Example Data Table
| Case | Method | V | Geometry inputs | Output unit | Shear stress (approx.) |
|---|---|---|---|---|---|
| 1 | VQ / I b | 1200 N | Q=1.75e5 mm³, I=8.40e6 mm⁴, b=40 mm | MPa | 0.625 MPa |
| 2 | Rectangular max | 5 kN | b=50 mm, h=120 mm | MPa | 2.5 MPa |
| 3 | Circular max | 800 N | d=30 mm | MPa | 1.51 MPa |
Formula Used
General shear stress at a point:
τ = (V × Q) / (I × b)
- V is internal shear force at the section.
- Q is first moment of area about the neutral axis for the area above/below the point.
- I is second moment of area about the neutral axis.
- b is width (thickness) of the section where stress is evaluated.
Quick maximum shear stress:
- Rectangle: τmax = 1.5 V / A
- Circle: τmax = 4 V / (3 A)
- A is the cross‑sectional area.
How to Use This Calculator
- Select a method based on your cross‑section and what you need.
- Enter the shear force V and choose its unit.
- Choose a length unit that matches your geometric properties.
- For VQ/Ib, enter Q, I, and local b.
- For quick maxima, enter the rectangle dimensions or diameter.
- Pick your preferred output unit, then press Calculate.
- Use CSV for spreadsheets and PDF for reports or sharing.
Beam Shear Stress Article
1) Role of shear stress in beams
Beam shear stress describes how internal shear force transfers load across a cross-section. It is highest near the neutral axis for many shapes, and it controls web design, adhesive joints, and fastener spacing in built-up members. This page helps you compute stress consistently and export results for documentation.
2) General point method with section properties
The most general approach uses τ = VQ/(Ib). Here I is the second moment of area (length4) and Q is the first moment of area (length3). Because Q changes with location, this method is ideal for I-beams where the web thickness b differs from flange width.
3) Quick maxima for common shapes
For a solid rectangle, the maximum shear stress at the neutral axis equals 1.5V/A, which is 50% higher than the average V/A. For a solid circle, the peak at the center equals 4V/(3A), about 33.3% above average. These relationships are built into the fast options.
4) Typical input ranges and units
In lab and small-machine components, shear forces often fall between 10 N and 20 kN, while section dimensions commonly range from 1 mm to 300 mm. The calculator accepts N, kN, and lbf, and converts mm, cm, m, in, and ft into consistent base units before computing stress.
5) Interpreting the result for design checks
Compare computed shear stress with an allowable value from your material specification and safety factors. As a rough reference, many structural steels have yield strengths around 250–350 MPa, and shear capacity is usually lower than tensile capacity. Always follow your governing code and connection details.
6) Where engineers use the VQ/Ib result
Use the general method for webs of I-sections, thin-walled box beams, and laminated members where shear flow matters. When you know Q and I from section tables, you can evaluate stress at a specific height and check whether web thickness is adequate for the applied shear force.
7) Common mistakes to avoid
The most frequent errors are mixing units (for example, entering Q in cm3 while I is in mm4), using an external load instead of internal shear force, and entering b as flange width rather than the local thickness at the point of interest. Keeping one length unit for all geometric values prevents these issues.
8) Reporting and traceability
Engineering reviews often require traceable calculations. After you compute, export CSV for spreadsheets or PDF for design notes. Store the method label, inputs, and output unit together so reviewers can reproduce results and verify that the correct section properties were used.
FAQs
1) What does Q represent in VQ/Ib?
Q is the first moment of area about the neutral axis for the area above or below the evaluated point. It depends on where you are in the cross-section, so it changes with height.
2) When should I use the rectangular maximum option?
Use it for solid rectangular sections when you need the peak shear stress quickly. It assumes the classic parabolic distribution and returns τ_{max}=1.5V/A at the neutral axis.
3) Is the circular maximum option valid for hollow tubes?
No. The 4V/(3A) peak relation is for a solid circular cross-section. For hollow tubes or thin-walled pipes, use the general method with the correct properties or a shear flow approach.
4) Why does the calculator ask for b at the point?
In VQ/Ib, b is the local width (often web thickness) where the shear stress is evaluated. In non-uniform sections, using the correct local thickness is essential.
5) What if my input gives an extremely large stress?
First check unit consistency for Q (length3) and I (length4). Then confirm you used internal shear force at the section, not an external point load.
6) Does this include shear due to torsion?
No. This tool covers transverse shear in bending. Torsional shear stress requires polar properties and torque inputs. Use a torsion calculator for circular shafts or thin-walled torsion problems.
7) Which output unit should I choose?
Choose MPa for most mechanical and structural work, kPa for low-stress materials, and psi for customary-unit reports. The calculator computes in Pa internally and converts to your selected unit.