Q(y) is the first moment of the area beyond height y about the neutral axis, I the second moment of area, b(y) the width at that height. Rectangles are parabolic; in thin I-beams the small web b concentrates shear, with a step in τ at the flange/web boundary.
How to read it
The section sketch shows how a thinner web concentrates shear into a smaller area.
The profile plot shows the peak around the neutral-axis region.
The map highlights unsafe combinations of shear force and web thickness.
Learn Beam Shear Stress Distribution by dialogue
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When reading Beam Shear Stress Distribution, where should I look first? Moving Shear force V changes both the plots and the result cards.
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Start with Max shear stress, but do not treat the number as the whole answer. Use Section sketch to confirm the assumed state, then read Shear stress profile for the distribution or trend. The section sketch shows how a thinner web concentrates shear into a smaller area.
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I can see why Shear force V changes Max shear stress. How should I judge the influence of Web thickness b?
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Move Web thickness b in small steps and watch Average shear stress. That reveals which term is controlling the result. For rectangular sections, peak shear stress is about 1.5 times the average. For thin I-sections, the web carries most of the shear. In VQ/Ib, Q and b change with depth. A single operating point is not enough; sweep the realistic scatter range.
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What is Utilization map for? It feels like the ordinary curve already tells the story.
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Utilization map is for finding boundaries where the condition becomes risky or margin collapses quickly. The profile plot shows the peak around the neutral-axis region. In Checking web shear in I-beams or box sections, the important question is often what happens after a small change, not only the nominal value.
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So if Max shear stress is within the target, can I accept the condition?
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Treat this as a first-pass review. It helps with Comparing web thickness changes during preliminary sizing and Finding shear-governed short-span beams that bending checks may miss, but final decisions still need standards, measured data, detailed analysis, and vendor limits. The map highlights unsafe combinations of shear force and web thickness.
Practical use
Checking web shear in I-beams or box sections.
Comparing web thickness changes during preliminary sizing.
Finding shear-governed short-span beams that bending checks may miss.
FAQ
Start with Max shear stress and Average shear stress. Then use Section sketch to confirm the assumed state and Shear stress profile to read distribution or bias. The section sketch shows how a thinner web concentrates shear into a smaller area
Move Shear force V alone, then move Web thickness b by a comparable amount and compare the change in Max shear stress. Utilization map shows combinations where margin or performance changes quickly.
Use it for Checking web shear in I-beams or box sections. Instead of trusting a single point, widen the input range and check whether Max shear stress keeps enough margin before moving to detailed analysis.
For rectangular sections, peak shear stress is about 1.5 times the average. For thin I-sections, the web carries most of the shear. In VQ/Ib, Q and b change with depth. Final decisions still require standards, measured data, detailed analysis, and vendor limits.
How to Use
Enter the shear force (in kN) applied to your beam cross-section in the Shear Force field.
Input the web thickness (in mm) and overall section height (in mm) for your I-beam or channel profile.
Set the shape factor (typically 1.2–1.5 for rolled steel sections) to account for non-uniform stress distribution across the web.
The simulator calculates maximum shear stress using τ_max = (V × Q) / (I × t_w) and displays utilization against 120 MPa design limit.
Worked Example
A structural steel I-beam (IPE 300) carries shear force V = 85 kN with web thickness t_w = 7.1 mm and height h = 300 mm. Using shape factor k = 1.2: Average shear stress = 85,000 N / (7.1 × 300) = 40.1 MPa. Maximum shear stress = 40.1 × 1.2 = 48.1 MPa. Web area = 2,130 mm². Utilization ratio = 48.1 / 120 = 0.40 (40% of limit), indicating safe design with adequate reserve.
Practical Notes
For composite beams, increase shape factor to 1.4–1.5 to reflect stress concentration near neutral axis.
Rolled steel sections typically have k = 1.2; welded plate girders may require k = 1.0–1.1 if flange transitions are gradual.
If utilization exceeds 85%, consider increasing web thickness or reducing applied shear through additional supports.
Shear stress dominates in short-span beams (L/h < 10); verify bending stress separately for longer spans.