lilernoEngineeringOpening Lilerno
Chapter 11 · Guided self-study
Intro + external course studyEstimate deformation and identify a likely failure mode.
Build the idea
An original introduction, worked example and practice, followed by a curated reading sequence. The external courses supply deeper teaching and problem sets.
This guide is an orientation, not a complete university module. Practical work needs suitable facilities, safety review and supervision.
Start with these prerequisites
Shared science foundations
Equilibrium finds loads. Mechanics of materials connects those loads to stress, strain and deformation under stated material and geometry assumptions.
Module lens
Nominal stress is a first model of how an axial load is distributed over a section.
For a straight axially loaded member, average normal stress is force divided by cross-sectional area. Holes, notches and load introduction can produce local concentrations. Nominal stress alone does not predict every failure mode.
In one-dimensional linear elasticity, stress equals Young's modulus times strain. Strain is extension divided by original length. Check units and the validity of small deformation and material assumptions before extending the formula to bending or buckling.
See the relationship
Change one quantity, watch the graph respond, then explain the result in your own words.
Predict → change → explain
Double the area while preserving force. What happens to nominal stress?
Axes: Area (mm²) → Stress (MPa). Bounds may rescale when inputs change.
σ = 10 MPa. 1 N/mm² = 1 MPa. This is not a load rating.
Straight uniform axial bar; average stress F/A. No stress concentration, buckling, fatigue or allowable strength is modelled.
Original Lilerno illustration. Inputs are illustrative; this is not experimental evidence or a design rating.
| Series | Area (mm²) | Stress (MPa) |
|---|---|---|
| Nominal stress | 20 | 50 |
| Nominal stress | 22.25 | 44.94 |
| Nominal stress | 24.5 | 40.82 |
| Nominal stress | 26.75 | 37.38 |
| Nominal stress | 29 | 34.48 |
| Nominal stress | 31.25 | 32 |
| Nominal stress | 33.5 | 29.85 |
| Nominal stress | 35.75 | 27.97 |
| Nominal stress | 38 | 26.32 |
| Nominal stress | 40.25 | 24.84 |
| Nominal stress | 42.5 | 23.53 |
| Nominal stress | 44.75 | 22.35 |
| Nominal stress | 47 | 21.28 |
| Nominal stress | 49.25 | 20.3 |
| Nominal stress | 51.5 | 19.42 |
| Nominal stress | 53.75 | 18.6 |
| Nominal stress | 56 | 17.86 |
| Nominal stress | 58.25 | 17.17 |
| Nominal stress | 60.5 | 16.53 |
| Nominal stress | 62.75 | 15.94 |
| Nominal stress | 65 | 15.38 |
| Nominal stress | 67.25 | 14.87 |
| Nominal stress | 69.5 | 14.39 |
| Nominal stress | 71.75 | 13.94 |
| Nominal stress | 74 | 13.51 |
| Nominal stress | 76.25 | 13.11 |
| Nominal stress | 78.5 | 12.74 |
| Nominal stress | 80.75 | 12.38 |
| Nominal stress | 83 | 12.05 |
| Nominal stress | 85.25 | 11.73 |
| Nominal stress | 87.5 | 11.43 |
| Nominal stress | 89.75 | 11.14 |
| Nominal stress | 92 | 10.87 |
| Nominal stress | 94.25 | 10.61 |
| Nominal stress | 96.5 | 10.36 |
| Nominal stress | 98.75 | 10.13 |
| Nominal stress | 101 | 9.901 |
| Nominal stress | 103.3 | 9.685 |
| Nominal stress | 105.5 | 9.479 |
| Nominal stress | 107.8 | 9.281 |
| Nominal stress | 110 | 9.091 |
| Nominal stress | 112.3 | 8.909 |
| Nominal stress | 114.5 | 8.734 |
| Nominal stress | 116.8 | 8.565 |
| Nominal stress | 119 | 8.403 |
| Nominal stress | 121.3 | 8.247 |
| Nominal stress | 123.5 | 8.097 |
| Nominal stress | 125.8 | 7.952 |
| Nominal stress | 128 | 7.813 |
| Nominal stress | 130.3 | 7.678 |
| Nominal stress | 132.5 | 7.547 |
| Nominal stress | 134.8 | 7.421 |
| Nominal stress | 137 | 7.299 |
| Nominal stress | 139.3 | 7.181 |
| Nominal stress | 141.5 | 7.067 |
| Nominal stress | 143.8 | 6.957 |
| Nominal stress | 146 | 6.849 |
| Nominal stress | 148.3 | 6.745 |
| Nominal stress | 150.5 | 6.645 |
| Nominal stress | 152.8 | 6.547 |
| Nominal stress | 155 | 6.452 |
| Nominal stress | 157.3 | 6.359 |
| Nominal stress | 159.5 | 6.27 |
| Nominal stress | 161.8 | 6.182 |
| Nominal stress | 164 | 6.098 |
| Nominal stress | 166.3 | 6.015 |
| Nominal stress | 168.5 | 5.935 |
| Nominal stress | 170.8 | 5.857 |
| Nominal stress | 173 | 5.78 |
| Nominal stress | 175.3 | 5.706 |
| Nominal stress | 177.5 | 5.634 |
| Nominal stress | 179.8 | 5.563 |
| Nominal stress | 182 | 5.495 |
| Nominal stress | 184.3 | 5.427 |
| Nominal stress | 186.5 | 5.362 |
| Nominal stress | 188.8 | 5.298 |
| Nominal stress | 191 | 5.236 |
| Nominal stress | 193.3 | 5.175 |
| Nominal stress | 195.5 | 5.115 |
| Nominal stress | 197.8 | 5.057 |
| Nominal stress | 200 | 5 |
| Chosen section | 100 | 10 |
Save your place when you finish reading.
Original Lilerno example
An ideal axial bar carries 1,000 N through an area of 100 mm². Find average stress.
Use σ = F/A.
1,000/100 = 10 N/mm².
1 N/mm² = 1 MPa, so average stress is 10 MPa.
Test the model
Open learning, traceable sources
Work in this order. These links open the publisher’s material; free access does not always permit republication.
MIT OpenCourseWare · Spring 2004
Start with: Mechanical behaviour, deformation and failure
Use the course materials for constitutive response and failure. Extend the basics through axial, bending, torsion and buckling exercises.
Daniel W. Baker and William Haynes
Start with: Internal forces and moments
Identify the internal resultants before evaluating stress.
Recall, then record
Close the explanation and answer these in your own words. Return tomorrow, then again later in the week.
Is this stress local or average?
Which constitutive law are you using?
What other failure modes are possible?
Make a units-checked axial stress and deformation calculation with explicitly assumed geometry and modulus. Do not use it as a fabrication specification.
Self-reported tasks, not an assessment of mastery or university credit. Reading a page does not complete a chapter.
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Open learning, traceable sources
Original Lilerno lessons and diagrams, supported by these references. Free access does not always permit republication. Links open the publisher’s material.
Forces, free-body diagrams, equilibrium, and structures.
CC BY-NC-SA 4.0; reference only. Embedded tools have separate terms.
Open source ↗Rights / publisher record ↗Mechanical behaviour, material selection, and experimental work.
CC BY-NC-SA, except marked exceptions; external study only.
Open source ↗Rights / publisher record ↗