= Four-point flexural test
= Four-point bending test
{synonym}
A \b[four-point flexural test] bends a specimen using two outer supports and two inner loading contacts. For symmetric loading, the interval between the inner contacts has constant <bending moment> and zero <transverse shear force>, approximating <pure bending> away from contact disturbances. The Illinois laboratory uses adjustable spans and records force and deflection with a mechanical testing frame.<Bending Test at the University of Illinois Mechanical Testing Instructional Laboratory>[Bending Test, fixtures and electronic readout]{ref}
Let the support span be $L$, the distance from each support to its nearest loading contact be $a$, and the \i[total] downward applied force be $P$. Each loading contact and each support carries force magnitude $P/2$. Static equilibrium gives
$$
M(x)=\begin{cases}
Px/2,&0\le x\le a,\\
Pa/2,&a\le x\le L-a,\\
P(L-x)/2,&L-a\le x\le L.
\end{cases}
$$
The central constant-moment region has length $L-2a$. Specifying whether a force symbol means total force or force at each nose prevents a factor-of-two error.
For an original example, $L=180\,\mathrm{mm}$, $a=60\,\mathrm{mm}$ and $P=80\,\mathrm N$ give reactions $40\,\mathrm N$ and central moment $2.4\,\mathrm{N\,m}$. A rectangular specimen with width $b=20\,\mathrm{mm}$ and thickness $h=5\,\mathrm{mm}$ has $I=bh^3/12=208.33\,\mathrm{mm^4}$. The nominal maximum <bending stress> magnitude is $M(h/2)/I=28.8\,\mathrm{MPa}$.
The apparatus measures force and a chosen displacement; the beam model converts them into stress, strain or <flexural modulus>. Midpoint displacement and displacement at the inner loading contacts are generally different. Fixture motion can additionally include <machine compliance> and contact indentation. Record the displacement location and both spans along with specimen dimensions.<Flex Testing by Instron>[test configuration and span-dependent calculations]{ref}
Unlike a central three-point load, this geometry provides a finite interval of maximum nominal moment. It tests a larger highly stressed region, so flaw distribution and where failure begins can matter when comparing results between fixtures.
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