the soil just below the load point is given by ______, where Z-vertical distance between point load and the stress and Q- point load.
