Beam shear angle
= Beam shear angle
{title2=$\gamma=w_x-\theta$}
The \b[beam shear angle] is the small-angle difference between centreline <slope> and material-section <beam cross-section rotation>:
$$
\gamma=w_x-\theta.
$$
With transverse coordinate $z$ and kinematics $u_x=-z\theta(x)$, $u_z=w(x)$, the engineering <shear strain> is $\partial_z u_x+\partial_x u_z=\gamma$. The <Euler-Bernoulli beam equation> imposes $\gamma=0$; a shear-deformable model permits $w$ and $\theta$ to vary independently. The primary beam account distinguishes these kinematics and relates transverse force to the resulting shear measure.<Applied Mechanics of Solids by A. F. Bower>[§8.7.2, Summary of beam theory, Timoshenko rotation and force/displacement relation]{ref}
For an original local example, suppose shape measurements give $w_x=0.015$, while section markers give $\theta=0.010$ radians in the same sign convention. Then $\gamma=0.005$, about $0.286$ degrees. Setting the section rotation equal to the observed slope would erase this measured discrepancy by assumption.
In a simple linear shear model, the transverse force resultant is $V=S\gamma$, with <effective beam shear rigidity> $S=k_sGA$. Here $G$ is the <shear modulus>, $A$ the material area, and $k_s$ a section correction coefficient. Stipulating $G=1.0\,\mathrm{GPa}$, $A=20\,\mathrm{mm^2}$ and $k_s=5/6$ gives $S=16667\,\mathrm N$ and $V\approx83.3\,\mathrm N$. The correction coefficient accounts for using a reduced section model; it is not universally fixed at $5/6$.
A physical test must measure both the centreline shape and section orientation, for example by tracking markers during loading. Shape alone determines $w_x$ but cannot independently determine $\gamma$ without section-rotation information or an additional mechanical model. The comparison also requires compatible spatial resolution and angular <measurement calibration>.