Member Stress Analysis for Beams and 3D Frames

Calculate elastic stress from the forces in every beam and column, then inspect axial, bending, shear, torsion, principal, and equivalent stress as colour contours on the actual 3D member geometry.

Inspect elastic member stress by station and across the rendered section surface

10 Member Stress Results in Structural FEA

A single peak stress can hide where the demand occurs. AutoCalcs calculates stress at stations along each member and maps supported results over the section surface, so you can review the governing member, station, and fibre. All 10 contours below are available in the structural analysis workspace.

1

Total Normal Stress σx (N + M)

Find the governing tensile or compressive normal stress from axial force plus biaxial bending.

Based on: Wireframe shows the signed governing extreme-fibre value at each station; rendered and outlined views map the signed stress over the section surface.

2

Axial Normal Stress σx,N

Isolate uniform tension or compression caused by the member axial force.

Based on: Signed axial stress N/A at each station.

3

Bending Normal Stress |σx,M|

See where strong-axis and weak-axis bending create the largest normal stress.

Based on: Magnitude of the normal-stress contribution from My and Mz, without N/A.

4

Torsional Shear Stress τT

Review elastic shear stress caused by twisting moment about the member axis.

Based on: Saint-Venant torsional shear from T and the section torsion properties.

5

Total Shear Stress τ

Inspect the combined shear field from transverse shear forces and torsion.

Based on: Section-point recovery using Vy, Vz, and T.

6

Max Principal Stress σ1

Locate the most tensile principal stress in the recovered beam stress state.

Based on: Maximum signed principal stress from the local normal and shear stress.

7

Min Principal Stress σ2

Locate the most compressive principal stress in the recovered beam stress state.

Based on: Minimum signed principal stress from the local normal and shear stress.

8

von Mises Equivalent Stress

Compare the combined beam section-point stress state with uniaxial yield for ductile metals.

Based on: Distortion-energy equivalent stress from the local normal and shear stress.

9

Tresca Equivalent Stress

Apply the maximum-shear-stress yield criterion for ductile metals.

Based on: Equivalent stress equal to the difference between the maximum and minimum principal stresses.

10

Rankine Stress (Max Principal Tension)

Screen the maximum principal tensile stress, commonly relevant to brittle behaviour.

Based on: The tensile maximum principal stress at each recovered section point.

Beam Stress Formulas Used in Member Analysis

For a beam-column section, longitudinal normal stress at a point is the sum of axial and biaxial bending stress:

σx = N/A + Mzy/Izz + Myz/Iyy

The solver obtains N, Vy, Vz, T, My, and Mz from the finite element model. Stress recovery then uses the selected section's area, second moments of area, torsion properties, geometry, and supported shear model. This is more useful than a one-span formula when load sharing, continuity, releases, 3D framing, or biaxial bending controls.

How to Calculate Beam and Frame Stress

  1. Create the model. Draw beams and columns or open a sample frame.
  2. Assign sections and materials. Recovery uses the actual section properties and orientation.
  3. Add supports and loads. Apply the loading and combinations required for the model.
  4. Run the analysis. Solve a load case or load combination.
  5. Choose a stress contour. Switch between the 10 results and inspect member surfaces.

How to Interpret Member Stress Results

Use total normal stress to find critical tension and compression fibres, then separate axial and bending stress to understand the peak. Review total and torsional shear around webs and walls. For ductile metals, von Mises or Tresca can screen elastic yielding; for brittle behaviour, principal and Rankine stress are often more relevant.

These contours are analysis results, not proof of member capacity. Final design still needs the applicable material code, stability, buckling length, section classification, resistance factors, serviceability, and load combinations. AutoCalcs provides separate member design checks for supported standards.

Scope and Limitations

  • Contours report elastic beam-theory stress recovered from 1D member actions and section geometry. They do not resolve local web or flange effects or stress concentrations around supports, load-introduction points, welds, bolts, or connections.
  • Saint-Venant torsion is included; restrained warping normal stress and warping torsion are outside the standard 6-DOF frame formulation.
  • Transverse shear recovery depends on the section family. The result legend warns when transverse-shear recovery is unavailable.
  • Some custom drawn sections support normal stress only unless detailed recovery data is available.
  • Von Mises and Tresca are ductile-metal yield measures and are unavailable for concrete and timber. Concrete and timber contours are indicative gross-section elastic results only, not code capacity checks; concrete results do not include reinforcement, cracking, or transformed-section properties.

Beam Stress Calculator FAQ

What does a beam stress calculator calculate?

A beam stress calculator converts member actions into elastic stresses using the cross-section properties. AutoCalcs recovers normal stress from axial force and biaxial bending, shear stress from transverse shear and torsion, and then derives principal and equivalent stresses along the member.

What is the formula for combined beam stress?

At a section point, normal stress is the axial term N/A plus the bending terms from My and Mz. The signs depend on the member local axes and point location, so a 3D contour shows which flange, web, or face governs.

Can I calculate stress for a full frame instead of one beam?

Yes. Structural FEA solves the connected 3D model, recovers member actions at stations along every beam and column, and displays the selected stress result for a load case or load combination.

Is member stress the same as a design-code check?

No. Member stress is elastic analysis output. A code check also considers resistance factors, section classification, buckling, unbraced length, stability, material rules, and interaction equations.

Try Member Stress Analysis Free

Open Structural FEA to analyse connected beams and frames, review load cases and combinations, and switch between wireframe station gradients and rendered or outlined per-fibre stress contours. For an isolated material-point calculation, use the von Mises stress calculator.

Run Member Stress Analysis Now

Open the sample portal frame, run the analysis, and switch between all 10 member stress contours directly in your browser.

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