Stress & Strain Calculator | Young's Modulus & Deformation
Assumes a homogeneous, isotropic member under uniform uniaxial load in the elastic range (Hooke's law). Results are screening calculations, not code-compliant design approval. Typical material values vary with grade, temper and temperature [mdash] always verify against your own datasheet.
Inputs
Results
Step-by-step calculation
Solve for any variable
Yield / factor-of-safety check
Tensile-test curve analysis
Paste two columns of data (strain, stress) [mdash] CSV, TSV or spaces. Header lines and force/extension data are auto-skipped or detected. Units: strain in mm/mm (decimal), stress in MPa.
Engineering and true stress / strain
Formulas used in the calculations
Core relations
[sigma] = F / A [eps] = [Delta]L / L[sub0] E = [sigma] / [eps] [sigma] = E[middot][eps]
[Delta]L = F[middot]L[sub0] / (A[middot]E) (elastic deformation)
L[subF] = L[sub0] + [Delta]L (final length)
k = A[middot]E / L[sub0] (axial stiffness)
Reverse solving
F = [sigma][middot]A A = F / [sigma] [eps] = [sigma] / E [Delta]L = [eps][middot]L[sub0] L[sub0] = [Delta]L / [eps]
Geometry
A_round = [pi][middot]d[sq] / 4 A_tube = ([pi]/4)[middot](D[sub0][sq] [minus] D[subI][sq])
A_rect = b[middot]h A_hollow rect = b[middot]h [minus] b[subI][middot]h[subI]
Engineering vs true values
[eps][subT] = ln(1 + [eps][subE]) [sigma][subT] [approx] [sigma][subE][middot](1 + [eps][subE]) (before necking)
Safety and energy
FoS = [sigma][subY] / [sigma] U[subY] = ([sigma] / [sigma][subY])[middot]100% u = [half][middot][sigma][middot][eps] U = [half][middot]F[middot][Delta]L
Strain conversions
[eps]_% = [eps] [times] 100 [mu][eps] = [eps] [times] 10[sup6] [sigma]_psi = [sigma]_MPa [times] 145.038
Worked example: 50 kN on a 20 mm steel rod
Given: F = 50 kN, d = 20 mm, L0 = 2000 mm, E = 200 GPa, [sigma]y = 250 MPa.
Stress and strain quick reference
| Quantity | Formula | Common units |
|---|---|---|
| Normal stress [sigma] | F / A | Pa, MPa, psi, ksi (1 MPa = 1 N/mm[sq]) |
| Strain [eps] | [Delta]L / L[sub0] | dimensionless (decimal, %, [mu][eps]) |
| Young's modulus E | [sigma] / [eps] | GPa, MPa, psi, Msi |
| Elongation [Delta]L | [eps] L[sub0] = FL[sub0]/(AE) | mm, in |
| Factor of safety | [sigma]y / [sigma] | dimensionless |
| True strain | ln(1 + [eps]e) | dimensionless |
Frequently asked questions
What is the formula for stress?
Stress is the internal force per unit cross-sectional area: [sigma] = F/A. With F in newtons and A in mm[sq], [sigma] comes out directly in N/mm[sq], which equals MPa.
What is the formula for strain?
Engineering strain is the change in length divided by the original length: [eps] = [Delta]L / L[sub0]. It is dimensionless and is often expressed as a percentage or in microstrain ([mu][eps]).
How do you calculate Young's modulus?
Within the elastic range, E = [sigma] / [eps]. From test data, the best practice (per ASTM E111) is a linear regression over the elastic portion of the curve rather than a single point [mdash] the Curve Analysis tab does this automatically.
What is the unit of stress?
The SI unit is the pascal (Pa = N/m[sq]). Engineering practice favors MPa (equal to N/mm[sq]); US practice uses psi and ksi (1 MPa = 145.038 psi).
Is strain dimensionless?
Yes. Strain is a ratio of two lengths, so it has no units. Common expressions are decimal (0.0005), percent (0.05%) and microstrain (500 [mu][eps]).
What is the difference between engineering and true stress/strain?
Engineering values use the original area and length; true values use the instantaneous ones: [eps]t = ln(1+[eps]e) and [sigma]t [approx] [sigma]e[middot](1+[eps]e). They diverge at large strain, especially after necking.
How do you calculate elongation?
[Delta]L = [eps][middot]L[sub0] = F[middot]L[sub0] / (A[middot]E). A 2 m steel rod at 159 MPa stretches about 1.6 mm.
What is the 0.2% offset yield strength?
For materials without a sharp yield point, a line is drawn parallel to the elastic slope but offset by 0.2% strain; its intersection with the stress-strain curve defines the 0.2% proof stress. The Curve Analysis tab computes it for you.
When is Hooke's law valid?
Only in the linear-elastic range, below the proportional/yield limit. Above yield, [sigma] = E[middot][eps] no longer applies and elastic-deformation formulas should not be used to predict permanent deformation.
What is factor of safety?
FoS = [sigma]y / [sigma] for yield-based design (or [sigma]u / [sigma] against ultimate). It is a screening check here, not a substitute for code-compliant design (AISC, ASME, Eurocode).
Accuracy note: this tool performs exact algebraic unit conversions and round-trip checks internally, but rounded material preset values are typical literature values, not guaranteed properties of your specific alloy, temper or temperature.
Stress and Strain Calculator All Calculators Mechanical Engineering Tools
Stress and Strain Calculator
The Complete Engineer's User Guide
Learn how to use the free online axial stress, strain, elongation and factor-of-safety calculator for mechanical, civil and structural engineering. Field-by-field guide, worked examples, unit conversions, code compliance and FAQs [mdash] all in one page.
A complete, field-by-field user guide for the SteelSolver.com Stress and Strain Calculator [mdash] the free online axial stress, strain, elongation and factor-of-safety tool for mechanical, civil and structural engineers. Learn what every input means, which units to use, which formulas the tool applies, and how to interpret the results in real design work.
What Is Axial Stress and Strain Calculation Used For?
Axial stress and strain calculation predicts how a straight structural member (rod, bar, cable, bolt, column, or tube) deforms when a force is applied along its axis. It answers four everyday engineering questions:
- Will it hold? [mdash] Is the internal stress [sigma] below the material's yield strength [sigma]y?
- How much will it stretch? [mdash] What is the elongation [Delta]L under service load?
- How stiff is it? [mdash] What is the axial stiffness k = AE/L[sub0] in N/mm or MN/m?
- What is the factor of safety? [mdash] FoS = [sigma]y / [sigma] for yield-based design.
Core formulas used by the calculator
[sigma] = F / A [eps] = [Delta]L / L[sub0] E = [sigma] / [eps] [Delta]L = F[middot]L[sub0] / (A[middot]E)
[sigma][subT] [approx] [sigma][subE][middot](1 + [eps][subE]) [eps][subT] = ln(1 + [eps][subE])
All formulas assume linear-elastic, homogeneous, isotropic material behaviour under uniform uniaxial load, well below the yield strength [mdash] the classic Hooke's law regime.
Quick reference table
| Quantity | Symbol | Formula | Typical units |
|---|---|---|---|
| Normal stress | [sigma] | F / A | MPa, psi, ksi |
| Engineering strain | [eps] | [Delta]L / L[sub0] | dimensionless, %, [mu][eps] |
| Young's modulus | E | [sigma] / [eps] | GPa, Msi |
| Elongation | [Delta]L | F[middot]L[sub0] / (A[middot]E) | mm, in |
| Axial stiffness | k | A[middot]E / L[sub0] | N/mm, MN/m |
| Factor of safety | FoS | [sigma]y / [sigma] | dimensionless |
Where Engineers Apply Axial Stress and Strain Calculations
This is not a niche formula. It sits at the heart of dozens of everyday design and inspection tasks:
1. Structural steel design
Checking tension members, hangers, bracing rods and anchor bolts against AISC 360 (LRFD/ASD). Example: verifying a 20 mm anchor bolt in a column base plate under a 50 kN uplift.
2. Mechanical component design
Sizing tie rods, push rods, piston rods, threaded fasteners and machine screws. Example: calculating the preload stretch of a Grade 8.8 M12 bolt.
3. Pressure vessel and piping
Estimating axial stress in pipe walls, support rods and vessel skirt bolts under thermal or pressure load [mdash] screening check before ASME BPVC calculations.
4. Civil infrastructure
Tension in bridge hangers, suspension cable segments, prestressing strands and tie-backs. Used for preliminary sizing before AASHTO / Eurocode detailing.
5. Material testing laboratories
Converting load-extension data from a universal testing machine (UTM) into stress-strain curves, and computing Young's modulus per ASTM E111 and 0.2% offset proof stress per ASTM E8.
6. Education and exam preparation
FE / PE exam practice, university mechanics-of-materials courses, and homework verification where students need a quick cross-check.
Field-by-Field Input Guide
Every input in the calculator is explained below with its symbol, unit options, typical range and what happens if you enter it wrong.
Axial force F
What it is
The total external load applied along the member's centroidal axis, in newtons, kilonewtons, meganewtons, pounds-force or kips.
Sign convention
- Positive (+) [mdash] tension: the member is being pulled, so [sigma] and [eps] come out positive.
- Negative ([minus]) [mdash] compression: the member is being pushed, so [sigma] and [eps] come out negative.
Typical values
- Small bolted joint: 5-50 kN
- Bridge hanger: 200-2000 kN
- Prestressing strand: 100-250 kN per strand
Cross-section geometry
The calculator accepts six standard cross-section shapes. Pick the one that matches your member:
| Shape | Required inputs | Area formula |
|---|---|---|
| Round solid bar | Diameter d | [pi]d[sq] / 4 |
| Hollow tube | Outer Do, inner Di | ([pi]/4)(Do[sq] [minus] Di[sq]) |
| Rectangle | Width b, height h | b[middot]h |
| Square | Side a | a[sq] |
| Hollow rectangle | B, H, Bi, Hi | BH [minus] BiHi |
| Custom area | Area A | user-supplied |
Original length L[sub0]
The undeformed length of the member between the two points where displacement is measured. For a bolt, L[sub0] is the grip length, not the total bolt length. For a tensile test specimen, L[sub0] is the gauge length.
- Typical structural member: 500-6000 mm
- ASTM E8 round specimen gauge length: 50 mm (2 in)
- Fastener grip length: 10-200 mm
Length-change mode: [Delta]L or Lf
You can enter either the change in length [Delta]L (preferred) or the final length Lf. If you leave both blank and provide E, the tool computes [Delta]L from Hooke's law: [Delta]L = F[middot]L[sub0] / (A[middot]E).
Young's modulus E
The slope of the linear-elastic portion of the stress-strain curve. Selecting a material preset auto-fills a typical literature value:
| Material | E (GPa) | [sigma]y (MPa) | UTS (MPa) |
|---|---|---|---|
| Structural steel (mild) | 200 | 250 | 400 |
| Carbon steel (A36) | 200 | 250 | 450 |
| Stainless steel (304) | 193 | 215 | 505 |
| Aluminum (6061-T6) | 68.9 | 276 | 310 |
| Copper (annealed) | 117 | 70 | 220 |
| Brass (C36000) | 97 | 105 | 340 |
| Titanium (Ti-6Al-4V) | 113.8 | 880 | 950 |
| Magnesium (AZ31B) | 45 | 200 | 260 |
| Cast iron (gray) | 100 | [mdash] | 250 |
Yield strength [sigma]y and UTS
Optional but strongly recommended. When supplied, the calculator shows the factor of safety, yield utilization %, remaining load capacity, and load at yield/UTS. Without these, no safety status is shown.
Units and Unit Conversions
Every numeric input has an adjacent unit selector. The calculator converts everything to SI internally (N, mm, mm[sq], MPa), computes the result, and then displays it in the chosen unit.
| Quantity | Available units | Conversion to SI |
|---|---|---|
| Force | N, kN, MN, lbf, kip | 1 kN = 1000 N; 1 kip = 4448.22 N |
| Length | mm, cm, m, in, ft, [mu]m | 1 in = 25.4 mm; 1 ft = 304.8 mm |
| Area | mm[sq], cm[sq], m[sq], in[sq], ft[sq] | 1 in[sq] = 645.16 mm[sq] |
| Modulus / stress | GPa, MPa, psi, ksi, Msi | 1 MPa = 145.038 psi |
Visual: How Uniform Axial Loading Works
The diagram below shows a prismatic bar of original length L[sub0] and cross-section area A, loaded by two equal and opposite axial forces F. Under tension, the bar elongates by [Delta]L in the elastic range.
Reading the diagram
- Orange rectangle [mdash] the original undeformed bar of length L[sub0] and cross-section A.
- Dashed outline [mdash] the deformed shape after elongation [Delta]L.
- Orange arrows [mdash] the two equal and opposite axial forces F applied at each end.
- Green dimension [mdash] elongation [Delta]L, positive in tension, negative in compression.
Worked Example: 50 kN on a 20 mm Steel Rod
Problem statement
A 2 m long, 20 mm diameter mild-steel rod carries an axial tensile load of 50 kN. The rod is made of structural steel with E = 200 GPa and [sigma]y = 250 MPa. Find the axial stress, strain, elongation, factor of safety, and axial stiffness.
Step 1 [mdash] Cross-sectional area
A = [pi]d[sq]/4 = [pi](20)[sq]/4 = 314.16 mm[sq]
Step 2 [mdash] Normal stress
[sigma] = F/A = 50,000 N / 314.16 mm[sq] = 159.2 MPa
Step 3 [mdash] Strain
[eps] = [sigma]/E = 159.2 / 200,000 = 0.000796 = 0.0796 %
Step 4 [mdash] Elongation and final length
[Delta]L = [eps][middot]L[sub0] = 0.000796 [times] 2000 = 1.59 mm
Lf = L[sub0] + [Delta]L = 2000 + 1.59 = 2001.59 mm
Step 5 [mdash] Factor of safety
FoS = [sigma]y / [sigma] = 250 / 159.2 = 1.57
Step 6 [mdash] Axial stiffness
k = A[middot]E/L[sub0] = 314.16 [times] 200,000 / 2000 = 31,416 N/mm = 31.4 MN/m
Step 7 [mdash] Load at yield
Fy = [sigma]y[middot]A = 250 [times] 314.16 = 78.5 kN
A second example [mdash] hollow aluminium tube
A 30 kN tensile load is applied to a 6061-T6 aluminium tube with outer diameter 40 mm, inner diameter 32 mm, and length 1200 mm. Find stress, elongation and FoS.
A = ([pi]/4)(40[sq] [minus] 32[sq]) = ([pi]/4)(1600 [minus] 1024) = 452.4 mm[sq]
[sigma] = 30,000 / 452.4 = 66.3 MPa
[Delta]L = 30,000 [times] 1200 / (452.4 [times] 68,900) = 1.16 mm
FoS = 276 / 66.3 = 4.16
Very safe design [mdash] aluminium tube is lightly loaded at 24 % of yield.
A third example [mdash] compression in a short column
A 100 mm [times] 100 mm square steel post is loaded in compression by 400 kN. Length 2500 mm. Find stress and shortening.
A = 100 [times] 100 = 10,000 mm[sq]
[sigma] = [minus]400,000 / 10,000 = [minus]40 MPa (compression)
[Delta]L = [minus]40 [times] 2500 / 200,000 = [minus]0.5 mm (shortening)
Note: for a 2.5 m long 100 mm square post, buckling must also be checked [mdash] this tool does not check stability.
Common Mistakes to Avoid
These are the ten most frequent errors engineers and students make when using axial stress and strain calculations:
1. Confusing tension and compression signs
Always enter tensile force as positive and compressive force as negative. If you reverse the sign, [sigma] and [eps] flip but the magnitude stays the same, which can hide a buckling risk.
2. Mixing diameter and radius
The round-bar formula uses diameter squared: A = [pi]d[sq]/4. If you enter radius r instead of diameter d, the area is off by a factor of 4.
3. Using total bolt length instead of grip length
For a bolt, L[sub0] is the grip length [mdash] the clamped thickness, not the entire shank. Using the full bolt length overestimates elongation.
4. Entering load with safety factor already included
The FoS output is meaningful only when the input force is the actual applied load. If you pre-multiply by 1.5, the calculated FoS is 1.5 [times] too small.
5. Using the wrong Young's modulus
Steel is 200 GPa, aluminium is 69 GPa, titanium is 114 GPa. Using steel E for an aluminium member understates the elongation by nearly 3[times].
6. Applying Hooke's law above yield
[sigma] = E[middot][eps] is valid only in the linear-elastic range. If [sigma] exceeds [sigma]y, the tool flags it [mdash] the elastic formula no longer predicts actual elongation.
7. Ignoring buckling in compression
A slender member can fail by elastic instability long before the compressive stress reaches [sigma]y. This tool does not check Euler buckling; use a column calculator for that.
8. Forgetting stress concentrations
Holes, fillets, threads and keyways raise local stress by factors of 2-4. This tool computes nominal axial stress only [mdash] multiply by Kt for fatigue or fracture checks.
9. Omitting temperature effects
Young's modulus drops roughly 3-5 % per 100 [deg]C for steels. Above 200 [deg]C, use temperature-corrected E from ASME or Eurocode tables.
10. Forgetting residual or preload stress
A preloaded bolt already carries stress before any external load. The total stress is preload plus the fraction of external load not absorbed by joint stiffness.
Real-World Usage and Case Studies
Case 1 [mdash] Anchor bolt uplift check (structural)
A base plate in a wind-loaded steel frame transfers a 45 kN uplift into four M20 Grade 8.8 anchor bolts. The engineer uses this calculator to confirm stress [sigma] = 45,000/(4 [times] 245) [approx] 46 MPa, well below 640 MPa yield, FoS [approx] 14. The check confirms bolts are governed by pull-out and edge distance, not by tensile stress.
Case 2 [mdash] Preload stretch of a bolt (mechanical)
A Grade 8.8 M12 bolt with 60 mm grip is preloaded to 50 kN. Using A = 84.3 mm[sq] and E = 200 GPa, the tool returns 0.178 mm stretch. This value is used to calibrate the torque-tension relationship in the assembly line.
Case 3 [mdash] Suspension bridge hanger sizing (civil)
A hanger carries 800 kN dead + live load. The designer evaluates several diameters and material grades and picks the lightest option that keeps FoS above 2.5 under service load and above 1.67 under factored load, consistent with AASHTO LRFD.
Case 4 [mdash] Tensile test curve analysis (laboratory)
A lab technician plots load-extension data from a universal testing machine. The tool performs linear regression over the first 25 % of the elastic region to extract E per ASTM E111, then finds the 0.2 % offset yield per ASTM E8.
Case 5 [mdash] Piping support rod check (process plant)
A pipe support rod transfers 12 kN from a 6 m span. The piping engineer checks [sigma] = 12,000/314 = 38 MPa on an M20 rod, and confirms FoS above 5 [mdash] acceptable as a secondary support per ASME B31.3.
Accuracy, Assumptions and Limitations
What the tool assumes
- Homogeneous, isotropic, linear-elastic material behaviour
- Uniform uniaxial load through the centroid
- Prismatic cross-section (constant A along L[sub0])
- Small strain [mdash] no geometric nonlinearity
- Isothermal conditions
- No residual stress, no preload, no stress concentration
Numerical accuracy
All unit conversions use exact SI definitions (1 in = 25.4 mm exactly, 1 lbf = 4.4482216152605 N exactly). Results are computed in double precision and displayed to 4-5 significant figures. Round-trip checks confirm no drift from repeated conversions.
What the tool does NOT do
- Buckling or column stability checks (use Euler / AISC Chapter E)
- Fatigue analysis or S-N curves
- Stress concentration factors (Kt)
- Combined bending, torsion or shear
- Temperature-dependent material properties
- Plastic or post-yield deformation
- Residual stress or preload effects
Code Compliance: AISC, ASCE, Eurocode
This calculator performs the basic mechanics check that underlies the tension and axial-compression provisions of the major structural codes. It does not replace the code itself.
| Code | Relevant provision | How this tool helps |
|---|---|---|
| AISC 360-22 | Chapter D [mdash] Design of Members for Tension | Computes gross-section yielding stress; you then compare to [phi]Fy or Fy/[Omega] |
| AISC 360-22 | Chapter E [mdash] Design of Members for Compression | Provides axial stress before applying the slenderness reduction factor |
| ASCE 7-22 | Load combinations | Feed factored loads from LRFD combos into this tool |
| Eurocode 3 (EN 1993-1-1) | [section]6.2.4 [mdash] Resistance of cross-sections in tension | Nominal stress check against fy/[gamma]M0 |
| Eurocode 3 (EN 1993-1-8) | Bolted connection design | Bolt tensile stress and stiffness under external load |
| ASME BPVC Section VIII Div. 1 | Allowable stress basis | Nominal axial stress versus tabulated allowable stress |
Key User Pain Points and How This Solves Them
Engineers, students and inspectors face recurring friction when they need a quick axial stress check. Here is how SteelSolver.com - Stress and Strain Calculator addresses each pain point directly.
| Pain point | What users experience | How solves it |
|---|---|---|
| Unit conversion errors | Mixing kN with lbf, mm with inches, MPa with psi produces answers off by orders of magnitude | Every input has a built-in unit selector; internal conversion to SI is exact; results shown in both SI and imperial |
| Spreadsheet fatigue | Rebuilding the same [sigma] = F/A sheet for every new problem | Zero setup [mdash] enter force, geometry and material, get stress, strain, elongation, FoS and stiffness instantly |
| Wrong cross-section formula | Forgetting the difference between [pi]d[sq]/4 and [pi]r[sq]; mis-applying hollow-tube formulas | Six preset geometries (solid, hollow, rectangle, square, hollow rect, custom) auto-compute area with no memorisation |
| No safety-check feedback | Getting a stress value but not knowing if it is safe | Real-time status: green elastic, amber approaching yield, red above yield [mdash] with FoS, utilisation % and remaining capacity |
| Unclear material properties | Not knowing E, [sigma]y, UTS for common alloys | Nine built-in material presets covering steel, stainless, aluminium, titanium, copper, brass, magnesium, cast iron |
| No reverse calculation | Needing to find area from allowable stress, or modulus from [sigma] and [eps], without algebra | Dedicated "Solve For" tab computes any single variable from the other two |
| Test-data analysis is manual | Plotting stress-strain curves and finding 0.2 % offset yield by hand | Curve Analysis tab ingests CSV data, auto-fits elastic modulus per ASTM E111, and finds offset yield, UTS, toughness and resilience |
| True vs engineering confusion | Mixing up [sigma]e with [sigma]t, especially past yield | Dedicated converter: [sigma]t = [sigma]e(1+[eps]e), [eps]t = ln(1+[eps]e), with a warning above 5 % strain |
| Mobile and tablet access | Spreadsheets are painful on phones | Responsive design works on any device; formulas render as Unicode without heavy libraries |
| Copy-paste reporting | Reformatting results into emails or reports | Copy Results, Copy All Data, Copy Shareable Link, and Print / PDF buttons produce clean, engineer-ready output |
Frequently Asked Questions
What is the formula for axial stress?
Axial normal stress is force divided by cross-sectional area: [sigma] = F/A. If F is in newtons and A is in square millimetres, the result is in N/mm[sq], which is numerically identical to MPa.
What is the formula for axial strain?
Engineering strain is change in length divided by original length: [eps] = [Delta]L/L[sub0]. It is dimensionless and is often reported as a percentage or in microstrain ([mu][eps]).
How do I calculate Young's modulus from stress and strain?
E = [sigma]/[eps]. In the elastic region, the best practice per ASTM E111 is a linear regression over many points rather than a single-point calculation. The Curve Analysis tab does this automatically.
What is the SI unit of stress?
The pascal (Pa = N/m[sq]). Practical engineering units are MPa (= N/mm[sq]) and GPa. US customary units are psi and ksi, where 1 MPa = 145.038 psi.
Is strain dimensionless?
Yes. Strain is a ratio of two lengths, so it has no units. It is normally expressed as a decimal (0.001), a percentage (0.1 %), or in microstrain (1000 [mu][eps]).
What is the difference between engineering and true stress?
Engineering stress uses the original cross-section area: [sigma]e = F/A[sub0]. True stress uses the instantaneous area: [sigma]t = F/A. Before necking, [sigma]t [approx] [sigma]e(1+[eps]e). After necking, the simple conversion breaks down and instantaneous area measurements are required.
When is Hooke's law valid?
Only in the linear-elastic range, below the proportional limit (typically 60-70 % of [sigma]y for metals). Above yield, [sigma] = E[middot][eps] no longer applies and plastic-deformation formulas must be used instead.
How do I calculate elongation of a steel rod?
Use [Delta]L = F[middot]L[sub0]/(A[middot]E). For a 2 m, 20 mm diameter steel rod under 50 kN: A = 314.16 mm[sq], E = 200,000 MPa, so [Delta]L = 1.59 mm. The tool computes this instantly.
What is the 0.2 % offset yield strength?
For materials without a sharp yield point (aluminium, stainless, titanium), a line parallel to the elastic slope is offset by 0.2 % strain. Its intersection with the stress-strain curve defines the 0.2 % proof stress, per ASTM E8. The Curve Analysis tab computes it automatically.
What is a good factor of safety for axial loading?
Typical values: 1.5-2.0 for static steel structures (AISC ASD uses 1.67 for yielding), 2.0-2.5 for machine components, 3.0-4.0 for castings and brittle materials, and 4.0+ for critical or fatigue-loaded joints. Always follow the governing code for your industry.
Does this tool check buckling?
No. It computes nominal axial stress only. For compression members with slenderness above roughly L/r = 20, you must also check Euler or AISC Chapter E buckling. A dedicated column calculator is recommended.
Can I use this for a bolt under preload?
Yes, for the elastic stretch and stress caused by the preload itself. But the total bolt stress under external load also depends on joint stiffness and the preload fraction [mdash] that calculation requires a bolted-joint analysis, not just [sigma] = F/A.
Is this calculator accurate enough for final design?
It is accurate for what it does: nominal elastic axial stress and strain. It is a screening tool. Final design must consider buckling, fatigue, stress concentration, temperature, residual stress, code load factors and connection detailing.
Does it work offline?
Once the page is loaded in your browser, all calculations run client-side in JavaScript. No data leaves your device and no internet connection is needed for the math itself.
Have a question that is not covered? The interactive calculator above accepts URL parameters (force, geometry, E, [sigma]y, UTS) so you can bookmark or share a specific problem with your team.
Ready to run your own numbers?
Open the SteelSolver.com - Stress and Strain Calculator and apply everything you just learned. Free, offline-capable, no sign-up required.
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