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Scaling in Newmark's 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.

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

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

  • The chart has a scale line OQ. The length OQ represents the depth zz (the circles are drawn for radius ratios R/zR/z, with OQ as the unit).
  • Draw the plan of the loaded area on tracing paper to a scale at which the depth zz equals the length OQ of the chart. The drawing scale is therefore OQ : zz.
  • 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 Δσz=I N q\Delta\sigma_z = I\,N\,q.

✓ Answer checked by Claude Opus 5.5 (high effort)

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