A beam of metal supported at the two edges is loaded at the centre. The depression at the centre is proportional to
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For a beam, the depression at the centre is given by, are constants for a particular beam i.e.,
For the same cross-sectional area and for a given load, the ratio of depressions for the beam of a square
cross-section and circular cross-section is
, where load, length of beam and is geometrical moment of inertia for rectangular beam, where breadth and depth
For square beam
For a beam of circular cross-section,
(for sq. cross section)
and
(for circular cross-section)
Now
( i.e., they have same cross-sectional area)
A steel wire of original length and cross-sectional area is clamped at the two ends so that
it lies horizontally and without tension. If a load of is suspended from the middle point of the wire,
what would be its vertical depression?
Y of the steel . Take
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