CIV-37

Shear flow q = VQ/I

q = V Q / I. Force per unit length at a glued or welded joint.

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ShearShear flow q

Governing equation

q=VQ/I

$V \in \left[1, 600\right]$

where

V: Shear (kN)
Q: First moment (cm^3)
I: Second moment (cm^4)
q: Shear flow (kN/m)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

q=VQ/I

$V \in \left[1, 600\right]$

$V = 1$ $q = 0.002$

Along the curve

②

Domain of the variable — blue

V_{\min} = 1,\quad V_{\max} = 600

$V \in \left[1, 600\right]$

$V = 1$ $V = 1$

Along the curve

③

Response curve — green

q=VQ/I

$V \in \left[1, 600\right]$

$V = 1$ $q = 0.002$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}q}{\mathrm{d}V}

$V \in \left[1, 600\right]$

$V = 4.767$ $q^{\prime} = 0.002$

Along the curve

Lecture brief

Historical brief

From Euler’s 1744 elastica and Navier’s beam theory to Mohr’s circle and transformed-section RC, structural mechanics grew as a closed-form craft before finite elements. The lab keeps those governing lines for buckling, flexure, joints and influence. This sheet (CIV-37 — Shear flow q = VQ/I) is the form associated with Shear flow q. Working symbols: $V$ , $Q$ , $I$ $\rightarrow$ $q$ . Integrate τ t along a cut. Fastener pitch s then carries q s.

Purpose

Purpose: compute

q

from

V

Q

I

in Structural & civil via

q=VQ/I

q = V Q / I. Force per unit length at a glued or welded joint. Use it when a real structural & civil question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

V = 90.000\,\mathrm{kN}

Q = 350.000\,\mathrm{cm^3}

I = 15000.000\,\mathrm{cm^4}

, the governing relation

q=VQ/I

yields

q = 0.21\,\mathrm{kN/m}

. A built-up beam, a glue line, a flow q. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Shear V90 kNFirst moment Q350 cm^3Second moment I15000 cm^4

Outputs

Shear flow q0.21 kN/m

Reading speed

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Narration of this film

A built-up beam, a glue line, a flow q.

Integrate τ t along a cut. Fastener pitch s then carries q s.

Reading speed

Watch on YouTube