---
title: "Scaling in Newmark's method"
subject: "Soil Mechanics"
chapter: 8
key: "semester_4/soil_mechanics:newmark-scaling"
source: https://www.bctengineer.com/q/semester_4/soil_mechanics/newmark-scaling
site: BCT Engineering
---

# Scaling in Newmark's method

Soil Mechanics · Chapter 8: Vertical Stresses Below Applied Loads

- Asked in: 2079 Asoj, 2 marks
- Video: [Newmarks Influence Chart | Vertical Stress distribution | vertical stress in soil | Soil Mechanics](https://www.youtube.com/watch?v=nQu7qiIlds8) — Civil Engineering Exam
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/soil_mechanics/newmark-scaling
- Whole chapter: https://www.bctengineer.com/md/semester_4/soil_mechanics/chapter-8

## Question

How is the scaling done in Newmark's analysis method?

## Short answer

The loaded area plan is drawn to a scale where depth z equals chart length OQ. The point of interest is centred, and the number of covered elements N is counted. The stress increase is Δσz = I·N·q, where I=0.005.

## Answer

Scaling in Newmark's method makes the chart consistent with the depth $z$ at which the stress is required.

- The chart has a scale line OQ. The length OQ represents the depth $z$ (the circles are drawn for radius ratios $R/z$, with OQ as the unit).
- Draw the plan of the loaded area on tracing paper to a scale at which the depth $z$ equals the length OQ of the chart. The drawing scale is therefore OQ : $z$.
- Place the point at which the stress is required over the centre of the chart, and count the elements covered by the plan.

For a different depth, redraw the plan to a new scale (same chart). The stress is then $\Delta\sigma_z = I\,N\,q$.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What does OQ represent?
   A. Depth z
   B. Load
   C. Width
   D. Influence value
   Answer: A. OQ equals the depth at which stress is required. (Key point: Scale line)

2. The plan is drawn to a scale such that:
   A. z equals OQ
   B. B equals OQ
   C. q equals OQ
   D. L equals z
   Answer: A. Scale is OQ/z. (Key point: Scale)

3. Where is the point of interest placed on the chart?
   A. At the centre
   B. At the edge
   C. At Q
   D. Anywhere
   Answer: A. Centre of chart. (Key point: Position)

4. For a different depth you:
   A. Redraw plan to a new scale
   B. Use a different chart only
   C. Change q
   D. Change I
   Answer: A. Same chart, new plan scale. (Key point: Different depth)

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