Calculator Inputs
Calculation History
Example Data Table
| Units | Lb | fy | Iz | J | Iw | Wpl | C1 | MEd | Estimated Mb,Rd | Status |
|---|---|---|---|---|---|---|---|---|---|---|
| SI | 4500 mm | 355 MPa | 9.0E7 mm^4 | 1.8E5 mm^4 | 2.5E11 mm^6 | 7.0E5 mm^3 | 1.13 | 160 kN·m | 207.9 kN·m | PASS |
| SI | 7000 mm | 355 MPa | 1.2E8 mm^4 | 2.1E5 mm^4 | 3.2E11 mm^6 | 8.6E5 mm^3 | 1.00 | 220 kN·m | 186.8 kN·m | FAIL |
| Imperial | 180 in | 50 ksi | 350 in^4 | 2.4 in^4 | 5200 in^6 | 85 in^3 | 1.20 | 140 kip-ft | 315.4 kip-ft | PASS |
Formula Used
This tool uses an elastic critical moment formulation for lateral-torsional buckling and a reduction factor approach to obtain design resistance. It is intended for open sections where warping matters.
- C1 approximates the moment diagram effect along Lb.
- αLT is selected from curve a-d or entered manually.
- Always match inputs, curves, and factors to your governing code.
How to Use This Calculator
- Choose your units and enter the applied bending moment MEd.
- Enter the unbraced length Lb between effective restraints.
- Provide material properties (E, G, fy) and select ν if needed.
- Paste section properties Iz, J, Iw, and Wpl from tables.
- Set C1 and the LTB curve (αLT) per your standard.
- Press “Check Buckling Capacity” to get PASS/FAIL and utilization.
- Download CSV or PDF to attach to design notes and QA records.
Professional Notes on Beam Lateral‑Torsional Buckling
1) What this check is solving
Lateral‑torsional buckling (LTB) occurs when a beam in bending deflects laterally and twists, reducing usable bending strength before yielding is fully developed. The calculator screens this risk by estimating an elastic critical moment, then applying a reduction factor to obtain a design resistance moment for comparison with the applied demand.
2) Inputs that dominate elastic critical moment
The elastic critical moment Mcr is strongly influenced by unbraced length Lb. Because the leading term varies with 1/Lb2, doubling Lb can reduce the critical level by roughly four times, before warping and torsion terms are considered. Increasing Iz and Iw generally improves stability, while a larger J improves torsional stiffness.
3) Typical material properties used in practice
For carbon steel design, engineers commonly use E around 200–210 GPa and shear modulus G around 77–81 GPa, with Poisson’s ratio ν near 0.30. Yield strength fy often ranges from 235 to 460 MPa in many building projects, while common North American grades are frequently taken as 50 ksi (about 345 MPa).
4) Section properties and reliable data sources
Iz, J, Iw, and Wpl should come from verified section tables or manufacturer catalogs. Warping constant Iw is especially important for open shapes and can differ significantly across similar depths. If you are using a built‑up section, confirm that the properties reflect the actual connection details and plate layout.
5) Moment gradient factor C1 and load realism
C1 accounts for the shape of the bending moment diagram between restraints. For nearly uniform bending, C1 is often close to 1.0; for favorable gradients, it can be higher. Use values consistent with your standard and ensure they match the governing load case, not an average condition.
6) Reading the outputs: λLT, χLT, and utilization
The non‑dimensional slenderness λLT is a quick indicator of sensitivity to LTB. When λLT is small, χLT is near 1.0 and the section can develop close to its plastic moment. As λLT increases, χLT drops and the design resistance moment decreases, raising utilization toward failure.
7) Practical bracing strategies on site
Bracing reduces effective Lb and can dramatically increase capacity. Common methods include intermediate lateral restraints, diaphragm action from decking, and torsional bracing through cross‑frames. Even a modest reduction in unbraced length can provide large benefits because the critical level scales strongly with Lb.
8) Quality checks before accepting a PASS result
Confirm restraint locations, end conditions, and whether the beam is free to warp. Verify that the selected imperfection curve αLT aligns with your section type and fabrication quality. Finally, document the governing inputs, calculated Mb,Rd, and utilization; the included CSV/PDF exports support quick QA and design record keeping.
FAQs
1) Which axis should I use for Iz and Wpl?
Use the properties about the bending axis that corresponds to your applied moment. If the beam bends about the major axis, use the major‑axis plastic modulus and the appropriate minor‑axis inertia required by your chosen LTB formulation.
2) What should I enter for G if I only know E?
If you do not have G, keep ν at about 0.30 and let the calculator compute G = E / (2(1+ν)). This is standard for many steels and is adequate for screening checks.
3) How do I choose a reasonable C1 value?
C1 depends on the moment diagram between restraints. For near‑uniform bending, start near 1.0. For strong gradients with a peak near mid‑span, a higher C1 may be justified per your design standard.
4) Why does a longer unbraced length reduce capacity so much?
Mcr has a dominant term proportional to 1/Lb2. As Lb increases, lateral deflection and twist become easier, the reduction factor drops, and the design resistance moment decreases quickly.
5) Can I use this for closed box sections?
This tool is most suitable for open sections where warping effects are relevant. Closed sections behave differently and often have higher torsional stiffness. Use a code‑specific method for box sections and verify section constants carefully.
6) What does PASS mean in this calculator?
PASS means the applied moment MEd is less than or equal to the computed design resistance moment Mb,Rd for the provided inputs, giving utilization at or below 100% for this screening check.
7) What should I do if it fails?
Typical fixes include reducing Lb with added restraints, selecting a section with larger Iz, J, or Iw, reducing demand with load redistribution, or confirming that C1 and boundary assumptions are not overly conservative.