cantilever experiment

8/2/2019 Cantilever Experiment

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The axial bending stress varies throughout the

cross-section and tends to be a maximum at

either the top or bottom and is zero at the neutral

axis (which is the centroid of the cross-section for

homogeneous cross-sections). In this case, it is

tensile on top and compressive on the bottom.

The shear stress likewise varies over the cross-section, is zero at the top and bottom of the cross-

section, and is a maximum at the neutral axis

(centroid of the cross-section for homogeneous

cross-sections).

After loading, we note that the top line has

stretched (tension) and the bottom line has

shortened (compression). If measured carefully,

we see that the longitudinal line at the center has

not changed length (at centroid). The longitudinal

lines now appear to form concentric circular lines.

A beam deforms and stresses develop inside itwhen a transverse load is applied on it. In a

horizontal beam supported at the ends and loaded

downwards in the middle, the material at the over-side of the beam is compressed while the material at the underside

is stretched. There are two forms of internal stresses caused by lateral loads:

Shear stress parallel to the lateral loading plus complementary shear stress on planes perpendicular to the load

direction;

Direct compressive stress in the upper region of the beam, and direct tensile stress in the lower region of the beam.

These last two forces form a couple ormoment as they are equal in magnitude and opposite in direction.

This bending moment resists the sagging deformation characteristic of a beam experiencing bending. The stress

distribution in a beam can be predicted quite accurately even when some simplifying assumptions are used.

When loads are applied to a beam their originally straight axes become curved. Displacements from the initial axes

are called bending or flexural deflections. The amount of flexural deflection in a beam is related to the beams area

moment of inertia (I), the single applied concentrated load (P), length of the beam (L), the modulus of elasticity (E),

and the position of the applied load on the beam.

The beam is divided into compressive and tensile regions separated by a neutral surface. The beam may be

assumed to be composed of an infinite number of longitudinal fibres. Due to the bending, fibres in the lower part of

the beam extend and those in the upper part are shortened. Some where in between, there would be a layer of fibre

which has undergone no extension or change in length. This is known as the neutral surface.For consideration ofplastic flow processes in metals and in sufficiently hot ceramics, the relevant microscale involves the network of

dislocation lines that move within crystals. These lines shift atom positions relative to one another by one atomicspacing as they move along slip planes.
http://en.wikipedia.org/wiki/Compressive_stresshttp://en.wikipedia.org/wiki/Tensile_stresshttp://en.wikipedia.org/wiki/Couple_%28mechanics%29http://en.wikipedia.org/wiki/Moment_%28physics%29http://en.wikipedia.org/wiki/Bending_momenthttp://en.wikipedia.org/wiki/Bending_momenthttp://en.wikipedia.org/wiki/Moment_%28physics%29http://en.wikipedia.org/wiki/Couple_%28mechanics%29http://en.wikipedia.org/wiki/Tensile_stresshttp://en.wikipedia.org/wiki/Compressive_stress

cantilever experiment

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