Experimental apparatus for unsymmetrical bending and shear-centre determination of cantilever beams
A cantilever beam clamped in a rotating chuck — with an angular scale and an adjustable load-eccentricity — produces on demand pure symmetrical bending, pure unsymmetrical bending, or combined bending-and-torsion. Two dial gauges record the horizontal and vertical components of the free-end deflection. A set of three cross-sections (I, L, U) lets the student build Mohr's circle of the second moments of area from measured data, locate the shear centre of the U-profile, and observe the effect of shear flow.
Experiments
Bernoulli hypothesis
Axial second moments of area and product moment of inertia
Symmetrical (uniaxial) bending of a beam, with I, L and U profiles
Unsymmetrical (complex) bending of a beam with an L profile; calculation of the neutral axis
Combined bending and torsion by eccentric force application
Determination of the shear centre on a beam with a U profile
Familiarisation with shear flow in open cross-sections
Comparison of calculated and measured values
Cantilever beams
Deformed length500 mm
Materialaluminium
ProfilesI · L · U — three cross-sections
Clamping & loading
Clamping flangefree to rotate in any direction about the beam axis
Angle scale0…360°, graduation 1°
Load-point eccentricity0…25 mm, continuously adjustable
Measurement
Horizontal & vertical deflection2 × dial gauge, 0…10 mm, graduation 0.01 mm
Load set
Weights1 × 2.5 N hanger · 1 × 2.5 N · 3 × 5 N
Delivery
Experimental unit on baseplate with rotating clamping flange